非标准抛物线型变截面板簧力学特性解析计算

Analytical calculation of mechanical properties for nonstandard parabolic tapered leaf spring

为了满足实际悬架刚度的设计要求,通常抛物线型变截面板簧的抛物线段的坐标原点不在力的作用点上,即非标准抛物线型变截面板簧。然而,其变形及应力一直未给出可靠的解析计算公式。根据单片非标准抛物线型变截面板簧的力学模型,利用莫尔积分,建立了变形、刚度的解析计算公式,并分析了坐标偏移量对板簧结构及力学特性的影响;在此基础上,根据少片簧与各片板簧之间的刚度与载荷的关系,建立少片非标准抛物线型变截面板簧的变形、刚度和应力的解析计算公式。通过实例对少片非标准抛物线型变截面板簧的变形、刚度及应力进行解析计算和仿真验证,解析计算值与仿真值均吻合,变形相对偏差在0.7%以内,应力相对偏差在2.3%以内,结果表明所建立的解析计算方法是正确的。最后,对少片簧进行了刚度测试试验。结果表明,刚度解析值与试验值吻合,相对偏差在4.2%以内,进一步验证所建模型和方法的可靠性。

To meet the design requirements of the actual suspension stiffness,generally the coordinate origin of the parabolic tapered leaf spring does not coincide with the action point of the force,that is,nonstandard parabolic tapered leaf spring.However,there are no exact deformation and stress analytical calculation formulas for it.Based on the mechanical model of the single-chip nonstandard parabolic tapered leaf spring,this study established the analytical formulas of its stiffness and stress by using Moore integral.Then,the influence of the coordinate offset on its structure and mechanical properties is analyzed.On this basis,the deformation,stiffness,and the stress analytical formulas were derived for the few-chip parabolic tapered leaf spring according to the relationship between the stiffness and load between the few-chip and the single-chip leaf spring.With a case study,the deformation and the stress were computed and simulated,the results of which show that the values computed are close to those simulated.The deformation relative deviations are not more than 0.7%,the stress relative deviations are not more than 2.3%,which means that the established analytical formulas are accurate.Finally,a stiffness test was performed on the few-chip leaf spring.The results show that the computed stiffness values are close to those tested and the relative deviations are not more than 4.2%.This further verifies the reliability of the established model and method.