非圓柱形螺旋壓縮彈簧特性研究

The Study of the Behavior of Non-cylindrical Helical Compression Springs

方亮彬(Lian-Bin Fang) ； 張恭翰(Kun-Han Chang) ； 呂明芳(Ming-Fang Lu) ； 陳威廷(Wei-Ting Chen)

《建國科大學報》 29卷1期 (2009/10) Pp. 23-40

https://doi.org/10.6995/JCTU.200910.0023

摘要

在本文中以非線性有限元素法研究圓錐形、桶形和鼓形等非圓柱形螺旋壓縮彈簧作用力與位移，以及各圈斷面上應力分佈的情形，以期瞭解非圓柱形壓縮彈簧因壓縮力作用而產生相鄰各圈間，或是彈簧各圈與底座接觸時，作用力與位移，以及彈簧中斷面上應力變化的情形，同時將以計算結果說明線材半徑(r)與彈簧平均半徑(R)比值，以及螺距對各圈斷面上應力分佈所造成的影響。由所得的結果發現，不同於圓柱形的壓縮彈簧，非圓柱形的壓縮彈簧，各圈具有不同的平均半徑，會於作用力大時產生接觸現象，使得斷面內應力產生變化，對於較小的線徑(r)與平均半徑(R)比的彈簧而言，其以忽略曲率變化的公式估算時，應力值的誤差約在6~12%之間；而對於位移與力量關係而言，即使是壓縮彈簧在面臨壓縮接觸的情形，以非線性有限元素分析的結果，誤差可控制於2%左右，而於本文分析例中，以鼓形彈簧之應力分佈受到接觸的影響較大。由此可知，非圓柱形彈簧承受壓縮力作用時，其應力分佈，以及位移與力量關係，不是單純地與線材半徑與彈簧平均半徑比值，或是螺距有關，因此在設計時，對於非圓柱形壓縮彈簧因彈簧接觸所造成的影響應謹慎地加以考量。

關鍵字

壓縮彈簧 ； 接觸 ； 有限元素分析

並列摘要

In this paper, nonlinear finite element method was used to investigate the behavior of non-cylindrical helical springs including conical, barrel and hyperboloidal, under compression for the sake of understanding the variations of the relationship between load and displacement, and the distribution of stresses on the cross section of each coil of the non-cylindrical helical springs while the coils contacts each other or the base of the springs. Besides, the results from the finite element analysis were used to illustrate the effect of the ratio of average radius of springs to the radius of winding line of springs, and the effect of the pitch of springs to the distribution of stresses on the cross section of each coil. The results show that the error of the distribution of stresses on the cross section is approximately 6~12% for the springs with smaller ratio of r/R while estimated with the formula neglecting the effect of curvature. Nevertheless, the error for the relationship between load and displacement can be control within 2% for the non-cylindrical springs even under the condition of contacting while using the nonlinear finite element analysis. The hyperboloidal one among the cases of non-cylindrical helical springs used shows more significant variation of stresses on the cross section when contacting condition occurred. Non-cylindrical helical springs are with different behavior compared with the cylindrical ones due to the variations of average radius that cause the coils of the springs contact each other or the base of the springs under higher loadings, which causes the variation of the distribution of stresses on the cross section of the coils, and not merely for the reasons of the effect of the ratio of average radius of springs to the radius of winding line of springs and pitch of springs. Therefore, we should pay more attention to the effects arising from the contact of coils of non-cylindrical springs when the design is proceeded.

並列關鍵字

Compression springs ； Contact ； finite element analysis