Tolerances and fits.This book includes tables and calculations for easy option of fits of machine parts and determination of their dimensional tolerances and deviations. Using this tool the following tasks can be solved: 

 

1. Selection of suitable fits of machine parts according to the international standard ISO 286.

2. Determination of dimensional tolerances and deviations of machine parts according to the international standard ISO 286.

3. Selection of preferred fits of machine parts and determination of their dimensional tolerances and deviations according to ANSI B4.1.

4. Determination of non-prescribed limit deviations of linear and angular dimensions according to ISO 2768.

5. Automatic design of a fit for the given clearance or fit interference respectively.

The data, procedures, algorithms and specialized literature and standards ANSI, ISO, DIN and others were used in the calculations.List of standards: ANSI B4.1, ANSI B4.2, ISO 286, ISO 1829, ISO 2768, EN 20286, JIS B 0401

Control, structure and syntax of calculations.Information on the syntax and control of the calculation can be found in the document "Control, structure and syntax of calculations".

Basic terms.It is necessary that the dimensions, shape and mutual position of surfaces of individual parts of mechanical engineering products are kept within a certain accuracy to achieve their correct and reliable functioning. Routine production processes do not allow maintenance (or measurement) of the given geometrical properties with absolute accuracy. Actual surfaces of the produced parts therefore differ from ideal surfaces prescribed in drawings. Deviations of actual surfaces are divided into four groups to enable assessment, prescription and checking of the permitted inaccuracy during production:

Dimensional deviations

Shape deviations

Position deviations

Surface roughness deviations

This toll includes the first group and can therefore be used to determine dimensional tolerances and deviations of machine parts.

 

As mentioned above, it is principally impossible to produce machine parts with absolute dimensional accuracy. In fact, it is not necessary or useful. It is quite sufficient that the actual dimension of the part is found between two limit dimensions and a permissible deviation is kept with production to ensure correct functioning of engineering products. The required level of accuracy of production of the given part is then given by the dimensional tolerance which is prescribed in the drawing. The production accuracy is prescribed with regards to the functionality of the product and to the economy of production as well.

A coupling of two parts creates a fit whose functional character is determined by differences of their dimensions before their coupling.

where:

d=D ... basic sizeDmax , Dmin ... limits of size for the holedmax , dmin ... limits of size for the shaftES ... hole upper deviation EI ... hole lower deviationes ... shaft upper deviationei ... shaft lower deviation

 

Depending on the mutual position of tolerance zones of the coupled parts, 3 types of fit can be distinguished:

A. Clearance fit

B. Transition fit

C. Interference fit

ISO 286:  ISO system of limits and fits. [1]This paragraph can be used to choose a fit and determine tolerances and deviations of machine parts according to the standard ISO 286:1988. This standard is identical with the European standard EN 20286:1993 and defines an internationally recognized system of tolerances, deviations and fits. The standard ISO 286 is used as an international standard for linear dimension tolerances and has been accepted in most industrially developed countries in identical or modified wording as a national standard (JIS B 0401, DIN ISO 286, BS EN 20286, CSN EN 20286, etc.). 

The system of tolerances and fits ISO can be applied in tolerances and deviations of smooth parts and for fits created by their coupling. It is used particularly for cylindrical parts with round sections. Tolerances and deviations in this standard can also be applied in smooth parts of other sections. Similarly, the system can be used for coupling (fits) of cylindrical parts and for fits with parts having two parallel surfaces (e.g. fits of keys in grooves). The term "shaft", used in this standard has a wide meaning and serves for specification of all outer elements of the part, including those elements which do not have cylindrical shapes. Also, the term "hole" can be used for specification of all inner elements regardless of their shape. 

Note: All numerical values of tolerances and deviations mentioned in this paragraph are given in the metric system and relate to parts with dimensions specified at 20 °C.

1.1 Basic size.It is the size whose limit dimensions are specified using the upper and lower deviations. In case of a fit, the basic size of both connected elements must be the same.

Attention: The standard ISO 286 defines the system of tolerances, deviations and fits only for basic sizes up to 3150 mm. 

1.2 Tolerance of a basic size for specific tolerance grade.The tolerance of a size is defined as the difference between the upper and lower limit dimensions of the part. In order to meet the requirements of various production branches for accuracy of the product, the system ISO implements 20 grades of accuracy. Each of the tolerances of this system is marked "IT" with attached grade of accuracy (IT01, IT0, IT1 ... IT18).

Field of use of individual tolerances of the system ISO:IT01 to IT6 For production of gauges and measuring instruments

IT5 to IT12 For fits in precision and general engineering

IT11 to IT16 For production of semi-products

IT16 to IT18 For structures

IT11 to IT18 For specification of limit deviations of non-tolerated dimensions

Note: When choosing a suitable dimension it is necessary to also take into account the used method of machining of the part in the production process. The dependency between the tolerance and modification of the surface can be found in the table in paragraph [5].

1.3 Hole tolerance zones.The tolerance zone is defined as a spherical zone limited by the upper and lower limit dimensions of the part. The tolerance zone is therefore determined by the amount of the tolerance and its position related to the basic size. The position of the tolerance zone, related to the basic size (zero line), is determined in the ISO system by a so-called basic deviation. The system ISO defines 28 classes of basic deviations for holes. These classes are marked by capital letters (A, B, C, ... ZC). The tolerance zone for the specified dimensions is prescribed in the drawing by a tolerance mark, which consists of a letter marking of the basic deviation and a numerical marking of the tolerance grade (e.g. H7, H8, D5, etc.). This paragraph includes graphic illustrations of all tolerance zones of a hole which are applicable for the specified basic size [1.1] and the tolerance grade IT chosen from the pop-up list. 

Though the general sets of basic deviations (A ... ZC) and tolerance grades (IT1 ... IT18) can be used for prescriptions of hole tolerance zones by their mutual combinations, in practice only a limited range of tolerance zones is used. An overview of tolerance zones for general use can be found in the following table. The tolerance zones not included in this table are considered special zones and their use is recommended only in technically well-grounded cases.

Prescribed hole tolerance zones for routine use (for basic sizes up to 3150 mm):

             

 B8

C8

A9B9

C9

A10B10

C10

A11B11

C11

A12B12

C12

A13B13

C13         

       

  

E5

CD6D6

E6

CD7D7

E7

CD8D8

E8

CD9D9

E9

CD10

D10

E10

 D11

 

 D12

 

 D13

          

   EF3F3

EF4F4

EF5F5

EF6F6

EF7F7

EF8F8

EF9F9

EF10

F10               

   FG3G3

FG4G4

FG5G5

FG6G6

FG7G7

FG8G8

FG9G9

FG10

G10               

H1 H2 H3 H4 H5 H6 H7 H8 H9 H10 H11 H12 H13 H14 H15 H16 H17

H18

JS1 JS2 JS3 JS4 JS5 JS6 JS7 JS8 JS9 JS10

JS11

JS12

JS13

JS14 JS15 JS16 JS17

JS18

    

K3 

K4 

K5J6K6

J7K7

J8K8                    

   M3N3

M4N4

M5N5

M6N6

M7N7

M8N8

M9N9

M10N10

 N11              

    P3 P4 P5 P6 P7 P8 P9 P10                

    R3 R4 R5 R6 R7 R8 R9 R10                

    S3 S4 S5 S6 S7 S8 S9 S10                

        T5 T6 T7 T8                    

U5 U6 U7 U8 U9 U10

       

V5X5

 

V6X6

Y6

V7X7

Y7

V8X8

Y8

 X9

Y9

 X10

Y10               

         Z6

ZA6Z7

ZA7Z8

ZA8Z9

ZA9

Z10ZA10

Z11ZA11

             

           ZB7ZC7

ZB8ZC8

ZB9ZC9

ZB10

ZC10

ZB11

ZC11

             

Note: Tolerance zones with thin print are specified only for basic sizes up to 500 mm. 

Hint: For hole tolerances, tolerance zones H7, H8, H9 and H11 are used preferably.

1.4 Shaft tolerance zones.The tolerance zone is defined as a spherical zone limited by the upper and lower limit dimensions of the part. The tolerance zone is therefore determined by the amount of the tolerance and its position related to the basic size. The position of the tolerance zone, related to the basic size (zero line), is determined in the ISO system by a so-called basic deviation. The system ISO defines 28 classes of basic deviations for shafts. These classes are marked by lower case letters (a, b, c, ... zc). The tolerance zone for the specified dimensions is prescribed in the drawing by a tolerance mark, which consists of a letter marking of the basic deviation and a numerical marking of the tolerance grade (e.g. h7, h6, g5, etc.). This paragraph includes graphic illustrations of all tolerance zones of a shaft which are applicable for the specified basic size [1.1] and the tolerance grade IT chosen from the pop-up list. 

Though the general sets of basic deviations (a ... zc) and tolerance grades (IT1 ... IT18) can be used for prescriptions of shaft tolerance zones by their mutual combinations, in practice only a limited range of tolerance zones is used. An overview of tolerance zones for general use can be found in the following table. The tolerance zones not included in this table are considered special zones and their use is recommended only in technically well-grounded cases.

Prescribed shaft tolerance zones for routine use (for basic sizes up to 3150 mm):

             

  

c8

a9b9

c9

a10b10

c10

a11b11

c11

a12b12

c12

a13b13

           

       cd5d5

cd6d6

cd7d7

cd8d8

cd9d9

cd10

d10

 d11

 d12

 d13          

    

ef3

 ef4

e5ef5

e6ef6

e7ef7

e8ef8

e9ef9

e10ef10                

   f3

fg3f4

fg4f5

fg5f6fg6

f7fg7

f8fg8

f9fg9

f10fg10                

    g3 g4 g5 g6 g7 g8 g9 g10                

h1 h2 h3 h4 h5 h6 h7 h8 h9 h10 h11 h12 h13 h14 h15 h16 h17

h18

js1 js2 js3 js4 js5 js6 js7 js8 js9 js10 js11 js12 js13 js14 js15 js16 js17

js18

    

k3 

k4 j5k5

j6k6

j7k7

 k8

 k9

 k10 

 k11 

 k12 

 k13           

   m3n3

m4n4

m5n5

m6n6

m7n7

m8n8

m9n9                  

    p3 p4 p5 p6 p7 p8 p9 p10                

    r3 r4 r5 r6 r7 r8 r9 r10                

    s3 s4 s5 s6 s7 s8 s9 s10                

        t5 t6 t7 t8                    

u5 u6 u7 u8 u9

       

v5x5

 

v6x6

y6

v7x7

y7

v8x8

y8

 x9

y9

 x10

y10               

         z6za6

z7za7

z8za8

z9za9

z10za10

z11za11

             

           zb7zc7

zb8zc8

zb9zc9

zb10

zc10

zb11

zc11             

Note: Tolerance zones with thin print are specified only for basic sizes up to 500 mm. 

Hint: For shaft tolerances, tolerance zones h6, h7, h9 and h11 are used preferably.

1.5 Selection of fit.This paragraph can be used to choose a recommended fit. If you wish to use another fit than the recommended one, define hole and shaft tolerance zones directly in the paragraphs [1.9, 1.10]. When designing the fit itself, it is recommended to follow several principles:

Design a fit in a hole basis system in a shaft basis system.

Use hole tolerances greater or equal to the shaft tolerance.

Tolerances of the hole and shaft should not differ by more than two grades.

Hint: In case you wish to find a suitable standardized fit with regard to its specific properties (a fixed amount of clearance or fit interference is required), use the function of automatic fit design in paragraph [4].

1.6 System of fit.Although there can be generally coupled parts without any tolerance zones, only two methods of coupling of holes and shafts are recommended due to constructional, technological and economic reasons.

A. Hole basis systemThe desired clearances and interferences in the fit are achieved by combinations of various shaft tolerance zones with the hole tolerance zone "H". In this system of tolerances and fits, the lower deviation of the hole is always equal to zero.

B. Shaft basis systemThe desired clearances and interferences in the fit are achieved by combinations of various hole tolerance zones with the shaft tolerance zone "h". In this system of tolerances and fits, the upper deviation of the hole is always equal to zero.

where:

d=D ... basic size////  ... hole tolerance zone\\\\  ... shaft tolerance zone

 

The option of the system for the specified type of product or production is always influenced by the following factors:

Constructional design of the product and the method of assembly.

Production procedure and costs for machining the part.

Type of semi-product and consumption of material.

Costs for purchase, maintenance and storage of gauges and production tools.

Machine holding of the plant.

Options in use of standardized parts. 

Hint: Although both systems are equivalent in the view of functional properties, the hole basis system is used preferably.

1.7 Type of fit.Depending on the mutual position of tolerance zones of the coupled parts, 3 types of fit can be distinguished:

A. Clearance fitIt is a fit that always enables a clearance between the hole and shaft in the coupling. The lower limit size of the hole is greater or at least equal to the upper limit size of the shaft.

B. Transition fitIt is a fit where (depending on the actual sizes of the hole and shaft) both clearance and interference may occur in the coupling. Tolerance zones of the hole and shaft partly or completely interfere.

C. Interference fitIt is a fit always ensuring some interference between the hole and shaft in the coupling. The upper limit size of the hole is smaller or at least equal to the lower limit size of the shaft.

