谐波力激励下螺旋形弹簧的拉扭耦合动力响应

DYNAMIC RESPONSE OF COUPLED TENSIONAL-TORSIONAL HELICAL SPRING UNDER HARMONIC FORCE EXCITATION

建立一种普遍的解析理论 ,利用简正模态法研究确定性载荷作用下拉扭耦合螺旋形弹簧的动力响应。假定确定性载荷是谐波变化的 ,得到各种谐波激励下封闭形式的解 ,并对动力拉伸位移和扭转位移的数值结果进行讨论 。

The helical spring is usually regarded as a linear extension/torsion element, but in fact the general characteristics of helical spring is that its static response is coupled, that is a tension load will cause both axial and torsional displacements at the same time, and conversely, a torque will result in rotation as well as extension. Such coupled behavior has a great influence on the dynamic response of the helical spring. The free vibration analysis of a coupled extensional torsional helical spring has been investigated by a number of authors in recent years, but there appears to be little work reported on the forced vibration characteristics of coupled extensional torsional helical spring. The problem is addresses in this paper. A general analytical theory is developed. The dynamic response of coupled tensional torsional helical spring under deterministic load is investigated by using normal mode method. The deterministic load is assumed to be harmonic varying. The theoretic expressions for the displacement response of helical spring subjected to concentrated or distributed harmonic loads are obtained. The method is illustrated by its application to investigate the effects of axial force on the torsion displacement response and the torque on the axial displacement response of a fixed free helical spring. Representative results for the dynamic axial and torsional displacements are given and discussed for two applications: one when the deterministic load is a harmonically varying concentrated axial force at the tip of the fixed free helical spring, and the other when the deterministic load is a harmonically varying concentrated torque at the tip of the fixed free helical spring. Although the example given in this paper is that of a simple helical spring, the theory is fairly general and can be used for other types of deterministic load and different boundary conditions of the helical spring.