矩形截面非圆柱螺旋弹簧的模态分析
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同济大学航空航天与力学学院,同济大学航空航天与力学学院

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国家自然科学基金项目(面上项目,重点项目,重大项目)


Modal analysis of non-cylindrical helical springs with rectangular cross-section
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School of Aerospace Engineering and Applied Mechanics,School of Aerospace Engineering and Applied Mechanics

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The National Natural Science Foundation of China (General Program, Key Program, Major Research Plan)

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    摘要:

    对非圆柱(锥形、桶形、双曲形)矩形截面螺旋弹簧的自由振动问题进行了研究。在弹簧的运动微分方程中,所有的位移函数和广义翘曲坐标均定义在形心主轴上,并首次考虑了簧丝截面的翘曲变形对固有频率的影响。本文采用改进的Riccati传递矩阵法对包括14个自由度的一阶变系数常微分方程组进行了求解。在簧丝截面为矩形的情况下,给出了各种参数变化如截面的宽高比、螺旋角、有效圈数和非圆柱螺旋线最小与最大半径之比对两端固支矩形截面锥形弹簧固有频率的影响。为了证明理论的有效性,对两端固支矩形截面锥形弹簧的固有频率和振动模态进行了求解,并同ANASY三维实体单元(Solid45)的结果进行了比较。计算表明,簧丝截面的翘曲变形对矩形截面非圆柱螺旋弹簧的固有频率有着重大的影响,在自由振动分析中必须加以考虑。

    Abstract:

    Free vibration analysis of non-cylindrical (conical, barrel, and hyperboloidal types) helical springs with rectangular cross-section is performed. In the differential equations of motion for the springs, all displacement functions and a generalized coordinate for warping are defined at the centroidal principal axes. The effect of warping deformation on the natural frequencies is first studied. Improved Riccati transfer matrix method is introduced to solve the first order ordinary differential equations with variable coefficients, which consist of 14 degrees of freedom. For the rectangular cross-section, the effects of the aspect ratio , the helix pitch angle , the number of active turns and the ratio of radii of the minimum cylinder to the maximum cylinder on the natural frequencies of the clamped–clamped conical springs are investigated. The natural frequencies and vibration modes of conical spring of rectangular cross-section with clamped-clamped boundary condition are simulated to validate the proposed method, which is also compared with a finite element model using three-dimensional solid elements (Solid 45) in ANSYS code. Numerical results reveal that the effect of warping deformation on the natural frequencies of the springs is prominent which should be taken into consideration in their free vibration analysis

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引用本文

郝颖,虞爱民.矩形截面非圆柱螺旋弹簧的模态分析[J].振动工程学报,2012,25(3).[HAO Ying,虞爱民. Modal analysis of non-cylindrical helical springs with rectangular cross-section[J]. Journal of Vibration Engineering,2012,25(3).]

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历史
  • 收稿日期:2011-08-11
  • 最后修改日期:2012-05-25
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  • 在线发布日期: 2012-06-12
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