Calculation of a helical-toothed cylindrical gear pair

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Contents

1 Messages 3
2 Overview 3
3 Tooth geometry 3
4 Materials 3
4.1 Roughnesses 4
4.2 Lubrication 4
5 Geometry 4
5.1 Reference profiles 4
5.2 Basic data 5
5.3 Diameters and their allowances 5
5.4 Tip clearances and tooth heights 6
5.5 Roll angle 6
5.6 Tooth thickness and pitch 6
5.7 Sliding 6
5.8 Contact ratios 7
6 General influence factors 7
6.1 Forces and circumferential speed 7
6.2 Contact stiffness 8
6.3 Calculation of K factors 8
6.4 K factors 8
7 Calculation of tooth root strength (fracture) 9
7.1 Safety factors 9
8 Calculation of flank strength (pitting) 9
8.1 Safety factors 10
9 Micropitting 10
10 Scuffing load capacity 10
10.1 Flash temperature-criteria 11
10.2 Integral temperature-criteria 11
11 Measurements for tooth thickness 11
11.1 Tooth thickness tolerances 11
11.2 Base tangent lengths 11
11.3 Measurement over balls and pins 12
11.4 Tooth thickness 12
11.5 Backlash 12
12 Toothing tolerances 12
13 Modifications and determination of the tooth form 13
13.1 Data for the tooth form calculation 13
14 Supplementary data 13
14.1 Masses, stiffnesses and moments of inertia 13
14.2 Wear, power loss, sound pressure level 13
15 Service life, damage 14
15.1 Damage 14
16 Remarks 14
16.1 Conventions 14
16.2 Calculations and factors 14

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1 Messages

No messages occurred during the calculation.

2 Overview

Calculation method ISO 6336:2019

Drawing or article number:

Gear 1: 0.000.0
Gear 2: 0.000.0
------- Gear 1 ----------------- Gear 2 -------
Power (kW) [P] 140.290
Speed (1/min) [n] 950.0 321.1

Number of load cycles (in mio.) [NL] 1140.000 385.352

Torque (Nm) [T] 1410.2 4171.8

Application factor [KA] 1.25
Required service life (h) [H] 20000.00

Gear driving (+) / driven (-) + -

Working flank Gear 1: Right flank
Gear 1 direction of rotation: Clockwise

3 Tooth geometry

Geometry calculation according to ISO 21771:2007

------- Gear 1 ----------------- Gear 2 -------

Center distance (mm) [a] 145.000
Center distance tolerance ISO 286:2010 Measure js7
Normal module (mm) [mn] 3.0000
Normal pressure angle (°) [αn] 20.0000
Helix angle at reference circle (°) [β] 10.0000
Number of teeth [z] 24 71
Facewidth (mm) [b] 100.00 100.00
Hand of gear left right
Accuracy grade [Q-ISO 1328:2013] A6 A6
Inner diameter (mm) [di] 0.00 0.00
Inner diameter of gear rim (mm) [dbi] 0.00 0.00

4 Materials

Gear 1
18CrNiMo7-6, Case hardening steel, case-hardened, ISO 6336-5 Figure 9/10 (MQ), Core hardness >=25HRC Jominy J=12mm<HRC28

Gear 2
18CrNiMo7-6, Case hardening steel, case-hardened, ISO 6336-5 Figure 9/10 (MQ), Core hardness >=25HRC Jominy J=12mm<HRC28

------- Gear 1 ----------------- Gear 2 -------

Surface hardness HRC 61 HRC 61

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Material treatment according to ISO 6336:2006 Normal, Life factors ZNT and YNT ≥ 0.85
Infinite life strength for tooth root stress (N/mm²) [σFlim] 430.00 430.00
Fatigue strength for Hertzian pressure (N/mm²) [σHlim] 1500.00 1500.00
Young's modulus (N/mm²) [E] 206000 206000
Poisson's ratio [ν] 0.300 0.300
Tensile strength (N/mm²) [σB] 1200.00 1200.00
Yield point (N/mm²) [σS] 850.00 850.00

