Page 274 - Analysis and Design of Machine Elements

Analysis and Design of Machine Elements
252
Steps Computation Results Units
2) Parameters and dimensions of the wormgear z = 2 mm
1
The number of wormgear teeth z = 41; Profile shift z = 41
2
coefficient x =−0.5; 2
2
Check the speed ratio x =−0.5
2
z 41
i = 2 = = 20.5 d = 328
2
z 1 2
The error of speed ratio
20.5 − 20
= 2.5%
20
It is acceptable.
Reference diameter of the wormgear
d = mz = 8 × 41 = 328 mm
2
2
4. Check Check the bending strength of the wormgear teeth
the bending by Eq. (9.18)
strength = 0.666KT 2 Y Y Y ≤ [ ]
of wormgear F d d m Fa2 Sa2 F
1 2
teeth
Virtual number of teeth Y = 2.87
z 41 Fa2
z = 2 = ∘ = 43.48 Y = 1.47
v2
3
cos cos 11.31 Sa2
3
From Table 8.4, by interpolating, we have wormgear
tooth form factor Y = 2.87, and stress correction
Fa2
factor Y Sa2 = 1.47.

Helix angle factor Y = 0.906
∘
11.31
Y = 1 − = 1 − = 0.906
∘ ∘
120 120
Specify basic allowable bending stress from Table 9.2
for ZCuSnl0P1 wormgear as [ ] =56 MPa.
′
F
Bending life factor
√ √
9 10 6 10 6
K = = 9 = 0.657
FN N 4.38 × 10 7
Allowable bending stress is
′
[ ]= K [ ] =56 × 0.657 = 36.8MPa
F FN F
The bending stress is
0.666KT 2
Y
= Y Fa2 Sa2
Y
F
d d m
1 2
0.666 × 1.21 × 0.94 × 10 6
=
80 × 328 × 8
×2.87 × 1.47 × 0.906 = 13.79 MPa
< [ ]
F F
Therefore, bending strength is satisfactory.
5. Thermal Omitted
analysis
6. Structural Omitted
design