Nonlinear Dynamic Analysis of a Trochoid Cam Gear

Abstract A trochoid cam gear (TCG) is a kind of precise transmission device with high performance, such as non-backlash, high-precision, low noise, etc. However, the nonlinear dynamics has not been studied. In the present paper, the nonlinear dynamic differential equation of the TCG is constructed. First, the trochoid equation and the tooth profile equation are deduced to satisfy the conditions of the continuous transmission. Second, a pure torsional nonlinear dynamic model is established to further construct the nonlinear model of the TCG according to a Lagrange equation. Finally, the dynamic characteristics of the TCG are investigated. For the short amplitude coefficient K, break of quasiperiodic torus is the main reason for the chaotic vibration. By increasing K, the performance of TCG can be improved to maintain stable motion.

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Nonlinear Dynamic Analysis and Chaos Prediction of Grinding Motorized Spindle System

Shock and Vibration ◽

10.1155/2019/9643124 ◽

2019 ◽

Vol 2019 ◽

pp. 1-10

Author(s):

Weitao Jia ◽

Feng Gao ◽

Yan Li ◽

Wenwu Wu ◽

Zhongwei Li

Keyword(s):

Nonlinear Dynamic ◽

High Speed ◽

Chaotic Behavior ◽

Nonlinear Dynamic Analysis ◽

Phase Portraits ◽

Impact Factors ◽

Nonlinear Dynamic Model ◽

Motorized Spindle ◽

Spindle System ◽

The Impact

The paper determines the impact factors of dynamics of a motorized spindle rotor system due to high speed: centrifugal force and bearing stiffness softening. A nonlinear dynamic model of the grinding motorized spindle system considering the above impact factors is constructed. Through system simulation including phase portraits and Poincaré map, the periodic behavior and chaotic behavior of the nonlinear grinding motorized spindle system are revealed. The threshold curve of chaos motion is obtained through the Melnikov method. The conclusion can provide a theoretical basis for researching deeply the dynamic behaviors of the grinding motorized spindle system.

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Based on the Nonlinear Dynamic Analysis of Linkage Vibration and Prevention

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.971-973.410 ◽

2014 ◽

Vol 971-973 ◽

pp. 410-413

Author(s):

Wen Juan Zhao

Keyword(s):

Control Strategy ◽

Nonlinear Dynamic ◽

High Speed ◽

Preventive Measures ◽

Mechanical Vibration ◽

Nonlinear Dynamic Analysis ◽

Connecting Rod ◽

Nonlinear Dynamic Model ◽

Set Up ◽

And Control

connecting rod mechanism under the condition of high speed operation, organization, the elastic dynamic response of not only make the institutions of trajectory deviation, also can cause fatigue failure, this paper set up an accurate view of the nonlinear dynamic model of analysis of linkage performance and characteristics of mechanical vibration, look for the causes of various vibration, and puts forward corresponding preventive measures and control strategy.

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Nonlinear dynamic analysis of spur gear system based on fractional-order calculus

Modern Physics Letters B ◽

10.1142/s0217984920504205 ◽

2020 ◽

Vol 34 (36) ◽

pp. 2050420

Author(s):

Jingyu Hou ◽

Shaopu Yang ◽

Qiang Li ◽

Yongqiang Liu

Keyword(s):

Fractional Order ◽

Nonlinear Dynamic ◽

Numerical Solutions ◽

Nonlinear Dynamic Analysis ◽

Harmonic Balance Method ◽

Spur Gear ◽

Nonlinear Dynamic Model ◽

Mesh Stiffness ◽

Incremental Harmonic Balance Method ◽

Internal Excitation

In this paper, nonlinear dynamic model of spur gear pairs with fractional-order damping under the condition of time-varying stiffness, backlash and static transmission error is established. The general formula of fractional-order damping term is derived by using the incremental harmonic balance method (IHBM), and the approximate analytical solution of the system is obtained by use of the iterative formula. The correctness of the results is verified by comparing with the numerical solutions in the existing literature. The effects of mesh stiffness, internal excitation amplitude and fractional order on the dynamic behavior of the system are analyzed. The results show that changing the fractional order can effectively control the resonance position and amplitude in the meshing process. Both the mesh stiffness and internal excitation can control the collision state and the stability.

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Nonlinear Dynamics and Analysis of a Planar Multilink Complex Mechanism with Clearance

Shock and Vibration ◽

10.1155/2018/6172676 ◽

2018 ◽

Vol 2018 ◽

pp. 1-17 ◽

Cited By ~ 3

Author(s):

Xiulong Chen ◽

Shuai Jiang ◽

Yu Deng ◽

Qing Wang

Keyword(s):

Nonlinear Dynamics ◽

Dynamic Response ◽

Phase Diagrams ◽

Dynamic Model ◽

Dynamic Behavior ◽

Nonlinear Dynamic ◽

Lagrange Equation ◽

Nonlinear Dynamic Model ◽

Planar Mechanism ◽

Driving Speed

In order to understand the nonlinear dynamic behavior of a planar mechanism with clearance, the nonlinear dynamic model of the 2-DOF nine-bar mechanism with a revolute clearance is proposed; the dynamic response, phase diagrams, Poincaré portraits, and largest Lyapunov exponents (LLEs) of mechanism are investigated. The nonlinear dynamic model of 2-DOF nine-bar mechanism containing a revolute clearance is established by using the Lagrange equation. Dynamic response of the slider’s kinematics characteristic, contact force, driving torque, shaft center trajectory, and the penetration depth for 2-DOF nine-bar mechanism are all analyzed. Chaos phenomenon existed in the mechanism has been identified by using the phase diagrams, the Poincaré portraits, and LLEs. The effects of the different clearance sizes, different friction coefficients, and different driving speeds on dynamic behavior are studied. Bifurcation diagrams with changing clearance value, friction coefficient, and driving speed are drawn. The research could provide important technical support and theoretical basis for the further study of the nonlinear dynamics of planar mechanism.

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