Table 3.4

Standard values of m_n

Series 1	1.0	1.25	1.5	2.0	2.5	3.0	4.0	5.0	6.0	8.0	10.0	12.0
Series 2	1.125	1.375	1.75	2.25	2.75	3.5	4.5	5.5	7.0	9.0	11.0	14.0

Note. Series 1 should be preferred to Series 2

3.5. Determine the total number of teeth

Obtained value of z _Σ should be rounded off to the nearest integer numeral.

3.6. Determine the number of teeth of the pinion

,

where z_min =17 for straight spur gears.

Obtained value of z^p should be rounded off to the nearest integer numeral. If z^p <17 it is necessary to decrease the module or to use nonstandard toothed wheels. For our case

.

Round off z^p to the nearest integer numeral. Assume z^p=27

3.7. Determine the number of teeth of the gear

Upper sign is right for gears with external toothing and down sign is used for gears with internal toothing.

3.8. Specify the velocity ratio of the gearing

u_act= .

The error ε = should be less or equal to 4%. Otherwise the number of teeth z^p, z^g and z _S must be rounded off to the other side.

In our case condition is satisfied, because

3.9. Determine the nominal pitch circles diameters for the pinion and the gear

d^p = m· z^p =2∙27=54 mm,

d^g = 2·a_w d^p =2∙160-54=266 mm.

3.10. Determine the addendum circles diameters for the pinion and the gear

= d^p + 2·m =54+2∙2=58 mm,

= d^g ± 2·m =266+2∙2=270 mm.

3.11. Determine the dedendum circles diameters for the pinion and the gear

= d^p-2.5·m =54-2.5∙2=49 mm,

= d^g 2.5·m =266-2.5∙2=261 mm.

3.12. Determine forces that act in the engagement of straight spur gears:

- turning force ;

- radial force ,

where α _w =20˚ is the pressure angle for the pitch circle.

3.13. Determine the maximum contact stress that develops in the contact zone of teeth

where T^p is the torque at the pinion shaft in N×mm; K_H is the design load factor that is determined as K_H=K_{H b}× K_HV, where K_{H b} is the load concentration factor; K_HV is the dynamic load factor.

The load concentration factor K_{H b} is specified by table 3.2 depending upon ψ _bd = . That is why K_{H b}=1.11.

In order to determine K_HV it is necessary to find the peripheral speed V^g of the gear

m/sec,

where ω ^g is the angular velocity of the gear and the gearing accuracy of manufacturing (table 3.5).

The dynamic load factor K_HV is determined by table 3.6. In our case K_HV =1,24

Table 3.5