1.8 Recommended fits.A sufficient fit can be selected in the pop-up list.

The list of recommended fits given here is for information only and cannot be taken as a fixed listing. The enumeration of actually used fits may differ depending on the type and field of production, local standards and national usage and last but not least, depending on the plant practices. Properties and field of use of some selected fits are described in the following overview. When selecting a fit it is often necessary to take into account not only constructional and technological views, but also economic aspects. Selection of a suitable fit is important particularly in view of those measuring instruments, gauges and tools which are implemented in the production. Therefore, follow proven plant practices when selecting a fit.

Fields of use of selected fits (preferred fits are in bold):Clearance fits:

H11/a11,   H11/c11 , H11/c9, H11/d11, A11/h11,   C11/h11 , D11/h11 Fits with great clearances with parts having great tolerances.Use: Pivots, latches, fits of parts exposed to corrosive effects, contamination with dust and thermal or mechanical deformations.

H9/C9, H9/d10,   H9/d9 , H8/d9, H8/d8,   D10/h9 , D9/h9, D9/h8 Running fits with greater clearances without any special requirements for accuracy of guiding shafts. Use: Multiple fits of shafts of production and piston machines, parts rotating very rarely or only swinging.

H9/e9 ,   H8/e8 , H7/e7,   E9/h9 , E8/h8, E8/h7 Running fits with greater clearances without any special requirements for fit accuracy.Use: Fits of long shafts, e.g. in agricultural machines, bearings of pumps, fans and piston machines.

H9/f8, H8/f8,   H8/f7 ,   H7/f7 , F8/h7,   F8/h6 Running fits with smaller clearances with general requirements for fit accuracy. Use: Main fits of machine tools. General fits of shafts, regulator bearings, machine tool spindles, sliding rods.

H8/g7,   H7/g6 ,   G7/h6 Running fits with very small clearances for accurate guiding of shafts. Without any noticeable clearance after assembly.Use: Parts of machine tools, sliding gears and clutch disks, crankshaft journals, pistons of hydraulic machines, rods sliding in bearings, grinding machine spindles.

H11/h11, H11/h9Slipping fits of parts with great tolerances. The parts can easily be slid one into the other and turn.Use: Easily demountable parts, distance rings, parts of machines fixed to shafts using pins, bolts, rivets or welds.

H8/h9, H8/h8, H8/h7,   H7/h6 Sliding fits with very small clearances for precise guiding and centring of parts. Mounting by sliding on without use of any great force, after lubrication the parts can be turned and slid by hand. Use: Precise guiding of machines and preparations, exchangeable wheels, roller guides. 

Transition fits:

H8/j7, H7/js6,   H7/j6 , J7/h6 Tight fits with small clearances or negligible interference. The parts can be assembled or disassembled manually.Use: Easily dismountable fits of hubs of gears, pulleys and bushings, retaining rings, frequently removed bearing bushings.

H8/k7,   H7/k6 , K8/h7,   K7/h6 Similar fits with small clearances or small interferences. The parts can be assembled or disassembled without great force using a rubber mallet.Use: Demountable fits of hubs of gears and pulleys, manual wheels, clutches, brake disks.

H8/p7, H8/m7, H8/n7, H7/m6,   H7/n6 , M8/h6, N8/h7,   N7/h6 Fixed fits with negligible clearances or small interferences. Mounting of fits using pressing and light force.Use: Fixed plugs, driven bushings, armatures of electric motors on shafts, gear rims, flushed bolts.

Interference fits:

H8/r7,   H7/p6 ,   H7/r6 ,   P7/h6 , R7/h6 Pressed fits with guaranteed interference. Assembly of the parts can be carried out using cold pressing.Use: Hubs of clutch disks, bearing bushings.

H8/s7, H8/t7,   H7/s6 , H7/t6,   S7/h6 , T7/h6 Pressed fits with medium interference. Assembly of parts using hot pressing. Assembly using cold pressing only with use of large forces.Use: Permanent coupling of gears with shafts, bearing bushings.

H8/u8, H8/u7, H8/x8, H7/u6, U8/h7, U7/h6Pressed fits with big interferences. Assembly using pressing and great forces under different temperatures of the parts.Use: permanent couplings of gears with shafts, flanges. 

Hint: If not in contradiction with constructional and technological requirements, preferably use some of the preferred fits. Preferred fits are marked by asterisk "*" in the list.

Note: Preferred fits designed for preferred use in the USA are defined in ANSI B4.2. This standard prescribes the following groups of preferred fits:- Clearance fits: H11/c11, H9/d9, H8/f7, H7/g6, H7/h6, C11/h11, D9/h9, F8/h7, G7/h6- Transition fits: H7/k6, H7/n6, K7/h6, N7/h6- Interference fits: H7/p6, H7/s6, H7/u6, P7/h6, S7/h6, U7/h6

1.9 Hole tolerance zone.Limit deviations of the hole tolerance zone are calculated in this paragraph for the specified basic size [1.1] and selected hole tolerance zone. 

The respective hole tolerance zone is automatically set up in the listing during selection of any of the recommended fits from the list in row [1.8]. If you wish to use another tolerance zone for the hole, select the corresponding combination of a basic deviation (A ... ZC) and a tolerance zone (1 ... 18) in pop-up lists in this row.

Though the general sets of basic deviations (A ... ZC) and tolerance grades (IT1 ... IT18) can be used for prescriptions of hole tolerance zones by their mutual combinations, in practice only a limited range of tolerance zones is used. An overview of tolerance zones specified for general use can be found in the table in paragraph [1.3]. The tolerance zones which are not included in the selection are considered special zones and their use is recommended only in technically well-grounded cases.

Attention: In case you select a hole tolerance zone which is not defined in the ISO system for the specified basic size, limit deviations will be equal to zero and the tolerance mark will be displayed in red.

Hint: For hole tolerances, tolerance zones H7, H8, H9 and H11 are used preferably.

1.10 Shaft tolerance zones.Limit deviations of the hole tolerance zone are calculated in this paragraph for the specified basic size [1.1] and selected shaft tolerance zone. 

The respective shaft tolerance zone is automatically set up in the listing during selection of any of the recommended fits from the list in row [1.8]. If you wish to use another tolerance zone for the shaft, select the corresponding combination of a basic deviation (a ... zc) and a tolerance zone (1 ... 18) in pop-up lists in this row.

Though the general sets of basic deviations (a ... zc) and tolerance grades (IT1 ... IT18) can be used for prescriptions of shaft tolerance zones by their mutual combinations, in practice only a limited range of tolerance zones is used. An overview

of tolerance zones specified for general use can be found in the table in paragraph [1.3]. The tolerance zones which are not included in the selection are considered special zones and their use is recommended only in technically well-grounded cases.

Attention: In case you select a shaft tolerance zone which is not defined in the ISO system for the specified basic size, limit deviations will be equal to zero and the tolerance mark will be displayed in red.

Hint: For shaft tolerances, tolerance zones h6, h7, h9 and h11 are used preferably.

1.11 Parameters of the selected fit.Parameters of the selected fit are calculated and mutual positions of tolerance zones of the hole and shaft are displayed in this paragraph. 

Note: Dimensional data on this picture are given in m.

ANSI B4.1:  Preferred limits and fits for cylindrical parts. [2]This paragraph can be used for selection of a preferred fit of cylindrical parts according to ANSI B4.1. This standard defines a system of dimensional tolerances and prescribes a series of those preferred fits of cylindrical part, which are specified for preferred use. 

Note: All numerical values of tolerances and deviations given in this paragraph are related to those parts, whose dimensions are determined at 68 °F.

2.1 Basic size.It is the size whose limit dimensions are specified using the upper and lower deviations. In case of a fit, the basic size of both connected elements must be the same.

Note: Standard ANSI B4.1 defines a system of preferred fits only for basic sizes up to 16.69 in.

2.2 Tolerance of a basic size for specific tolerance grade.The tolerance of a size is defined as the difference between the upper and lower limit dimensions of the part. The standard ANSI B4.1 implements 10 tolerance grades to meet the requirements of various production branches for accuracy of products. The system of tolerances is prescribed by the standard for basic sizes up to 200 in. 

Note: When choosing a suitable dimension it is necessary to also take into account the used method of machining of the part in the production process. The dependency between the tolerance and modification of the surface can be found in the table in paragraph [5].

2.4 System of fits.The standard ANSI B4.1 defines two basic methods of coupling of holes and shafts for the selected series of preferred fits.

A. Hole basis systemIn this system of tolerances and fits, the lower deviation of the hole is always equal to zero.

B. Shaft basis systemIn this system of tolerances and fits, the upper deviation of the hole is always equal to zero.

where:

d=D ... basic size////  ... hole tolerance zone\\\\  ... shaft tolerance zone

 

The option of the system for the specified type of product or production is always influenced by the following factors:

Constructional design of the product and the method of assembly.

Production procedure and costs for machining the part.

Type of semi-product and consumption of material.

Costs for purchase, maintenance and storage of gauges and production tools.

Machine holding of the plant.

Options in use of standardized parts. 

Hint: Although both systems are equivalent in the view of functional properties, the hole basis system is used preferably.

2.5 Type of fit.The standard ANSI B4.1 divides the series of preferred fits into three basic groups according to the type and field of use. 

A. Running or sliding fits [RC]This includes fits with guaranteed clearances which are specified for movable couplings of those parts which have to run or slide one against the other. 

B. Locational fits [LC, LT, LN]This includes clearance or interference fits specified for precise locational positioning of coupled parts. The coupled parts must be fixed mechanically to prevent one moving against the other during assembly. Depending on the locational positioning of tolerance zones of the coupled parts, 3 types of these fits may be distinguished: Clearance fits [LC], interference fits [LN] and transition fits [LT].

C. Force or shrink fits [FN]This includes guaranteed interference fits specified for fixed (non-demountable) couplings of parts.

Each of these groups is marked using a literal abbreviation, which together with a numerical specification of the class of fit unambiguously defines the selected fit.

2.6 Fit.Select a suitable fit from the pop-up list.

Properties and field of use of preferred fits are described in the following overview. When selecting a fit it is often necessary to take into account not only constructional and technological but also economic aspects. Selection of a suitable fit is important particularly in view of those measuring instruments, gauges and tools which are implemented in the production. Therefore, follow proven plant practices when selecting a fit.

Field of use of preferred fits:

Running or sliding clearance fits [RC]:Fits with guaranteed clearance designed for movable couplings of parts (pivots, running and sliding fits of shafts, guiding bushings, sliding gears and clutch disks, pistons of hydraulic machines, etc.). The parts can be easily slid one into the other and turn. The tolerance of the coupled parts and fit clearance increases with increasing class of the fit.

RC 1: Close sliding fits with negligible clearances for precise guiding of shafts with high requirements for fit accuracy. No noticeable clearance after assembly. This type is not designed for free run.

RC 2: Sliding fits with small clearances for precise guiding of shafts with high requirements for fit precision. This type is not designed for free run; in case of greater sizes a seizure of the parts may occur even at low temperatures.

RC 3: Precision running fits with small clearances with increased requirements for fit precision. Designed for precision machines running at low speeds and low bearing pressures. Not suitable where noticeable temperature differences occur. 

RC 4: Close running fits with smaller clearances with higher requirements for fit precision. Designed for precise machines with moderate circumferential speeds and bearing pressures.

RC 5,   RC 6 : Medium running fits with greater clearances with common requirements for fit precision. Designed for machines running at higher speeds and considerable bearing pressures.

RC 7: Free running fits without any special requirements for precise guiding of shafts. Suitable for great temperature variations.

RC 8, RC 9: Loose running fits with great clearances with parts having great tolerances. Fits exposed to effects of corrosion, contamination by dust and thermal or mechanical deformations.

Locational clearance fits [LC]:Fits with guaranteed clearances, designed for unmovable couplings where easy assembly and disassembly is required (precise fits of machines and preparations, exchangeable wheels, bearing bushings, retaining and distance rings, parts of machines fixed to shafts using pins, bolts, rivets or welds, etc.). The coupled parts must be fixed mechanically to prevent one moving against the other during assembly. These fits are defined by the standard in a wide range of tolerances and clearances, from tight fits with negligible clearances designed for precise guiding and centring of parts [LC 1, LC 2] up to free fits with great clearances and maximum tolerances [LC 10, LC 11] where easy assembly is the primary requirement. The tolerance of coupled parts and fit clearance increases with increasing class of the fit.

Locational transition fits [LT]:

These types include clearance or interference fits designed for demountable unmovable couplings where precision of fits of the coupled parts is the main requirement. The part must be fixed mechanically to prevent one moving against the other during assembly.

LT 1, LT_2: Tight fits with small clearances or negligible interferences (easy detachable fits of hubs of gears, pulleys and bushings, retaining rings, bearing bushings, etc.). The part can be assembled or disassembled manually.

LT 3, LT_4: Similar fits with small clearances or interferences (demountable fits of hubs of gears and pulleys, manual wheels, clutches, brake disks, etc.). The parts can be coupled or disassembled without any great force by using a rubber mallet.

LT 5, LT_6: Fixed fits with negligible clearances or small interferences (fixed plugs, driven bushings, armatures of electric motors on shafts, gear rims, flushed bolts, etc.). Assembly of parts using low pressing forces.

