螺旋彈簧之幾何參數對勁度與應力影響之研究

螺旋彈簧是機械中重要的元件，以其製作容易、儲能效率高、受力與位移關係靈敏等優點而被廣泛使用。本研究利用電腦輔助工程分析軟體，對非圓形截面、變節距與非圓柱形之螺旋彈簧進行模擬分析。在固定截面形心位置與截面積之下，Oval-1-H95為最佳截面形狀，其最大應力較參考彈簧降低約2%~4%，而勁度幾乎不變。在不同彈簧指數下，相同卵形截面對勁度與應力的影響，是彈簧指數越小，勁度提升越多，不過最大應力與彈簧指數之間則無明顯的相關性。　　若將限制條件改變為固定彈簧外徑及體積，則Oval-2截面同時在提高勁度與降低最大應力上有最佳之表現，其中Oval-2-H85是降低彈簧應力的最佳截面形狀，比參考彈簧降低約6%；而Oval-2-H80是提高勁度之最佳截面形狀，可在最大應力小於參考彈簧的前提下，提高勁度達15%。本研究透過改變截面形狀為卵形，達到增強彈簧勁度及降低彈簧素線表面應力之結果。　　變節距以及非圓柱形彈簧，可以使彈簧勁度為非線性漸硬，且素線上的應力在相鄰的螺旋壓實之後便不再增加。而變節距彈簧的非線性範圍又較非圓柱形彈簧來的大，且勁度增加的曲線也較為平滑。

關鍵字

螺旋彈簧；截面形狀；變節距；非圓柱形

並列摘要

Helical springs are an important element in the machinery and widely used. In this study, with CAE software package, one is to study the stiffness and the stress distribution on wire surface of the spring by changing the profile of its cross section, and study the effects of variable pitch and non-cylindrical springs. It is found that when the centroid and area of cross-section is fixed, the Oval-1-H95 is the optimal shape, it reduces the maximal stress by 2%~4% from the reference spring, when the stiffness is identical. On the other hand, when one comes to fix the outer diameter and the volume of springs, the Oval-2 is the optimal shape, it reduces the maximal stress and also strengthens the stiffness. The Oval-2-H85 is the best in reducing the maximal stress, it is 6% lower than that of the reference spring. And the Oval-2-H80 is the best in strengthening the stiffness, it is 15% higher than that of the reference spring, under the premise of lower stress than the reference spring.

並列關鍵字

Helical springs ； Cross-section shape ； Variable pitch ； Non-cylindrical

參考文獻

3. K. Nagaya, “Stresses in a helical spring of arbitrary cross section with consideration of end effects,” Journal of Vibration, Acoustics, Stress and Reliability in Design, Vol. 109, 1987, pp. 289–301.

5. N. Kamiya and E. Kita, “Boundary element method for quasi-harmonic differential equation with application to stress analysis and shape optimization of helical spring,” Computers & Structures, Vol. 37, No.1, 1990, pp. 81-86.

6. T. Imaizumi, T. Ohkouchi and S. Ichikawa, “Shape optimization of the wire cross section of helical springs,” JSME International Journal, Series C, Vol. 36, No. 4, 1993, pp. 507-514.

7. Y. Lin and A. P. Pisano, “The differential geometry of the general helix as applied to mechanical springs,” Journal of Applied Mechanics, Vol. 55, 1988, pp. 831-836.

8. V. Yildirim, “Expressions for predicting fundamental natural frequencies of non-cylindrical helical springs,” Journal of Sound and Vibration, Vol. 252, No. 3, 2002, pp. 479-491.

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螺旋彈簧之幾何參數對勁度與應力影響之研究

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