# Constraint conditions of minimum center distance for two stage spur gears

① According to the contact fatigue strength formula of tooth surface, the

The constraint conditions of tooth surface are obtained

Where k is the load factor, T1 is the torque of the pinion, T2 is the torque of the pinion, ad is the material factor, [σ H] is the allowable stress of the gear, s is the safety factor, khn1 is the life factor, σ Lim1 is the fatigue limit, and ψ D is the tooth width factor.

② According to the condition of bending fatigue strength of tooth root, it is divided into three parts

The constraint conditions of the two stages (high speed and low speed) at the root of the tooth are different

Where [σ F] is the allowable stress, where s is the safety factor, kfn1 is the life factor, and σ Lim1 is the fatigue limit.

③ Torque transmitted by high speed and low speed gears:

Where, the transmission efficiency between the high-speed stage and the low-speed stage is 0.95.

④ In order to make the pitch of addendum circle of high-speed stage and low-speed stage gear reasonable, according to the experience, take e = 50mm, the normal tooth height coefficient of addendum circle radius of high-speed stage gear to normal tooth Han = 1, and the center distance of low-speed stage gear pair 