# 臺灣博碩士論文加值系統

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 線性滑軌主要用來支撐和引導運動部件按給定的方向做往復直線運動，其結構由導軌、滑塊、滾動體等附件組成。線性滑軌具備高精度定位與低摩擦力等特性，且被廣泛運用在具有線性運動功能之機械設備上。滾柱型線性滑軌為線接觸模式相較於一般滾珠型線性滑軌的點接觸模式，在相同外徑條件下提供更高的負載能力。本文主要是研究滾柱型線性滑軌在不同材質和幾何參數對接觸應力、變形量、安全係數及模態頻率分析。利用Hertz接觸理論和理論公式，計算出滾柱型線性滑軌的接觸應力、變形量、安全係數及使用壽命。接著應用SolidWorks軟體建構滾柱型線性滑軌3D實體模型，並使用SolidWorks Simulation進行有限元素分析。針對滾柱型線性滑軌不同材質、滾柱數量和幾何參數，探討對應力、變形量、安全係數及模態頻率之影響。本研究分析結果顯示，使用理論公式與有限元素分析法都可得到相近結果，且誤差率皆小於2%內。結果顯示當滾柱數增加或滾柱直徑長度比上升時，應力與變形量皆會下降，而安全係數則會上升。本研究結果期望能有助於滾柱型線性滑軌之應用，並提供業界作為線性滑軌設計之參考。
 Linear guideways are mainly used to support and guide moving parts to perform reciprocating linear motion in a given direction. The structure is composed of guide rails, sliders, rolling elements and other accessories. Linear guideways have the characteristics of high-precision positioning and low friction, and are widely used in mechanical equipment with linear motion functions. Compared with the point contact mode of general ball linear guideway, the line contact mode of the roller type linear guideway provides a higher load capacity under the same outer diameter condition.This paper mainly studies the contact stress, deformation, safety factor and modal frequency analysis of roller-type linear guideway in different materials and geometric parameters. Using Hertz contact theory and theoretical formulas, the contact stress, deformation, safety factor and service life of the roller-type linear guideway are calculated. Then SolidWorks software was used to construct a 3D solid model of the roller-type linear guideway, and SolidWorks Simulation was used for finite element analysis. According to different materials, roller numbers and geometric parameters of roller-type linear guideways, the effects on stress, deformation, safety factor and modal frequency are discussed. The analysis results of this study show that similar results can be obtained by using the theoretical formula and finite element analysis method, and the error rate is less than 2%. The results show that when the number of rollers increases or the diameter-to-length ratio of rollers increases, the stress and deformation will decrease, while the safety factor will increase. The results of this study are expected to contribute to the application of roller-type linear guideways and provide references for design in the industry.
 致謝 I摘要 IIAbstract III目錄 IV表目錄 VII圖目錄 VIII符號說明 XII第一章 緒論 11-1前言 11-2滾柱型線性滑軌的種類與應用 41-3文獻回顧 101-4研究動機與目的 131-5論文架構 14第二章 滾柱型線性滑軌之幾何理論分析 152-1 Hertz彈性接觸理論 162-2滾柱型線性滑軌接觸應力 172-3滾柱型線性滑軌接觸變形量 192-4滾柱型線性滑軌安全係數及壽命 20第三章 滾柱型線性滑軌有限元素分析 233-1滾柱型線性滑軌3D建模 243-2 SolidWorks Simulation電腦輔助工程分析流程 253-2-1前處理(Preprocessing) 25 3-2-1-1選擇材料以及單位 25 3-2-1-2選擇滾柱型線性滑軌的接觸結合面 26 3-2-1-3滾柱型線性滑軌固定端設定 26 3-2-1-4滾柱型線性滑軌負載設定 27 3-2-2求解(Solution) 27 3-2-2-1網格 27 3-2-3後處理(Post-processing) 28 3-2-3-1執行滾柱型線性滑軌分析並探討結果 28 3-3安全係數分析 31 3-4模態頻率分析 32第四章 結果與討論 374-1正向力對滾柱型線性滑軌滾道材質之接觸應力分析 374-2正向力對滾柱型線性滑軌滾道材質之變形量分析 394-3正向力對滾柱型線性滑軌材質之安全係數分析 414-4滾柱型線性滑軌壽命評估 434-5理論公式與有限元素分析誤差比較 444-6滾柱型線性滑軌應力及變形量有限元素分析 454-7滾柱型線性滑軌安全係數有限元素分析 524-8滾柱型線性滑軌模態頻率有限元素分析 55第五章 結論與未來研究方向 585-1結論 585-2未來研究方向 59參考文獻 60
