Allowable bending stresses

Mechanical characteristics of the worm gear material are given in table 6.1.

Durability factor K_bL is determined as

,

where N_b0= 1·10⁶ is the base number of cycles;

N_bi = 60·n^g·t·K_bi is the design number of stress cycles;

n^g is the rotational speed of the worm gear;

t = L×365×K_a×24×K_d is the service life in hours;

L is the service life in years; K_a is the annual utilization factor; K_d is the daily utilization factor;

Obtained magnitude of K_bL should satisfy to the following condition:

0.543 ≤ K_bL≤1.

Otherwise, for further calculations we take the extreme values of the mentioned above inequality.

In our case the service life of the gearing is 8 years, K_a = 0.7, K_d= 0.3,

.

N_bi = 60·22.1·14716.8= 19.144·10⁶; N_b0= 1·10⁶;

Condition0.543 ≤ K_bL≤1 is satisfied.

For bronze and non-reversed transmission

[σ_b] = (0.08·490 + 0.25·195)·0.719 = 63.24 MPa

6.5.Calculate the worm gear for strength.

6.5.1. Determine the center distance of the worm gearing

,

where T^g is the torque at the worm gear shaft in N×mm;

z^g = z^w×u ≥28 is the number of teeth of the worm gear (it should be rounded off to the nearest integer numeral); z^w is the number of threads of the worm that is determined according to table 6.4; q^w is the worm diameter factor whose minimum value is found as = 0.212×z^g (obtained magnitude of q^w must be rounded off to the greater side according to the following standard series 8; 10; 12.5; 14; 16; 20); E_tr is the transformed modulus of elasticity that is determined by the formula

.

where E^w is the worm material modulus of elasticity (for steels E = 2.1×10⁵ MPa); E^g is the worm gear material modulus of elasticity (for bronzes and cast irons E ≈ 0.9×10⁵ MPa).

Table 6.4