MACHINE TOOL GEAR BOX

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D.P.Bhaskar, Sanjivani COE Kopargaon

Give FEEDBACK: [email protected]

1. Lathe 2. Shaping 3. Milling 4. Drilling

Multi‐speed Gear Box of Machine Tool

Single input speed (Motor speed) = nem Multi‐Speeds on Spindle shaft (Spindle Speeds)

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n1 ,n2 ,n3 ,n4 n5 ,n6 ,n7 , nz

The extreme spindle speeds n1 = nmin nZ = nmax

Why Multi‐Speeds ?

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Different : • Feeds • W/P Materials • W/P Dimensions [D] • Cutting tool materials

n1 n2 n3 n4 n5 n6 n7 n8 N9= nz

nem


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Speed Regulations

Stepped Regulations

Stepples Regulations

Discrete speed steps Continuous speed steps

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n1 n2 n3 n4 n5 nz

nem


Why Progressions *To find different speed steps *Find relation of two speed steps

1. Arithmetic progression (AP) 2. Geometric Progression (GP) 3. Harmonic Progression (HP)

Progression Laws

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Types of Progression Laws


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Difference between 2 successive speeds is constant = at at= (n2 – n1)= (n3– n2)= (n4 – n3)= (nz– nz‐1)

Z=Total speed steps (speeds) on spindle. (n1, n2, n3, n4,……………………….., nz‐1,nz..)

LAW

Ration of 2 successive Speeds= Ø=Speed Ratio

nmax =Maximum spindle speed (rpm)= nz nmin= Minimum spindle speed (rpm)= n1

n ( )

n1 =nmin

n2 =n1 + at n3 = n2 + at =n1 + 2at n4 = n3 + at =n1 + 3at nz = n(z‐1) + at =n1 + (z‐1)at

Dk = Diameters to be Machined at Specific cutting speed (v) =Upper limit of Diameter

∆

∆Dk = Diameters Range = (D2‐D1) = (D3‐D2) ………

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AP

Maximum spindle speed (rpm), nmax =445 rpm Minimum spindle speed (rpm), nmin=35 rpm Number of speed steps, Z=12 Cutting speed, v=20 m/min.

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Arithmetic progression

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Remarks @ AP

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At high spindle speeds, the diameter range is very narrow and hence some of the speed steps are redundant.

At low spindle speeds the diameter range is wide hence needs to add more speed steps between calculated values.


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GP


Geometric progression

Range Ratio

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Geometric Progression Ratio

Speed Ratio

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Progression ratio/ Speed ratio Progression ratio/ Speed ratio

Geometric progression (also inaccurately known as a geometric series) is a sequence of speeds such that the ratio of any two successive speeds of the sequence is a constant called the Geometric progression ratio (speed ratio) of the sequence.

Range ratio

It ratio of maximum and minimum speed

GP

Maximum spindle speed (rpm), nmax =445 rpm Minimum spindle speed (rpm), nmin=35 rpm Number of speed steps, Z=12 Cutting speed, v=20 m/min.

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Remarks @ AP

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At high spindle speeds, the diameter range is very narrow and hence some of the speed steps are redundant.

At low spindle speeds the diameter range is wide hence needs to add more speed steps between calculated values.


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Variation in Diameters is wide in AP than GP

AP or GP?

GP gives Optimum Distribution Of Gear Speeds compared to

AP

AP – GP‐ HP Comparison AP – GP‐ HP Comparison

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Z Z N N

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Effect of GP ratio

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In gearbox design a set of preferred step ratio or preferred numbers is used to obtain the series of output speed of gearbox. The preferred step ratio is mentioned as basic series named as R5, R10,R20,R40 and R80. Each basic series has a specific step ratio. R [Charles Renard]

Definition of preferred number/speed series

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Structural Formula

Structural Diagram

Ray Diagram

Speed chart

Gearing Diagram 1

2

3

4

5 Sequence

Z =P1(x1)*P2(x2)*....Pu(xu) Structural Formula

The maximum number of speed that can be obtained from two shafts is three. Hence its necessary to use intermediate shafts between the input shaft and output shaft. The structural formula helps to arrive the number of stages and required gears to obtain the desired speeds.

Structural Formula

P : Speed steps/ Pairs in any stage X : Characteristic in stage

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RULE

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HL=Z=6 VL=N+1=3


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1) MAX Node addition=7.5 2) P of Stage one should be less

BEST

RULE

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BEST D.P.Bhaskar, Sanjivani COE Kopargaon

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Z=9

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Z=12

For More than 2 stages 1st and last stage P should be less BEST

RULE

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Optimum SF


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A ray diagram is a representation of structural formula. It provides information such as speed in each stage, the transmission ratio in each stage, The total number of speeds and its values.

Definition

Ray diagram for Z=4


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RULE

Ray Diagram Speed chart

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Ray Diagram Kinematic/Gearing Layout A kinematic layout is a pictorial representation of a gearbox, describing the arrangement of gears. It provides information like number of stages, number of shafts used, number of gear pairs and its arrangement.

Definition

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RULE


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Gearing Diagram


Z=12

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Gearing Diagram

Number of Teeth and Speed deviation diagram

Write best Structural formula, Draw Structural Diagram, Ray Diagram, Speed Chart, Gearing Diagram, No of teeth, Speed Deviation Diagram


Question

Sppeds n1 n2 n3 n4 n5 6 Calculated 100 158 252.8 395 632 995.4 Round off 100 160 250 400 630 1000

e

Ray Diagram, Speed Chart Gearing Diagram

Spindle speeds

Stage 1 No. Of Teeth Calculation Ray Diagram

No deviation in speeds in stage 1

ZA=20 ZA’=50 GA=2.5 ZB=27 ZB’=43 GB=1.59 C1=70

Stage 1 No. Of Teeth Calculation




Ray Diagram

Deviation in speeds in stage 2 ZC=20 ZC’=80 GE=4 ZD=38 ZD’=61 GD=1.631 ZE=61 ZE’=39 GC=0.639 C2=100



GE=4 GD=1.6 GC=0.635

GE=4 GD=1.631 GC=0.639

′′ ′ 400′ /GD=400/1.635=244.64

′ 630′ /GD=630/1.635=385.32

′′ ′ 400′ /GC=400/0.639=626

′ 630′ /GC=630/0.639=986

n(TH) n(PR) 100 100 160 160 250 244.64 400 385.32 630 626 100 986

Deviated Speeds

Speed Deviation ∆n

nth 100 160 250 400 630 1000 nact 100 160 244.64 385.32 4 986 ∆n 0 0 ‐2.144 ‐3.67 ‐0.639 ‐1.40

Limit for speed deviations ∆n < ± 10(ɸ‐1)٪ ∆n < ± 10(1.58‐1)=5.8٪

Speed Deviation Diagram

Difference between number of teeth on successive gears in change gear box

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•Input speed= 120 RPM •Draw structure diagram •Find Spindle speeds. •Speed trapped for given position •Speed ratio?

SPPU Questions


SPPU Questions


MACHINE TOOL GEAR BOX

Engineering

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