1 Tooth fracture on worm shafts
2 State of the art
2.1 Stress calculation in worm gears
2.2 Load distribution in worm gears
2.3 Stress calculation in helical spur gears
3 General stress in worm shafts
Variable | Unit | Value | Material data, load data and load distribution | ||
---|---|---|---|---|---|
a | [mm] | 100 | Material Worm, Wheel | [−] | 16MnCr5/CuSn12-C-GZ |
z2/z1 | [−] | 41/2 | E1/E2 | [N/mm2] | 210,000/98,100 |
q | [−] | 9 | υ1/υ2 | [−] | 0.3/0.35 |
Mx | [mm] | 4 | T2 | [Nm] | 1350 |
α0 | [°] | 20 | n1 | [rpm] | 60 |
rf1 | [mm] | 1.52 | Line load F | [N/mm] |
×
|
Hf* | [−] | 1.25 | σH,max | [N/mm2] | 694,54 |
ha* | [−] | 1.00 |
×
| ||
b1 | [mm] | 65 | |||
b2 | [mm] | 30 | |||
l1 | [mm] | 160 |
3.1 FEM-Model for calculating the stress in the tooth fillet
4 Analytical calculation model
4.1 Numerical calculation of the distribution of force and moment on a curved plate
4.2 Approximate function for the distribution of force and moment
5 Calculation of the stress distribution
6 Validation and discussion
7 Summary and conclusion
8 Nomenclature
a | Centre distance [mm] |
b1, b2 | Worm thread width, wheel width [mm] |
da1, df1, dm1 | Diameters of the worm shaft [mm] |
h, hFe | Lever arm and effective lever arm [mm] |
ha1*, hf1* | Worms tooth height factors [−] |
k1, k2, k3 | Coefficients of parameter functions [−] |
l1 | Bearing distance of the worm [mm] |
Mx, mn | Axial modulus, normal modulus [mm] |
n1 | Rotational speed of the worm [rpm] |
p1 ,p2 | Parameters of distribution functions [−] |
q | Form factor [−] |
r | Radius of the force application point[mm] |
rf1 | Tooth root radius |
Sfn /fx/fγ/mx | Tooth widths of the worm [mm] |
t | Depth coordinate [mm] |
x, y, z | Cartesian coordinate directions [mm] |
z1, z2 | Number of threads of the worm and teeth of the worm wheel [−] |
A | Surface area [mm2] |
Start point of the contact path [−] | |
D | Distribution functions [−] |
E | End point of the contact path [−] |
E1, E2 | Youngs modulus of worm and wheel [N/mm2] |
F | Point force [N] or line load [N/mm] |
KS | Support effect function [−] |
Mb | Bending moment [Nm] |
PF | Force application point [−] |
T2 | Moment on the worm wheel [Nm] |
SF | Safety factor against tooth fracture [−] |
SFmin | Minimum safety factor [−] |
Wb | Section modulus [mm3] |
YF, YS, Yβ, YB, YDT | Tooth bending stress correction factors [−] |
α0 | Normal engagement angle [°] |
α | Force angle in yz-plane [°] |
β | Position on the tooth root [°] |
βrf1 | Position on the tooth root rounding [°] |
γF | Force angle in xz-plane [°] |
σ | Normal stress [N/mm2] |
σFG, σFP | Stress limit and permissible stress [N/mm2] |
σF, σF0 | Maximum local and nominal stress [N/mm2] |
σ1 | Maximum principal stress [N/mm2] |
σHmax | Maximum Hertzian contact pressure [N/mm2] |
τ | Shear stress [N/mm2] |
τFG | Shear stress limit [N/mm2] |
τF | Maximum local shear stress [N/mm2] |
υ1, υ2 | Poisson ratio of worm and wheel [−] |