- 學位論文
平面凸輪機構之機械誤差分析及其應用
Analysis of Mechanical Errors in Planar Cam Mechanisms and Its Applications
摘要
凸輪機構已被廣泛地應用於各種機器與機械裝置中。至今，凸輪仍在機械工業中扮演不可取代的重要角色。由於凸輪為不規則形狀的機械元件，其輪廓較不容易被精確地加工。因此，凸輪輪廓的公差設定及誤差檢測成為設計與製造精密凸輪機構時的重要工作。 凸輪機構的機械誤差分析旨在建立各設計參數之公差量（或偏差量）與從動件運動誤差之間的理論關係。換言之，機械誤差分析為精密凸輪機構之公差設計的基礎。本論文的主要目的為提出一套簡易且有系統的解析方法以進行平面凸輪機構的機械誤差分析。此解析方法並可延伸應用於平面凸輪機構的公差最佳化配置，以及應用於盤形凸輪與共軛凸輪的輪廓誤差檢測。 首先，藉由等效連桿的概念，以及透過凸輪輪廓的徑向尺寸誤差與法線方向誤差間之理論關係的建立，本研究發展出一套稱為等效連桿法的解析方法以預測由盤形凸輪機構之各設計參數偏差量所導致的從動件運動誤差。此方法可以簡易且有系統地進行平面凸輪機構的機械誤差分析，以推導出從動件的位置、速度及加速度誤差方程式。此方法透過分析一個具有確切解的偏心圓凸輪機構以及評估一個因誤用從動件運動曲線所導致之凸輪輪廓誤差的誇張案例以進行理論上的驗證。然後，此方法透過四種常用盤形凸輪機構及一平面凸輪從動件式取放裝置的機械誤差分析以進行演示。 其次，結合等效連桿法以及易製性與易組裝性設計的概念，本研究發展出一套平面凸輪機構的公差最佳化配置程序。此最佳化程序的目標在於使凸輪機構達到最大的易製性與易組裝性，同時確保從動件維持所需的運動精度。此最佳化程序透過一平面凸輪從動件式取放裝置的公差配置以進行演示。 再者，為了檢測盤形凸輪的輪廓誤差，本研究提出一直接且簡潔的解析方式以處理由三次元量床所量得的座標量測資料。此方法是基於盤形凸輪輪廓的徑向尺寸誤差與法線方向誤差間之理論關係。為了驗證此方法，一對盤形共軛凸輪的檢測實驗被加以進行。由此方法所得到的實驗結果與Hermite內插法進行比較。結果顯示此方法可以精確且更有效率地處理座標量測資料以進行盤形凸輪的輪廓誤差檢測。 本研究亦說明如何使用特殊的檢測治具以量測組裝式共軛凸輪機構之共軛條件，以間接地評估共軛凸輪輪廓的誤差量；對於這種間接量測方法，所需要的量具只有針盤指示錶。對於被檢測的共軛凸輪機構，利用等效連桿法，可推導出共軛條件變化量與凸輪輪廓誤差量之間的理論關係。基於此理論關係，用於組裝式共軛凸輪之品質管制的保守準則被加以提出。此間接量測方法特別適用於大量生產之共軛凸輪的品質管制。此外，如果能額外再備有一對已知輪廓誤差之樣板共軛凸輪的話，則透過檢測由一個樣板凸輪併合另一個是待檢測凸輪所搭配組成之共軛凸輪時所量得的共軛條件變化量，將可以估算出待檢測凸輪的輪廓誤差。此間接量測方法透過兩實例以進行演示。同時，一對盤形共軛凸輪透過此方法以進行檢測，並使用三次元量床進行量測，以測試此方法的精確度。結果顯示預測值與實驗值之間具有相當良好的吻合度。 綜合以上所述，本論文提供簡單且有效率的方法以進行各種盤形凸輪與共軛凸輪的機械誤差分析、公差配置與輪廓誤差檢測。
並列摘要
Cam mechanisms have been applied in a wide variety of machines and mechanical devices. Up to now, cams still play an important role in the mechanical industry and cannot be superseded. Because cams are irregular-shaped mechanical components, their profiles cannot be accurately machined with relative ease. Therefore, the cam profile tolerancing and error inspection become important tasks in the design and manufacture of precision cam mechanisms. The purpose of the mechanical error analysis of the cam mechanism is to establish the theoretical correlation between the tolerance (or deviation) of each design parameter and the follower motion deviation. That is, the analysis of mechanical errors is a fundamental of tolerance design of precision cam mechanisms. The main purpose of this dissertation is to present a relatively simple and systematic analytical method to perform the mechanical error analysis of planar cam mechanisms. This analytical method can also be extended to apply to the optimal tolerance allocation for planar cam mechanisms and to the profile error inspection of disk cams and conjugate cams. Firstly, by employing the concept of equivalent linkage and the derived correlation between the radial-dimension errors and the normal-direction errors of the cam profile, an analytical method, called the equivalent linkage method, is developed to analytically predict the kinematic errors of the follower caused by the deviation in each design parameter of planar cam mechanisms. This method can effectively and systematically perform the mechanical error analysis of planar cam mechanisms to obtain the displacement, velocity, and acceleration error equations of the follower motion. Here, this method is validated through analyzing an eccentric circular cam mechanism whose exact solution is available, and also examined through evaluating the profile error of an exaggerated case whose relatively large profile error is caused by adopting an incorrect follower motion program. Then the method is illustrated through analyzing the mechanical errors of all four types of commonly used disk cam mechanisms and a planar cam-follower type pick-and-place device. Secondly, by incorporating the equivalent linkage method and the concept of design for manufacture and assembly (DFMA), this study develops a procedure of optimal tolerance allocation for planar cam mechanisms. The objective of this optimal procedure is to maximize the manufacturability and assembility of the cam mechanism while maintaining acceptable kinematic accuracy of the follower motion. This optimal procedure is illustrated by allocating the tolerances in a planar cam-follower type pick-and-place device. Furthermore, in order to inspect the profile deviations of disk cams, a direct and concise analytical method for dealing with the coordinate measurement data obtained from a coordinate measuring machine (CMM) is proposed. The method is based on the derived correlation between the radial-dimension errors and the normal-direction errors of disk cam profiles. To verify this method, an experiment of inspecting a pair of conjugate disk cams was conducted. The experimental results obtained from the proposed method were compared with those obtained by using the Hermite interpolation method. It shows that this method is accurate and more efficient for dealing with the coordinate measurement data to inspect the profile errors of disk cams. This study also demonstrates how to use a special measuring fixture to measure the conjugate condition of an assembled conjugate cam mechanism so as to indirectly evaluate the deviations of conjugate cam profiles; for such an indirect measurement method, the only required measuring instrument is a dial indicator. For a conjugate cam mechanism being examined, by employing the equivalent linkage method, the correlation between the conjugate condition variations and the cam profile errors can be derived analytically. Based on the correlation, conservative criteria for qualify control of assembled conjugate cams are proposed. This indirect measurement method is particularly suitable for the quality control in mass production of conjugate cams. Furthermore, if a pair of master conjugate cams with known profile errors is additionally available, through the measured conjugate condition variations of a pair of assembled conjugate cams consisting of one master cam and the other being an inspected cam, then the profile errors of each individual inspected cam can be estimated. This indirect measurement method is illustrated by two examples. Also, a pair of conjugate cams were examined by the method and also measured using a CMM to test the accuracy of the method. It shows quite a good agreement between prediction and experimental results. In summary, this dissertation provides simple and efficient means for analyzing the mechanical errors, for allocating the tolerances, and for examining the profile errors of various types of disk cams and conjugate cams.