Forces acting on the driven gear can be calculated perEquations (16-25).

(16-25)

If the Σ term in Equation (16-25) is 90º, it becomesidentical to Equation (16-20). Figure 16-16 presentsthe direction of forces in a screw gear mesh when theshaft angle Σ = 90º and β1 = β2 = 45º.

SECTION 17 STRENGTH AND DURABILITY OF GEARS The strength of gears is generally expressed in terms ofbending strength and surface durability. These areindependent criteria which can have differing criticalness,although usually both are important. Discussions in this section are based upon equationspublished in the literature of the Japanese GearManufacturer Association (JGMA). Reference is made tothe following JGMA specifications: Specifications of JGMA:

JGMA 401-01 JGMA 402-01 JGMA 403-01 JGMA 404-01 JGMA 405-01

Bending Strength Formula of SpurGears and Helical Gears Surface Durability Formula of SpurGears and Helical Gears Bending Strength Formula of BevelGears Surface Durability Formula of BevelGears The Strength Formula of Worm Gears

Generally, bending strength and durability specificationsare applied to spur and helical gears (including doublehelical and internal gears) used in industrial machines inthe following range:

Module: Pitch Diameter: Tangential Speed: Rotating Speed:

mdvn

1.5 to 25 mm25 to 3200 mmless than 25m/secless than 3600 rpm

Conversion Formulas: Power, Torque and Force Gear strength and durability relate to the power and forces to betransmitted. Thus, the equations that relate tangential force at thepitch circle, Ft(kgf), power, P (kw), and torque, T (kgf.m) are basic tothe calculations. The relations are as follows: Ft = 102P = 1.95x106P = 2000T (17-1) V dwn dw

P = Ftv = 10-6 = Ftdwn (17-2) 102 1.95 T = Ftdw = 974P (17-3) 2000 n where: v : Tangential Speed of Working Pitch Circle (m/sec) v : dwn 19100 dw : Working Pitch Diameter (mm) n : Rotating Speed (rpm)

17.1 Bending Strength Of Spur And Helical Gears In order to confirm an acceptable safe bending strength, it isnecessary to analyze the applied tangential force at the working pitchcircle, Ft, vs. allowable force, Ftlim This is stated as: Ft < Ftlim (17-4) It should be noted that the greatest bending stress is at the root ofthe flank or base of the dedendum. Thus, it can be stated: σF = actual stress on dedendum at root σFtlim = allowable stressThen Equation(17-4) becomes Equation(17-5) σF ≤ σFlim (17-5)Equation(17-6) presents the calculation of Ftlim:

(17-6)

Equation (17-6) can be converted into stress by Equation (17-7):

(17-7)

17.1.1 Determination of Factors in the Bending Strength Equation If the gears in a pair have different blank widths, let the wider onebe bw and the narrower one be bs. And if: bw - bs ≤ mn bw and bs can be put directly into Equation (17-6). bw - bs ≤ mn the wider one would be changed to bs + mn and the narrower one, bs would be unchanged.17.1.2 Tooth Profile Factor, YF The factor YF is obtainable from Figure 17-1 based on theequivalent number of teeth, Zv and coefficient of profile shift, x, if thegear has a standard tooth profile with 20º pressure angle, per JIS B1701. The theoretical limit of undercut is shown. Also, for profileshifted gears the limit of too narrow (sharp) a tooth top land is given.For internal gears, obtain the factor by considering the equivalentracks. 17.1.3 Load Distribution Factor, Yε Load distribution factor is the reciprocal of radial contact ratio. Yε = 1 (17-8) εα Table 17-1 shows the radial contact ratio of a standard spur gear.

400

401

17.1.4 Helix Angle Factor, Yβ Helix angle factor can be obtained from Equation(17-9).

(17-9)

17.1.5 Life Factor, KL We can choose the proper life factor, KL from Table 17-2.The number of cyclic repetitions means the total loadedmeshings during its lifetime.

17.1.6 Dimension Factor of Root Stress, KFX Generally, this factor is unity. KFX = 1.00 (17-10)17.1.7 Dynamic Load Factor, KV Dynamic load factor can be obtained from Table 17-3 basedon the precision of the gear and its pitch line linear speed.

17.1.8 Overload Factor, Ko Overload factor, Ko, is the quotient of actual tangential forcedivided by nominal tangential force, Ft. If tangential force isunknown, Table 17-4 provides guiding values. Ko = Actual tangential force (17-11) Nominal tangential force, F1 17.1.9 Safety Factor for Bending Failure, SF Safety factor, SF, is too complicated to be decided precisely.Usually, it is set to at least 1.2.17.1.10 Allowable Bending Stress at Root, σFlim For the unidirectionally loaded gear, the allowable bendingstresses at the root are shown in Tables 17-5 to 17-8. In thesetables, the value of aF,m is the quotient of the tensile fatiguelimit divided by the stress concentration factor 1.4. If the load isbidirectional, and both sides of the tooth are equally loaded, thevalue of allowable bending stress should be taken as 2/3 of thegiven value in the table. The core hardness means hardness atthe center region of the root.

Table 17-2 Life Factor, KLNumber of Cyclic

RepetitionsHardness (1)

HB 120 ... 220Hardness(2)Over HB 220

Gears with Carburizing Gears withNitriding

Under 10000 1.4 1.5 1.5Approx. 105 1.2 1.4 1.5

Approx. 106 1.1 1.1 1.1

Approx. 107 1.0 1.0 1.0NOTES: (1) Cast iron gears apply to this column. (2) For induction hardened gears, use the core hardness.

Table 17-3 Dynamic Load Factor, KvPrecision Grade of Gears form JIS B1702 Tangential Speed at Pitch Line (m/s)

Tooth ProfileUnder 1 1 to less

than 33 to lessthan 5

5 to lessthan 8

8 to lessthan 18

12 to lessthan 18

18 to lessthan 25Unmodified Modified

1 - - 1.0 1.0 1.1 1.2 1.3

1 2 - 1.0 1.05 1.1 1.2 1.3 1.5

2 3 1.0 1.1 1.15 1.2 1.3 1.5

3 4 1.0 1.2 1.3 1.4 1.5

4 - 1.0 1.3 1.4 1.5

5 - 1.1 1.4 1.5

6 - 1.2 1.5 Table 17-4 Overload Factor, Ko

Impact from Prime MoverImpact from Load Side of Machine

Uniform Load Medium Impact load Heavy Impact loadUniform Load (Motor, Turbine, Hydraulic Motor) 1.0 1.25 1.75

Light Impact Load (Multicylinder Engine) 1.25 1.5 2.0Medium Impact Load (Single Cylinder Engine) 1.5 1.75 2.25

402

See Table 17-5 for sFlim of gears without case hardening.Table 17-6 gives sFlim of gears that are induction hardened;and Tables 17-7 and 17-8 give the values for carburized andnitrided

gears, respectively. In Tables 17-8A and 17-8B, examples ofcalculations are given.