4.1 Roughnesses

------- Gear 1 ----------------- Gear 2 -------

Roughness average value DS, flank (µm) [RAH] 0.60 0.60
Roughness average value DS, root (µm) [RAF] 3.00 3.00
Mean roughness height, Rz, flank (µm) [RZH] 4.80 4.80
Mean roughness height, Rz, root (µm) [RZF] 20.00 20.00

4.2 Lubrication

Lubrication type Oil bath lubrication

Type of oil ISO-VG 220
Lubricant base Mineral-oil base
Oil nominal kinematic viscosity at 40°C (mm²/s) [ν40] 220.00
Oil nominal kinematic viscosity at 100°C (mm²/s) [ν100] 17.50
Specific density at 15°C (kg/dm³) [ρ] 0.895
Oil temperature (°C) [TS] 70.000

5 Geometry

5.1 Reference profiles

Gear reference profile 1

Reference profile 1.25 / 0.38 / 1.0 ISO 53:1998 Profil A
Dedendum coefficient [hfP*] 1.250
Root radius factor [ρfP*] 0.380
[ρfPmax*] 0.472
Addendum coefficient [haP*] 1.000
Tip radius factor [ρaP*] 0.000
Protuberance height coefficient [hprP*] 0.000
Protuberance angle [αprP] 0.000
Tip form height coefficient [hFaP*] 0.000
Ramp angle [αKP] 0.000
not topping
Smallest radius of curvature, root rounding (mm) [ρmin.e/i] 1.294 / 1.301

Gear reference profile 2

Reference profile 1.25 / 0.38 / 1.0 ISO 53:1998 Profil A
Dedendum coefficient [hfP*] 1.250
Root radius factor [ρfP*] 0.380
[ρfPmax*] 0.472
Addendum coefficient [haP*] 1.000
Tip radius factor [ρaP*] 0.000
Protuberance height coefficient [hprP*] 0.000
Protuberance angle [αprP] 0.000
Tip form height coefficient [hFaP*] 0.000
Ramp angle [αKP] 0.000
not topping
Smallest radius of curvature, root rounding (mm) [ρmin.e/i] 1.206 / 1.209

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5.1.1 Information on final machining
------- Gear 1 ----------------- Gear 2 -------
Dedendum reference profile [hfP*] 1.250 1.250
Tooth root radius Refer. profile [ρfP*] 0.380 0.380
Addendum Reference profile [haP*] 1.000 1.000
Protuberance height coefficient [hprP*] 0.000 0.000
Protuberance angle (°) [αprP] 0.000 0.000
Tip form height coefficient [hFaP*] 0.000 0.000
Ramp angle (°) [αKP] 0.000 0.000

Type of profile modification: none (only running-in)

Tip relief by running in (µm) [Ca L/R] 2.0 / 2.0 2.0 / 2.0

5.2 Basic data

Overall transmission ratio [itot] -2.958

Gear ratio [u] 2.958
Transverse module (mm) [mt] 3.046
Transverse pressure angle (°) [αt] 20.284
Working pressure angle (°) [αwt] 20.604
(°) [αwt.e/i] 20.625 /20.583
Working pressure angle at normal section (°) [αwn] 20.315
Base helix angle (°) [βb] 9.391
Helix angle at operating pitch circle (°) [βw] 10.020
Reference center distance (mm) [ad] 144.698
Sum of profile shift coefficients [Σxi] 0.1013

------- Gear 1 ----------------- Gear 2 -------

Profile shift coefficient [x] 0.0853 0.0160
Generating profile shift coefficient [xE.e/i] 0.0533/ 0.0350 -0.0275/-0.0504
Virtual gear no. of teeth [zn] 25.037 74.067
Involute length (mm) [l_dFa-l_dFf] 5.635 6.083

5.3 Diameters and their allowances

------- Gear 1 ----------------- Gear 2 -------

Reference diameter (mm) [d] 73.111 216.286
Base diameter (mm) [db] 68.577 202.874
Tip alteration (mm) [k*mn] -0.002 -0.002

