Bevel gearing with straight, oblique and curved teeth [mm/DIN]

i Pinion Gear

ii

?

1.0

1.1 Transferred power Pw [kW] 50,000 49,325

1.2 Speed (Pinion / Gear) n [/min] 1000,0 403,8 [/min]

1.3 Torsional moment (Pinion / Gear) Mk [Nm] 477,50 1166,41 [Nm]

1.4 Transmission ratio / from table i 2,48

1.5 Actual transmission ratio / deviation i 2,4762 0,00%

2.0

2.0 Material identification according standard :

2.1 Material of the pinion :

2.2 Material of the gear :

2.3 Loading of the gearbox, driving machine - examples

2.4 Loading of gearbox, driven machine - examples

2.5 Type of gearing mounting

2.6

2.7 Coefficient of one-off overloading KAS

2,8 Desired service life Lh [h]

2.9 Coefficient of safety (contact/bend) SH / SF 1,30 1,60

2.10 Automatic design

3.0

3.1 Guiding curve of the toothing (Type of toothing)

3.2 Addendum - Coefficient of the height of the tooth head ha* 1,000 1,000 [modul]

3.3 Unit head clearance c* 0,200 0,200 [modul]

3.4 Recommended coefficient of the root radius 0,293 0,293 [modul]

3.5 Coefficient of the root radius rf* 0,293 0,293 [modul]

4.0

4.1 Number of teeth Pinion / Gear z 21 52

4.2 Angle of shaft axes S 90 [°]

4.3 Pressure angle a 20,0 [°]

4.4 Base helix angle bm 23,3 [°]

4.5 Direction of the teeth pitch (pinion)

4.6 Width of toothing to the surface straight line of the cone (b/Re)

4.7 Width of toothing to the surface straight line of the cone (b/Re) Re/b 0,35 < 0.35

4.8 Module mmn 12,000 [mm]

4.9 Face width / max. recommendet value b 130 < 151 [mm]

4.10 Approximate weight of the gearing m [kg]

4.11 Minimum coefficient of safety SH / SF 1,877 16,984

Comments

Basic Info

Project No.

File name

Parameters of the tooth profile, gearing type

Accuracy grade - DIN3965 / ISO1328 |Ra max|v max

Options of material, loading conditions, operational and production parameters

Bevel gearing with straight, oblique and curved teeth [mm/DIN]

20000

Project information

Check lines:11.7;

Project Notes

Bevel gearing: Beta=23,31; mmn=12; b=130; z1=21; z2=52; n1=1000; n2=403,8; i=2,48; P=50 [kW]

111-111

Bevel Gear

Gear2_02.xls

Project Name

John Doe 3/11/2014

Input section

256,085

2,00

Options of basic input parameters

Date

Design of a module (Diametral Pitch) and geometry of toothing

Author

100

200

300

A...Continuous

A...Continuous

A...Carbon structural steel Ck 60 (Rm=660 MPa) normalized

A...Overhung both wheels - type 1

6 / 7…....(Ra max.= 1,6 / v max.= 12)

B. Helical gearing

90

20,0

25

Left-Hand

A,B. Straight line, type I (Standard straight and oblique toothing)