Locational interference fits [LN]:Fits with small interferences designed for fixed couplings where precision and rigidity of fits of the coupled parts is the main requirement. These fits cannot be used for transfers of torsional moments using friction forces only; the parts must be secured to prevent one moving against the other. The parts can be assembled or disassembled using cold pressing and greater forces or hot pressing.

Force or shrink fits [FN]:Fits with guaranteed interferences designed for fixed (undetachable) coupling of parts (permanent couplings of gears with shafts, bearing bushings, flanges, etc.). These fits are designed, above all, for transfers of torsional moments using friction forces between shafts and hubs. The amount of interference (loading capacity of the fit) increases with increasing class of the fit. Mounting of the parts using cold pressing with great pressing forces at different temperatures of the parts.

FN 1: Light drive fits with small interferences designed for thin sections, long fits or fits with cast iron external members.

FN 2: Medium drive fits with medium interferences designed for ordinary steel parts or fits with high-grade cast iron external members.

FN 3: Heavy drive fits with great interferences designed for heavier steel parts.

FN 4, FN_5: Force fits with maximum interferences designed for highly loaded couplings.

2.7 Hole tolerance zone.The tolerance zone is defined as a spherical zone limited by the upper and lower limit dimensions of the part. The tolerance zone is therefore determined by the amount of the tolerance and its position related to the basic size.

Limit deviations of the hole tolerance zone are calculated in this paragraph for the specified basic size [2.1] and selected hole tolerance zone. The respective hole tolerance zone is set up according to the preferred fit selected in row [2.6].

2.8 Shaft tolerance zone.The tolerance zone is defined as a spherical zone limited by the upper and lower limit dimensions of the part. The tolerance zone is therefore determined by the amount of the tolerance and its position related to the basic size.

Limit deviations of the shaft tolerance zone are calculated in this paragraph for the specified basic size [2.1] and selected shaft tolerance zone. The respective shaft tolerance zone is set up according to the preferred fit selected in row [2.6].

2.9 Parameters of the selected fit.Parameters of the selected fit are calculated and mutual positions of tolerance zones of the hole and shaft are displayed in this paragraph.

Note: Dimensional data in the picture are given in thousandths of inches.

ISO 2768-1:  General tolerances for linear and angular dimensions without individual tolerance indications. [3]All dimensions of machine parts prescribed in the production documentation should be specified using limit dimensions (tolerances) to avoid any uncertainty and dispute during production, checks and assembly. Important functional dimensions (particularly those that could cause confusion in mounting of the parts) are tolerated usually individually by the addition of a tolerance mark or numerical value of the deviation to the respective basic size. Other dimensions where high precision of production is not required can be tolerated using a general record in the drawing. The standard ISO 2768-1:1989 is an internationally recognized standard for tolerancing of these linear and angular dimensions.

The standard ISO 2768-1 is designed for tolerancing of dimensions of machine parts produced using cutting operations or forming of sheets. It is advisable to use limit deviations defined here also with non-metallic materials. This standard prescribes limit deviations of linear and angular dimensions in four classes of accuracy. When choosing a tolerance class it is necessary (in addition to the constructional aspects) to also take into account, above all, the usual accuracy of the production shop. 

General limit deviations according to ISO 2768-1 are divided into 3 groups (tables): Limit deviations for linear dimensions [3.1], limit deviations for broken edges [3.2] and limit deviations for angular dimensions [3.3]. With dimensions up to 0.5mm (tables [3.1, 3.2]) the limit deviations are prescribed right after the respective basic size.

Note: In case general limit deviations of dimensions according to this standard have to be applied, a respective record must be placed in the drawing (in the description field or in its vicinity). E.g. for the medium tolerance class "ISO 2768 - m".

Hint: If not in contradiction with constructional and technological requirements, use preferably a medium class of accuracy "m" for machined metal parts.

Design of fit for specific allowance. [4]This paragraph can be used for a design (matching) of a suitable standardized fit of machine parts for a known clearance or interference respectively. The fit design is based on the standard ISO 286 (see [1]). The fit design is processed automatically and after its completion, the calculation provides the user with a set of 15 fits whose parameters meet the best requirements entered in paragraph [4.1]. 

4.2 System of fit.Although there can be generally coupled parts without any tolerance zones, only two methods of coupling of holes and shafts are recommended due to constructional, technological and economic reasons.

A. Hole basis systemThe desired clearances and interferences in the fit are achieved by combinations of various shaft tolerance zones with the hole tolerance zone "H". In this system of tolerances and fits, the lower deviation of the hole is always equal to zero.

B. Shaft basis systemThe desired clearances and interferences in the fit are achieved by combinations of various hole tolerance zones with the shaft tolerance zone "h". In this system of tolerances and fits, the upper deviation of the hole is always equal to zero.

where:

d=D ... basic size////  ... hole tolerance zone\\\\  ... shaft tolerance zone

 

The option of the system for the specified type of product or production is always influenced by the following factors:

Constructional design of the product and the method of assembly.

Production procedure and costs for machining the part.

Type of semi-product and consumption of material.

Costs for purchase, maintenance and storage of gauges and production tools.

Machine holding of the plant.

Options in use of standardized parts. 

Hint: Although both systems are equivalent in the view of functional properties, the hole basis system is used preferably.

4.3 Type of fit.Depending on the mutual position of tolerance zones of the coupled parts, 3 types of fit can be distinguished:

A. Clearance fitIt is a fit that always enables a clearance between the hole and shaft in the coupling. The lower limit size of the hole is greater or at least equal to the upper limit size of the shaft.

B. Transition fitIt is a fit where (depending on the actual sizes of the hole and shaft) both clearance and interference may occur in the coupling. Tolerance zones of the hole and shaft partly or completely interfere.

C. Interference fitIt is a fit always ensuring some interference between the hole and shaft in the coupling. The upper limit size of the hole is smaller or at least equal to the lower limit size of the shaft.

4.4 Basic size.Enter a common theoretical size of the coupled parts. 

Attention: The standard ISO 286 defines the system of tolerances, deviations and fits only for basic sizes up to 3150 mm. 

4.5, 4.6 Limit deviations for the fit.Depending on the selected type of fit [1.3], enter desired limit values of clearance or interference resp. of the designed fit in rows [4.5, 4.6].

4.7 Design and selection of the fit.This paragraph can be used for the fit design itself. After setting all desired parameters of the fit in paragraph [4.1], initiate automatic fit design using the button on this row. The design processes all combinations of prescribed hole and shaft tolerance zones (see tables in paragraphs [1.3, 1.4]) and selects 15 optimal standardized fits. The user is informed on processing of the calculations in a dialogue.

The qualitative criterion for selection of a fit includes a sum of deviations (in absolute values) of limit values of the clearance or interference resp. of the designed fit from desired values [4.5, 4.6]. After completion of calculations, the selected fits are transferred to the table. The table of designed fits is divided into two parts. The lower part includes selected fits listed from the best to the least optimal. The upper part of the table gives one of the preferred fits, particularly the one whose parameters best meet the desired limit deviations [4.5, 4.6]. After selection of any fit in the table, its parameters are displayed in paragraph [4.8]. 

Note: Dimensional data in the table are given in m.

4.8 Parameters of the selected fit.Parameters of the selected fit are calculated and mutual positions of tolerance zones of the hole and shaft are displayed in this paragraph. 

Note: Dimensional data on this picture are given in m.

Relationship of tolerance to surface finish. [5]This paragraph includes a table describing the relationship of surfaces of machine parts to their dimensional tolerances. Individual tolerance grades available for the given method of machining of the parts are marked in the table using a green field.

Hint: A table describing the relationship between surface roughness and the method of machining of machine parts can be found in the book "Units converter".

Setting calculations, change the language.Information on setting of calculation parameters and setting of the language can be found in the document "Setting calculations, change the language".

Workbook modifications (calculation).General information on how to modify and extend calculation workbooks is mentioned in the document "Workbook (calculation) modifications

GD&T Basic(s) True Position and TolerancesBy Otto Belden

This post is a very simple explanation of Position as used in Geometric Dimensioning and Tolerancing. Why am I writing about Position? One of the most frequent questions people ask me regarding Geometric Dimensioning and Tolerancing is "what does that target bulls-eye symbol mean". That bulls-eye symbol is called Position and it seems to be the most confusing and mysterious symbols in GD&T for some people. Before I talk about Position you should go back and read - or read if you haven't read already - THIS post that I wrote about tolerances and size and maybe even THIS post I wrote awhile back. There is nothing really mysterious or even complicated about the concept of Position and how it's used with Basic Dimensions in GD&T. The application can get pretty scary and complicated sometimes but the concept is pretty straight forward. I'm going to try and explain it in a overly simple way and later tie all these Design Related posts together as I write more of them.  Square Tolerance ZonesThe first thing that is important to point out is that Geometric Dimensioning and Tolerancing is all about the dimensions tolerances so I'm going to compare the 'traditional' method of tolerancing to Position as a starting point. So to start with have a look at a 'traditional' drawing below that uses linear coordinate dimensions. On a 'traditional' drawing that is using linear dimensions the tolerances are put on each of the dimensions either directly as in the picture below or in the title block (or notes) on the drawing. Have a look at the below drawings 2A and 2B that are dimensioned 'traditionally' with the tolerances on the dimensions themselves. I have left the dimensions of the block itself off the drawing for clarity.

Linear Dimensions with a Square Tolerance Zone

  In the top view of the above picture (2A above) there is a rectangular block and a couple of dimensions to a point near the middle. Imagine that you want to drill a hole 1.5 inches from the left side and 1 inch from the top as the dimensions show. Note that each dimension has a tolerance of +/-.25 inches so to get the hole in the right spot you first measure down from the top of the block 1 inch +/- .25 inches, giving you a total tolerance of .50 inches. Same thing with the other dimension, measure from the left 1.50 inches +/-.25 inches - again giving you a total tolerance of .5 inches. To get the hole in the right spot according to the dimensions (and the tolerances) you would have to drill the hole so that the center of the hole was somewhere inside that .5 inch square tolerance zone. Does that make sense? It seems strange if you think about it that a round hole would be positioned in a square tolerance zone doesn't it? Read more and this will start to make sense...

So looking at the above drawing 2A again there is a square tolerance zone created by the +/- tolerance on each of the dimensions. The point in the center of the tolerance zone is the Nominal position or the exactly perfect place for the center of the hole. In other words the dimensions are to the nominally perfect point that the hole center can be and the tolerances are showing how far away from that nominally perfect point the center of the hole can be.     Another way of thinking about this is: The dimensions on a drawing are locating tolerance zones and not the features themselves. Read that last sentence again and keep it in mind because it's a important concept and will be really important soon. So in the picture above the 1.50 and 1.0 dimensions are not dimensioning to the hole they are dimensioning to the tolerance zone that the center of the hole has to be in. It's easy to look at a drawing like the one above and think that the "dimensions are to the hole" but in reality they are not really dimensions to the hole, they are dimensions to the area that the center of the hole can be in. I'm going on and on about this concept because it's important to understand especially later (in future posts) when I'm going to write about more dimensioning concepts.   In 2B of the drawing above you can see the square tolerance zone with a dimension from the nominally perfect point in the center to the corner of the square tolerance zone. That diagonal dimension is .354 inches and that is the worst case position that the center of the hole can be in, or the farthest off nominal that the center of the hole can be and still be OK."Really, the hole can be off .354 inches" you ask?At first glance you might think that the worst case position that the hole can be off from nominal is .25 inches, after all the dimensions are +/- .25 inches, but that isn't the case because the tolerance zone is square shaped. Now have a look at the drawing below of the square tolerance zone that has two possible positions for the center of the hole, both .354 inches from Nominal.

The Pitfalls of Square Tolerance Zones

The drawing above shows the square tolerance zone and a couple dimensions to possible center points for the hole. Notice that the orange .354 dimension to a possible hole center is outside the tolerance zone but the black .354 dimension is just inside it.  The center of the hole can be off Nominal by .354 inches but only if the hole is off diagonally from the nominal point. If the center of the hole is off by .354 either horizontally or vertically then the hole is out of the tolerance zone and the part is considered to be bad. That is a very odd

way to dimension hole because the hole is round and it usually doesn't matter which direction a round hole is off from nominal, because the hole is round! A round hole can usually be off a little bit in any direction and still work in the design. If you dimension the drawing with a square tolerance zone you would have to reject all the parts that had holes off by .354 inches unless they were off diagonally. This odd situation is the  result caused by the square tolerance zone.    In the picture above I put a bunch of points where you might expect to see the centers of holes if you were to make a bunch of parts and measure the hole centers on all of them. When you mass produce parts you tend to get aNormal Distribution around the nominal position for all the dimensions, those points represent what you might see if you made a bunch of parts and measured to the hole centers on all of them. Using a square tolerance zone would mean that a lot of parts would be rejected and possibly scrapped because the hole centers were outside the square tolerance zone even though the parts would probably work OK.    Round Tolerance ZonesAt this point I want to finally talk about Position and what it means in GD&T. In a huge oversimplification I'm going to say that in this example "Position is a round tolerance zone". I'll probably get a lot of emails (ottobelden.@yahoo.com) and maybe even nasty comments on this Blog about that last sentence because Position is a lot more than a 'round tolerance zone' but for now in the context of this post, think of Position as a round tolerance zone (it's actually cylindrical in this case but for now just think of it as round). To start this off I've redrawn the above drawing of the block with the hole in it using Position. Have a look at the drawing below and notice all the rectangles with numbers in them. The drawing looks complicated but really it's almost the same drawing as I did above.