Tip diameter (mm) [da] 79.619 222.378

(mm) [da.e/i] 79.619 /79.589 222.378 /222.332

Tip diameter allowances (mm) [Ada.e/i] 0.000 /-0.030 0.000 /-0.046

Tip form diameter (mm) [dFa] 79.619 222.378

(mm) [dFa.e/i] 79.619 /79.589 222.378 /222.332

Active tip diameter (mm) [dNa] 79.619 222.378

(mm) [dNa.e/i] 79.619 /79.589 222.378 /222.332

Operating pitch diameter (mm) [dw] 73.263 216.737

(mm) [dw.e/i] 73.273 /73.253 216.767 /216.707

Root diameter (mm) [df] 66.123 208.882

Generated root diameter with xE (mm) [df.e/i] 65.930 /65.821 208.621 /208.483

Active root diameter (mm) [dNf] 69.450 212.019

(mm) [dNf.e/i] 69.486 /69.432 212.070 /211.986

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Root form diameter (mm) [dFf] 69.234 210.988
(mm) [dFf.e/i] 69.160 /69.120 210.782 /210.675

5.4 Tip clearances and tooth heights

------- Gear 1 ----------------- Gear 2 -------

Theoretical tip clearance (mm) [c] 0.750 0.750
Effective tip clearance (mm) [c.e/i] 0.984 / 0.860 0.944 / 0.826

Reserve (dNf-dFf)/2 (mm) [cF.e/i] 0.183 / 0.136 0.697 / 0.602

Addendum, mn(haP *+x+k) (mm) [ha] 3.254 3.046

(mm) [ha.e/i] 3.254 / 3.239 3.046 / 3.023

Dedendum, mn(hfP *-x) (mm) [hf] 3.494 3.702

(mm) [hf.e/i] 3.590 / 3.645 3.833 / 3.901

Tooth height (mm) [h] 6.748 6.748

5.5 Roll angle

------- Gear 1 ----------------- Gear 2 -------

Roll angle at dFa (°) [ξFa.e/i] 33.797 /33.748 25.721 /25.689
Roll angle to dNf (°) [ξNf.e/i] 9.362 / 9.078 17.446 /17.365
Roll angle at dFf (°) [ξFf.e/i] 7.486 / 7.221 16.153 /16.041

5.6 Tooth thickness and pitch

------- Gear 1 ----------------- Gear 2 -------

Tooth thickness, arc, in module [sn*] 1.6329 1.5824
Normal tooth thickness at tip circle (mm) [san] 2.086 2.384
(mm) [san.e/i] 2.026 / 1.966 2.306 / 2.235

Normal tooth thickness at tip form circle (mm) [sFan] 2.086 2.384
(mm) [sFan.e/i] 2.026 / 1.966 2.306 / 2.235

Normal space width at root circle (mm) [efn] 0.000 2.292

(mm) [efn.e/i] 0.000 / 0.000 2.319 / 2.333

Pitch on reference circle (mm) [pt] 9.570 9.570

Base pitch (mm) [pbt] 8.977 8.977
Transverse pitch on contact-path (mm) [pet] 8.977 8.977
Lead height (mm) [pz] 1302.603 3853.534
Axial pitch (mm) [px] 54.275 54.275

5.7 Sliding

------- Gear 1 ----------------- Gear 2 -------

Max. sliding velocity at tip (m/s) [vga] 0.976 0.985
Specific sliding at the tip [ζa] 0.485 0.643
Specific sliding at the root [ζf] -1.804 -0.943
Mean specific sliding [ζm] 0.565

Sliding factor on tip [Kga] 0.268 0.270

Sliding factor on root [Kgf] -0.270 -0.268

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5.8 Contact ratios

------------------ Pair ----------------------

Minimal length of contact line (mm) [Lmin] 163.284
Transverse contact ratio [εα] 1.642
[εα.e/m/i] 1.648 / 1.637/ 1.626
Overlap ratio [εβ] 1.842
Total contact ratio [εγ] 3.484
[εγ.e/m/i] 3.490 / 3.479/ 3.468
Length of path of contact (mm) [ga] 14.736
(mm) [ga.e/i] 14.793 /14.594

