Considering the random fluctuation of the input torque and the load torque and the random meshing error

a lateral- torsional coupling dynamic model of single stage spur gear transmissions is built. By the numerical method

the dynamic stresses on the gear tooth are obtained. The process of dynamic stress during the work period is regard as a random process

and the probability distribution model of the maxima stress is equivalent to the effect of this random process in the random process

then

the probability distribution model of stress is obtained. After that

the probability distribution model of allowable stress is obtained by the Monte Carlo method. Based on the stress- strength interference theory

a dynamic reliability model of gear transmissions considering the correlation between the tooth root bending fatigue failure and the tooth surface contact fatigue failure is built. This research shows that the larger the meshing error is

the lower the reliability of system is.