Block and Hole Redrawn with a Position Tolerance(the square tolerance zone is shown for reference only)

  In the drawing 2C above I redrew the block and the hole but this time a equivalent Position tolerance is used instead of the square tolerance zone. The first thing that is different between the drawings is the 1.50 inch and 1.00 inch dimensions have boxes around them. When you put a box around a dimension it's called a Basic Dimension and Basic dimensions don't have any tolerance associated with them, they are perfect. Most people freak out at this point and say "you can't have perfect dimensions without tolerances" because nothing can be made perfect. That is true, all dimensions must have tolerances but the tolerances don't necessarily have to be on the dimensions themselves. With basic dimensions the tolerance is someplace else and not on the dimensions.   

The concept of having 'perfect' Basic dimensions is not really that different from the +/- toleranced dimensions in the first drawings 2A and 2B above. With the +/- toleranced dimensions the 1.50 and 1.00 dimensions are dimensioning to the Nominally perfect center of the square tolerance zone so they are really perfect right? In the case of Basic dimensions (with the box around them) the 1.00 and 1.50 are dimensioning to the Nominally perfect center of a round tolerance zone and they are perfect too. The same perfect dimensions with just different shaped tolerance zones. The Basic box around the dimensions is really just a reminder telling you that the tolerance isn't associated with the dimension as it was with the +/- dimensions, the tolerances are someplace else.  Have a look again at the 2C drawing above. The 1.50 and the 1.00 Basic dimensions are locating the center of a round tolerance zone that is .708 inches in diameter. The .708 inch diameter tolerance zone is being defined in the rectangular box under the hole diameter with the "target bulls-eye symbol" Position symbol. The rectangular box under the hole dimension is called the Feature Control Frame and just like it's name it is controlling the Position of the feature (in this case the hole). This is a handy way of specifying the location of the hole because the location tolerance for the hole is right next to the hole diameter.   In drawing 2C I drew in the old square tolerance zone for comparison to the new round Position tolerance zone. Notice that the square tolerance zone is circumscribed by the round Position tolerance zone. That is because the .708 inch diameter round tolerance zone is 2X the .354 worst case square tolerance zone hole center location shown in drawing 2B above. Remember in the case of the square tolerance zone the hole could be off nominal by .354 inches only in the diagonal directions and not horizontally or vertically. The .708 inch round tolerance zone allows the center of the hole to be located .354 inches off nominal in any direction! With the position tolerance not only is the round hole being located with a round tolerance zone but if you make a bunch of parts and the hole centers are normally distributed around the nominal 'perfect dimensions' all the parts will be OK and not rejected.

Cylindrical Tolerance Zone with Position

Earlier in this post I said that Position tolerance zones are round but that wasn't exactly correct. Position tolerance zones are actually cylindrical in this case because in the real world parts are 3 dimensional objects. Position tolerance zones can be other shapes too and I'll write about those cases in another post, for simplicity in this case think of Position tolerances as cylindrical.In the Feature Control Frame below the hole diameter I've added the letter A in it's own box. The letter A in this case is referencing a Datum that is being defined in the lower view of the part. What this means is that

the .708 diameter Position tolerance zone is located in relation to Datum A, in this case the flat face of the rectangular block. Have a look at drawing 2D above to see what I mean and note that the round tolerance zone shown in the top view is extending through the entire part perpendicular to the flat surface datum A.   Remember that for the part to be OK the center of the hole has to be inside the tolerance zone. The center of a hole is really the center axis of the hole because the hole is a 3 dimensional feature. Because the Position tolerance is referencing Datum A the cylindrical tolerance zone is Perpendicular to the flat face of the part. What this all means is that the center axis of the hole must be completely inside the cylindrical Position tolerance zone as shown in drawing 2D above. The Position tolerance is controlling not only the location of the center of the hole but also how perpendicular the hole must be to the Datum face A. Isn't Position cool?   In the drawing 2D above the hole isn't exactly Perpendicular to the face of the part but the center axis is entirely within the tolerance zone so the part is OK. If you wanted the hole to be even more perpendicular to the face of the part (but not change the tolerance zone) you have several options and I'll write about those in another post. For now the important concepts to remember are:Dimensions on drawing are to tolerance zones and not to the features themselves.

Position tolerance zones are 3 dimensional and the center of whatever they are dimensioning must be entirely within the position tolerance.

Basic dimensions have a box around them and they are perfect, the tolerance for Basic dimensions is someplace else on the drawing.

Square tolerance zones allow things to be farther out from Nominal than the tolerance on the dimensions state because the tolerance zones are square!

This post is a simple explanation of the Geometric Dimensioning and Tolerancing concepts of Basic Dimensions, (True) Position and Datum's. There is a lot more to all these concepts that I didn't cover in this post in the interests of keeping it simple. I intend to elaborate on not only the concepts in this post but the other posts where I wrote about GD&T HERE and HERE and tie them all together. I will also cover other Position concepts as well as  lots of other fun and exciting GD&T stuff!! If you have any questions or see something I might have missed please leave a comment or send me an email at ottobelden@yahoo.com and I'll be happy to get back to you!

4.2.

As already indicated, tolerance can be defined as the magnitude of permissible variation of

a dimension or other measured or control criterion from the specified value. Tolerances have to be

allowed because of the inevitable human failings and machine limitations which prevent ideal

achievements during fabrication. In order to maintain economic production and facilitate the

assembly of components it is necessary to allow a limited deviation from the designed size. Due to

its inevitability, tolerances constitute an engineering legality for deviation from the ideal value,

and like any other legal matter, formulation of tolerances must also be given due consideration,

and much thought and planning should go into it. The various factors affecting the choice of

tolerances should be given due consideration, as the setting of tolerances is not an arbitrary matter.

Though functional requirement is the primary consideration, i.e. the permitted deviation in size

must permit the assembly to function correctly for its designed life, there are other factors like

standardisation, manufacturing needs etc., which also influence the choice of tolerances and the

primary consideration of functional requirement sometimes requires compromise with these

factors.

The primary purpose of tolerances is to permit variation in dimensions without degradation

of the performance beyond the limits established by the specification of the design. Where high

performance is the criterion, there the functional requirements will be the dominating factor in

setting tolerances. However, where the functional performance provides some latitude, then

tolerance choice may be influenced and determined by factors like standardisation, methods of

tooling, and available manufacturing equipment.

The numerical values of tolerances may range across the entire spectrum of measurements

and if in all the cases, the functional requirement is taken as the only criterion to decide the value

of tolerance then there may be serious disadvantages like—too many different tolerances which

means excessive amounts of calculations and studies to establish tolerance values, excessive

amount of special tooling, complications in inspection etc. If a limited number of standard tolerances

are established, and the tolerances are chosen from these so that these are slightly closer than the

function dictates, then we get the advantages of fewer varieties of tooling, few calculations and

increased unit quantities because of repeated use of the same designs.

Functional and Non-functional Dimensions.Functional dimensions are those which

have to be machined and fit with other mating components. Non-functional dimensions are those

which need not be machined to a high degree of accuracy. These have no effect on the quality

performance of the component or assembly.

4.2.1.

Why tolerances are specified ?Ideal conditions would call for parts without any

kind of dimensional variation, but in actual practice it is impossible due to following reasons :

(i) Variations in the properties of the material being machined introduce errors.

(ii) The production machines themselves have some inherent inaccuracies built into them

and have the limitations to produce perfect parts.

(iii) It is impossible for an operator to make perfect settings. In setting up the machine, i.e.

in adjusting the tools and workpiece on the machine, some errors are likely to creep in.

An attempt to entirely overcome these factors with a view to obtain ideal conditions would

result into exhorbitant costs. The parts should, therefore, be made as inaccurate as tolerable to

satisfy the functional requirements. Thus tolerances are specified to the dimensions of all manufac-

tured parts and these should be just enough to do the intended job and no better. The tolerance is

a compromise between accuracy required for proper functioning and the ability to economically

produce this accuracy.

4.2.2.

Design Considerations in the Selection of Engineering Tolerances.The estab-

lishment of correct engineering or manufacturing tolerances is a matter of serious concern because

both too tight and too loose tolerances result in excessive cost. Tight tolerances result in unnecessary

machining and inspection time, high rejects, and adversary relationship between design, manufac-

turing, and inspection. Loose tolerances result in assembly problems and poor product performance.

The designer for selection of tolerances must have broad knowledge of engineering metrology,

must thoroughly understand how the part is to be measured. He should also be familiar with

capability of a wide range of manufacturing processes. He must also have a clear understanding of

the functional requirements of the piece part in assembly and operation with the other components

of the system.

Reasons for tendency to select tight tolerances. The unexperienced designer in order to protect

himself specifies significantly tighter tolerance than necessary for the following reasons: the creed

for precision, fear of interference or excessive clearance between assembled parts, selection of

tolerances from company or vender standards which tend to favour tight tolerances or selection

from similar previous design which may have been established on unrealistic tolerances, practice

of considering tight tolerances synonymous with good quality.

Optimum tolerance. A good designer must explore information and techniques available as

guidance in the establishment of realistic and, where possible, optimum engineering tolerances.

It must be remembered that the cost of machining and finishing to tighter tolerances

increases rapidly. One should have fairly good idea of relative cost of producing parts with different

tolerances. The standard products available within the specified tolerances should be considered.

One should also have good understanding of tolerances resulting from various production processes.

The understanding of statistical tools is of great help. It can be safely assumed that the most

of the manufacturing processes produce parts which are normally distributed. For normal distribu-

tion, 95% of all production lies within ±2 standard deviations and 99.7% within ±3 standard

deviations. It should be remembered that in a random assembly, probability of all large parts being

assembled with large parts, or of all small parts likewise being assembled together, is extremely

small. With this approach it is possible to use wider tolerances.

The use of quality control charts also enables one to be more realistic in selection of

tolerances. Quality control chart is a powerful tool for the definition of the potential dimensional

accuracy of manufacturing processes. Quality control charts are based on the assumption of normal

distribution, random sampling, and independence between samples. Control charts are good guide

for the design office in establishing of realistic specifications.

It is very important that the designer understands the capability of manufacturing process

in producing parts to a given tolerance. Computer simulation techniques are used to provide

understanding of the tolerance requirement of product of design. Computer simulation provides

data on the probability of parts of a certain tolerance range interfering at assembly.

4.2.3.

What is a basic dimension ?A basic dimension is the dimension, as worked out by

purely design considerations. Since the ideal conditions of producing basic dimension, do not exist,

the basic dimension can be treated as theoretical or nominal size, and it has only to be approximated.

A study of function of machine parts would reveal that it is unnecessary to attain perfection because

some variations in dimentions (however small) can be tolerated on sizes of various parts. It is, thus,

general practice to specify a basic dimension and then indicate by tolerances as to how much

variation in the basic dimension can be tolerated without affecting the functioning of the assembly

into which this part will be used.

4.2.4.

Different ways of expressing Tolerances.Tolerances are basically specified in two

forms, i.e. unilateral and bilateral. In unilateral tolerances, the total tolerance as related to a basic

dimension is in one direction only. This form of tolerance is usually indicated when the machining

of mating parts is called for, as this greatly assists the operator. This form of tolerance is usually

indicated when the machining of mating parts is called for, as this greatly assists the operator. The

operator machines to the upper limit of shaft (lower limit for a hole) knowing fully well that he still

has the whole tolerance left for machining before the parts are rejected. In case of bilateral

tolerances, the total tolerance is specified on both sides (plus and minus) of the basic dimension.

Bilateral tolerances usually have plus and minus tolerance of equal amount, but not necessarily

always. This system permits operator to take full advantage of the limit system especially in

positioning a hole.

In the case of unilateral tolerances, the dimension is allowed to vary only in one direction.

This system is used in machining processes like drilling in which case the dimensions are most

likely to deviate in one direction only (in drilling, hole is always of over size rather than undersize).

Bilateral tolerance system defines the theoretically desired size and the probable deviation

permitted on either side of the basic size. This system is used in mass production techniques where

machine setting is done for the basic size. Under such conditions, if tolerances are specified as

unilateral, then these should be changed into bilateral tolerances by changing the basic size. The

basic size should be mid way between upper and lower limits.

4.2.5.

Specifying tolerances for given assemblies.The type of assembly, i.e. fit between

two mating components is decided based on functional requirements. Based on it, tolerances on

shaft and hole are decided using two approaches, viz. complete interchangeability, or statistical

approach. In complete interchangeability approach, no risk is taken about even a single non-con-

forming assembly. If the fit between a shaft and hole is a clearance type, then for complete

interchangeable approach (referring to Fig. 4.2 it will be seen that) tolerance on shaft = tolerance

on hole = half the maximum clearance—half the minimum clearance.

