汽車扭力樑強度與疲勞特性之有限元素法分析

Finite Element Analysis on the Strength and Fatigue Properties of an Automotive Twist Beam

謝志輝(Chih-Hui Hsieh)

指導教授 ： 陳復國

國立臺灣大學/工學院/機械工程學研究所/碩士(2018年)

https://doi.org/10.6342/NTU201803859

摘要

後懸吊系統在車輛系統中扮演重要角色，可決定車輛之舒適度及操作性，因此其在設計及分析中受到業界之重視。設計，能經由扭力樑造型修改以達到期望之性能；分析，可透過CAE有限元素軟體建立準確分析，以有效率方式瞭解其設計扭力樑之性能是否可行。
本論文討論扭力樑強度分析方法之建立，由於知道不同元素或種類對於分析結果會有很大差異，因此本論文探討使用不同元素種類進行扭力樑強度分析，並得出最佳元素種類建議。由研究可知，對殼元素而言建議使用一階線性四邊形減積分；對實體元素而言建議使用一階線性六面體非協調性積分，以此兩種元素能快速且得到準確之結果。
透過確定分析模型正確性後，可進一步了解扭力樑在進行強度分析之受力機制，透過等效受力方法將其受力大致分成扭轉與彎曲，可知其中又以扭轉為造成扭力樑應力大之原因。了解其受力情形後，為能更進一步應用於所有扭力樑，因此建立簡化分析以利在僅有單支扭力樑下時使用，其方法可透過對等效受力方向施予扭轉力矩或角度進行分析以了解扭力樑之性能。
本論文除常見靜態分析外亦探討動態工況分析，透過分析結果可知，依據工況設計扭力樑變形情形大致可分為扭轉與彎曲，而其中又以左側深坑與左轉工況受力最大。
後懸吊系統在進行設計時最重要兩項分析分別為強度分析以及疲勞分析，強度分析可了解其性能並與產品壽命有一定指標性，但仍無法準確瞭解其疲勞壽命，因此本論文將討論透過建立材料疲勞試驗之模型分析並與真實試驗驗證以確立分析準確性。一般在汽車產業中進行
S-N曲線疲勞試驗大多應力比值R為0.1，此對於分析時使用會造成困難，須透過平均應力公式修正，這邊建議使用modified Gerber平均應力公式修正，再透過假設疲勞強度為0.5倍抗拉強度可推得其R=-1之S-N曲線，在進行單軸受力分析問題時應力指標可使用von Mises stress或Max principal stress，而平均應力修正式建議使用Gerber修正式，此分析結果與真實試驗接近。
由於S-N曲線取得不易且耗時，此為疲勞分析最大困難處，因此此論文討論出幾種預測S-N曲線之方法並應用，這邊透過與真實試驗比較可知，針對材料S550MC使用Schijve’s method與試驗結果最接近。
確立其疲勞分析之方法後，可對扭力樑台架試驗進行疲勞分析，由結果可知，在多軸受力情形下，使用不同應力指標其疲勞壽命結果不同，使用Max von Mises stress可能會有虛假破裂處之結果，而使用Max principal stress其結果則會過於保守，但其計算方式較可靠，因此可使用Max principal stress確定破裂發生處，再配合使用von Mises stress以得其疲勞壽命。
最後，由於已知扭力樑強度與疲勞有直接之關聯性，因此本研究將不同扭力樑應力與疲勞壽命討論其關連性，可知此兩參數成指數關係，也就是說當應力越低時，其影響疲勞壽命之變化越大。
一般來說，業界會依據車型需求訂定扭力樑疲勞壽命要求，多會以17.5萬次或加嚴標準24萬次，透過前面討論強度與疲勞之趨勢關係可知，其應力要求需分別低於392.0MPa或371.4MPa才能符合要求。

