Mechanical characteristics of materials of the worm gear ring

Material	Slippage speed Vs, m/sec	Casting method	Mechanical characteristics, MPa
Yield point sy	Ultimate strength
in tension sul t	in bending sul b
Tin bronzes
Bronze(10Sn-1Ni-1P)	Over 5	Centrifugal casting
Bronze(10Sn-1P)	Over 5	Chill casting
Bronze(10Sn-1P)	Over 5	Sand casting
Tinless bronzes
Bronze(9Al-4Fe)	2…5	Centrifugal casting
Bronze(9Al-4Fe)	2…5	Chill casting
Bronze(9Al-4Fe)	2…5	Sand casting
Cast-irons
Grey cast iron 12	Up to 2	Sand casting	-
Grey cast iron 18	Up to 2	Sand casting	-

6.3. Determine the allowable contact stress.

a) For the worm gear made of tin bronzes the allowable contact stress is determined from the condition to prevent fatigue pitting

[s_H] = s_lim·C_v·K_HL,

where s_lim is the limit of contact endurance that is determined as s_lim = 0.9·s_ult; s_ult is the ultimate strength in tension (table 6.1); C_v is the factor that takes into account the wear rate of a worm gear tooth depending upon the slippage speed (table 6.2); K_HL is the durability factor.

Table 6.2

Values of C_v

Slippage speed Vsl, m/sec
Cv	0.95	0.88	0.83	0.8

Durability factor K_HL is found in the following way:

,

where N_HO =10⁷ is the base number of cycles;

N_Hi = 60·n^g·t 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_HL should satisfy to the following condition:

0.67 ≤ K_HL≤1.15.

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

b) For the worm gear made of either tinless bronzes or cast irons, the allowable contact stress is determined to avoid seizure:

- for tinless bronzes [s_H] = 300 - 25∙V_sl;

- for cast iron [s_H] = 175 - 35∙V_sl.

In our case: [s_H] = 300 - 25∙2.4 = 240 MPa

6.4. Determine the allowable bending stress.

For this purpose we use table 6.3, where s_{ul t} is the ultimate strength in tension; s_{ul b} is the ultimate strength in bending; s_y is the yield point; K_bL is the durability factor.

Table 6.3