The transmission diagram of the reducer is shown in the figure, and the optimization design is carried out according to the minimum total center distance a ∑. The expression of center distance of reducer is as follows:
Where, Mn1 and Mn2 are the module of high and low speed gears respectively; Z1 and Z3 are the number of teeth of high and low speed gears respectively; I1 and I2 are the transmission ratio of high and low speed gears respectively; β is the helix angle of gear pair.
If the total transmission ratio I of the reducer is known, the transmission ratio expression of the low speed stage is I2 = I / I1