web-offset press is a kind of coupling nonlinear dynamic system.We use the lumped mass method

Newton's second law

the differential equations and series theory and method to establish the gear system nonlinear dynamic modeling of web-offset printing machine wherein the time-varying meshing stiffness

backlash

dynamic transmission error and other nonlinear factors were considered.the concept of general time-state space comprising of state variables

control variable and time

t

is established.Then the model of web-offset printing machine can be transformed into a state equation of nonlinear system.In order to solve the state equati

on of nonlinear control systems

at the operation point of general time-state space

the right side of the state equation can be expanded as Taylor series about time.Then the series solution of the nonlinear control state equation

for which the solution is expression in time series

can be obtained by using direct-integrating approach.Then we use Matlab to simulate the equation of the web-offset printing machine's gear system.We obtain the curves of the relationship of gear's angular velocity and time and the relationship of angular acceleration and time.we contrast these curves and the facts.the contrast result verifies the validity of the dynamic model and the analytic solution of the system equation.