柔性杆与凸轮斜碰撞特性分析

Dynamical analysis of the ?exible beam-cam oblique-impact system

在计入柔性杆横向变形及其二阶耦合量的条件下,利用Hamilton最小作用原理建立柔性杆与凸轮斜碰撞系统的动力学方程,提出了柔性杆与凸轮碰撞点的确定方法,实现了柔性杆自由下落后的碰撞前、碰撞过程和碰撞后3个阶段的动力学行为仿真.通过分析柔性杆的碰撞运动规律,发现杆的柔性、大范围运动和碰撞三者间存在耦合,碰撞后柔性杆的转角随时间波动变化,转角波动的幅值随时间增大总趋势在减小,但规律性较差.

A mechanical system is often modeled as a multi-body system with non-smoothness. Typical examples are the noises and vibrations produced in railway brakes, impact print hammers, or chattering of machine tools. These effects are due to the non-smooth characteristics such as clearance, impact, intermittent contact, dry friction, or a combination of these effects. In a non-smooth system, neither of the time evolutions of the displacements and the velocities are requested to be smooth. Beam-cam device is an important kind of impacting system which has a wide range of applications. The rotation of the cam at some constant speed provides a force to operate the beam. The most common example is the valve trains of internal combustion engines, where the rotation of the cam imparts the proper motion to the engine valves through the follower while a spring provides a restoring force necessary to maintain contact between the components. The impact on beam-cam is a typical oblique-impact. It has been observed that under variations of the cam rotational speed and other parameters, the follower can exhibit a complex behavior including bifurcations and chaos. We study a rigid flexible coupling system, which moves in the horizontal plane, and is composed of the hub, the flexible beam and a cam with constant rotating speed. Considering the second-order coupling of axial displacement which is caused by the transverse deformation of the beam, the kinetic energy and the potential energy of the whole system are calculated. The governing equations of the flexible beam-cam oblique-impact system are derived from Hamilton theory, when taking into account the second-order coupling quantity of axial displacement caused by the transverse displacement of the beam. Hertz contact theory and nonlinear damping theories are used to establish the contact model. By the equivalent conversion method in structural mechanics, the deflection curve of flexible beam is calculated. The acceleration at the contact point of beam and cam is used to judge whether they are separate, or contacted, or impacting. Due to the flexibility of beam, the impact point of beam-cam always changes with time and speed. We propose a method, which is a trial calculation method, to determine the impact point of flexible beam-cam. Simulation results show that there is transverse vibration at the free end of flexible beam. There is inter-coupling among the flexible of beam, the large range of motion, and the impact. After the impact, the rotation angle of the flexible beam changes with time and the angle amplitude mainly decreases with the increase of the time, but the regularity is poor.