Table 17-5 Gears Without Case Hardening

Material Arrow Indicate the rangesHardness Tensile Strength Lower

limit kgf/mm²(Refrence)σFlim

kgf/mm²HB HV

CastSteelGear

SC37SC42SC46SC49SCC3

37 10.442 12.046 13.249 14.255 15.860 17.2

NormalizationCarbon Steel

Gear

120 126 39 13.8130 136 42 14.8140 147 45 15.8150 157 48 16.8160 167 51 17.6170 178 55 18.4180 189 58 19.0190 200 61 19.5200 210 64 20210 221 68 20.5220 231 71 21230 242 74 21.5240 252 77 22250 263 81 22.5

Quenched andTempered

Carbon SteelGear

160 167 51 18.2170 178 55 19.4180 189 58 20.2190 200 61 21200 210 64 22210 221 68 23220 231 71 23.5230 242 74 24240 252 77 24.5250 263 81 25260 273 84 25.5270 284 87 26280 295 90 26290 305 93 26.5

Quenched andTempered Alloy

Steel Gear

220 231 71 25230 242 74 26240 252 77 27.5250 263 81 28.5260 273 84 29.5270 284 87 31280 295 90 32290 305 93 33300 316 97 34310 327 100 35320 337 103 36.5330 347 106 37.5340 358 110 39350 369 113 40360 380 117 41

403

Table 17-6 Induction Hardened Gears

Material Arrow indicate the rangeHeat Treatmentbefore Induction

Hardening

Core Hardness SurfaceHardness

HV

sFlimKgf/mm²HB HV

StructuralCarbon

Steel HardenedThroughout

Normalized

160 167 More than 550 21180 189 " 21220 231 " 21.5240 252 " 22

Quenched andTempered

200 210 More than 550 23210 221 " 23.5220 231 " 24230 242 " 24.5240 252 " 25250 263 " 25

Structural Alloy Steel Hardened

Throughout

Quenched andTempered

230 242 More than 550 27240 252 " 28250 263 " 29260 273 " 30270 284 " 31280 295 " 32290 305 " 33300 316 " 34310 327 " 35320 337 " 36.5

Hardened ExceptRoot Area

75%of theabove

NOTES: 1. if a gear is not quenched completely, or not evenly, or has quenching cracks, the σFlim will drop dramatically. 2. If the hardness after quenching is relatively low, the value of σFlim should be that given in Table 17-5.

Table 17-7 Carburized Gears

Material Arrows indicate the rangescore hardness σFlim

Kgf/mm²HB HV

StructuralcarbonSteel

S15CS15CK

140 147 18.2150 157 19.6160 167 21170 178 22180 189 23190 200 24

StructuralAlloySteel

220 231 34230 242 36240 252 38250 263 39260 273 41270 284 42.5280 295 44290 305 45300 316 46310 327 47320 337 48330 347 49340 358 50350 369 51360 380 51.5370 390 52

Table 17-8 Nitrided Gears

Material Surface Hardness (Reference) Core HardnessσFlim

kgf/mm²

Alloy Steel exceptNitriding Steel More than HV 650

220 231 30240 252 33260 273 36280 295 38300 316 40320 337 42340 358 44360 380 46

Nitriding SteelSACM645 More than HV 650

220 231 32240 252 35260 273 38280 295 41300 316 44

NOTE: The above two tables apply only to those gears which have adequate depth of surface hardness. Otherwise, the gears should be rated according to Table 17-5.

404

17.1.11 Example of Bending Strength CalculationTable 17-8A Bending Strength Factors

No. Item Symbol Unit Pinion Gear1 Normal Module mn mm 22 Normal Pressure Angle αn degree

20º3 Helix Angle b 0º4 Number of Teeth z 20 405 Center Distance ax mm 606 Coefficient of Profile Shift x +0.15 -0.157 Pitch Circle Diameter d

mm40.000 80.000

8 Working Pitch Circle Diameter dw 40.000 80.0009 Tooth Width b 20 2010 Precision Grade

JIS 5 JIS 5

11 Manufacturing Method Hobbing12 Surface Roughness 12.5 µm13 Revolutions per Minute n rpm 1500 75014 Linear Speed v m/s 3.14215 Direction of Load Unidictional16 Duty Cycle Cycles Over 107 cycles17 Material

SCM 415

18 Heat Treatment Carburizing19 Surface Hardness HV 600 ...64020 Core Hardness HB 260 ... 28021 Effective Carburized Depth mm 0.3 ... 0.5

Table 17-8B Bending Strength FactorsNo. Item Symbol Unit Pinion Gear1 Allowable Bending Stress at Root σFlim kgf/mm² 42.52 Normal Module mn mm

23 Tooth Width b 204 Tooth Profile Factor YF 2.568 2.5355 Load Distribution Factor Yε 0.6196 Helix Angle Factor Yβ 1.07 Life Factor KL 1.08 Dimension Factor of Root Stress KFX 1.09 Dynamic Load Factor KV 1.410 Overload Factor KO 1.011 Safety Factor SF 1.2

12 Allowable Tangential Force on Working PitchCircle

Ftlim kgf 636.5 644.8

17.2 Surface Strength Of Spur And Helical Gears The following equations can be applied to both spur andhelical gears, including double helical and internal gears,used in power transmission. The general range ofapplication is:

Module:Pitch Circle:Linear Speed:Rotating Speed:

mdvn

1 .5 to 25 mm25 to 3200 mmless than 25 m/secless than 3600 rpm

17.2.1 Conversion Formulas To rate gears, the required transmitted power andtorques must be converted to tooth forces. The sameconversion formulas, Equations (17-1), (17-2) and(17-3), of SECTION 17 are applicable to surface strengthcalculations.