A. Transverse pressure angle

B. Normal module (mean)

A...Carbon structural steel Ck 60 (Rm=740 MPa) heat treated

DIN

5.0

5.1 Correction type

5.2 Recommendet value x1 / xt1 0,000 0,000

5.3 - Permissible undercutting of teeth (min. value) x1 / x2 -0,6360 -8,1756

5.4 - Preventing undercutting of teeth (min. value) x1 / x2 -0,4693 -8,0090

5.5 Pinion addendum modification coefficient setting

5.6 Addendum modification coefficient Pinion / Gear x1 / x2 -0,3000 0,3000

5.7 Tooth thicknes modification coefficient xt1 / xt2 -0,0300 0,0300

5.8 Total contact ratio eg

5.9 Unit tooth thickness on the tip diameter sae* 0,7512 1,4340

5.10 Safety coefficient for surface durability SH 2,130 1,877

5.11 Safety coefficient for bending durability SF 16,98 18,94

6.0

6.1 Number of teeth Pinion / Gear z 21 52

6.2 Transverse module (outer, midle, inner) met,mmt,mit 13,0665 10,7484 [mm]

6.3 Normal module (outer, midle, inner) men,mmn,min 12,0000 9,8711 [mm]

6.4 Cone length (outer, midle, inner) Re,Rm,Ri 366,387 301,387 [mm]

6.5 Pitch cone angle d 21,9911 68,0089 [°]

6.6 Addendum cone angle da 23,4212 70,6633 [°]

6.7 Dedendum cone angle df 18,9290 66,1705 [°]

6.8 Tip diameter (outer) dae 343,049 814,979 [mm]

6.9 Tip diameter (midle) dam 291,359 692,181 [mm]

6.10 Tip diameter (inner) dai 239,670 569,383 [mm]

6.11 Pitch diameter (outer) de 323,077 800,001 [mm]

6.12 Pitch diameter (midle) dm 274,397 679,459 [mm]

6.13 Pitch diameter (inner) di 225,717 558,918 [mm]

6.14 Root diameter (outer) dfe 280,281 789,631 [mm]

6.15 Root diameter (midle) dfm 238,050 670,652 [mm]

6.16 Root diameter (inner) dfi 195,818 551,673 [mm]

6.17 Addendum angle qa 1,4300 2,6545 [°]

6.18 Dedendum angle qf 3,0621 1,8384 [°]

6.19 Addendum (outer) hae 10,7692 20,0000 [mm]

6.20 Addendum (midle) ha 9,1466 16,9865 [mm]

6.21 Addendum (inner) hai 7,5239 13,9729 [mm]

6.22 Dedendum (outer) hfe 23,0769 13,8462 [mm]

6.23 Dedendum (midle) hf 19,5998 11,7599 [mm]

6.24 Dedendum (inner) hfi 16,1226 9,6736 [mm]

14,1289

431,387

2,9531

15,3846

Basic dimensions of gearing

Correction of toothing (Addendum modification)