------- Gear 1 ----------------- Gear 2 -------

Addendum contact ratio [ε] 0.817 0.824
[ε.e/i] 0.819 / 0.812 0.829 / 0.813

Length T1-A and T2-A (mm) [T1A,T2A] 5.490 45.536

(mm) [.e/i] 5.433 / 5.603 45.536 / 45.480
Length T1-B and T2-B (mm) [T1B,T2B] 11.249 39.777
(mm) [.e/i] 11.249 / 11.220 39.720 / 39.863
Length T1-C and T2-C (mm) [T1C,T2C] 12.891 38.135
(mm) [.e/i] 12.876 / 12.905 38.093 / 38.178
Length T1-D and T2-D (mm) [T1D,T2D] 14.466 36.559
(mm) [.e/i] 14.410 / 14.579 36.559 / 36.503
Length T1-E and T2-E (mm) [T1E,T2E] 20.226 30.800
(mm) [.e/i] 20.226 / 20.196 30.743 / 30.886
Length T1-T2 (mm) [T1T2] 51.026
(mm) [.e/i] 50.969 / 51.083

Diameter of single contact point B (mm) [d-B] 72.173 217.914

(mm) [d-B.e/i] 72.173 / 72.155 217.872 /217.977
Diameter of single contact point D (mm) [d-D] 74.431 215.648
(mm) [d-D.e/i] 74.386 / 74.519 215.648 /215.610

6 General influence factors

6.1 Forces and circumferential speed

------- Gear 1 ----------------- Gear 2 -------

Nominal circum. force at pitch circle (N) [Ft] 38576.6
Axial force (N) [Fa] 6802.1 6802.1
Radial force (N) [Fr] 14257.3 14257.3
Normal force (N) [Fnorm] 41685.6 41685.6
Nominal circumferential force per mm (N/mm) [w] 385.77

Only as information: Forces at operating pitch circle:

Nominal circumferential force (N) [Ftw] 38496.3
Axial force (N) [Faw] 6802.1 6802.1
Radial force (N) [Frw] 14472.7

Circumferential speed reference circle (m/s) [v] 3.64

Circumferential speed operating pitch circle (m/s) [v(dw)] 3.64

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6.2 Contact stiffness

Running-in value (µm) [yp] 0.6

Running-in value (µm) [yf] 0.7
Correction factor [CM] 0.800
Gear blank factor [CR] 1.000
Basic rack factor [CBS] 0.975
Material coefficient [E/Est] 1.000
Singular tooth stiffness (N/mm/µm) [c'] 13.732
Meshing stiffness (N/mm/µm) [cγα] 20.339
Meshing stiffness (N/mm/µm) [cγβ] 17.288
Reduced mass (kg/mm) [mRed] 0.01655
Resonance speed (min-1) [nE1] 13950
Resonance ratio (-) [N] 0.068
Subcritical range

6.3 Calculation of K factors

Running-in value (µm) [yα] 0.7

Bearing distance l of pinion shaft (mm) [l] 200.000
Distance s of pinion shaft (mm) [s] 20.000
Outside diameter of pinion shaft (mm) [dsh] 66.500
Load in accordance with Figure 13, ISO 6336-1:2006 [-] 4
0:a), 1:b), 2:c), 3:d), 4:e)
Coefficient K' according to Figure 13, ISO 6336-1:2006 [K'] -1.00
Without stiffening
Tooth trace deviation (active) (µm) [Fβy] 9.65
from deformation of shaft (µm) [fsh*B1] 14.55
fsh (µm) [fsh] 14.55
B1 [B1] 1.00
fHβ5 (µm) [fHβ5] 8.00
Tooth without flank line modification
Position of contact pattern: favorable
from production tolerances (µm) [fmα*B2] 16.28
B2=1.00
Tooth trace deviation, theoretical (µm) [Fβx] 11.35
Running-in value (µm) [yβ] 1.70

6.4 K factors

Dynamic factor [Kv] 1.011

Width factors
- Flank [KHβ] 1.171
- Tooth root [KFβ] 1.158
- Scuffing [KBβ] 1.171