17.2.2 Surface Strength Equations As stated in SECTION 17.1. the tangential force. Ft, isnot to exceed the allowable tangential force, Ftlim Thesame is true for

the allowable Hertz surface stress, σHlim The Hertz stress σH iscalculated from the tangential force, Ft For an acceptable design, itmust be less than the allowable Hertz stress σHlim That is:

σH ≤ σHlim (17-12) The tangential force, Ftlim, in kgf, at the standard pitch circle, canbe calculated from Equation(17-13).

The Hertz stress σH (kgf/mm²) is calculated from Equation(17-14). where u is the ratio of numbers of teeth in the gear pair.

The "+" symbol in Equations (17-13) and (17-14) applies totwo external gears in mesh, whereas the "-" symbol is used for aninternal gear and an external gear mesh. For the case of a rack andgear, the quantity u/(u±1) becomes 1.

405

7.2.3 Determination of Factors In the Surface StrengthEquations

17.2.3.A Effective Tooth Width, bH(mm) The narrower face width of the meshed gear pair is assumedto be the effective width for surface strength. However, if thereare tooth modifications, such as chamfer, tip relief or crowning,an appropriate amount should be substracted to obtain theeffective tooth width.

17.2.3.B Zone Factor, ZH The zone factor is defined as:

(17-15)

where: βb = tan-1(tanβ cosαt) The zone factors are presented in Figure 17-2 for toothprofiles per JIS B 1701, specified in terms of profile shiftcoefficients x1, and x2, numbers of teeth Z1 and Z2 and helixangle β. The "+" symbol in Figure 17-2 applies to external gearmeshes, whereas the "-" is used for internal gear and externalgear meshes.

17.2.3.C Material Factor, ZM

(17-16)

where: ν = Poisson's Ratio, and E = Young's Modulus

Table 17-9 contains several combinations of material andtheir material factor. 17.2.4 Contact Ratio Factor, Zε This factor is fixed at 1.0 for spur gears. For helical gear meshes, Zε is calculated as follows: Helical gear: When εβ ≤ 1,

(17-17)

where: εα = Radial contact ratio εβ = Overlap ratio

406

Table 17-9 Material Factor, ZmGear Meshing Gears Material

FactorZM

(kgf/mm²)0.5Material Symbol

EYoung'sModuluskgf/mm²

Poison'sRatio Material Symbol

EYoung'sModuluskgf/mm²

Poisson'sRatio

StructuralSteel * 21000

0.3

Structural Steel * 21000

0.3

60.6Cast Steel SC 20500 60.2

Ductile Cast Iron FCD 17600 57.9Gray Cast Iron FC 12000 51.7

Cast Steel SC 20500Cast Steel SC 20500 59.9

Ductile Cast Iron FCD 17600 57.6Gray Cast Iron FC 12000 51.5

Ductile CastIron FCD 17600

Ductile Cast Iron FCD 17600 55.5Gray Cast Iron FC 12000 50.0

Gray CastIron FC 12000 Gray Cast Iron FC 12000 45.8

* NOTE: Structural steels are S...C, SNC, SNCM, SCr, SCM, etc.

17.2.5 Helix Angle Factor, Zb, This is a difficult parameter to evaluate. Therefore, it isassumed to be 1.0 unless better information is available. Zβ= 1.0 (17-18)17.2.6 Life Factor, KHL This factor reflects the number of repetitious stress cycles.Generally, it is taken as 1.0. Also, when the number of cycles isunknown, it is assumed to be 1.0. When the number of stress cycles is below 10 million, thevalues of Table 17-10 can be applied.

Table 17-10 Life Factor, KHLDuty Cycles Life Factorless than 105 1.5

approx. 105 1.3

approx. 106 1.15

above 107 1.0

NOTES: 1. The duty cycle is the meshing cycles during a lifetime. 2. Although an idler has two meshing points in one cycle, it is still regarded as one repetition. 3. For bidirectional gear drives, the larger loaded direction is taken as the number of cyclic loads.

17.2.7 Lubricant Factor, ZL The lubricant factor is based upon the lubricant's kinematicviscosity at 50ºC. See Figure 17-3.

The Kinematic Viscosity at 50ºC, cStNOTE: Normalized gears include quenched and tempered gearsFig. 17-3 Lubricant Factor, ZL

17.2.8 Surface Roughness Factor, ZR This factor is obtained from Figure 17-4 on the basis of theaverage roughness Rmaxm (µm). The average roughness iscalculated by Equation (17-19) using the surface roughnessvalues of the pinion and gear, Rmax1 and Rmax2, and thecenter distance, a, in mm.

(17-19)

407

17.2.9 Sliding Speed Factor, Zv This factor relates to the linear speed of the pitch line. SeeFigure 17-5.

17.2.10 Hardness Ratio Factor, Zw The hardness ratio factor applies only to the gear that is inmesh with a pinion which is quenched and ground. The ratio iscalculated by Equation (17-20). Zw = 1.2 - HB2 - 130 (17-20) 1700 where: HB2 = Brinell hardness of gear range: 130 ≤ HB2 ≤ 470If a gear is out of this range, the Zw is assumed to be 1.0.

17.2.11 Dimension Factor, KHX Because the conditions affecting this parameter are oftenunknown, the factor is usually set at 1.0.

KHX = 1.0 (17-21)

17.2.12 Tooth Flank Load Distribution Factor, KHβ (a) When tooth contact under load is not predictable:This case relates the ratio of the gear face width to the pitchdiameter, the shaft bearing mounting positions, and the shaftsturdiness. See Table 17-11. This attempts to take into accountthe case where the tooth contact under load is not good orknown. (b) When tooth contact under load is good: In this case,the shafts are rugged and the bearings are in good closeproximity to the gears, resulting in good contact over the fullwidth and working depth of the tooth flanks. Then the factor isin a narrow range, as specified below: KHβ = 1.0 ... 1.2 (17-22) 17.2.13 Dynamic Load Factor, Kv Dynamic load factor is obtainable from Table 17-3 accordingto the gear's precision grade and pitch line linear speed. 17.2.14 Overload Factor, Ko The overload factor is obtained from either Equation (17-11)or from Table 17-4. 17.2.15 Safety Factor for Pitting, SH The causes of pitting involves many environmental factors andusually is difficult to precisely define. Therefore, it is advisedthat a factor of at least 1.15 be used. 17.2.16 Allowable Hertz Stress, σHlim The values of allowable Hertz stress for various gear materialsare listed in Tables 17-12 through 17-16. Values for hardnessnot listed can be estimated by interpolation. Surface hardness isdefined as hardness in the pitch circle region.

