Abstract：Considering backlash of gear pairs, time-varying mesh stiffness and friction, a nonlinear dynamic model of scissor gear transmission with seven degree-of-freedom was established by analytical mechanics theory. An example scissor gear was used to investigate the effects of rotational speed, backlash, stiffness and preload of torsional spring on the nonlinear dynamic behavior of the system with Runge-Kutta method. The results showed that the system went into a chaotic motion with increase in speed, and it is at the medium speed that the nonlinear dynamic behavior of the system was more sensitive to the change of the speed. When the backlash increased, the speed interval of chaos became larger and the chaotic characteristic was enhanced. It was the nonlinear dynamic characteristic, not the gear teeth off, that was profoundly influenced by the torsional stiffness of spring. And the smaller torsional stiffness would be more helpful to avoiding the separating and impacting status of the gear pair. Preload of torsional spring affected the meshing states of the scissor gear transmission. Minimum preload torque was almost in direct proportion to the load torque.
[1] 高卫.弹簧消隙小模数齿轮传动链回差计算分析及工程应用[J].火控雷达技术,1999,28(4):31-34.
Gao Wei. Analysis of backlash in spring anti-backlash small modulus gear drive train and its engineering application [J]. Fire Control Radar Technology, 1999, 28(4): 31-34.
[2] 石辉,杨锡和.双片齿轮用弹簧的弹性力计算[J].雷达与对抗, 2000(3):45-50.
Shi Hui, Yang Xihe. Spring's elastic force computation for double gear [J]. Radar & Ecm., 2000(3):45-50.
[3] 董懿琼,杨雪春.无间隙齿轮在汽车发动机降噪中的应用尝试[J].南昌大学学报•工科版,2006,28(3):250-255.
Dong Yiqiong, Yang Xuechun. Experimental application of gapless gear pairs to noise reduction of automobile engine [J]. Journal of Nanchang University (Engineering & Technology), 2006, 28(3): 250-255.
[4] 李国民.双片齿轮固有频率计算分析[J].电子机械工程, 2001(3): 11-12.
Li Guoming. Calculation and analysis of double gear's inherent frequency [J]. Electro-Mechanical Engineering, 2001(3): 11-12.
[5] KWON Y S, HWANG H Y, LEE H R, et al. Rate loop control based on torque compensation in anti-backlash geared servo system [C]. American Control Conference, June 30-July 2,2004, Boston, MA, United Stated: Institute of Electrical and Electronics Engineers Inc, 2004: 3327-3332.
[6] ALLAN P M, LEVY N M. The determination of minimum pre-load torque for anti-backlash gears in a positional servomechanism [J]. IEEE Transactions on Industrial Electronics and Control Instrumentation, 1980, 27: 1232-1239.
[7] 杨政,尚建忠,罗自荣,等.扭簧加载双片齿轮消隙机构综合啮合刚度[J].机械工程学报,2013,49(1):23-30.
Yang Zheng, Shang Jianzhong, Luo Zirong, et al. Research on synthesis meshing stiffness of torsional spring-loaded double-gear anti-backlash mechanism [J]. Journal of Mechanical Engineering, 2013, 49(1): 23-30.
[8] Yang Zheng, Shang Jianzhong, Luo Zirong. Effect analysis of friction and damping on anti-backlash gear based on dynamics model with time-varying mesh stiffness [J]. J. Cent. South Univ., 2013(20):3461-3470.
[9] 日本机械学会.齿轮强度设计资料[M].李茹贞,赵清慧,译.北京:机械工业出版社, 1984:30-32.
JSME. The strength design document of gear [M]. Translated by Li Ruzhen, Zhao Qinghui. Beijing: China Machines Press, 1984.
[10] Benedict G H, Kelley B W. Instantaneous coefficients of gear tooth friction [J]. Transactions of the American Society of Lubrication Engineers, 1961, 4:59-70.
[11] 李润方,王建军.齿轮系统动力学——振动、冲击、噪声[M].北京:科学出版社,1997.
[12] Wolf A, Swift J B, Swinney H L. Determining lyapunov exponents from a time series [J]. Physica D, 1985, 16:285-317.
[13] 王峰，方宗德，李声晋.重合度对人字齿轮非线性系统振动特性的影响分析[J].振动与冲击,2014,33(3):18-22.
WANG Feng,FAMG Zong-de,LI Sheng-jin.Effect of contact ratio on dynamic behavior of a double-helical gear nonlinear system[J].Journal of Vibration and Shock,2014,33(3):18-22.