Transverse load factors

- Flank [KHα] 1.050
- Tooth root [KFα] 1.050
- Scuffing [KBα] 1.050

Application factor [KA] 1.250

Distribution factor [Kγ] 1.000

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7 Calculation of tooth root strength (fracture)

Calculation of Tooth form coefficients according method: B

------- Gear 1 ----------------- Gear 2 -------
Calculated with generating profile shift coefficient [xE.i] 0.0350 -0.0504
Tooth form factor [YF] 1.10 1.04
Stress correction factor [YS] 1.92 2.05
Load application angle (°) [αFen] 18.89 19.95
Load distribution influence factor [fε] 0.770
Load application diameter (mm) [den] 74.241 217.738
Bending moment arm (mm) [hF] 2.94 3.31
Tooth thickness at root (mm) [sFn] 6.10 6.65
Tooth root radius (mm) [ρF] 1.65 1.49
Bending moment arm (-) [hF/mn] 0.979 1.102
Tooth thickness at root (-) [sFn/mn] 2.034 2.216
Tooth root radius (-) [ρF/mn] 0.548 0.498
Calculation cross section diameter (mm) [dsFn] 67.006 209.707
Tangents on calculation cross section (°) [αsFn] 30.000 30.000
Notch parameter [qs ] 1.854 2.226

Helix angle factor [Yβ] 0.960

Deep tooth factor [YDT] 1.000
Gear rim factor [YB] 1.00 1.00
Effective facewidth (mm) [beff] 100.00 100.00
Nominal stress at tooth root (N/mm²) [σF0] 260.69 262.98
Tooth root stress (N/mm²) [σF] 400.63 404.14

Permissible bending stress at root of Test-gear

Notch sensitivity factor [YdrelT] 0.994 0.997
Surface factor [YRrelT] 0.957 0.957
Size factor, tooth root [YX] 1.000 1.000
Life factor [YNT] 0.888 0.907
YdrelT*YRrelT*YX *YNT 0.844 0.866
Alternating bending factor, mean stress influence coefficient
[YM] 1.000 1.000
Stress correction factor [YST] 2.00
YST*σFlim (N/mm²) [σFE] 860.00 860.00
Permissible tooth root stress σFG/SFmin (N/mm²) [σFP] 518.40 531.82
Limit strength tooth root (N/mm²) [σFG] 725.76 744.55

7.1 Safety factors

------- Gear 1 ----------------- Gear 2 -------

Required safety [SFmin] 1.40 1.40
Safety for tooth root stress [SF=σFG/σF] 1.81 1.84
Transmittable power (kW) [kWRating] 181.53 184.61

8 Calculation of flank strength (pitting)

------- Gear 1 ----------------- Gear 2 -------

Zone factor [ZH] 2.442
Elasticity factor (√N/mm²) [ZE] 189.812
Contact ratio factor [Zε] 0.780
Helix angle factor [Zβ] 1.008
Effective facewidth (mm) [beff] 100.00
Nominal contact stress (N/mm²) [σH0] 968.81

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Contact stress at operating pitch circle (N/mm²) [σHw] 1207.54
Coefficient [fZCa] 1.20 (Helical gear sets without flank modifications)
Single tooth contact factor [ZB,ZD] 1.10 1.10
Contact stress (N/mm²) [σHB, σHD] 1322.80 1322.80

Lubricant coefficient for NL [ZL] 1.020 1.020

Speed factor at nL [ZV] 0.975 0.975
Roughness factor for NL [ZR] 0.962 0.962
Material hardening factor for NL [ZW] 1.000 1.000
Life factor [ZNT] 0.909 0.939
[ZL*ZV*ZR*ZNT] 0.870 0.899
Limited pitting is permissible: No
Size factor (flank) [ZX] 1.000 1.000

Permissible contact stress, σHG/SHmin (N/mm²) [σHP] 1304.26 1348.38

Pitting stress limit (N/mm²) [σHG] 1304.26 1348.38

8.1 Safety factors

------- Gear 1 ----------------- Gear 2 -------

Required safety [SHmin] 1.00 1.00
Safety factor for contact stress on operating pitch circle [SHw] 1.08 1.12
Safety against pressure, σHG/σHBD Single contact [SHBD] 0.99 1.02
Safety regarding transmittable torque [SHBD²] 0.97 1.04
Transmittable power (kW) [kWRating] 136.39 145.77