Table 17-11 Tooth Flank Load Distribution Factor for Surface Strength,

b d1

method of Gear Shaft Supportbearings on Both Ends

Bearing on OneEndGear Equidistant

from BearingsGear Close to One

End (Rugged Shaft)Gear close to OneEnd (weak Shaft)

0.2 1.0 1.0 1.1 1.20.4 1.0 1.1 1.3 1.450.6 1.05 1.2 1.5 1.650.8 1.1 1.3 1.7 1.851.0 1.2 1.45 1.85 2.01.2 1.3 1.6 2.0 2.151.4 1.4 1.8 2.1 -1.6 1.5 2.05 2.2 -4.8 1.8 - - -2.0 2.1 - - -

NOTES: 1. The b means effective face width of spur & helical gears. For double helical gears, b is face width including central groove. 2. Tooth contact must be good under no load. 3. The values in this table are not applicable to gears with two or more mesh points, such as an idler.

408

Table 17-12 Gears without Case without Case Hardening - Allowable Hertz Stress

Material Arrows Indicate the rangesSurface

HardnessLower Limit of

Tensile Strengthkgf/mm²

(Refrence)

σHlimkgf/mm²

HB HV

Cast Steel

SC37SC42SC46SC49SCC3

37 3442 3546 3649 3755 3960 40

NormalizedStructural Steel

120 126 39 41.5130 136 42 42.5140 147 45 44150 157 48 45160 167 51 46.5170 178 55 47.5180 189 58 49190 200 61 50200 210 64 51.5210 221 68 52.5220 231 71 54230 242 74 55240 253 77 56.5250 263 81 57.5

Quenched andTempered

Structural Steel

160 167 51 51170 178 55 52.5180 189 58 54190 200 61 55.5200 210 64 57210 221 68 58.5220 231 71 60230 242 74 61240 252 77 62.5250 263 81 64260 273 84 65.5270 284 87 67280 295 90 68.5290 305 93 70300 316 97 71310 327 100 72.5320 337 103 74330 347 106 75.5340 358 110 77350 369 113 78.5

Quenched andTempered Alloy

Steel

220 231 71 70230 242 74 71.5240 252 77 73250 263 81 74.5260 273 84 76270 284 87 77.5280 295 90 79290 305 93 81300 316 97 82.5310 327 100 84320 337 103 85.5330 347 106 87340 358 110 88.5350 369 113 90360 380 117 92370 391 121 93.5380 402 126 95390 413 130 96.5400 424 135 98

409

Table 17-13 Gears with Induction Hardening - Allowable Hertz Stress

Material Heat Treatment beforeInduction Hardening

Surface Hardeness HV(Quenched)

σ H lim

StructuralCarbon Steel

S43C

S48CNormalized

420 77440 80460 82480 85500 87520 90540 92560 93.5580 95

600 and above 96

StructuralAlloySteel

SMn443SCM435SCM440SNC836

SNCM439

Quenchedand

Tempered

500 109520 112540 115560 117580 119600 121620 123640 124660 125

680 and above 126Table 17-14 Carburized Gears- Allowable Hertz Stress

Material Effective CarburizedDepth

Surface Hardeness HV(Quenched)

σ H limkgf/mm²

Structural Carbon SteelS15C

S15CK

Relatively Shallow (SeeTable 17-14A,

row A)

580 115600 117620 118640 119660 120680 120700 120720 119740 118760 117780 115800 113

Structural Alloy Steel

SCM415

SCM420

SNC420

SNC815

SNCM420

Relatively Shallow (SeeTable 17-14A,

row A)

580 131600 134620 137640 138660 138680 138700 138720 137740 136760 134780 132800 130

Relatively Thick(See

Table 17-14A, row A)

580 156600 160620 164640 166660 166680 166700 164720 161740 158760 154780 150800 146

NOTES: 1. Gears with thin effective carburized depth have "A" row values in the Table 17-14A. For thicker depths, use "B values. The effective carburized depth is defined as the depth which has the hardness greater than HV 513 or HRC 50. 2. The effective carburizing depth of ground gears is defined as the residual layer depth after grinding to final dimensions.

410

Table 17-14AModule 1.5 2 3 4 5 6 8 10 15 20 25

Depth,mm

A 0.2 0.2 0.3 0.4 0.5 0.6 0.7 0.9 1.2 1.5 1.8B 0.3 0.3 0.5 0.7 0.8 0.9 1.1 1.4 2.0 2.5 3.4

NOTE:For two gears with large numbers of teeth in mesh, themaximum shear stress point occurs in the inner part ofthe tooth beyond the carburized depth. In such a case, alarger safety factor, SH, should be used.

Table 17-15 Gears with Nitriding- Allowable Hertz Stress

Material Surface Hardness(Refrence)

σ H lim kgf/mm²

Nitriding Steel SAC 645 etc. Over HV 650Standard Processing Time 120

Extra Long Processing Time 130...140Note: In order to ensure me proper strength, this table applies only to those gears whicn have adequate depth of nitriding. Gears with insufficient nitnding or where the maximum shear stress point occurs much deeper than the nitriding depth should have a larger safety factor, SH.

Table 17-16 Gears with Soft Nitriding(1) - Allowable Hertz Stress

Materialnitriding

TimeHours

σHlim kgf/mm²

Relative Radius of Curvature mm(2)Less than 10 10 to 20 more than 20

Structural Steel or AlloySteel

2 100 90 804 110 100 906 120 110 100

Note: (1) Applicable to salt bath soft nitriding and gas soft nitriding gears (2) Relative radius of curvature is obtained from Figure 17-6. 17.2.17 Example of Surface Strength Calculation

Table 17-16A Spur Gear Design DetailsNo. Item symbol Unit Pinion Gear1 Normal Module mn mm 22 Normal Pressure Angle αn degree

20º3 Helix Angle β 0º4 Number of Teeth z 20 405 Center Distance αx mm 60

6 Coefficient of Profile Shift x +0.15 -0.157 Pitch Circle Diameter d

mm40.000 80.000

8 Working Pitch Circle Diameter dw 40.000 80.0009 Tooth Width b 20 2010 Precision Grade

JIS 5 JIS 5

11 Manufacturing Method Hobbing12 Surface Roughness 12.5 µm13 Revolutions per Minute n rpm 1500 75014 Linear Speed v m/s 3.14215 Direction of Load Unidirectional16 Duty Cycle cycle Over 107 Cycles17 Material