Results section

-300

-200

-100

0

-500 -400 -300 -200 -100 0 100 200 300 400 500

E. Curved teeth

6.25 Normal pressure angle an [°]

6.26 Transverse pressure angle at [°]

6.27 Helix angle b [°]

6.28 Base helix angle bb [°]

6.29 Pressure angle at the pitch cylinder awn [°]

6.30 Transverse pressure angle at the pitch cylinder awt [°]

6.31 Circular pitch pe [mm]

6.32 Transverse circular pitch pte [mm]

6.33 Tooth thickness on the pitch diameter sne 18,6843 25,7030 [mm]

6.34 Tooth thickness on the pitch diameter sn 15,8690 21,8301 [mm]

6.35 Tooth thickness on the pitch diameter sni 13,0537 17,9573 [mm]

6.36 Tooth thickness on the tip diameter sae 10,6136 20,2613 [mm]

6.37 Tooth thickness on the tip diameter sa 9,0144 17,2084 [mm]

6.38 Tooth thickness on the tip diameter sai 7,4152 14,1555 [mm]

6.39 Unit tooth thickness on the tip diameter sae* 0,7512 1,4340 [modul]

7.0

7.1 Number of teeth of a virtual wheel with oblique teeth zvn' 22,648 138,866

7.2 Number of teeth of a virtual wheel with straight teeth zv 29,239 179,280

7.3 Reference diameter dv' 295,928 1814,490 [mm]

7.4 Tip diameter dva' 314,221 1848,462 [mm]

7.5 Base diameter dvb' 278,082 1705,062 [mm]

7.6 Root diameter dvf' 256,729 1790,970 [mm]

7.7 Virtual center distance av [mm]

7.8 Virtual Gear Ratio iv

8.0

8.1 Transverse contact ratio / overlap ratio ea | eb 1,7933 1,1599

8.2 Total contact ratio eg

8.3 Resonance speed nE1 [ /min]

8.4 Resonance ratio N

8.5 Approximate weight of the gearing m [kg]

8.6 Efficiency of the gearing m

8.7 Selected / Recomended lubricant viscosity v50 50 50 [mm2/sec]

9.0

Common for the gearing

9.1 Stiffness of a tooth pair c'

9.2 Meshing stiffness per unit face width cg

9.4 Application factor KA

9.5 Dynamic factor KV

9.6 Number of cycles NK 1,20E+09 4,85E+08

For pitting safety calculation

9.7 Face load factor (contact stress) KHb

9.8 Transverse load factor (contact stress) KHa

9.9 Total factor of additional loads KH

9.10 Elasticity factor ZE

9.11 Zone factor ZH

9.12 Helix angle factor Zbeta

9.13 Contact ratio factor Zeps

9.14 Size factor ZX 1,000 1,000

9.15 Lubricant factor ZL 0,916 0,916

9.16 Peripheral speed factor ZV 1,022 1,022

9.17 Roughness factor affecting surface durability ZR 0,945 0,945

9.18 Bevel gear factor (flank) ZK

9.19 Life factor for contact stress ZN 0,850 0,850

9.20 Single pair tooth contact factor ZB / ZD 1,000 1,000

For bending safety calculation

9.21 Face load factor (root stress) KFb

9.22 Transverse load factor (root stress) KFa

16,85

4,562

189,81

0,747

0,958

2,087

2,402

23,31

22,0425

1,500

0,850

2,087

1,500

4044,79

Coefficients for safety calculation

2,9531

18,4828

48,332

Virtual spur gear toothing

256,0848

1055,2089

98,65%

6,1315

18,4828

20,0000

20,0000

44,387

Qualitative indexes of a gearing

0,25

10,56

1,000

1,457

n=∞; ZN=0.85

Mineral oil

Automatic

9.23 Total factor of additional loads KF

9.24 Helix angle factor Ybeta

9.25 Contact ratio factor Yeps

9.26 Notch sensitivity factor Ydelta 0,994 1,016

9.27 Size factor YX 0,958 0,958

9.28 Tooth-root surface factor YR 1,003 1,003

9.29 Alternating load factor YA

9.30 Production technology factor YT

9.31 Life factor for bending stress YN 0,850 0,850

9.32 Tip factor, equal (YFa YSa) YFS 4,212 3,502

10.0

10.1 Safety coefficient for surface durability SH 2,13 1,88

10.2 Safety coefficient for bending durability SF 16,98 18,94

10.3 Safety in contact in one-time overloading SHst 2,90 2,47

10.4 Safety in bending in one-time overloading SFst 25,07 27,35

10.5 Nominal contact stress SigmaH0

10.6 Contact stress SigmaH 208,39 208,39

10.7 Pitting stress limit SigmaHG 443,80 391,15

10.8 Permissible contact stress SigmaHP 341,38 300,88

10.9 Nominal tooth-root stress SigmaF0 4,73 3,93

10.10 Tooth-root stress SigmaF 21,59 17,95

10.11 Tooth-root stress limit SigmaFG 366,68 340,05

10.12 Permissible bending stress SigmaFP 229,17 212,53

11.0

11.1 Tangential force Ft [N]

11.2 Normal force Fn [N]

11.3 Axial force - (rotation acc. to the picture) Fa 1864,84 613,04 [N]

11.4 Radial force (rotation acc. to the picture) Fr 613,04 1864,84

11.5 Axial force (rotation opposite to the picture) Fa -916,14 1736,13 [N]

11.6 Radial force (rotation opposite to the picture) Fr 1736,13 -916,14

11.7 Peripheral speed on the pitch diameter v | vmax 14,37 < 12 [m/s]

11.8 Specific load / Unit load wt | wt* 31,50 2,62 [N/mm | MPa]

12.0

12.1 Density Ro 7870 7870 [kg/m^3]

12.2 Young's Modulus (Modulus of Elasticity) E 206 206 [GPa]

12.3 Tensile Strength, Ultimate Rm 740 660 [MPa]

12.4 Tensile Strength, Yield Rp0.2 440 380 [MPa]

12.5 Poison's Ratio 0,3 0,3

12.6 Contact Fatigue Limit SHlim 590 520 [MPa]

12.7 Bending Fatigue Limit SFlim 452 410 [MPa]

12.8 Tooth Hardness - Side VHV 235 200 [HV]

12.9 Tooth Hardness - Core JHV 235 200 [HV]

12.10 Base Number of Load Cycles in Contact NHlim 5,00E+07 5,00E+07

12.11 Wohler Curve Exponent for Contact qH 10 10

12.12 Base Number of Load Cycles in Bend NFlim 3,00E+06 3,00E+06

12.13 Wohler Curve Exponent for Bend qF 6 6

1,000

1,000

3480,36

0,806

Safety coefficients

97,56

4,562

Additions section

Parameters of the chosen material

0,625

3995,79

Force conditions (forces acting on the toothing)

n=∞; YN=0.85

13.0

13.1 Ambient air temperature [°C]

13.2 Maximum oil temperature [°C]

13.3 Coefficient of heat dissipation [W/m2/K]

13.4 Power losses [kW]

13.5 Gearbox surface (min.) [m2]

14.0

Recommended shaft diameter for:

14.1 - Main power-transmitting shafts DA 95,57 128,68 [mm]

14.2 - Small, short shafts DB 74,27 99,99 [mm]

15.0

15.1 Transmission ratio calculation using the number of teeth z1,z2 = i 21 52 = 2,4762

15.2 Transmission ratio calculation using the speed n1,n2 = i 2000,0 750,0 = 2,6667

15.3 Power calculation using the pinion speed and torque moment Mk1,n1=Pw1 270,0 1600,0 = 45,2356

16.0

16.1 2D drawing output to:

16.2 2D Drawing scale

16.3 Detail:

Graphical output, CAD systems

Auxiliary calculations

Preliminary design of shaft diameters (steel)

1,69

60,00

0,68

10,00

20,00

Power, warming-up, gearbox surface

DXF File

Automatic

Gear