The statistical approach bases the permissible tolerances on the normal distribution curve,

considering that only 0.3% components would lie beyond ± 3o limits. This approach, obviously,

allows wider tolerances compared to complete interchangeability approach. The statistical approach

thus permits cheaper production methods but can be used when components are produced in bulk.

If all the assignable causes of variation are fully controlled, then expected frequency curves of shafts

and holes will be normal frequency curves, and accordingly the expected frequency of the clearances

will also be the normal curve.

It is estimated that about 33% more tolerance is permitted by statistical approach in

comparison to total interchangeability approach.

4.2.6.

Tolerance Accumulation.If a part comprises of several steps, each step having some

tolerance over its length, then overall tolerance on complete length will be sum of the tolerances on

individual length.

It would be appreciated that this practice of specifying tolerances would result in high

tolerances on the overall length. The effect of accumulation of tolerances can be minimised by

adopting progressive dimensioning from a datum as shown in Fig. 4.4.

4.2.7.

Compound Tolerances.Compound tolerances

are those which are derived by considering the effect of toleran-

ces of more than one dimension. For example, in Fig. 4.5, the

tolerances on dimension I are dependent on tolerances on L, h

and 8. Thus compound tolerance of T is the combined effect of

these three tolerances. The minimum tolerance on T will be

corresponding to L – b, 6 + a and h + c.

Interchangeability (Metrology)

An interchangeable part is one which can be substituted for similar part manufactured to

the same drawing.

In earlier times production used to be confined to small number of units and the same

operator could adjust the mating components to obtain desired fit. With time the concept of

manufacturing techniques kept on changing and today the same operator is no more responsible

for manufacture and assembly too. With economic oriented approach, mass production techniques

were inevitable, that led to breaking up of a complete process into several smaller activities and

this led to specialisation. As a result various mating components will come from several shops, even

a small component would undergo production on several machines. Under such conditions it

becomes absolutely essential to have strict control over the dimensions of portions which have to

match with other parts. Any one component selected at random should assemble correctly with any

other mating component, that too selected at random. When a system of this kind is ensured it is

known as interchangeable system. Interchangeability ensures increased output with reduced

production cost.

In interchangeable system, every operator being concerned only with a limited portion of

overall work, he can easily specialise himself in that work and give best results leading to superior

quality. He need not waste his skill in fitting the components by hit and trial and assembly time is

reduced considerably. In the case of big assemblies, several units to manufacture individual parts

can be located in different parts of country depending on availability of specialised labour, raw

material, power, water and other facilities and final assembly of all individual components

manufactured in several units can be done at one place. The replacement of worn out or defective

parts and repairs is rendered very easy and the cost of maintenance is very much reduced and shut

down time also reduced to minimum.

Interchangeability is possible only when certain standards are strictly followed. Universal

interchangeability (i.e. parts drawn from any two altogether different manufacturing sources for

mating purposes) is desirable and for this it is essential that common standards be followed by all,

and all standards used by various manufacturing units

should be traceable to a single source, i.e. international

standards. When all parts to be assembled are made

in the same manufacturing unit, local standards may

be followed (condition being known as local interchan-

geability) but for reasons of obtaining spares from any

other source it is again desirable that these local stand-

ards be also traceable to international standards.

The required fit in an assembly can be obtained

in two ways, namely (i) universal or full interchan-

geability, and (ii) selective assembly. Full interchan-

geability means that any component will mat with any

other mating component without classifying manufactured components in subgroup or without

carrying out any minor alterations for mating purposes. This type of interchangeability is not must

for interchangeable production and many times not feasible also as it requires machines capable of

maintaining high process capability and very high accuracy, and very close supervision on produc-

tion from time to time. (Process capability of a machine is defined as its ± 3o spread of dimensions

of components produced by it. If a plot is drawn of the actual dimensions of the similar components

produced by a machine, it is found to follow natural law of distribution, i.e. having mean of all the

components at central value with a spread of ± 3o value, a being known as standard deviation, and

±3oas the process capability of machine). For full interchangeable assembly it is essential that only

such machines be selected for manufacturing whose process capability is equal to or less than the

manufacturing tolerance allowed for that part. Only then every component will be within desired

tolerance and capable of mating with any other mating component.

4.3.1.

Selective Assembly.Today the consumer not only wants quality, precision and

trouble free products but also he wants them at attractive prices. This has become possible only by

adopting automatic gauging for selective assembly whereby parts manufactured to rather wide

tolerances fit and function as though they were precisely manufactured in precision laboratory to

very close tolerances. This is a concept which does away with old idea of inspection in which part

is identified as ‘good’ or ‘bad’; good part being used for assembly and bad used to be scraped. In

selective assembly the components produced by a machine are classified into several groups

according to size. This is done both for hole and shaft and then the corresponding groups will match

properly.

If some parts (shaft and holes) to be assembled are manufactured to normal tolerances of

0.01 mm (and both are within the curve of normal distribution), an automatic gauge can segregate

them into ten different groups with a 0.001 mm limit for selective assembly of the individual parts.

Thus parts with tolerances of 0.0001 mm are obtained (due to segregation) and both the

conditions of high quality and low cost can be served by selective assembly technique. However, it

is very important that the two component parts to be fitted together must be kept within the normal

distribution, i.e. the central or mean value should be at desired calculated value and the process

capability of two machines producing shafts and holes must be identical otherwise for some

components the mating components will not be available. If not so, then other techniques need to

be adopted which are described below :

Fig. 4.7 shows a case in which the process capability of both shaft and hole producing

machines is same but tolerances on parts are desired as one-tenth of process capability of machines.

In such a case the parts are segregated by automatic inspection into ten groups and parts in shaft

region Si are matched with parts in hole region Hh S2 with H2 and so on. This results in matching •

of parts having tolerances l/10th of machine capability. In this case as the process capability of both

machines is same, equal number of parts are available in each segregated zone and no wastage will

be there.

Fig. 4.8 shows another case in which the process capability of hole making machine is much

wider than the tolerance of part but shaft making machine can produce component to the desired

tolerance. In such a case the parts with hole are segregated into adequate number of groups

depending on the desired tolerance.

This curve when broken into several groups enables to determine the number of components likely

to be produced in each group. The shafts are ‘therefore’ so produced that their setting needs to be

changed as many number of times as there are groups formed for the holes and at the mean value

Shaft production (Area under curve dictates number of parts

to be produced for each setting)

Fig. 4.8

of each sub-group. The number of shafts to be produced for each setting is determined by earlier

curve for holes.

Another typical case can be when the process capability of both shaft producing and hole

making machines are different and much wider than the permissible tolerances. In such a case the

process having worst process capability is broken into adequate number of sub-groups as described

before. The other process is then broken into adequate groups with their set points so adjusted that

the number of components produced in this process corresponding to various groups made in earlier

process will be same and as such no wastage will be there.

It will be noted that selective assembly technique can be followed for latter two cases also

but is little complicated and the first case is more preferred one for selective assembly.

It would now be obvious that the selectively assembly is based on the natural distribution

of components produced by a machine ; and proper means being available to ensure mean value

and the dispersion of the process and the segregation of parts by automatic gauging. Thus machine

produces parts of wider tolerance (cost being low) but for assembly, parts of one-tenth of tolerance

of machine required for optimum performance are available. This is the best and cheapest method

of assembling parts and is widely used in industry. Selective assembly is often followed in air craft,

automobile industries and in ball and roller bearing unit as the tolerances desired in such industries

are very narrow and not possible by any sophisticated machine at reasonable costs. The selective

assembly, however enables such tolerances to be arranged without their actually being produced

as discussed above.

Limits of Size

There are three considerations in deciding the limits necessary for a particular dimension,

viz. functional requirement (function of the component, what it is required to do), interchangeability

(ease of replacement in the event of failure), and economics (minimisation of production time and

cost). As already pointed earlier, the degree of tolerance thus calls for a compromise. To assist the

designer in his choice of limits and fits, and to encourage uniformity throughout, a number of

standards on limit and fit system have been published which must be strictly followed.

A limit system consists of a series of tolerances arranged to suit a specific range of sizes and

functions, so that limits of size may be selected and given to mating components to ensure specific

classes of fit.

Plain Gauges (Metrology)

 

4.12.

Gauges are inspection tools of rigid design, without a scale, which serve to check the

dimensions of manufactured parts. Gauges do not indicate the actual value of the inspected

dimension on the work. They can only be used for determining as to whether the inspected parts

are made within the specified limits.

Plain gauges are used for checking plain (unthreaded) holes and shafts. Gauges are classified.

(1) According to their type :

(a) Standard and limit gauges,

(b) Limit gauges.

(2) According to their purposes :

(a) Workshop.

(b) Inspection.

(c) Reference or master gauges. These are better known as control gauges and comprise

the setting plug gauges and wear check plug gauges and are mainly used for

controlling the dimensions of ring gauges and for checking their wear during use.

(3) According to the form of the tested surface :

(a) Plug gauges for checking holes.

(b) Snap and ring gauges for checking shafts.

(4) According to their design :

(a) Single limit and double limit gauges,

(b) Single ended and double ended gauges,

(c) Fixed and adjustable gauges.Advantage of fixed gauges

The various advantages of fixed gauges in comparison to comparator type gauges are :

(i) Fixed gauges are essentially free from errors due to drift and the original adjustment,

non-linear response, effect of power supply variations and other extraneous factors which neces-

sitate regular calibration and occasional correction on comparator type gauges.

(ii) These provide positive dimensional information.

(iii) These are portable and independent of power supply availability.

(iv) These involve no other auxiliary equipment and set ups.

(v) These can be designed to check combinations of several dimensions comprising lengths,

diameters and angles.

(vi) These can be designed to inspect interrelated features, for size, location, form, alignment

etc. so as to check the virtual size of a member (combined effect of all parameters with regard to

the functional adequacy of the inspected features.)

(vii) These are particularly useful in the checking of part members whose meaningful

geometric irregularities can’t be readily detected by gauges which do not provide complete

reverse

replica of the part portions.

(viii) These provide uniform reference standards.

(ix) These are not expensive.

(x) Comparator have to be set from time to time using master fixed gauges.

4.12.1.Inspection Gauging of Plain Workpieces.

As per IS : 3455—1971, in order to

avoid any dispute, the manufacturer and purchaser should use gauges as follows :

The inspection department should normally use the same types of gauges as used in the

workshop. However in order to attain same results by both workshop and inspection department,

it is recommended that workshop should use new or only slightly worn gauges and inspection

department should use gauges with their size nearer the permissible wear limits.

As regards purchaser, he can either use the gauges of manufacturer, after ensuring their

accuracy, or use gauges having their sizes near the wear limit ; or use gauges having tolerance

zones so disposed so as to ensure acceptance of sizes which are within the specified limits.

As the dimensions for workpieces and inspection instruments are specified at 20°C, all

measurements should normally be carried out at 20°C. However if, both gauges and workpieces

are

of same material or materials having same coefficient of linear expansion then checking

tempera-

ture may deviate from 20°C without deteriment to the result, provided same temperature is

attained

both by workpiece and gauges.

4.12.2.Types of Gauges.

The gauges for cylindrical holes and internal screw-threads are

customarily in the form of a cylindrical plug, plain or screwed, with a convenient handle. The

gauging portion of the gauge may be either integral with the handle or the whole gauge may be

machined from one piece of metal. Such gauges are usually called ‘solid gauges’. Alternatively,

the

gauging portion and the handle may be separately manufactured and, for use, are engaged

together

to form a rigid assembly by means of a suitable locking device. The latter type is generally called

as ‘renewable end’ type of gauges. The ‘Go’ and ‘No Go’ gauges may be in the form of separate

single-ended gauge, or may be combined on one handle to form a double-ended gauge. In the

case

of plain plug gauges a form of convenient combined ‘Go’ and ‘No Go’ gauge is the progressive

gauge,

which is single-ended gauge with one gauging member having two diameters to the ‘Go’ and

‘No

Go’ limits respectively. In the case of plain plug gauges of diameter larger than 75 mm, which

are

very heavy, it is common practice to use bar type (segmental type) of gauges, because the

efficiency

of the gauge would decrease rapidly if the sensitiveness of user is impaired by weight.

Another serious problem encountered in plug gauges is of

inserting it into the bore of a component, because the axes of gauge

and hole should be made coincident before entering which is a

difficult task specially with heavy gauges. If this condition is not

satisfied, gauges will have tendency to jam in the hole. In order to

overcome these difficulties it is usual to provide a lead in chamber

(Fig. 4.27) which minimises damages to holes and saves time.

The gauges for shafts and external threads are either of

‘ring” gauge form or of’gap’ gauge form. Ring gauges are generally

of non-adjustable type and separate gauges are used for ‘Go’ and ‘No Go’ gauging. Gap gauges

for

plain work may be either of the solid, non-adjustable type or may be of the adjustable type. Gap

gauges for screw threads are invariably of the adjustable type. Either the separate gauges may be

used for ‘Go’ and ‘No Go’ gauging or a combined ‘Go’ and ‘No Go’ gauge may be used, and the

adjustable gap gauges are generally of the latter form.