SCM 41518 Heat Treatment Carburizing19 Surface Hardness HV 600 ... 64020 Core Hardness HB 260 ... 28021 Effective Carburized Depth 0.3 ... 0.5

411

17.3 Bending Strength Of Bevel Gears This information is valid for bevel gears which are used inpower transmission in general industrial machines. Theapplicable ranges are:

Module:Pitch Diameter:

Linear Speed:Rotating Speed:

md vn

1.5 to 25 mmless than 1600 mm for straight bevelgearsless than 1000 mm for spiral bevelgearsless than 25 m/secless than 3600 rpm

17.3.1 Conversion Formulas In calculating strength, tangential force at the pitch circle,Ftm, in kgf; power, P, in kW, and torque, T, in kgf.m, arethe design criteria. Their basic relationships are expressed inEquations (17-23) through (17-25). Ftm = 102P = 1.95 x 106P = 2000T (17-23) Vm dmn dm P = FtmVm = 5.13 X 10-7 Ftmdmn (17-24) 102 T = Ftmdm = 974P (17-25) 2000 n where: Vm : Tangential speed at the central pitch circle Vm : dmn 19100 dm : Central pitch circle diameter dm : d - bsinδ 17.3.2 Bending Strength Equations The tangential force, Ftm, acting at the central pitch circleshould be less than the allowable tangential force, Ftm lim,which is based upon the allowable bending stress σFlim. Thatis: Ftm ≤ Ftm lim (17-26) The bending stress at the root, σF which is derived fromFtm should be less than the allowable bending stress σFlim.

σF ≤ σFlim (17-27) The tangential force at the central pitch circle, Ftmlim(kgf), is obtained

from Equation (17-28).

where: βm : Central spiral angle (degrees) m : Radial module (mm) Ra : Cone distance (mm) And the bending strength σF (kgf/mm²) at the root of tooth iscalculated from Equation (17-29).

17.3.3 Determination of Factors in Bending StrengthEquations 17.3.3.A Tooth Width, b (mm) The term b is defined as the tooth width on the pitch cone,analogous to face width of spur or helical gears. For the meshedpair, the narrower one is used for strength calculations. 17.3.3.B Tooth Profile Factor, YF The tooth profile factor is a function of profile shift, in both theradial and axial directions.

Using the equivalent(virtual) spur gear toothnumber, the first step isto determine the radialtooth profile factor, YFO,from Figure 17-8 forstraight bevel gears andFigure 17-9 for spiralbevel gears. Next,determine the axial shiftfactor, K, with Equation(17-33) from which theaxial shift correctionfactor, C, can beobtained using Figure17-7. Finally, calculateYF by Equation(17-30).

YF = CYFO (17-30)

412

Should the bevel gear pair not have any axial shift, thenthe coefficient C is 1, as per Figure17-7. The tooth profilefactor, YF, per Equation (17-31) is simply the YFO Thisvalue is from Figure 17-8 or 17-9, depending uponwhether it is a straight or spiral bevel gear pair. The graphentry parameter values are per Equation (17-32). YF = YFO (17-31)

(17-32)

where: ha = Addendum at outer end (mm) hao = Addendum of standard form (mm) m = Radial module (mm) The axial shift factor, K, is computed from the formula:

(17-33)

17.3.3.C Load Distribution Factor, Yε Load distribution factor is the reciprocal of radial contact ratio. Yε = 1 (17-34) εα The radial contact ratio for a straight bevel gear mesh is:

(17-35)

413

See Table 17-17 through 17-19 for some calculate examplesof radial contact ratio for various bevel gear pairs.

414

17.3.3.D Spiral Angle Factor, Yβ The spiral angle factor is a function of the spiral angle. Thevalue is arbitrarily set by the following conditions:

(17-36)

17.3.3.E Cutter Diameter Effect Factor, Yc This factor of cutter diameter, Yc, can be obtained from Table17-20 by the value of tooth flank length, b / cosβm (mm), overcutter diameter. If cutter diameter is not known, assume Yc =1.00.

17.3.3.F Life Factor, KL We can choose a proper life factor, KL, from Table 17-2similarly to calculating the bending strength of spur and helicalgears. 17.3.3.G Dimension Factor of Root Bending Stress, KFX This is a size factor that is a function of the radial module, m.Refer to Table 17-21 for values.

17.3.3.H Tooth Flank Load Distribution Factor, KM Tooth flank load distribution factor, KM, is obtained fromTable 17-22 or Table 17-23.

17.3.3.l Dynamic Load Factor, Kv Dynamic load factor, Kv, is a function of the precision grade ofthe gear and the tangential speed at the outer pitch circle, asshown in Table 17-24.

17.3.3.J Overload Factor, KO Overload factor, KO, can be computed from Equation(17-11) or obtained from Table 17-4, identical to the case ofspur and helical gears.

17.3.3.K Reliability Factor, KR The reliability factor should be assumed to be as follows:1. General case: KR=1.2 2. When all other factors can be determined accurately: KR= 1.0 3. When all or some of the factors cannot be known withcertainty: KR = 1.4

17.3.3.L Allowable Bending Stress at Root, σFlim The allowable stress at root σFlim can be obtained fromTables 17-5 through 17-8, similar to the case of spur andhelical gears.

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17.3.4 Examples of Bevel Gear Bending Strength Calculations

Table 17-24A Gleason Straight Bevel Gear Design DetailsNo. Item Symbol Unit Pinion Gear1 Shaft Angle Σ degree 90º2 Module m mm 23 Pressure Angle α

degree20º

4 Central Spiral Angle βm 0º5 Number Of Teeth z 20 406 Pitch Circle Diameter d mm 40.000 80.0007 Pitch Cone Angle δ degree 26.56505º 63.43495º8 Cone Distance Re

mm44.721

9 Tooth Width b 15 10 Central Pitch Circle Diameter dm 33.292 66.58411 Precision Grade

JIS 3 JIS 3

12 Manufacturing Method Gleason No. 10413 Surface Roughness 12.5 µm 12.5 µm14 Revolutions per Minute n rpm 1500 75015 Linear Speed v m/s 3.14216 Direction of Load Unidirectional17 Duty Cycle Cycle More than 107 Cycles18 Material

SCM 415

19 Heat Treatment Carburized20 Surface Hardness HV 600 ... 64021 Core Hardness HB 260 ... 28022 Effective Carburized Depth mm 0.3 ... 0.5