 1.上銀科技, “線性滑軌產品介紹”, https://www.hiwin.tw/ , 2022。2.D. Xu and R. Kang, “Characteristic analysis with CAE and experiment of linear rolling guideways,”2010 International Conference on Computer, Mechatronics, Control and Electronic Engineering, Vol. 2, pp. 506-509, 2010.3.J. S. Wu, J. C. Chang, G. A. Tsai, C. Y. Lin, F. M. Ou, “The effect of bending loads on the dynamic behaviors of a rolling guide,” Journal of Mechanical Science and Technology, Vol. 26, pp. 671-680, 2012.4.T. Horng, “The study of contact pressure analyses and prediction of dynamic fatigue life for linear guideways system,” Modern Mechanical Engineering, Vol. 3, pp. 69-76, 2013.5.W. Sun, X. Kong, B. Wang, “Precise finite element modeling and analysis of dynamics of linear rolling guideway on supporting direction,” Journal of Vibroengineering, Vol. 15, pp. 1330–1340, 2013.6.W. Sun, X. Kong, B. Wang, X. Li, “Statics modeling and analysis of linear rolling guideway considering rolling balls contact,” Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, Vol. 229, pp. 168-179, 2015.7.A. Shaukharova,Y. Liang, H. Feng, B. Xu, “Study of stiffness of linear guide pairs by experiment and FEA,” World Journal of Engineering and Technology, Vol. 4, pp. 115-128, 2016.8.W. Tao, Y. Zhong, H. Feng, Y. Wang, “Model for wear prediction of roller linear guides,” Wear, Vol. 305, pp. 260-266, 2013.9.D. J. Cheng, T. J. Park, S. J. Kim, “Improved friction model for the roller LM guide considering mechanics analysis,” Journal of Mechanical Science and Technology, Vol. 32, pp. 2723-2734, 2018.10.X. Song, H. Chen, H. Jiang, X. Xu, Y. Li, Y. Zhang, “Improved design of roller linear guide for heavy load based on finite element method and measurement,” Advances in Mechanical Engineering, Vol. 10, pp. 1-8, 2018.11.X. Y. Wang, C. G. Zhou, Y. Ou, “Experimental analysis of the wear coefficient for the rolling linear guide,” Advances in Mechanical Engineering, Vol. 11, pp. 1-7, 2019.12.D. J. Cheng, F. Xu, S. H. Xu, S. J. Kim, “Investigation of the frictional behavior in a roller linear motion guide under mixed EHL,” Tribology Transactions, Vol. 63, pp. 528-542, 2020.13.S. H. Xu, D. J. Cheng, S. W. Zhang, “Analysis of friction fluctuations mechanism of a preloaded roller linear motion guide based on a new 5-DOF dynamic stiffness model,” Measurement, Vol. 190, Article 110768, 2022.14.R. Teutsch, B. Sauer, “An alternative slicing technique to consider pressure concentrations in Non-Hertzian line contacts,” Transactions of the ASME, Vol. 126, pp. 436-442, 2004.15.W. Wang, Y. Zhang, C. Li, “Dynamic reliability analysis of linear guides in positioning precision,” Mechanism and Machine Theory, Vol. 116, pp. 451-464, 2017.16.R. Jirova, L. Pesik, “Dynamical load of linear rolling guides,” MM Science Journal, June, pp. 3943-3949, 2020.17.D. J. Cheng, S. H. Xu, S. J. Kim, S. W. Zhang, “Analysis of non-uniform load distribution and stiffness for a preloaded roller linear motion guide,” Mechanism and Machine Theory, Vol. 164, Article 104407, 2020.18.K. Tanaka, T. Yamazaki, “Dynamic force behavior for linear guideways with balls of different materials,” Measurement: Sensors, Vol. 18, Article 100280, 2021.19.李東益，蔡傳暉， “線性滑軌接觸預壓力之振動特性與模態分析” ，華梵大學碩士學位論文，2006。20.陳世捷，鄧昭瑞， “滾柱型線性滑軌之容差分析” ，國立台灣科技大學碩士學位論文，2011。21.李太和，龔傑， “於線性滑軌上移動結構動態特性評估” ，遠東科技大學碩士學位論文，2014。22.PMI公司, “滾珠螺桿/線性滑軌/線性模組 綜合技術型錄”，2022。23.A. Tibrewala, T. J. Padave, “Finite element analysis of components using von mises criterion for optimized inlet guide valve in Centrifugal Air Compressor,” International Journal of Advanced Research in Engineering and Applied Sciences, Vol. 3, pp. 1-21, 2014.
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 1 於線性滑軌上移動結構動態特性評估 2 滾柱型線性滑軌之容差分析 3 滾珠螺桿應力與安全係數分析 4 球面滾子軸承應力與安全係數分析

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