Please use this identifier to cite or link to this item: http://hdl.handle.net/11455/1841
標題: 歌德曲面與球面接觸變形之探討
An Investigation on the Contact Deformation of Gothic and Spherical Surfaces
作者: 朱元一
Chu, Yuan Yi
關鍵字: Gothic profile surface;歌德曲面;contact;preload;interference;experience formula;接觸;預壓力;干涉量;經驗公式
出版社: 機械工程學系所
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摘要: 
歌德曲面為特殊曲面,與其它曲面接觸時具有多接觸點接觸較穩定的優點,故廣泛應用在各式傳動元件,如滾珠螺桿與線性滑軌。然而應用歌德曲面之傳動元件需有預壓力以產生運動剛性,故上述元件裝配時採用干涉配合,使接觸元件間產生預壓力以掌控其運動性能,本研究目標即在於探討歌德曲面與球面接觸之預壓力與干涉量之關聯性,並設計實驗進行比較。
本研究首先建構歌德曲面與球面接觸之模型,並以Hertz接觸模式與有限元素法進行理論分析,結果顯示兩曲面間的干涉量增加時,其接觸區域之接觸力呈現非線性增加。本研究進一步設計實驗以比對理論分析之合理性,實驗使用半徑10.287mm之雙凹球面歌德曲面,選用配合之鋼珠直徑由19.035mm增加至19.06mm,鋼珠直徑間距為5μm,施加之作用力分別由21.2N至增加282.8N。實驗結果顯示,作用力增加時,變形量隨作用力增加而呈非線性提升,此結果與Hertz接觸模式分析之趨勢相同;唯實驗結果之變形量較理論值高,推估主要原因為Hertz接觸模式假設接觸點未變,與實驗之實際狀況稍有出入。故本研究依據實驗結果進一步歸納出不同牙型係數之歌德曲面與球面接觸變形量及接觸剛性與接觸力之經驗公式,可供利用歌德曲面所設計之傳動元件,包括滾珠螺桿與線性滑軌之參考。

Gothic profile surface is a special surface that provides multi contact points with other surface and thus widely used in precise transmission components, such as ballscrew and linear guide. However, as the transmission component needs preload between moving elements to provide motion stiffness, interference assembly is introduced in these transmission compoments. This research is aimed to investigate the relationship between the preload and the interference of Gothic and spherical surfaces. Experiments are also designed and conducted as a comparison with the theoretical analysis.
The contact model of Gothic and spherical surfaces is first constructed and analyzed by Hertz contact model as well as by finite element method. The results reveal that the contact force increases, non-linearly, as the interference increases. Experiments measuring the force and the deformation of a fixture, with dual-spherical Gothic surfaces of radius 10.287mm, in contact with different steel balls are designed and conducted. The diameters of these steel balls are from 19.035mm to 19.06mm in 5μm increment with contact forces ranging from 21.2N to 282.2N. The experimental results showed that the deformation increases nonlinearly when contact force increases, in consistent with Hertz model. Nevertheless, the measured deformations are higher than theoretical values due to slippings between the contact elements in the experiments. The experience formula of deformation and stiffness with respect to the contact force for different profiles form factor are derived from the experimental data as a reference for the design and analysis of transmission components.
URI: http://hdl.handle.net/11455/1841
其他識別: U0005-1308200713123100
Appears in Collections:機械工程學系所

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