關鍵字

後懸吊系統 ； 扭力樑強度分析 ； 扭力樑受力機制 ； 有限元素法 ； 疲勞試驗 ； 推估S-N曲線之方法 ； 平均應力修正式 ； 應力比值 ； 後懸吊系統疲勞分析

並列摘要

Rear wheel suspension system play an important role in vehicle system. It can determine the comfort and operability of the vehicle. Therefore, it received the attention of industry in design and analysis. About design, it can achieve the desired performance by modified the shape of torsion beam; About accurate analysis, it can be established by CAE finite element software. Use efficient way to understand whether the performance of the design for the torsion beam is feasible or not.
This study discusses the establishment of the strength analysis method for torsion beam. Since it is known that different element types will make serious difference in analysis result, this study explores the strength analysis of torsion beam by using different element types and achieves the best suggestion of element types. According to the study, first-order linear quadrilateral reduced integration is recommended for shell element; First-order linear hexahedral incompatible integrals are recommended for solid elements. These two element types can quickly and accurately achieve the result.
After determining the correctness of the analytical model, we can further understand the dynamic mechanism of the torsion beam in strength analysis. The force mechanism is roughly divided into torsion and bending by the equivalent force method. It can be known that the twisting is the main reason to cause stress on torsion beam. By understanding the condition of the mechanism, it can further more applicate on every torsion beam.
Therefore, this study establishes a simplified analysis to use when there is only a single torsion beam. The method can be used to find out the performance of torsion beam by applying a torsional moment or angle of equivalent parameter.
In addition to the common static analysis, this paper also discusses dynamic working conditions analysis. According to the analysis results, we can know that the deformation of the torsion beam can be roughly divided into torsion and bending according to the working conditions. Among them, the stress on the left side deep pit and the left turn condition is higher.
The two most important analyses of the rear suspension system are strength analysis and fatigue analysis. Strength analysis can understand its performance and have representative indicator with product life, but still can not accurately understand its fatigue life. Therefore, this paper will discuss the establishment of material fatigue test model analysis and verification with real test to confirm the accuracy of the analysis. Generally, in the automotive industry, the stress ratio R of S-N curve fatigue test is 0.1, which is difficult to use for analysis and must be corrected by the mean stress correction. It is recommended to use the modified Gerber mean stress correction, and then the S-N curve with R=-1 can be derived by assuming a fatigue strength of 0.5 times the tensile strength. The stress indicator can use von Mises stress or Max principal stress when performing uniaxial stress analysis problems. The mean stress correction suggests to use the Gerber mean stress correction which analysis result is close to the actual test.
Since the S-N curve is not easy to obtain and time consuming, this is the most difficult part of fatigue analysis. Therefore, this study discusses several methods for predicting the SN curve and applies them. Comparing with the actual test, the Schijve's method is the closest to the test results for the material S550MC.
The torsion beam bench test can be performed fatigue analysis after determining the method of fatigue analysis. In the case of multi-axial stress, the fatigue life results are different using different stress indicators. Using von Mises stress might cause spurious hot spots. Using Max principal stress will be too conservative, but its calculation method is more reliable. Therefore, the Max principal stress can be used to determine where the crack occurs, and then use von Mises stress to obtain its fatigue life.
Finally, since the strength of torsion beam is known to be directly related to fatigue, this study discusses the relationship between different stresses and fatigue life. It can be seen that the two parameters are exponential, that is to say, the lower the stress, the greater the change in fatigue life.
In general, the industry will set the fatigue life requirements of torsion beam according to the needs of the vehicle model. Fatigue life target will be more than 175,000 times or tightened standard 240,000 times. Through the discussion of the relationship between strength and fatigue, the stress requirements must be lower than 392.0 MPa or 371.4 MPa to meet the target.

並列關鍵字

rear suspension system ； torsion beam strength analysis ； torsion beam dynamic mechanism ； finite element method ； fatigue test ； method for estimating the S-N curve ； mean stress correction ； stress ratio ； fatigue analysis of rear suspension system

參考文獻

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