Optimization objective function of single stage double circular arc spiral bevel gear

The single-stage nutation reducer is designed with the radial size less than 108 mm, the transmission power of 20 kW and the transmission ratio of about 10 as the design objectives, and the optimization model with the minimum volume of the reducer as the objective function is established.

The size of reducer is mainly determined by the number of teeth Z1 and Z2, tooth width b, nutation angle ε, pitch angle δ 1 and δ 2, helix angle β and normal surface modulus Mn. Under a given transmission condition, by establishing the relationship between nutation angle ε and pitch cone angle δ 1, δ 2, the value range of nutation angle ε is set, and they are used as known quantities and do not participate in optimization. According to the formula, when the transmission ratio is determined, the meshing bevel gears Z1 and Z2 are not independent of each other. Therefore, Z1 is taken as the design variable.

The design variables of single-stage nutation drive are as follows:

The objective function can be expressed as follows: