齒盤型態自行車傳動系統齒數比設計程序之研究

Abstract

國外自行車傳動零件大廠不斷推陳出新，國內自行車傳動零件製造廠為了提升競爭能力，須要一套設計程序用來設計具多齒數比的新傳動系統。然而國內自行車傳動零件製造廠在研發上，卻未針對傳動系統齒數比的設計方法，進行深入探討與研究。因此，本研究首先探討齒數比對人因及機構兩方面的影響，並以此為基礎，提出一齒盤型態自行車傳動系統齒數比之系統化設計程序。 當齒盤型態傳動系統的齒盤數增加，齒數比數量隨之增加，而換檔的複雜度也隨之增加。此時對騎乘者造成的困擾是：不知道該何時換檔？以及不知道該換到哪一檔？本研究提出最佳換檔時機的計算方式及最佳換檔策略的發展方式，以解決上述兩個問題。當騎乘者的踏速需要作改變，而進行換檔的時候，即稱為換檔時機，換檔前與換檔後騎乘者踏速的差距即稱為踏速區間寬度。騎乘者在騎乘過程中，從傳動系統所提供的所有齒數比中，選取數個作為實際會使用到的齒數比，此齒數比集合即稱為換檔策略。每一個換檔策略具有數個踏速區間寬度，其寬度平均值及標準差之權重和為最小者，即為最佳換檔策略。因此一套齒盤型態傳動系統的最佳人因品質，可以以其最佳換檔策略的權重和的大小來評比。至於在最佳機構品質的定義上，則以齒盤間換檔路徑的數目多寡來決定，其數目越多，則表示換檔所需時間越短。此系統化設計程序，以最佳換檔策略內的踏速區間寬度平均值及標準差之權重和，作為最佳化目標函數，以各齒片間所含換檔路徑數目作為最佳化限制條件，同時以齒數作為設計變數，由於齒盤的齒數為整數，因此選擇基因演算法求取最佳解。如此，藉由此設計程序所產出的齒盤型態傳動系統齒數比，便具有最佳之人因及機構設計的特性。

The manufacturers of bicycle transmissions in Taiwan need a design procedure of the freewheel-type bicycle transmission to develop new transmissions with plenty of gear ratios to promote their competition ability. However, these manufacturers did not make a study of the design procedure of gear ratios of a freewheel-type bicycle transmission in the past. On account of this reason, this study focuses on the ergonomic and mechanical analysis on the gear ratios and then proposes a systematic design procedure of a freewheel-type bicycle transmission. The number of gear ratios and the complexity of gear shifting increases with the number of sprockets provided by a freewheel-type bicycle transmission. The complexity may make a cyclist feel confused by when to shift gear and which gear to be shifted to. This study proposes the calculation of the shifting point and the development of the optimum shifting strategy to solve these problems. The shifting point represents the time at gear shifting. The difference between cadences before and after shifting is a cadence spread. To decrease the complexity of shifting, a cyclist may choose several gear ratios from all gear ratios provided by a freewheel-type bicycle transmission. These chosen gear ratios compose a shifting strategy. The shifting strategy whose weight sum of mean and standard deviation of cadence spreads is minimum is the optimum shifting strategy. Therefore, the ergonomic quality of a freewheel-type bicycle transmission can be defined as the weight sum of its optimum shifting strategy. On the other hand, the mechanical quality can be defined as the number of shifting path between two sprockets. The shifting time decreases while the number of shifting path increases. In this study, the weight sum of mean and standard deviation of cadence spreads in the optimum shifting strategy is defined as a cost function in the systematic design procedure. Besides, the number of shifting path between two sprockets is treated as a constraint. Meantime, the number of gears on each sprocket is regarded as a design variable. Since the design variables are integers, this procedure finds an optimum solution by genetic algorithm. Consequently, this procedure generates the freewheel-type bicycle transmission with the optimally ergonomic and mechanical qualities.