An original numerical calculation method for impacting contact model of spur gear under lightly loaded condition
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An original numerical calculation method for impacting contact model of spur gear under lightly loaded condition Fuhao Liu
. Liang Zhang . Hanjun Jiang . Jielu Zhang . Xuehua Yu
Received: 15 November 2019 / Accepted: 10 May 2020 Ó Springer Nature B.V. 2020
Abstract In this study, an impacting contact model of spur gear under lightly loaded condition is constructed by considering the pinion and the wheel as rigid body, in which the lubricant is modelled by a linear spring damper combination. The entire motion of the gear system is fell into three phases, i.e.,: meshing state, transient state and non-meshing state. An original numerical calculation method is proposed for this model, and its validation is confirmed by using the Co-simulation of Adams-Matlab/Simulink. Instead of using the Jacobian matrix, the proposed numerical method could effectively avoid the ill condition in the iteration on data resulting from the nonlinearity of gear backlash. The results in this study verified that the algorithm is useful not only can increase the accuracy, but also significantly decrease the calculation time of the entire system. And the original numerical calculation method is employed to illustrate and quantify the influences of the excitation F. Liu (&) L. Zhang H. Jiang School of Mechanical and Automotive Engineering, Qingdao University of Technology, Qingdao 266520, China e-mail: [email protected] F. Liu X. Yu College of Automobile Engineering, Yancheng Institute of Technology, Yancheng 224051, Jiangsu, China J. Zhang Jiangsu Tailong Decelerator Machinery Co., Ltd., Taixing 225400, Jiangsu, China
frequency on the impacting contact model of spur gears. Keywords Gear system Numerical method Impacting contact Nonlinear analysis List of symbols x Dynamical transmission errors x_ Relative speed x€ Relative acceleration L Length of gear backlash t Time in second Dt0 Time interval for any given time t0 Tf Time of one excitation period Time interval from lubricant contact to Dtm solid contact tn Time interval for the current step nth Dtmax Maximum time-step Dtmin Minimum time-step Ip;w Rotational inertia of pinion and gear Rotational displacements of pinion and hp;w gear Rotational velocity of pinion and gear h_ p;w € Rotational acceleration of pinion and gear hp;w Rp;w Base radius of pinion and gear Drag torque Tw Twm Mean part of drag torque j Amplitude of vibratory part of the jth Tpw harmonic for drag torque
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Meccanica
;j Tp Tpm i Tpp #i x P 2Dt e a1;2;3 c; k; fm;p e N Kd;c Cd;c
Initial phase of the jth harmonic for drag torque Driving torque Mean part of driving torque Amplitude of vibratory part of the jth harmonic for driving torque Initial phase of the jth harmonic for driving torque Excitation frequency Number of engine cylinders Short time duration of impact Coefficient of restitution Intermediate variables for Dtm Intermediate variables for government equation Precision tolerant Initial resolution of numerical solution Lubricant stiffness of drivin
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