Table 17-24B Bending Strength Factors for Gleason Straight Bevel GearNo. Item Symbol Unit Pinion Gear1 Central Spiral Angle βm degree 0º2 Allowable Bending Stress at Root σFlim kgf/mm² 42.5 42.53 Module m

mm2

4 Tooth Width b 155 Cone Distance Re 44.7216 Tooth Profile Factor YF

2.369 2.3877 Load Distribution Factor Yε 0.6138 Spiral Angle Factor Yβ 1.09 Cutter Diameter Effect Factor YC 1.1510 Life Factor KL 1.011 Dimension Factor KFX 1.012 Tooth Flank Load Distribution Factor KM 1.8 1.813 Dynamic Load Factor KV 1.414 Overload Factor KO 1.015 Reliability Factor KR 1.216 Allowable Tangential Force at Central Pitch Circle Ftlim kgf 178.6 177.3

17.4 Surface Strength Of Bevel Gears This information is valid for bevel gears which are used inpower transmission in general industrial machines. Theapplicable ranges are:

Radial Module:Pitch Diameter:

Linear Speed:Rotating Speed:

md

vn

1.5 to 25mmStraight bevel gear under 1600mmSpiral bevel gear under 1000mmless than 25 m/secless than 3600 rpm

17.4.1 Basic Conversion Formulas The same formulas of SECTION 17.3 apply. (See page 84).

17.4.2 Surface Strength Equations In order to obtain a proper surface strength, the tangential

force at the central pitch circle, Ftm, must remain below theallowable tangential force at the central pitch circle, Ftmlim,based on the allowable Hertz stress σHlim.

Ftm ≤ Ftmlim (17-37) Alternately, the Hertz stress σH, which is derived from thetangential force at the central pitch circle must be smaller thanthe allowable Hertz stress σHlim.

σH ≤ σHlim (17-38) The allowable tangential force at the central pitch circle,Ftmlim, in kgf can be calculated from Equation (17-39).

(17-39)

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The Hertz stress, σH (kgf/mm2) is calculated from Equation(17-40).

17.4.3 Determination of Factors In Surface StrengthEquations17.4.3.A Tooth Width, b (mm) This term is defined as the tooth width on the pitch cone. Fora meshed pair, the narrower gear's "b" is used for strengthcalculations.17.4.3.B Zone Factor, ZH The zone factor is defined as:

where: βm = Central spiral angle αn = Normal pressure angle

αt = Central radial pressure angle

βb = tan-1(tanβm cosαt)

If the normal pressure angle αn is 20º, 22.5º or 25º, the zonefactor can be obtained from Figure 17-10. 17.4.3.C Material Factor, ZM The material factor, ZM, is obtainable from Table 17-9. 17.4.3.D Contact Ratio Factor, Zε The contact ratio factor is calculated from the equationsbelow. Straight bevel gear: Zε = 1.0 Spiral bevel gear:

where: εα = Radial Contact Ratio εβ = Overlap Ratio

17.4.3.E Spiral Angle Factor, Zβ Little is known about these factors, so usually it is assumed tobe unity. Zβ = 1.0 (17-43)

17.4.3.F Life Factor, KHL The life factor for surface strength is obtainable from Table17-10.

17.4.3.G Lubricant Factor, ZL The lubricant factor, ZL, is found in Figure 17-3.

17.4.3.H Surface Roughness Factor, ZR The surface roughness factor is obtainable from Figure 17-11on the basis of average roughness, Rmaxm, in µm The averagesurface roughness is calculated by Equation (17-44) fromsurface roughnesses of the pinion and gear (Rmax1 andRmax2), and the center distance, a, in mm.

17.4.3.I Sliding Speed Factor, Zv The sliding speed factor is obtained from Figure 17-5 basedon the pitch circle linear speed.

17.4.3.J Hardness Ratio Factor, Zw The hardness ratio factor applies only to the gear that is inmesh with a pinion which is quenched and ground. The ratio iscalculated by Equation (17-45).

where Brinell hardness of the gear is: 130 ≤ HB2 ≤ 470

If the gear's hardness is outside of this range, Zw is assumedto be unity. Zw = 1.0 (17-46)

17.4.3.K Dimension Factor, KHX Since, often, little is known about this factor, it is assumed tobe unity. KHX = 1.0 (17-47)

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17.4.3.L Tooth Flank Load Distribution Factor, KHβ Factors are listed in Tables 17-25 and 17-26. If the gear andpinion are unhardened, the factors are to be reduced to 90% of thevalues in the table.

Table 17-25 Tooth Flank Load Distribution Factor for SpiralBevel Gears, Zerol Bevel Gears and Straight Bevel Gearswith Crownina. KHβ

Stiffness ofShaft, Gear

Box, etc.

Both GearsSupported On

Two Sides

One GearSupported on

One End

Both GearsSupported on

One EndVery Stiff 1.3 1.5 1.7Average 1.6 1.85 2.1

SomewhatWeak 1.75 2.1 2.5

Table 17-26 Tooth Flank Load Distribution Factor forStraight Bevel Gear without Crownina. KHβ

Stiffness ofShaft, Gear

Box, etc.

Both GearsSupported On

Two Sides

One GearSupported on

One End

Both GearsSupported on

One EndVery Stiff 1.3 1.5 1.7Average 1.85 2.1 2.6

somewhat Weak 2.8 3.3 3.8

17.4.3.M Dynamic Load Factor, Kv The dynamic load factor can be obtained from Table 17-24.

17.4.3.N Overload Factor, KO The overload factor can be computed by Equation 17-11 orfound in Table 17-4.

17.4.3.O Reliability Factor, CR The general practice is to assume CR to be at least 1.15.

17.4.3.P Allowable Hertz Stress, σHlim The values of allowable Hertz stress are given in Tables17-12 through 17-16.

17.4.4 Examples of Bevel Gear Surface StrengthCalculation Tables 17-26A and 17-26B give the calculations ofsurface strength factors of Gleason straight bevel gears.

