The total velocity ratio can be found by the formula

u = u _bd × u_hsg,

where u_bd. is the belt drive velocity ratio; u_hsg is the helical spur gearing velocity ratio.

First, determine the velocity ratio of speed reducer.

It should correspond to the following standard series^*.

^* - for spur and bevel gear speed reducers:

1.25; 1.4; 1.6; 1.8; 2.0; 2.24; 2.5; 2.8; 3.15; 3.55; 4.0; 4.5; 5.0; 5.6

Let us take u_hsg =5.6.

Then the velocity ratio u_bd =u/u_hsg=23.41/5.6=4.18 (for belt drives the obtained value of u_bd should range from 2 to 4; for chain drives u_cd = from 1.5 to 4).

1.8. Determine the rotational speed of all shafts.

n₁ = n_r = 1000 rpm;

The obtained value of n₃ must be equal to n_out according to the initial data. Error ε must be not more than 4%. In our case ε =2.7%.

1.9. Determine the angular velocity of all mechanical drive shafts:

1.10. Determine the power at mechanical drive shafts.

Calculation is carried out with respect to P_inp, determined in point 1.3.

P₁ = P_inp = 10.65 kW;

P₂ = P₁× h_bd× h_b = 10.65× 0.96× 0.99 = 10.12 kW;

P₃ = P₂× h_hsg× h²_b× = 10.12× 0.97× 0.99² = 9.62 kW;

The obtained magnitude of P₃ must be equal to P_out according to the initial data. Error should not be more than 1%. In our case ε =0.5%.

1.12. Determine the torques at all shafts.

Checking:

2. CALCULATION OF ALLOWABLE STRESSES

2.1. Select the material of toothed wheels.

The main material of toothed wheels is carbon and alloy steels. Depending on material hardness, toothed wheels are subdivided into two groups:

- toothed wheels with surface hardness H :

- toothed wheels with surface hardness H > 350 BHN Brinell hardness number.

For general purpose speed reducers, the following alternatives are possible:

a) A pinion and a gear are made of identical carbon or alloy steel, such as 45 (0.45C), 40X (0.40C-Cr), 40XH (0.40C-Cr-Ni). Heat treatment of both, the gear and the pinion is martempering. The pinion hardness is ranged from 269 to 302 BHN and the gear hardness is ranged from 235 to 262 BHN.

b) A pinion and a gear are made of identical alloy steel, such as 40X (0.40C-Cr), 40XH (0.40C-Cr-Ni), 35XM (0.35C-Cr-Mo). Heat treatment of the gear is martempering to hardness ranged from 269 to 302 BHN. Heat treatment of the pinion is martempering and surface (induction) hardening to hardness ranged from 45 to 50 HRC.

Toothed wheels of the straight and helical spur gears are recommended to produce according to the alternative a). If we deal with bevel gearing, the alternative b) is more preferable.

2.2. Determine the mean values of the gear and the pinion hardness:

- for the pinion

- for the gear

2.3. Determine the allowable contact stress for the pinion and gear.

Determine the limit of contact endurance for the pinion and for the gear according to table 2.1.

Table 2.1