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The state equation of the system is the physical variable that characterizes the internal state of the system with time. According to the bond graph model of the system, the generalized momentum p of the inertial element and the generalized displacement q of the capacitive element are the state variables. The stream and the stream are denoted by e and f, respectively, and the keys are uniformly numbered 120, wherein the subscripts of the variables p and q represent the part numbers, and the subscripts of the variables e and f represent the number of the keys. Each energy storage component of the system has an integral causal relationship. The state variables of the whole system are: X=[q0, p4, qH4, p1, q1, p1c, qH2, p2] T(1) according to system causality and power flow direction Obtain the state space equation of the system bond graph simulation: q0=-1I4 Sfp4=1C0q0-1CH4qH4qH4=1I4(2) where: m1=11 p;m2=p1 p;m3=11 p planetary gear characteristic parameter: p=z2z1 =10848, pc=z3z1c=84364 Dynamic simulation analysis of the system According to the parameters of the planetary gear transmission system and the mechanical properties of the material, the parameters of the inertia element I and the capacitive element C in the state equation are determined by the material mechanics [7] recommended formula. See the basic parameters of the system.
The basic parameters of the system category sun gear Z1 planetary gear Z6 inner ring gear Z2 sun gear Z1c planetary wheel Z5 inner ring gear Z3 tooth number 4830108362484 tooth width / mm5040 modulus / mm3 pressure angle / (b) 20 due to the corresponding parameter difference of each component Large, so the corresponding dimensionless processing of the coefficients in the equation of state, using the fourth-order Runge-Kutta method to solve the differential equation of the system state equation (2). In order to obtain the true output (T, X) of the system, the obtained generalized momentum p is divided by the inertia of the corresponding I component to obtain the rotational speed, and the obtained generalized displacement q is divided by the compliance of the corresponding C component to obtain the torque T. [6]. Obtain the deformation curve and output simulation result of the system planet carrier.
The conclusion can be seen from the simulation curve: 1Because the rigidity of the planet carrier 2 is smaller than that of the planet carrier 4, the deformation is large, but the deformation process is slower than 4, and the planet carrier 4 is integrated with the input shaft, and receives the input torque and the inner ring gear. At the same time as the sun wheel, the force is complicated and the deformation produces fluctuations.
2 Known by the formula X = p / I, the system is output by 2, and its rotational speed increases as the generalized momentum of 2 increases. The output speed curve can correctly reflect the actual situation. The output torque is affected by the deformation of the carrier 4, which causes fluctuations. As a kind of analysis method, 3 bond diagram is simple, accurate, reliable and has broad application prospects in system dynamics analysis.