Table 17-26A Gleason Straight Bevel Gear Design DetailsNo. Item Symbol Unit Pinion Gear1 Shaft Angle Σ degree 90º2 Module m mm 23 Pressure Angle α degree

20º4 Central Spiral Angle βm 0º5 Number of Teeth z 20 406 Pitch Circle Diameter d mm 40.000 80.0007 Pitch Cone Angle δ degree 26.565.5º 63.43495º8 Cone Distance Re

mm44.721

9 Tooth Width b 1510 Central Pitch Circle Diameter dm 33.292 66.58411 Precision Grade

JIS 3 JIS 3

12 Manufacturing Method Gleason No. 10413 Surface Roughness 12.5 µm 12.5 µm14 Revolutions per Minute n rpm 1500 75015 Linear Speed v m/s 3.14216 Direction of Load Unidirectional17 Duty Cycle cycle Over 107 cycles18 Material

SCM 415

19 Heat Treatment Carburized20 Surface Hardness HV 600 ... 64021 Core Hardness HB 260 ... 28022 Effective Carburized Depth mm 0.3 ... 0.5

418

Table 17-26B Surface Strength Factor of Gleason Straight Bevel GearNo. Item Symbol Unit Pinion Gear1 Allowable Hertz Stress σHlim kgf/mm² 1642 Pinion's Pitch Diameter d1 mm 40.0003 Pinion's Pitch Cone Angle δ1 degree 26.56505º4 Cone Distance Re mm

44.7215 Tooth Width b 156 Number of Teeth Ratio z2/z1 u 27 Zone Factor ZH 2.4958 Material Factor ZM (kgf/mm²) 60.69 Contact Ratio Zε

1.010 Spiral Angle Factor Zβ 1.011 Life Factor kHL 1.012 Lubricant Factor ZL 1.013 Surface Roughness Factor ZR 0.9014 Sliding Speed Factor ZV 0.9715 Hardness Ratio Factor ZW 1.016 Dimension Factor of Root Stress kHX 1.017 Load Distribution Factor kHβ 2.118 Dynamic Load Factor kV 1.419 Overload Factor KO 1.020 Reliability Factor CR 1.15

21 Allowable Tangential Force onCentral Pitch Circle

Ftlim kgf 103.0 103.0

17.5 Strength Of Worm Gearing This information is applicable for worm gear drives that areused to transmit power in general industrial machines with thefollowing parameters:

Axial Module:Pitch Diameter of Worm Gear:Sliding Speed: Rotating Speed, Worm Gear:

md2 v5n2

1 to 25 mmless than 900mm less than 30m/secless than 600 rpm

17.5.1 Basic Formulas: Sliding Speed, vs (m/s) Vs = d1n1 (17-48) 19100cosγ17.5.2 Torque, Tangential Force and Efficiency (1) Worm as Driver Gear (Speed Reducing)

where: T2 = Nominal torque of worm gear (kgf.m) T1 = Nominal torque of worm (kgf.m)

Ft = Nominal tangential force on worm gear's pitch circle (kgf)d2 = Pitch diameter of worm gear (mm)u = Teeth number ratio = z2 / zw ηR= Transmission efficiency, worm driving (not including bearingloss, lubricant agitation loss, etc.)µ = Friction coefficient

(2) Worm Gear as Driver Gear (Speed Increasing)

where: η1 = Transmission efficiency, worm gear driving (notincluding bearing loss, lubricant agitation loss, etc.)

17.5.3 Friction Coefficient, µ The friction factor varies as sliding speed changes. Thecombination of materials is important. For the case of a wormthat is carburized and ground, and mated with a phosphorousbronze worm gear, see Figure 17-12. For some othermaterials, see Table 17-27. For lack of data, friction coefficient of materials not listed inTable 17-27 are very difficult to obtain. H.E. Merritt has offeredsome further information on this topic. See Reference 9.

Table 17-27 Combinations of Materials and Their Coefficient of Friction, µCombination of Materials µ

Cast Iron and Phosphor BronzeCast Iron and Cast IronQuenched Steel and Aluminum AlloySteel and Steel

µ in Figure 17-12 times 1.15µ in Figure 17-12 times 1.33µ in Figure 17-12 times 1.33µ in Figure 17-12 times 2.00

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17.5.4 Surface Strength of Worm Gearing Mesh (1) Calculation of Basic Load Provided dimensions and materials of the worm pair areknown, the allowable load is as follows:

(2) Calculation of Equivalent Load The basic load Equations (17-51) and (17-52) areapplicable under the conditions of no impact and the pair canoperate for 26000 hours minimum. The condition of "no impact"is defined as the starting torque which must be less than 200%of the rated torque; and the frequency of starting should be lessthan twice per hour. An equivalent load is needed to compare with the basic load inorder to determine an actual design load, when the conditionsdeviate from the above. Equivalent load is then converted to an equivalent tangentialforce, Fte, in kgf: Fte = FtKhKs (17-53)and equivalent worm gear torque, T2e, in kgf.m: T2e = T2KhKS (17-54) (3) Determination of Load Under no impact condition, to have life expectancy of 26000hours, the following relationships must be satisfied: Ft ≤ Ftlim or T2 ≤ T2lim (17-55) For all other conditions: Fte ≤ Ftlim or T2e ≤ T2lim (17-56)NOTE: If load is variable, the maximum load should be used as the criterion.

17.5.5 Determination of Factors in Worm Gear SurfaceStrength Equations

17.5.5.A Tooth Width of Worm Gear, b2 (mm)

Tooth width of worm gear is defined as in Figure 17-13.

17.5.5.B Zone Factor, Z

where: Basic Zone Factor is obtained from Table 17-28 Q : Diameter factor = d1 mx Zw: number of worm threads

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17.5.5.C Sliding Speed Factor, Kv The sliding speed factor is obtainable from Figure 17-14,where the abscissa is the pitch line linear velocity. 17.5.5.D Rotating Speed Factor, Kn The rotating speed factor is presented in Figure 17-15 as afunction of the worm gear's rotating speed, n2.

17.5.5.E Lubricant Factor, ZL Let ZL = 1.0 if the lubricant is of proper viscosity and hasantiscoring additives. Some bearings in worm gear boxes may need a low viscositylubricant. Then ZL is to be less than 1.0. The recommendedkinetic viscosity of lubricant is given in Table 17-29.

