# Dynamics Analysis and Chaos Identification of Compound Pendulum Jaw Crusher with Joint Clearance
###### Abstract  
A dynamic model of the working mechanism of a compound pendulum jaw crusher with clearance is established by the Lagrange multiplier method (LMD) based on the L-N contact force model and modified Coulomb friction force model. The correctness of the dynamic model is verified by MATLAB and Adams comparison simulation, and the best selection range of driving speed and clearance size is determined according to the laminating crushing theory (LCT). The effects of driving speed and clearance size on the shock and chaos phenomenon in the clearance mechanism are analyzed, as well as the vibration force applied to the foundation. The results show that, under the premise of meeting the requirements of crusher production capacity, increasing the driving speed and reducing the clearance size can weaken the shock and chaos phenomenon during the operation of the mechanism, improve the dynamic performance and enhance the operation stability, and the service life of foundation is prolonged with the stability of vibration force. Furthermore, the optimal combination of driving speed and clearance size is determined, which provides a theoretical basis for the optimization of the vibration force of the jaw crusher. clearance; crusher; chaos; shock; vibration Article  
Dynamics Analysis and Chaos Identification of Compound Pendulum Jaw Crusher with Joint Clearance. 1  
Dynamics Analysis and Chaos Identification of Compound Pendulum Jaw Crusher with Joint Clearance. regression model of crusher performance was constructed. The amplitude of vibration force was greatly decreased by increasing the mass of the fixed cone for optimization. Current research on jaw crushers has concentrated on the design and optimization of the mechanism structure [9], ignoring the existence of joint clearance. When the crusher is operating at a high speed and under a heavy load, the revolute joint's elements will lose contact with one another. When they come into contact again owing to constraint and inertia, a collision will happen. At this point, the revolute joint's response force can be several times or even a dozen times as great as when there is no clearance [10], which invariably has an effect on the assessment of crusher vibration. The dynamic performance of the clearance mechanism system can be better described by chaos, and the stability of the mechanism operation can also be assessed by chaos [11]. [PERSON] [12] described the system dynamics for the planar slider-crank mechanism with multiple clearance joints by the correlation dimension and bifurcation actions. The dynamic equations of motion were derived using generalized coordinates and the Lagrange method, and the effects of clearance size and driving speed on system bifurcation were investigated. [PERSON] [13] utilized the KED method with the Lagrange method to establish a nonlinear dynamic model of a spatially parallel mechanism. The study showed the influence of various clearances on the parallel mechanism dynamics behavior, including chaos and bifurcation phenomenon, which provided a methodology for forecasting the dynamics behavior of parallel mechanisms with clearance and flexible links. By summarizing the above-mentioned research, one challenging issue exists in the jaw crusher. The presented idealized model does not accurately describe the dynamics of the crusher, which greatly affects the evaluation of the dynamic performance. Specifically, the existing research does not consider the effect of revolute joint with clearance and lacks comparative analysis of the dynamic characteristics under different working conditions. There is also a lack of specific analysis of the key parameters affecting the vibration force. Numerous scholars have used nonlinear dynamics techniques such as chaos to accomplish research and analysis in the field of mechanism with clearance, and they have produced a wealth of fruitful findings.