9 Micropitting

Calculation method according to ISO/TS 6336-22:2018

Calculation has not been carried out, lubricant: Load stage micropitting test not known

10 Scuffing load capacity

Calculation method according to ISO/TS 6336-20/21:2017

------- Gear 1 ----------------- Gear 2 -------

Thermal contact coefficient (N/mm/s^.5/K) [BM] 13.780 13.780
Relevant tip relief (µm) [Ca] 2.00 2.00
Optimal tip relief (µm) [Ceff] 23.71
Ca taken as optimal in the calculation. 0=no, 1=yes 0 0

------------------ Pair ----------------------

Helical load factor for scuffing [KBγ] 1.300
Lubrication coefficient for lubrication type [XS] 1.000
Scuffing test and load stage [FZGtest] FZG - Test A / 8.3 / 90 (ISO 14635 -
1) 12
Multiple meshing factor [Xmp] 1.000
Relative structural factor, scuffing [XWrelT] 1.000
Effective facewidth (mm) [beff] 100.000
Applicable circumferential force/facewidth (N/mm) [wBt] 599.305
KBγ = 1.300, wBt*KBγ = 779.087
Angle factor [Xαβ] 0.984
ε1 =0.817, ε2 =0.824

10/14
10.1 Flash temperature-criteria

------------------ Pair ----------------------

Lubricant factor [XL] 0.830
Tooth mass temperature (°C) [θMi] 81.88
θMi = θoil + XS *0.47*Xmp*θflm
Average flash temperature (°C) [θflm] 25.28
Scuffing temperature (°C) [θS] 348.81
Γ coordinates (point of highest temperature) [Γ] -0.574
[Γ.A]= -0.574, [Γ.E]= 0.569
Maximum contact temperature (°C) [θB] 152.39
Flash factor (°K*N^-.75*s^.5*m^-.5*mm) [XM] 50.058
Approach factor [XJ] 1.055
Load sharing factor [XΓ] 0.792
Dynamic viscosity (mPa*s) [ηM] 41.87 (70.0 °C)
Coefficient of friction [μm] 0.073
Required safety [SBmin] 2.000
Margin of safety for scuffing, flash temperature [SB] 3.384

10.2 Integral temperature-criteria

------------------ Pair ----------------------

Lubricant factor [XL] 1.000
Tooth mass temperature (°C) [θMC] 83.67
θMC = θoil + XS *0.70*θflaint
Integral scuffing temperature (°C) [θSint] 360.78
Flash factor (°K*N^-.75*s^.5*m^-.5*mm) [XM] 50.058
Running-in factor, well run in [XE] 1.000
Contact ratio factor [Xε] 0.260
Dynamic viscosity (mPa*s) [ηOil] 41.87 (70.0 °C)
Mean coefficient of friction [μm] 0.081
Geometry factor [XBE] 0.258
Meshing factor [XQ] 1.000
Tip relief factor [XCa] 1.115
Mean flash temperature (°C) [θflaint] 19.53
Integral tooth flank temperature (°C) [θint] 112.97
Required safety [SSmin] 1.800
Safety factor for scuffing (intg.-temp.) [SSint] 3.193
Safety factor for transmitted moment (int.-T.) [SSL] 6.766

11 Measurements for tooth thickness

11.1 Tooth thickness tolerances

------- Gear 1 ----------------- Gear 2 -------

Tooth thickness tolerance DIN 3967 cd25 DIN 3967 cd25
Tooth thickness allowance (normal section) (mm) [As.e/i] -0.070 /-0.110 -0.095 /-0.145

11.2 Base tangent lengths

------- Gear 1 ----------------- Gear 2 -------

Number of teeth spanned [k] 3.000 9.000
Base tangent length (no backlash) (mm) [Wk] 23.370 78.429
Base tangent length with allowance (mm) [Wk.e/i] 23.304 /23.266 78.339 /78.292
(mm) [ΔWk.e/i] -0.066 /-0.103 -0.089 /-0.136
Diameter of measuring circle (mm) [dMWk.m] 72.323 217.089

