基于精确几何模型梁单元的螺旋弹簧刚度分析

STIFFNESS ANALYSIS OF HELIX SPRING USING EXACT GEOMETRIC BEAM ELEMENT

以精确几何模型梁单元为基础,对圆截面螺旋弹簧刚度的非线性特性进行了分析。结合弹簧细长结构的变形特点,选取弹簧半径、弹簧高度、螺旋线极角和簧丝截面扭转角作为螺旋弹簧的描述变量;按照Bernoulli梁理论,通过形心曲线切矢量和簧丝截面扭转角建立截面坐标系;基于大转动梁的变形虚功率,获得螺旋弹簧曲率矢量,构建弹簧变形虚功率;应用柔体建模过程的滤除高频震荡分量方法修正弹簧系统动力学方程求得弹簧刚度,提高计算效率。数值算例表明,计算结果符合弹簧刚度的受力变形规律。同时与弹簧经典理论算法和传统有限元方法进行对比,验证了分析方法的正确性和合理性。

Based on the exact geometric beam element model,the nonlinear stiffness characteristic of helix spring with circular cross-sections was investigated.The way to choose descriptive variables of spring model was combined with deformation characteristics of slender helix spring,and the spring radius,height,helix polar angle and torsion angle of the cross-section of spring wire were selected as the descriptive variables of helix spring.According to the Bernoulli beam theory,the cross-section coordinate system was established by the centroid curve tangent vector and torsion angle of the cross-section.Spring deformation virtual power equation was built using curvature vector of helix spring which was based on the deformation virtual power of large rotating beam.The deformation virtual power equation of spring was built by using the method of removing high-frequency vibrations in flexible body systems.As validated by numerical examples,the results conformed to the deformation law of spring stiffness.In addition,compared with the classical theory algorithm and the traditional finite element method,the results proved the validity and rationality of the analytical procedure.