The entering end of the larger gauges, being liable to become burred if accidentally laid down

heavily on metal surfaces, is provided with a guard extension at the entering end of gauges. All

sharp edges on the gauging portions and handles should be removed and the larger and heavy

plug

gauges should be provided with venting holes.

The various type of limit plug gauges and limit snap gauges are shown below :

Fig. 4.27. Pilot plug gauge.

4.12.3.Plain Plug Gauges.

Generally the gauging members of the plain plug gauges are

made of suitable wear-resisting steel and the handles can be made of any suitable steel e.g.

handles

may be made of light metal alloys for heavy plain plug gauges, or suitable non-metallic handles

may be provided for smaller plain plug gauges. The gauging surface of plain plug gauges are

normally hardened to not less than 750 H.V. and suitably stabilised and ground and lapped.

The plain plug gauges are normally of double ended type for sizes upto 63 mm and of single

ended type for sizes above 63 mm.

The usual way of designating the plain plug gauges is by ‘Go’ and ‘No Go’ as applicable, the

nominal size, the tolerance of the work-piece to be gauged and the number of the standard

followed

e.g., a double ended ‘Go’ and ‘No Go’ plain plug gauge for gauging a bore of 10 mm with

tolerance

H7 and if designated according to Indian Standard (IS : 3484—1966) shall be designated as :

‘Go and No Go plain plug 10 H7, IS : 3484′.

The various types of plain plug gauges in common use are shown below :

(i) ‘Go’ and ‘No Go’ plain plug gauges for sizes upto 10 mm, (solid type). (Refer Fig. 4.29)

(ii) ‘Go’ and ‘No Go’ plain plug gauges for sizes over 10 and upto 30 mm (Taper Inserted type).

(Refer Fig. 4.30)

Fig. 4.30. Section of Handle.

(iii) ‘Go’ and ‘No Go’ plain plug gauges for sizes over 30 mm and upto 63 mm (Fastened type),

(Refer Fig. 4.31).

Fig. 4.31. Section of Handle.

Fig. 4.32. Section of Handle.

(iv) ‘Go’ and ‘No Go’ plain plug gauges for sizes over 63 mm and upto 100 mm (Fastened type).

(Refer Fig. 4.32)

(v) ‘Go’ and ‘No Go’ plain plug gauges for sizes over 100 mm and upto 250 mm (Flat type).

(Refer Fig. 4.33). This is a shell form plug gauge. Each plug is relieved to reduce weight.

Section of Handle

Fig. 4.33

For still further bigger holes and to restrict weight, use can be made of segmental cylindrical

ended gauges.

Spherically ended rods are used for very large holes. It would be noted that with such types

of gauges the full form of the gauge is lost and the errors of holes like ovality may not be

detected.

It is the general practice not to use cylindrical plugs above 100 mm diameter but to use

cylindrically

ended bars or spherically ended rods. Similarly Go gauges between the sizes of 100 and 200 mm

diameter can take the form of a cylindrically ended bar.

The plain gauges are marked with the following on their handles for their identification :

(i) Nominal size.

(ii) Class of tolerance.

(iii) The word ‘Go’ on the ‘Go’ side.

(iv) The words ‘No Go’ on the ‘No Go’ side.

(v) The actual values of tolerances.

(vi) Manufacturer’s name or trade mark.

The ‘No Go’ side is always painted with a red band. A typical example of the marking is

shown in Fig. 4.34. It is usual practice to apply suitable anti-corrosive coating to the plug gauges

in order to protect them against climatic conditions. In order to prevent damage in handling and

transit, these are packed in suitable cases. It may be mentioned that gauges with the gauging

portion integral with the handle are now becoming obsolete and gauges with renewable ends are

gaining popularity (Refer Fig. 4.35) because of the following advantages :

(i) Worn or damaged end can be replaced conveniently.

(ii) In the event of scraping of gauge, handle can be used for other gauge.

(iii) To reduce the weight, handle can be made of plastic which also facilitates in handling

the gauge, reduces cost and minimises risk of heat transfer.

For smaller through holes, another useful renewable and plug gauge is the progressive type

of gauge in which both GO and NOT GO gauging members are provided on same side separated

by

a small distance (Refer Fig. 4.36). First Go portion is inserted in the hole which would be further

obstructed by NOT GO portion if hole is of tolerable size.

Renewable end type plug gauge—single ended

Fig. 4.35

Progressive form of plug gauge

Fig. 4.36

4.12.4.Plain Ring Gauges.

The plain ring gauges are made of suitable wear resisting steel

and the gauging surfaces are hardened to a hardness of about 720 H.V. The gauging surfaces are

first suitably stabilised using proper heat treatment process and then ground and lapped and other

surfaces are finished smooth. These are protected against climatic conditions by applying a

suitable

anti-corrosive coating.

These are available in two designs, ‘Go’ and ‘No Go’. These are designated by ‘Go’ and ‘No

Go’ as may be applicable, the nominal size, the tolerance of the workpiece to be gauged, and the

number of the standard followed.

The general shapes of Go’ and ‘No Go’ gauges, for range from 3 to 70 mm in 10 steps, and

from 70 to 250 mm in 17 steps are shown in Figs. 4.37 and 4.38 and Figs. 4.39 and 4.40

respectively.

‘Go’ plain ring gauge for dimension dl from 3 to 70 mm in 10 steps

Fig. 4.37

For Fig. 4.37, dimension d2 varies from 22 mm (for range of di = 3—5 mm) to 112 mm (for

range of di = 60—70 mm). Correspondingly b varies from 5 to 22 mm and c from 0.4 to 1.6 mm.

‘Go’ plain ring gauge for dimension dx from 70 to 250 mm in 17 steps.

Fig. 4.38

‘No Go’ plain ring gauge for dimension d1 varying from 3 to 70 mm in 10 steps.

Fig. 4.39

For Fig. 4.38 dimension d2 varies from 125 mm (for range of dx = 70—80 mm) to 355 mm

(for range of di = 236—250 mm). Corresponding to dx = 120 to 355, dimension d2 varies from

100

mm to 280 mm ; b\ from 12 to 28 mm ; c from 2.5 to 4 mm ; r from 3 to 6 mm ; t from 3 to 8

mm.

For Fig. 4.39 dimension d2 varies from 22 mm for range di = 3—5 mm, to 112 mm for range

di = 60—70 mm. Correspondingly bi varies from 3 to 8 mm, c from 0.4 to 1.6 mm.

For Fig. 4.40 dimension d2 varies from 125 to 355 mm, d3 from 100 to 280, d4 from 113 to

335, &i from 10 to 25, b2 from 7 to 16, t from 1.5 to 4, c from 1 to 3, and r from 3 to 6 mm.

‘No Go’ plain ring gauge for dimension d1 varying from 70 to 250 mm.

Fig. 4.40

‘Go’ and ‘No Go’ snap gauges for sizes over 3 mm and upto 100 mm.

Fig. 4,41

4.12.5.Snap Gauges

4.12.5.1.Rib type snap gauges.

Double-ended type snap gauges can be conveniently used

for checking sizes in the range of 3 mm to 100 mm and single ended progressive type snap

gauges

are suitable for size range of 100 to 250 mm. The gauging surfaces of the snap gauges are

hardened

upto 720 HV and are suitably stabilised, ground and lapped. The other surfaces are finished

smooth.

The way of marking is also shown.

‘Go’ and ‘No Go’ snap gauges for sizes over 100 mm and upto 250 mm.

Fig. 4.42

4.12.5.2.

Plate snap gauges.

Double-ended type plate snap gauges are used for sizes in the

range of 2 to 100 mm and single-ended progressive type in the size range of 100 to 250 mm.

These

For sizes upto 10 mm For sizes above 10 mm

Fig. 4.43

are made of wear resistant steel of suitable quality. The gauging surfaces are properly hardened,

stabilised, ground and lapped. Other surfaces are smooth finished. The gauges are reasonably flat

and all sharp corners and edges are removed.

Plate snap gauges over 100 mm and upto 250 mm

Fig. 4.44

4.12.6.Adjustable Type Gap Gauges.

In these gauges the gauging anvils are adjustable

endwise in the horse-shoe frame. This type of gauge is set by means of slip gauges to any

particular

limit required. It is possible to set well made gauges to within about 0.002 mm of a desired size

and

thus their use enables fuller advantage to be taken of the manufacturing tolerance on the work

than when solid gauges with an appreciable manufacturing tolerance of their own are employed.

The adjustability also enables wear of the ‘Go’ anvils to be taken up at any time. If the anvil

faces

lose their flatness with use, they can bereground quite readily after removing them from the

frame.

The method of adjusting the anvils is usually by means of independent and finely threaded

screws

at the back end, and they are finally locked in position by some type of clamping screw.

For gap gauges the following conditions must be fulfilled :

(i) The frame should be of rigid design, and sufficiently strong to withstand workshop

conditions.

(ii) In order to provide suitable supports for clamping during manufacturing and subsequent

re-grinding, each side of the frame should have three finished coplanar faces, and these faces

should

be parallel.

(iii) The gauging anvils should have only a sliding and not a rotating movement for adjust-

ment.

(iv) The anvils should have a sufficient length of bearing on their shanks to ensure parallel

movement when being adjusted and also to obviate any tendency to tip when being locked or

when

in use.

(v) All adjustable parts should be close fitting.

(vi) The means of adjusting the gauging anvils should be simple.

(vii) The locking device for the anvils should be quite definite in its action.

(viii) There should be suitable provision for sealing the adjustment to prevent unauthorised

readjustment.

(ix) The distance between the ‘Go’ and ‘No Go’ anvil should be sufficient, when the gauge is

set for work of the largest diameter and largest tolerance, to enable the work to be in a free

position

when passing the ‘Go’ anvils and before meeting the ‘No Go’ anvils.

(x) The range over which the gauge can be adjusted should be marked on the frame.

4.12.7.Combined Limit Gauge. (Fig. 4.45).

In the case of gauging of cylindrical holes, it

is possible to combine both the ‘Go’ and ‘No Go’ dimensions of a plug gauge and thus a single

gauge

doing the work of checking both the upper and lower limits. It is achieved by employing a

spherically

ended gauge of the same diameter as the lower limiting dimen-

sion of the hole. Towards the outer edge of the spherical

member, a spherical projections is provided which is arranged

in such a way that the distance from the surface S to the

diametrically-opposite point on the spherical surface is equal

to the maximum limiting dimension of the hole. For checking

the hole for ‘Go’ position, the gauge is inserted into the hole

with the handle parallel to the axis of the hole. For checking

the hole for ‘No Go’ limit, the gauge is tilted so that the spherical

projections is normal to hole. The gauge in this position should

not enter the hole.

Other types of gauges in common use employ pilot

gauging methods. In pilot gauges, the possibility of the jam-

ming of ordinary plug gauge in the hole when inserted oblique-

ly, is eliminated. It is achieved by first proving a chamfer at the

end of plug gauge and then machining a narrow ring or pilot

after it.

4.12.8.Position Gauge.

There is a wide variety of position gauges in common use and their

design is based upon the shape of the work. Thus, practically a different position gauge is

required

for each design of work. The position gauges are employed for checking the position of some

feature

on the work in relation to another reference point or surface. Their design can be based either on

the principle of sighting the gauge and work, or on the method of feel.

Fig. 4.45. Combined Limit Gauge.

Fig. 4.46. Position gauge.

Fig. 4.47. Position gauge.

An simple gauge for checking the location of a recess in relation to a flat surface is shown in

Fig. 4.46. Another simple design in which the location of surface parallel to the reference surface

is to be located is shown in Fig. 4.47. It may be noted that no light will pass between the

reference

surface and gauge surface in contact with ‘Go’ side and light will pass with ‘No Go’ side.

4.12.9.Contour Gauges.

These are employed for checking the dimensional accuracy and

shape of irregular work. The contour gauges are made of similar profile as that of the work, e.g.

radius gauges are employed for checking the shape of fillets. The radius gauge which is used for

gauging both internal and external radii, contains a number of leaves having different radii

profile

and their radius being marked on the leaf. These leaves are hinged together at both the ends of a

base member provided with a clearance section hole and whole assembly is in the form of a

pocket-knife. Any leaf of desired radius can be slid outside and the rest remaining inside. These

leaves are made of hardened steel plates.

Other types of simple contour gauges are those for thread pitches, cutting tool angles, form

tools profiles and gear tooth profiles, etc.

4.12.10.Advantages of Fixed Gauges.

The advantages of fixed gauges are :

(i) These are consistent in form and dimension and thus virtually free from errors due to

drift of the original adjustment, non-linear response, and effect of power variation and other

extraneous factors, which call for frequent calibration.

(ii) Except for careful handling, human errors are nil.

(iii) These provide unambiguous ‘yes’ or ‘no’ decision regarding acceptability of inspected part.

(iv) These do not require auxiliary equipment and setups.

(v) These are portable and independent of power supply requirements.

(vi) These can be designed to check combinations of several dimensions comprising lengths,

diameters and angles. Other types of fixed gauges serve to inspect interrelated features for size,

location, form, alignment etc. to check the combined effect of several parameters with regard to

the

functional adequacy of the inspected feature, by determining the virtual size of the component.

(vii) These provide uniform reference standards.