11/14
11.3 Measurement over balls and pins

------- Gear 1 ----------------- Gear 2 -------

Theoretical diameter of ball/pin (mm) [DM] 5.220 5.059
Effective diameter of ball/pin (mm) [DMeff] 5.250 5.250
Radial single-ball measurement backlash free (mm) [MrK] 40.485 111.970
Radial single-ball measurement (mm) [MrK.e/i] 40.406 /40.360 111.849 /111.784

Diameter of measuring circle (mm) [dMMr.m] 73.498 216.519

Diametral measurement over two balls without clearance (mm) [MdK] 80.970 223.887
Diametral measurement over two balls (mm) [MdK.e/i] 80.812 /80.721 223.644 /223.515
Diametral measurement over pins without clearance (mm) [MdR] 80.970 223.940
Measurement over pins according to DIN 3960 (mm) [MdR.e/i] 80.812 /80.721 223.697 /223.568
Measurement over 2 pins, free, AGMA 2002 (mm) [dk2f.e/i] 0.000 / 0.000 223.642 /223.513
Measurement over 2 pins, transverse, AGMA 2002 (mm) [dk2t.e/i] 0.000 / 0.000 223.750 /223.621
Measurement over 3 pins, axial, AGMA 2002 (mm) [dk3A.e/i] 80.812 /80.721 223.697 /223.568

11.4 Tooth thickness

------- Gear 1 ----------------- Gear 2 -------

Reference chordal height from da.m (mm) [ha] 3.326 3.060
Chordal tooth thickness (mm) [sc] 4.895 4.747
(mm) [sc.e/i] 4.827 / 4.788 4.653 / 4.603

Tooth thickness, arc (mm) [sn] 4.899 4.747

(mm) [sn.e/i] 4.829 / 4.789 4.652 / 4.602

11.5 Backlash

------------------ Pair ----------------------

Circumferential backlash from Aa (mm) [jtw_Aa.e/i] 0.015 /-0.015
Radial backlash (mm) [jrw.e/i] 0.368 / 0.205
Circumferential backlash (transverse section) (mm) [jtw.e/i] 0.275 / 0.153
Normal backlash (mm) [jn.e/i] 0.253 / 0.141

Center distance allowances (mm) [Aa.e/i] 0.020 /-0.020

Backlash free center distance (mm) [aControl.e/i] 144.775 /144.652
Backlash free center distance, allowances (mm) [jta] -0.225 /-0.348

------- Gear 1 ----------------- Gear 2 -------

dNf.i with aControl (mm) [dNf0.i] 69.163 211.448
Reserve (dNf0.i-dFf.e)/2 (mm) [cF0.i] 0.002 0.333
Tip clearance (mm) [c0.i(aControl)] 0.532 0.498

Torsional angle on input with output fixed:

Total torsional angle (°) [j.tSys] 0.4294/ 0.2391

12 Toothing tolerances

------- Gear 1 ----------------- Gear 2 -------

According to ISO 1328-1:2013, ISO 1328-2:1997
Accuracy grade [Q] A6 A6
Single pitch deviation (µm) [fptT] 9.00 9.00
Base circle pitch deviation (µm) [fpbT] 8.44 8.44
Sector pitch deviation over k/8 pitches (µm) [Fpk/8T] 18.00 21.00
Profile form deviation (µm) [ffαT] 9.50 9.50
Profile slope deviation (µm) [fHαT] 7.50 7.50
Total profile deviation (µm) [FαT] 12.00 12.00

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Total profile deviation (µm) [FαT] 12.00 12.00
Helix form deviation (µm) [ffβT] 13.00 13.00
Helix slope deviation (µm) [fHβT] 11.00 12.00
Total helix deviation (µm) [FβT] 17.00 18.00
Total cumulative pitch deviation (µm) [FpT] 27.00 32.00
Adjacent pitch difference (µm) [fuT] 13.00 13.00
Runout (µm) [FrT] 24.00 29.00
Single flank composite, total (µm) [FisT] 35.00 41.00
Single flank composite, tooth-to-tooth (µm) [fisT] 8.50 8.50
Radial composite, total (µm) [FidT] 36.00 43.00
Radial composite, tooth-to-tooth (µm) [fidT] 14.00 15.00
FidT (Fi'') and fidT (fi'') according to ISO 1328:1997 calculated with the geometric mean values for mn and d.

