線性滑軌的剛性分析

The Rigid Analysis of Linear Guide

楊宜興(Yi-Xing Yang)

指導教授 ： 單秋成

國立臺灣大學/工學院/機械工程學研究所/碩士(2013年)

https://doi.org/10.6342/NTU.2013.10743

摘要

現代自動化應用要求移動裝置要有高速、高精度、低耗能的優良性能，而幫助達成此一要求的重要元件為線性滑軌，線性滑軌經過了二十多年的發展，具有結構緊湊、動摩擦係數小、承載能力大、安裝簡便、定位精度高、傳動平穩等優點。做為自動化應用的支撐部件、數位控制機床的應用越來越廣泛。而影響線軌精度之一關鍵性質為其剛性，因此透過對線性滑軌剛性的分析與驗證，對提高其性能的措施具有重要的意義。
本研究以理論分析、有限元素模擬、實驗驗證三個方面進行交互佐證，探討了市售六種不同負載等級的線性滑軌受靜態負載時，其剛性變化的情況，其細節如下:
一、根據線性滑軌的結構特點以及線性滑軌其力學狀態，利用赫茲接觸理論為基礎，分析鋼珠與滑塊、滑軌的接觸狀態，推導出負載與滑塊、滑軌間的相對位移量的關係。
二、使用有限元素法軟體Abaqus對此問題進行模擬分析。
三、以實驗的方式進行驗證，設計適當的位移計，利用萬能試驗機MTS810施加負載，量測滑塊與滑軌間的相對位移量。
將理論、模擬、實驗得到的數值互相佐證。確立三者數據的可信度。目前理論解與有限元素法模擬得到的數據已有吻合。兩者的誤差值在6%以下。藉由比較理論推導時使用的假設與模擬得到的數據，可以判斷假設是否合理。再加上實驗數據做為依據，再次討論理論與模擬的結果是否合理。最後可利用理論解估計線性滑軌的剛性。可減少模擬、實驗的成本。

關鍵字

線性滑軌 ； 剛性 ； 赫茲接觸 ； 球接觸 ； 有限元素

並列摘要

Modern industrial automation requires high-speed and high-precision and low energy consumption performance. Linear guide is an important component to achieve the purpose. Linear guide has a lot of features like compact structure, small dynamic friction coefficient, large carrying capacity, easy installation, high positioning accuracy and smooth transmission. The linear guide as an industrial automation supporting member, digital control machine tools get more widely. The rigid of the linear guide is a pivotal property to the accuracy. Therefore, through this research which analyzes and verifies the rigid of linear guide, we can improve its performance which is significant.
Observing the stiffness changing of the linear guide which endure static load is the topic of the research. There are six types of commercial linear guide which will be discussed in this research We will interact evidence in three aspects, theoretical analysis, finite element simulation, experiment. Details are as follows:
First, according to the structural characteristics of the linear guide and its mechanical state. We will simplify the model of the problem and analyze the contact condition of the ball between roller and slide by using Hertz contact theory. Driving the relationship of the load and relative displacement between roller and slide.
Second, using the finite element software, Abaqus, to simulate this problem.
Third, verifying the above results by experiment. Reference to theoretical solutions and finite element simulation's results. Designing an appropriate measuring tools and using material test systems to apply load on the linear guide. Measuring the relative displacement of the roller and the slide.
We will interact evidence in three aspects, theoretical analysis, finite element simulation, experiment. Unit now, theoretical solutions and finite element simulation solutions has been confirmed. The difference between theoretical solutions and finite element simulations are less than 6%. We can estimate the correction about assumption of theoretical derivation by comparing finite element simulation's data. Furthermore, according to the experiment data, we can estimate if aforementioned data was reasonable. Finally, establishing the credibility of the three data. We can only use theoretical solutions to accurately estimate the rigidity of the linear guide, and reduce the cost on the simulation and experiments

並列關鍵字

linear guide ； stiffness ； Hertz contact ； ball contact ； finite element

參考文獻

[1] Miko NAKAI, Masayuki YOKOI etc. Squealing of Cylindrical Roller Bearing. JSME Series3,1991,3:72-81

[2] T.E. Tallian Spalling Life Model With Relaxed Distribution Constraints , for Rough

Element Analyses of the Forced Response of A Frictionally Damped Beam, J. of

Journal No.664(1997):1-13

[7] S. Asaietal. Precision Linear Guide for Machine tools. NSK Technical Journal No.