(viii) Fixed gauges are particularly useful in the checking of part members whose meaningful

geometric irregularities cannot be readily detected by gauges which do not provide complete

reverse

replicas of the critical part portion.

(ix) Their moderate cost results in overall economy.

4.12.11.Miscellaneous Gauges.

Gauges are used not only for shaft and hole checking but

can be designed for all types of applications for checking purposes in production shop and also

for

gauge making and checking. Such gauges are usually complex.

As in slip gauges and angle gauges, all other gauges can also be of four types viz. master,

reference, check and workshop gauges. Master gauge, which is ultimate reference, is used for

controlling the reference gauges and can be found only in standards room. It is properly

calibrated

and its dimensional accuracy is beyond question. Reference gauge is used for checking check

gauges

and for arbitration purposes in case of doubt, and is reserved for reference purposes in an

inspection

department. Check gauge is used for testing the accuracy of workshop gauges. The general

checking

of component parts is carried out with workshop grade gauges.

4.12.12.Position Gauges.

Position gauges are used to check the geometrical relationship

of specific features, such as distance between two holes, distance of a hole from a reference

surface,

etc. Such gauges need not necessarily always be of solid form but can be designed with loose

‘Go’

and ‘No Go* feeler pieces which need to be inserted between the workpiece and the gauge

surfaces

in contact after the workpiece is inserted in position. In some applications dial indicators are also

used in conjunction with setting masters for contacting the work at the points to be gauged. Such

arrangements result in decreased cost of gauges and the increased efficiency.

4.12.13.Receiver Gauges.

Receiver gauges are designed to simultaneously check a number

of features of workpiece. These are often used for checking components before assembly.

4.12.14.Profile Gauges.

Profile gauges are used to check the form of the components.

Profiles are difficult to be checked by limit gauges and it is usual practice to use fixed gauges

mated

to profile for checking profiles. There are two methods of tolerancing the form of profile

(consisting

of straight lines and curves.)

(i) To provide a tolerance zone within which the finished profile must lie. This method

provides a uniform metal tolerance normal to the profile.

(ii) To use ordinates which are provided with individual tolerances. In this method the

tolerance, normal to the surface, will vary with the form of the profile.

Gauge Design (Metrology)

 

4.13.

To a greater or lesser extent, every gauge is a copy of the part which mates

with the part for

which the gauge is designed. For example, a bushing is made which is to

mate with a shaft; in this

case, the shaft is the opposed (mating part) part. The bushing is checked by

a plug gauge, which in

so far as the form of its surface and its size is concerned, is a copy of the

opposed part (shaft).

If a gauge is designed as an exact copy of the opposed part in so far as the

dimension to be

checked is concerned, it is called a ‘Standard Gauge’.

In design of a gauge, simplicity should be the main aim as simple gauges

can take

measurements continuously and accurately.

4.13.1.Taylor’s Principle.

According to Taylor, ‘Go’ and ‘No Go’ gauges should be designed

to check maximum and minimum material limits which are checked as

below.

‘Go’Limit. This designation is applied to that limit of the two limits of size

which corresponds

to the maximum material limit considerations, i.e. upper limit of a shaft and

lower limit of a hole.

The form of the ‘Go’ gauge should be such that it can check one feature of

the component in one

pass.

Wo Go’ Limit. This designation is applied to that limit of the two limits of

size which

corresponds to the minimum material condition, i.e. the lower limit of a

shaft and the upper limit

of a hole.

‘No Go’ gauge should check only one part or feature of the component at a

time, so that

specific discrepancies in shape or size can be detected. Thus a separate ‘No

Go’ gauge is required

for each different individual dimension.

Fig. 4.48. Plug gauge.

Fig. 4.49. Snap gauge.

The ‘Go’ plug gauge (Fig. 4.48) is the size of the minimum limit of the hole,

while the ‘No Go’

plug gauge corresponds to the maximum limit.

The ‘Go’ snap gauge (Fig. 4.49) on the other hand, is of a size

corresponding to the maximum

limit of the shaft, while the ‘No Go’ snap gauge corresponds to the minimum

limit. Gauging faces

of a normal snap or gap gauge must be parallel and square to each other

and the gauging points of

contact with the work should be in the same plane. The difference in size

between the ‘Go’ and ‘No

Go’ snap gauges, as well as the difference in size between the ‘GO’ and ‘No

GO’ plug gauges, is

approximately equal to the tolerance of the tested holeor shaft in case of

Standard Gauges, Rigidity

and robustness of snap gauges are important features so that gauges

function adequately and

maintain size. Gauging diameters of components that are slightly larger

than the gap setting can

produce high wielding action which may lead to gauge distortion and wrong

interpretation of

reading. Therefore, larger gap gauges should, preferably, be forged in a

deep I-section, ensuring

maximum rigidity in the plane of gauge and sufficient rigidity in lateral

direction.

Taylor’s principle states that the ‘Go’ gauges should check all the possible

elements of

dimensions at a time (roundness, size, location etc.) and the ‘No Go’ gauge

should check only one

element of the dimension at a time.

To ‘Go’ plug gauge must be of corresponding section and preferably full

length of hole so that

straightness of hole can also be checked. Thus it not only controls diameter

in any given section but

also ensures bore alignability. However it cannot check the degree of

ovality.

The ‘No Go’ plug gauge is relatively short and its function is dependent not

only on the

diameter but also on the circularity of the hole. Thus to some extent,

variation of hole shape can be

measured.

4.13.2.Wear Allowance Consideration on Gauge Maker’s Tolerance.

Since the gauge

maker can’t make absolutely accurately gauges, permissible deviation in

accuracy must be assigned

for gauge manufacture. Furthermore, the measuring surfaces of’Go’ gauges

which constantly rub

against the surfaces of parts in inspection, are consequently subjected to

wear and lose their initial

initial size. Thus due to wear, the size of’Go’ plug gauges is reduced, while

that of’Go’ snap gauges

is increased. It is of course desirable to prolong the service life of gauges

and, therefore, a special

allowance of metal, the wear allowance is added in a direction opposite to

the wear. For this reason

new ‘Go’ plug gauges are made with two positive deviations and ‘Go’ snap

gauges with two negative

deviations from the nominal size. (The nominal size on which limits of

gauges are based are the

limits of the parts to be checked.)

4.13.3.Important Points for Design.

(1) The form of’Go’ gauges should exactly coincide

with the form of the opposed (mating) parts.

(2) ‘Go’ gauges are complex gauges which enable several related

dimensions to be checked

simultaneously.

(3) In inspection, ‘Go’ gauges must always be put into conditions of

maximum impassability.

(4) ‘No Go’ gauges are gauges for checking a single element of feature.

(5) In inspection, ‘No Go’ gauges must always be put into conditions of

maximum passability.

4.13.4.Gauge maker’s Tolerance.

Keeping all above main points for gauge design in view

there are three methods of giving tolerances on gauges (snap and plug

gauges).

4.13.4.1.First system.

Workshop and Inspection Gauges (Fig. 4.50). In this method

workshop and inspection gauges are made separately and their tolerance

zones are different. This

was evolved many years ago in the development stage of limit gauges.

Fig. 4.50. Disposition of tolerances on workship and inspection

gauges.

According to this system the tolerances on the workshop gauge are

arranged to fall inside

the work tolerance, while the inspection gauge tolerances fall outside the

work tolerance. Further

in workshop gauges, ‘Go’ gauge should eat away 10% of work tolerance and

similarly the tolerance

on No Go’ gauge should be one-tenth of work tolerance, so if work tolerance

is 10 units then only

8 units will be left as the difference between the minimum of’No Go’ and

maximum of’Go’; the

tolerance on ‘Go’ as well as ‘No Go’ gauges individually being 1 unit each.

In Inspection Gauges, gauges are kept beyond work tolerance by 10% of its

value.

Disadvantages of Workshop and Inspection Gauges.

(1) Some of the components which are in work tolerance limits may be

rejected under

workshop gauges. So they are again checked by inspection gauges and may

be accepted after that.

(2) Some components which are not in work tolerance limits may be

accepted when tested

by inspection gauges.

(3) The workshop and inspection gauges are to be made separately as their

tolerance zones

are different.

4.13.4.2.Second system (Revised Gauge Limits).

Under this system the disadvantages

of inspection gauges are reduced by reducing the tolerance zone of

inspection gauge, and the

workshop gauge tolerance remains the same.

Fig. 4.51. Modified tolerances on inspection gauge.

For ‘Go’ and ‘No Go’ inspection gauges in this system, the 110% of the

range of work tolerance

is covered instead of 120% in the first system as shown in Fig. 4.51.

4.13.4.3.Third system (Present British System).

In new system, following principles are

followed along with Taylor’s principle.

(i) Tolerance should be as wide as is consistent with satisfactory

functioning, economical

production and inspection.

(ii) No work should be accepted which lies outside the drawing pacified

limits.

Thus modern system dispenses with workshop and inspection gauges and

we give the same

tolerance limits on workshop and inspection gauges and the same gauges

can be used for both

purposes.

The tolerance zone for the ‘Go’ gauges should be placed inside the work-

limits and tolerance

for the ‘No Go’ gauges outside the work-limits. Provision for wear of ‘Go’

gauges is made by

introduction of a margin between the tolerance zone for the gauge and

maximum metal limit of the

work. Wear should not be permitted beyond the maximum metal limit of the

work, when the limit

is of critical importance. Its magnitude is one-tenth of the gauge tolerance.

Thus when work

tolerance is less than 0.09 mm there is no need of giving allowance for

wear. If work tolerance is

more than 0.09 mm then 10% gauge tolerance is given only on ‘Go’ gauge

for wear.

The disposition of various tolerances and allowances on gauges according to

this system is

shown in Fig. 4.52 (a) and (b) and further clarified by the following example.

Fig. 4.52. Provision of margin for wear on GO gauges.

Indian Standards Gauging Practice for Plain Workpieces (Metrology)

 

4.14.

Generally inspection by limit gauges means an acceptable method for

dimensional conform-

ity to the specification of plain workpieces. The gauging of the workpieces is

carried out both by the

manufacturer as well as the purchaser. The tendency of the manufacturer is

to pass all such pieces

which are very close to the specified tolerance and the purchaser wants to

be very much on the safe

side. Moreover the purchaser does not rely on the manufacturer’s gauges.

The dispute requiring

the checking of the conformity of the gauges of the manufacturer may be

avoided by following the

procedure given below.

4.14.1.Inspection by the Manufacturer.

The best possible solution to avoid dispute is

that the inspection department of the manufacturer uses the same types of

gauges as those used

in the workshop. Further the difference between the results obtained by the

workshop and the

inspection department could be avoided by recommending the workshop to

use new or slightly worn

gauges and the inspection department to use gauges having sizes nearer

the permissible limit.

Inspection should be carried out at 20°C.

4.14.2.

Inspection by the Purchaser.

There can be three possibilities : (i) The purchaser

after ensuring the accuracy of the manufacturer’s gauges may use the

same; (ii) he may use gauges

in accordance with IS : 3455—1971 which have their sizes near the wear

limit in order to avoid

differences between the results obtained by the manufacturer and the

inspector ; (Hi) he may use

any type of gauges provided he ensures that the workpieces, the sizes of

which are within the

specified limits will not be rejected. Inspection should be carried out at

20°C reference temperature

only.

4.14.3.Taylor Principle.

This principle is based on the use of a correct system of limit

gauges to inspect shafts and holes. According to Taylor it is not adequate to

use simple Go gauge

on outer dimension only but the shape is an important factor, i.e. the Go

gauge should be full form

gauge and it should be constructed with reference to the geometrical form

of the part being checked,

in addition to its size. In other words, Go gauge should check all the

dimensions of a workpiece in

the maximum metal condition. As regards No Go gauges, Taylor was of the

view that it was useless

for Not Go gauge to be of full form, and each feature being dealt should be

checked with a specific

Not Go gauge. In other words, Not Go gauge shall check only one dimension

of the workpiece at a

time, for the minimum metal condition. Thus according to it, a hole should

completely assemble

with a ‘Go’ cylindrical plug gauge made to the specified ‘Go’ limit of the

hole, having a length at

least equal to the length of engagement of the hole and shaft. In addition,

the hole is measured or

gauged to check that its maximum diameter is not larger than the ‘No Go’

limit. The Taylor principle

interprets the limit of size for gauging holes and shafts as follows :

4.14.3.1.For holes.

If the Taylor principle is followed then the diameter of the largest perfect

imaginary cylinder which can be inscribed within the hole so that it just

contacts the highest points

of the surface, shall not be a diameter smaller than the ‘Go’ limit of size.

Further, the maximum

diameter at any position in the hole should not exceed the ‘No Go’ limit of

size.

4.14.3.2.For Shafts.

If the Taylor principle is followed then the diameter of the smallest

perfect imaginary cylinder which can be circumscribed about the shaft so

that it just contacts the

highest points of the surface, should not be a diameter larger than the ‘Go’

limit of size. Further

the minimum diameter at any position on the shaft should not be less than

the ‘No Go’ limit of the

size.

It may be noted that the Taylor principle does not take care of the error of

form, circularity

or straightness etc., the tolerances for which should be specified separately.