Table 17-29 Recommended Kinematic Viscosity of Lubricant Unit: cSt/37.8ºCOperating lubricant Temperature Sliding Speed (m/s)

Highest OperatingTemperature

Lubricant Temperature atStart of Operation Less than 2.5 2.5 to 5 More than 5

0ºC to less than 10ºC-10ºC ... 0ºC 110 ... 130 110 ... 130 110 ... 130

more than 0ºC 110 ... 150 110 ... 150 110 ... 15010ºC to less than 30ºC more than 0ºC 200 ... 245 150 ... 200 150 ... 20030ºC to less than 55ºC more than 0ºC 350 ... 510 245 ... 350 200 ... 24555ºC to less than 80ºC more than 0ºC 510 ... 780 350 ... 510 245 ... 35080ºC to less than 100ºC more than 0ºC 900 ... 1100 510 ... 780 350 ... 510

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17.5.5.F Lubrication Factor, ZM The lubrication factor, ZM, is obtained from Table 17-30. 17.5.5.G Surface Roughness Factor, ZR This factor is concerned with resistance to pitting of theworking surfaces of the teeth. Since there is insufficientknowledge about this phenomenon, the factor is assumed to be1.0. ZR = 1.0 (17-58) It should be noted that for Equation (17-58) to beapplicable, surfaces roughness of the worm and worm gear mustbe less than 3 mm and 12 mm respectively. If either is rougher,the factor is to be adjusted to a smaller value. 17.5.5.H Contact Factor, Kc Quality of tooth contact will affect load capacity dramatically.Generally, it is difficult to define precisely, but JIS B 1741 offersguidelines depending on the class of tooth contact.

Table 17-31 gives the general values of Kc depending on theJIS tooth contact class.

17.5.5.1 Starting Factor, Ks This factor depends upon the magnitude of starting torque andthe frequency of starts. When starting torque is less than 200%of rated torque, Ks factor is per Table 17-32.

17.5.5.J Time Factor, Kh This factor is a function of the desired life and the impactenvironment. See Table 17-33. The expected lives in betweenthe numbers shown in Table 17-33 can be interpolated.

17.5.5.K Allowable Stress Factor, Sclim Table 17-34 presents the allowable stress factors for variousmaterial combinations. Note that the table also specifiesgoverning limits of sliding speed, which must be adhered to ifscoring is to be avoided.

Table 17-30 Lubrication Factor, ZMSliding Speed (m/s) Less than 10 10 to 14 More than 14

Oil Bath Lubrication 1.0 0.85 -Forced Circulation Lubrication 1.0 1.0 1.0

Table 17-31 Classes of Tooth Contact and General_Values of Contact Factor, Kc

ClassProportion of Tooth Contact KcTooth Width Direction Tooth Height Direction

A More than 50%ofEffective Width of Tooth

More than 40% ofEffective Height of Tooth 1.0

B More than 35% ofEffective Width of Tooth

More than 30% ofEffective Height of Tooth 1.3 ... 1.4

C More than 20% ofEffective Width of Tooth

More than 20% ofEffective Height of Tooth 1.5 ... 1.7

Table 17-32 Starting Factor, Ks

Starting FactorStarting Frequency per Hour

Less than 2 2 ... 5 5 ... 10 More than 10Ks 1.0 1.07 1.13 1.18

Table 17-33 Time Factor, Kh

Impact from PrimeMover Expected Life

KhImpact from Load

Uniform Load Medium Impact Strong Impact

Uniform Load(Motor, Turbine,Hydulic Motor)

1500 Hours 5000 Hours

26000 Hours*60000 Hours

0.800.901.0 1.25

0.901.0 1.251.50

1.0 1.251.501.75

Light Impact(Multicylinderengine)

1500 Hours 5000 Hours

26000 Hours*60000 Hours

0.901.0 1.251.50

1.0 1.251.501.75

1.251.501.752.0

Medium Impact(Single cylinderengine)

1500 Hours 5000 Hours

26000 Hours*60000 Hours

1.0 1.251.501.75

1.251.501.702.0

1.501.752.0 2.25

*NOTE: For a machine that operates 10 hours a day, 260 days a year; this number corresponds to ten years of operating life.

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Table 17-34 Allowable Stress Factor for Surface Strength, Sclim Material ofworm Gear Material of Worm Sclim

Sliding Speed Limitbefore Scoring

(m/s)*

Phosphor Bronze CentrifugalCasting

Alloy Steel Carburized & QuenchedAlloy Steel HB 400Alloy Steel HB 250

1.551.341.12

302010

Phosphor BronzeChilled Casting

Alloy Steel Carburized & QuenchedAlloy Steel HB 400Alloy Steel HB 250

1.271.050.88

302010

Phosphor BronzeSand Molding or Forging

Alloy Steel Carburized & QuenchedAlloy Steel HB 400Alloy Steel HB 250

1.050.840.70

302010

Aluminum BronzeAlloy Steel Carburized & QuenchedAlloy Steel HB 400Alloy Steel HB 250

0.840.670.56

201510

Brass Alloy Steel HB 400Alloy Steel HB 250

0.490.42

85

Ductile Cast Iron Ductile Cast Iron but with a higher hardnessthan the worm gear 0.70 5

Cast Iron (Perlitic)Phosphor Bronze Casting and Forging 0.63 2.5Cast Iron but with a higher hardness thanthe worm gear 0.42 2.5

* Note: The value indicates the maximum sliding speed within the limit of the allowable stress factor, Sclim. Even when the allowable load is below the allowable stress level, if the sliding speed exceeds the indicated limit, there is danger of scoring gear surfaces.

17.5.6 Examples of worm Mesh Strength Calculation

Table 17-35A Worm and Worm Gears Design DetailsNo. Item Symbol Unit Worm Worm Gear1 Axial Module mx mm 22 Normal Pressure Angle αn degree 20º3 No. of Threads, No. of Teeth Zw,Z2 1 404 Pitch Diameter d mm 28 805 Lead Angle γ degree 4.085626 Diameter Factor Q 14 -7 Tooth Width b mm () 208 Manufacturing Method Grinding Hobbing9 Surface Roughness 3.23 µm 12.5 µm10 Revolutions per Minute n rpm 1500 37.511 Sliding Speed Vs m/s 2.20512 Material

S45C Aι BC2

13 Heat Treatment Induction Hardening -14 Surface Hardness Hs 63 ... 68 -

Table 17-35 Surface Strength Factors and Allowable ForceNo. Item Symbol Unit Worm Gear1 Axial Module mx

mm2

2 Worm Gear Pitch Diameter d2 803 Zone Factor Z

1.51574 Sliding Speed Factor Kv 0.495 Rotating Speed Factor Kn 0.666 Lubricant Factor ZL 1.07 Lubrication Factor ZM 1.08 Surface Roughness Factor ZR 1.09 Contact Factor KC 1.010 Allowable Stress Factor SClim 0.6711 Allowable Tangential Force Ftlim kgf 83.5

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