Abstract
Multistage planetary gear transmission system has been widely utilized in engineering practice due to the salient characteristics, such as high bearing load and large speed ratio. This paper addresses a two-stage planetary gearbox and establishes a system coupling torsional dynamical model which considers the time-varying mesh stiffness, friction forces, and interstage coupling factors. Meanwhile, the friction and lubrication states are classified to comprehensively analyze the calculation of friction coefficients under different conditions. Considering the time-varying influence of friction on the tooth surface under the condition of fluid lubrication, the vibration response under parametric excitation is solved by a numerical method. A multistage planetary transmission test bench is built in the back-to-back form so as to test the vibration of the two-stage planetary gearbox. It shows that the simulation results of the dynamical model are consistent with the test data. Consideration of the calculation of friction on the tooth surface and the friction coefficients is helpful for the establishment of the more accurate dynamical model and lays the foundation for the structural design, fault diagnosis, and dynamic optimization of the multistage planetary gear transmission system.
Highlights
Coupling Dynamical Model of the Two-Stage Planetary Gear Transmission SystemTwo planetary gear drive systems are considered, which are used to establish the dynamical model of the two-stage model, and there are a total of three planet wheels at each stage. e coupling between the two gears is considered as the torsional spring. e transmission coupling between stage I and stage II is expressed by the torsional springs and dampers. e internal transmission structure and the schematic diagram of the studied system are as shown in Figures 1(a) and 1(b), respectively
Is paper is organized as follows: first, a new coupling dynamical model is presented by using the lumpedparameter method on the basis of the Lagrange equation and geometric relation analysis. en, the vibration response under parametric excitation is solved by a numerical method, and the dynamic characteristics and parameter influence rules of the key components are obtained
Two planetary gear drive systems are considered, which are used to establish the dynamical model of the two-stage model, and there are a total of three planet wheels at each stage. e coupling between the two gears is considered as the torsional spring. e transmission coupling between stage I and stage II is expressed by the torsional springs and dampers. e internal transmission structure and the schematic diagram of the studied system are as shown in Figures 1(a) and 1(b), respectively
Summary
Two planetary gear drive systems are considered, which are used to establish the dynamical model of the two-stage model, and there are a total of three planet wheels at each stage. e coupling between the two gears is considered as the torsional spring. e transmission coupling between stage I and stage II is expressed by the torsional springs and dampers. e internal transmission structure and the schematic diagram of the studied system are as shown in Figures 1(a) and 1(b), respectively. E coupled torsional dynamic equation of the two-stage planetary gear transmission system with frictional force is formulated as the following equation:. Where superscripts I and II denote the 1st and 2cd stage of the two-stage gear system; Jj are the moments of inertia of each component; rj are the equivalent radii of the rotating parts; re is the radii of the shaft coupling; mp is the mass of a planet gear; Fsn, Frn are the nth planet-ring and planet-sun meshing forces; fsn, frn are the friction forces; Lsn, Lrn are the arm of friction forces; i1, i2 are the transmission ratios of the 1st and 2cd stage; and Tin, Tout are the input torque and load torque, respectively. Where x is the generalized coordinate vector; M is the mass matrix; C is the damping coefficient matrix; Kjt is the torsional support stiffness matrix; K(t) is the time-vary meshing stiffness matrix; and F1 and F2 are the external and internal loads, respectively
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