Thus according to Taylor principle we require a plug ring gauge having

exactly the ‘Go’ limit

diameter and a length equal to the engagement length of the fit to be made

for checking the ‘Go’

limit of the workpiece and this gauge must perfectly assemble with the

workpiece to be inspected.

The other gauge needed is the ‘No Go’ gauge which contacts the workpiece

surface only in two

diametrically opposite points and at those two points it should have exactly

‘No Go’ limit diameter.

This gauge should not be able to pass over in the workpiece in any

consecutive position in the various

diametric directions on the workpiece length.

In certain applications, the Taylor principle cannot be strictly and blindly

followed. The

following deviations are allowed which basically do not deviate from the

principle as such.

For ‘Go’ Limit, (i) In case the manufacturing process assures that the

error of straightness

will not affect the character of fit of the assembled workpieces, it is

advisable to go for standard

gauge blanks instead of using full form and length of engagement and make

the gauge unnecessarily

bulky and cumbersome and avoid the special gauge of exactly same working

length for one

workpiece.

(ii) If gauge happens to be too heavy, only segmental cylindrical bar could

be used provided

the manufacturing process ensures that errors of roundness will not have

any effect on the character

of fit of the assembled workpieces.

(iii) For shafts, particularly heavy ones ; it is generally not desirable to use

full form ring

gauges but only gap gauges. But for this purpose the manufacturing

process used should take care

of the error of roundness (especially lobing) and the error of straightness.

For ‘No Go’ Limit. The two-point checking devices are not feasible and

practicable in actual

practice because these are subjected to rapid wear etc. ; these can be safely

replaced by small

planes/cylindrical surfaces/spherical surfaces. For gauging very small holes

and in cases where

workpieces may be deformed to an oval by a two-point mechanical contact

device, the ‘No Go’ gauge

of full form may have to be used.

4.14.4.Allowable Deviation from the Taylor’s Principle.

In some applications, difficul-

ties are experienced in conveniently using gauges if they are strictly based

on Taylor’s principle.

Accordingly some deviations may be permitted.

According to Taylor’s principle a Go gauge should be of full form having

length equal to

engagement length of fit, but this is not always necessary. For example, if it

is known that the

manufacturing process ensures that error of straightness of hole or shaft is

so small that it would

not affect the desired fit of assembly, then length of Go cylindrical plug or

ring gauge may be less

than the length of engagement.

For very big holes, the full form gauge may be too heavy and inconvenient

to use. Therefore,

segmental cylindrical bar or spherical gauge may be used if it can be

assumed that the manufac-

turing process would not produce the error or roundness outside the

permissible limits to affect the

character of fit.

Similarly ‘Go’ gap gauge can be used in place of Go cylindrical ring gauge

(which is often

inconvenient for gauging shafts) provided manufacturing process can

ensure the errors of roundness

(lobing) and straightness of shaft within permissible limits. The straightness

of long shafts of small

diameter should be checked separately. Similarly, though Taylor’s principle

desired use of two-point

checking device to check No Go limit, but same is not always necessary in

following cases.

Since point contacts are subject to rapid wear, these can be replaced by

small plane,

cylindrical or spherical surfaces whenever appropriate. The two-point

checking device is also found

difficult to design and manufacturing for gauging very small holes and for

such cases No go plug

gauge of full cylindrical form can be used. However, possibility of accepting

workpieces having

diameters outside the No Go limit should be checked.

In certain cases the non-rigid workpiece may be deformed by 2-point

mechanical contact

device and in such cases No Go ring or plug gauges of full cylindrical form

have to be used.

No Go gauges of full cylindrical form can also be used for thin-walled

workpiece, which may

be out of round due to heat treatment, but would become circular when

such gauges are applied

with force just sufficient to convert the elastic deformation into circularity.

4.14.5.Limit Gauges.

The various types of limit gauges used for gauging internal diameters

or holes are :

(1) Full form cylindrical plug gauge. The gauging surface is in the form of

an external

cylinder. Generally a small circumferential groove is cut near the leading

end of the gauge and the

remaining short cylindrical surface is slightly reduced in order to act as a

pilot. The method of

attaching gauge to the handle should be such as not to affect the size and

form of the gauge by

producing undesirable stresses (Refer Fig. 4.57)

Fig. 4.57. Full form cylinderical plug gauge.

Fig. 4.58. Full form disc gauge.

(2) Full form spherical plug or disc gauge. This has gauging surface in the

form of a sphere

from which two equal segments are cut off by planes normal to the axis of

the handle. (Refer Fig.

4.58).

(3) Segmental cylindrical bar gauge. It has gauging surface in one of the

following two

forms : (i) External cylindrical form from which two axial segments are

made by lowering down

surface at other places (Refer Fig. 4.59) or {ii) External cylindrical form in

which segments are

formed by removing remaining material (Refer Fig. 4.60).

(4) Segmental spherical plug gauge. It is similar to full form spherical plug

or disc gauge but

has two equal segments cut off by planes parallel to the axis of the handle in

addition to the segments

cut off by planes normal to the axis of the handle. (Refer Fig. 4.61).

(5) Segmental cylindrical bar gauge with reduced measuring faces. It is

similar to segmental

cylindrical bar gauge but has reduced measuring faces in a plane parallel to

the axis of the handle.

(Refer Fig. 4.62).

Fig. 4.59. Segmental cylindrical bar gauge.

Fig. 4.60. Segmental cylindrical bar gauge.

Fig. 4.61. Segmental spherical gauge.

Fig. 4.62. Segmental cylindrical bar gauge.

(b) Rod gauge with spherical ends. It has spherical end surfaces which form

part of one single

sphere. (Refer Fig. 4.63).

The standard limit gauges used for gauging

external diameters or shafts are :

(i) Full form cylindrical ring gauge, which

has gauging surface, in the form of an internal

cylinder and whose wall is thick enough to avoid

deformation under normal conditions of use.

Fig. 4.63. Rod gauge with spherical ends.

(ii) Gap gauge. It generally has one flat surface and one cylindrical surface,

the axis of the

two surfaces being parallel to the axis of the shaft being checked. The

surfaces constituting the

working size may both be flat or both cylindrical also.

In order to inspect and adjust the limit gauges, the following gauges are

used :

(1) Reference gauges. These are either in the form of reference discs and

intended to be

used for setting gap gauges or in the form of cylindrical plug or ring gauges

for calibrating gauges

or indicating measuring instruments.

(2) Block gauges. These are standards of length having parallel plane end

surfaces which

are used for calibrating gauges of indicating measuring instruments.

Gauges for Tapers (Metrology)

 

4.15.

A taper is tested by using taper plug and ring gauges. The important thing

in testing a

tapered job is to check the diameter at bigger end and the change of

diameter per unit length. For

Fig. 4.64. Taper hole gauge.

Fig. 4.65. Taper plug gauge.

testing the correctness of a taper, three light lines are drawn with persian

blue about equidistant

along the length on the (male portion) plug gauge or spindle to be tested

and it is fitted in the gauge

(female) and rotated once or twice. If persian blue marks do not rub off

evenly, the taper is incorrect

and setting must be adjusted until persian blue marks are rubbed equally all

along its length.

4.15.1.Limit Gauges for Tapers.

For checking the diameter of bigger end, a mark is drawn

on the gauge to show the correct dimension for large end of taper. It is also

known as gauge plane

and taper actually starts from this plane. For bigger diameter (which is

situated in gauge plane)

the tolerance is ± IT6. Tolerance on smaller diameter will also be ± IT6 on

basic size calculated from

taper ratio.

Distance of bigger diameter from face depends upon the value of diameter

itself e.g. for 200

mm diameter it is 2 mm and varies from 0.5 to 2 mm. In Fig. 4.65, it is

represented by ‘Z’ length

for hole gauge.

On plug gauge, gauge plane is located at distance ‘a’ from free end and it

varies from 2 mm

to 12 mm. Tolerance for plug gauge on basic size is + IT5.

The diameter is tested for size by noting how far the gauge enters the

tapered hole or the

tapered spindle enters the gauge.

Wear allowance on gauges is not considered because of high costs involved

in manufacturing

to that accuracy.

A double ended gauge in this instance is unnecessary because the

difference in diameter

between the high and low limit of the tolerance is converted into a

lengthwise dimension and thus

the hole will be within the tolerance, when on inserting the gauge, the large

diameter of hole falls

between the gauge plane and the other line at distance Z from it.

Plug and Ring Gauges for Self-holding Tapers (Metrology)

 

4.16.

The most common use of self-holding tapers is in the machine spindle noses

and tool shanks

for the purpose of accurate alignment of tool and transmitting the torque.

Tapers can be both

internal as well as external and thus plug and ring gauges have to be

employed to check them. The

use of these gauges, of course, cannot help in arriving at the absolute

deviation of any particular

Fig. 4.66. Plug gauge, plain.

Fig. 4.67. Plug gauge, tanged.

dimension, but nevertheless it offers the easiest and quickest method of

verifying inter-chan-

geability of dimensions. The gauges are made from good quality steel and

suitably heat treated for

hardness (750 to 860 HV) and stabilisation. The gauges are generally well

finished and free from

crack, burrs, rust or other defects. The gauging surfaces are ground, lapped

and covered with a

suitable rust proof coating and packed in non-absorbent paper and packed

in boxes for safe handling.

Thus the plug and ring gauges for the self-holding tapers are of four types

as shown in Figs. 4.66

to 4.69.

4.16.1.Plug Gauges,

Plain. This is a full form ‘Go’ gauge representing a plain or tapped

end shank. It is provided with one ring marked on the gauge plane and

another ring to indicate the

minimum depth of the internal taper.

Fig. 4.68. Ring gauge, plain.

Fig. 4.69. Ring gauge, tanged.

Fig. 4.70. Testing taper of socket with plain plug gauge.

As it is used for the verification of internal taper of corresponding size and

thus the

dimensions of the gauging portion represent those of a plain end shank of

basic size. The distance

between the two ring marks ‘Z’ corresponds to the permissible deviation of

the gauge plane position

for the particular taper.

For testing the internal taper, the plug gauge is inserted as far as it goes

with light pressure.

At the extreme point the face of large end of internal taper shall lie within

the two ring marks given

on the plug gauge.

4.16.2.Plug Gauge, Tanged.

This is a full form ‘Go’ gauge representing the virtual size of

the shank of basic dimension having a tang which is on the top limit of its

thickness and eccentric

by the maximum permissible amount. It is used for the verification of

internal tapers in machine

tools or sockets and to ensure that the tang slot will accept the tang. It is

marked with a ring on

the gauge plane and another ring to indicate the minimum depth of internal

taper.

Fig. 4.71. Testing taper of socket with tanged plug gauge.

As it is intended to be used for the verification of internal taper of

corresponding size, the

plug gauge represents the size of the tanged end shank of the basic

dimensions but having the tang

of maximum permissible thickness which is eccentric by the maximum

permissible amount. A

further 0.01 mm is added to the tang thickness on either side to allow for

the eccentrictiy of the

tang of the plug gauge itself. The distance between the two ring marks ‘Z’

corresponds to the

permissible deviation of the gauge plane for particular taper. For testing

the internal taper of a

socket with a tanged end shank, the plug gauge is inserted as far as it goes

with light pressure. At

the extreme point, the face of large end of the internal taper should lie

within the two ring marks

given on the plug gauge.

4.16.3.Ring Gauge,

Plain. This gauge represents an internal taper of basic size. It is used

for verifying the taper of tapped or plain end shank.

As the ring gauge (plain) is intended to be used for verification of internal

taper of plain end

or tapped end shanks of corresponding size, the dimensions of its gauging

portion represent an

internal taper of basic size. For inspecting the external taper of a tapped Or

plain end shank, the

Fig. 4.72. Testing taper with ring gauge (plain).

ring gauge is inserted, as far as it goes with light pressure. At the extreme

position, the small end

of taper shank under test should lie flush or short of the face of the ring

gauge on the small end.

This can be verified with the help of a straight edge.

4.16.4.Ring gauge, Tanged.

The gauge represents an internal taper of basic size. A limit

step is provided at the small end of taper which verifies the length of shank

from the gauge plane

and also the combined effect of tang thickness and its offset. A ring gauge,

tanged represents the

basic dimensions of internal taper with a tang slot as it is used for the

verification of the external

taper of a tanged end shank of corresponding size. A step is provided to

verify that the tang slot

 

Fig. 4.73. Testing external taper with ring gauge (tanged).

will accept a shank even in the worst case. The step provided takes into

account the maximum

thickness of the tang which is eccentric by the maximum permissible

amount and a further tolerance

of 0.01 mm is allowed to offset the effect of variation in the manufacture or

measurement of the

ring gauge itself.

For testing the external taper of the tanged end shank, the ring gauge is

inserted, as far as

it goes with light pressure. At the extreme position, no part of the tang

under test should extend

beyond the surfaces A, B and C (Fig. 4.73). The shank surfaces may

however, lie flush with these

surfaces.

The plug and ring gauges are generally marked legibly and indeligible with

the designation

of taper manufacturer’s name, initials or recognised trade mark and the

year of manufacture. The

gauges are designated by the (i) commonly used name of the

gauges, (ii) designation of taper and

(iii) number of the standard followed.