Standard values of module m for worm gearing

m,mm	2.5; 3.15; 4; 5	6.3; 8; 10; 12.5
qw	8; 10; 12.5; 16; 20	8; 10; 12.5; 14; 16; 20

In our case:

6.5.3. In order to ensure standard value of the centre distance we use modified worm gear with offset factor x determined as

.

To avoid undercutting the following condition should be carried out

.

Otherwise it is necessary to change a_w, q^w or z^g.

In our case:

6.5.4. Specify the velocity ratio of the worm gearing

and determine the error that must be less or equal to 4%.

;

6.5.5. Determine the pitch diameter of the worm

d^w = m×q^w = 8×10 = 80 mm.

6.5.6. Determine the addendum circle diameter of the worm

.

6.5.7. Determine the dedendum circle diameter of the worm

.

6.5.8. Determine the threaded length of the worm by means of table 6.7.

Table 6.7

Threaded length of the worm b^w

Shift factor x	Number of threads of the worm zw
1; 2
	bw ³ (11+0.06×zg)·m	bw ³ (12.5+0.09×zg)·m
-0.5	bw ³ (8+0.06×zg)·m	bw ³ (9.5+0.09×zg)·m
-1.0	bw ³ (10.5+zw)·m	bw ³ (10.5+zw)·m
+0.5	bw ³ (11+0.1×zg)·m	bw ³ (12.5+0.1×zg)·m
+1.0	bw ³ (12+0.1×zg)·m	bw ³ (13+0.1×zg)·m

Note. From manufacturing consideration, the threaded length of hobbed and ground worms is increased by 25 mm at m <10 mm, by 35 to 40 mm at m =10 mm to 16 mm and by 50 mm at m>16 mm.

b^w ³ (11+0.06×40)·8 = 107.2 mm

Assume

6.5.9. Determine the lead angle of the worm

6.5.10. Determine the pitch diameter of the worm gear

d^g = m×z^g = 8×40 = 320 mm.

6.5.11. Determine the addendum circle diameter of the worm gear

6.5.12. Determine the dedendum circle diameter of the gear

6.5.13. Determine the maximum diameter of the worm gear

6.5.14. Determine the face width of the worm gear

for z^w =1; 2

for z^w = 4.

6.5.15. Determine the peripheral speed at the worm and the worm gear

;

and

6.5.16. Specify the slippage speed

6.5.17. Determine the efficiency of the worm gearing

,

where r' is the friction angle determined by means of table 6.8.

Table 6.8

Angle of friction r'

Slippage speed Vsl, m/s	Angle of friction, r'	Slippage speed Vsl, m/s	Angle of friction, r'
0.1	4°30¢ - 5°10¢	2.5	1°40¢ - 2°20¢
0.5	3°10¢ - 3°40¢		1°30¢ - 2°10¢
1.0	2°30¢ - 3°10¢		1°20¢ - 1°40¢
1.5	2°20¢ - 2°50¢		1°00¢ - 1°30¢
2.0	2°00¢ - 2°30¢		0°55¢ - 1°20¢

Note. Greater values of r' correspond to tinless worm gears.

In our case: r' = 2°10';

6.5.18. Determine forces in the engagement of the worm gearing

- turning force at the worm and axial force at the worm gear : ;

- axial force at the worm and turning force at the worm gear : ;

- radial force Fr:

.

6.5.19. Determine the maximum contact stress

,

where T^g is in N·mm; ξ = 0.75 is the factor which takes into account the fact that contact of the worm and the worm gear occurs not along the whole arc of contact defined by the gear face angle 2d (2d ≈ 100º = 1.75 rad); ε_α is the contact ratio determined as

;

K_H = K_Hb · K_HV is the design load factor.

Table 6.9

Worm deformation factor Θ

Number of threads of the worm zw	Worm deformation factor at q of
		12.5

is the load concentration factor; Q is the worm deformation factor (table 6.9); x₁ takes into account load nature (for constant load x₁=0.6); K_HV is the dynamic load factor determined by means of table 6.10 (for worm gearings we take 7 or 8 accuracy of manufacturing).

Table 6.10

Dynamic load factor K_HV

Degree of accuracy	Dynamic load factor KHV at Vsl (m/sec) of
up to 1.5	1.5 - 3	3 - 7.5	7.5 - 12
	1.0	1.0	1.1	1.2
	1.15	1.25	1.4	-
	1.25	-	-	-

Obtained value of σ_H should correspond to the following condition

σ_H = (0.8…1.1)·[σ_H ].

Otherwise it is necessary to change the center distance a_w and recalculate the gearing.

In our case: ;

; K_HV = 1.25;

K_H = 1.04 · 1.25 = 1.37; ξ = 0.75; 2d ≈ 100º;

Obtained value of σ _H should correspond to the following condition

σ _H =(0.8…1.1)·[σ _H ]=(0.8…1.1)·240=192…264 MPa.

Strength condition is satisfied.

6.5.20. Determine the maximum bending stress

,

where K_b is the design load factor (K_b =K_H); m_n= m×cosg is the module at the normal section; Y_b is the tooth form factor determined by means of table 6.11 depending on the number of teeth of the equivalent straight spur gear

.

Table 6.11

Tooth form factor Y_b

zv
Yb	1.8	1.76	1.71	1.61	1.55	1.48	1.45	1.4	1.34	1.3	1.27	1.24

In our case: m_n= 8×cos 11.3⁰ = 7.846; K_b =1.297;

;

From table 6.11 tooth form factor Y_b = 1.52;

Strength condition is satisfied.

6.6. Determine the temperature of the oil containing in the casing

,

where t_air = 20°C is the temperature of the air; P^w is the power at the worm in W; h is the efficiency of the worm gearing; K_t is the heat transfer factor (for cast iron casings K_t =15…18 W/m²×C°); A is the area of the cooling surface determined approximately depending upon the center distance a_w by means of table 6.12; [t_oil] is the allowable temperature of the oil (for industrial oils [t_oil] = 80…95°C).

Table 6.12