According to ISO 1328-2:2020

Accuracy grade [Q] R39 R40
Radial composite, total (µm) [FidT] 29.00 41.00
Radial composite, tooth-to-tooth (µm) [fidT] 13.00 17.00

Axis alignment tolerances recommendation acc. to ISO TR 10064-3:1996, Quality 6

Maximum value for deviation error of axis (µm) [fΣβ] 18.00 (Fβ=18.00)
Maximum value for inclination error of axes (µm) [fΣδ] 36.00

13 Modifications and determination of the tooth form

13.1 Data for the tooth form calculation

Data not available.

Please run the calculation in the "Tooth form" tab and open the main report again.

14 Supplementary data

Maximal possible center distance (eps_a=1.0) [aMAX] 147.126

14.1 Masses, stiffnesses and moments of inertia

------- Gear 1 ----------------- Gear 2 -------

Mass (kg) [m] 3.266 28.594
Total mass (kg) [mGes] 31.859
Moment of inertia for system, relative to the input:
calculation without consideration of the exact tooth shape
Single gears, (da+df)/2...di (kg*m²) [J] 0.00217 0.16619
System (da+df)/2...di (kg*m²) [J] 0.02116

14.2 Wear, power loss, sound pressure level

Torsional stiffness at driving gear with fixed driven gear:

Torsional stiffness (MNm/rad) [cr] 2.028
Torsion when subjected to nominal torque (°) [δcr] 0.040
Average coefficient of friction according to Niemann [μm] 0.075
Wear sliding coef. by Niemann [ζw] 0.927
Loss factor [HV] 0.125
Gear power loss (kW) [PVZ] 1.316
Meshing efficiency (%) [ηz] 99.062
Sound pressure level based on Masuda, without PPTE/δs [dB(A)] 81.613

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15 Service life, damage

Required safety for tooth root [SFmin] 1.40

Required safety for tooth flank [SHmin] 1.00
Required service life [H] 20000.00

Service life (calculated with required safeties):

System service life (h) [Hatt] 12627

------- Gear 1 ----------------- Gear 2 -------

Tooth root service life (h) [HFatt] 1e+06 1e+06
Tooth flank service life (h) [HHatt] 1.263e+04 3.736e+04
Note: The entry 1e+006 h means that the Service life > 1,000,000 h.

15.1 Damage

Damage relative to the required service life (H, 20000.0 h)

F1 (%) F2 (%) H1 (%) H2 (%)

0.0000 0.0000 158.3886 53.5398

Damage relative to the system service life (Hatt, 12627.2 h)

F1 (%) F2 (%) H1 (%) H2 (%)
0.0000 0.0000 100.0000 33.8028

16 Remarks

16.1 Conventions

- Specifications with .e/i mean: Maximum value .e and Minimum value .i, taking all tolerances into account.
- Specifications with .m mean: Mean value within tolerance.

- The center distance tolerances and the tooth thickness allowance are taken into account for the backlash tolerance. The maximum and
minimum clearance corresponding to the largest and smallest allowances are shown. The calculation is performed for the operating pitch
circle.

16.2 Calculations and factors

- Calculation of Zβ acc. to Corrigendum 1 ISO 6336-2:2008 with Zβ = 1/(COS(β)^0.5)

- Details of calculation method:
c γ according to Method B
Kv according to Method B
KHβ and KFβ according to Method C
fmα according to equation 64, fsh according to 57/58, Fβx according to 52/53/54
KHα, KFα according to Method B
- The logarithmically interpolated value must be entered for factors ZL, ZV , ZR, ZW , ZX , YdrelT, YRrelT and YX . This value is calculated from the
infinite life strength and static strength values, based on the number of load cycles.

End of report (lines: 619)

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