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  本文選題：非圓齒輪 + 齒形接觸分析　； 參考：《哈爾濱工業(yè)大學(xué)》2013年碩士論文

【摘要】：隨著計算機(jī)技術(shù)和數(shù)控加工的發(fā)展，非圓齒輪的設(shè)計和加工變得越來越容易。但是，根據(jù)齒輪副的實際齒廓精確計算其嚙合過程，評價其傳動性能的方法在非圓齒輪副傳動中是一個空白。為了解決這一問題，本論文從非圓齒輪齒廓離散數(shù)據(jù)點入手，通過曲線擬合得到非圓齒輪齒廓的統(tǒng)一數(shù)學(xué)描述，基于齒廓嚙合原理進(jìn)行非圓齒輪傳動數(shù)值模擬，構(gòu)建了完整的非圓齒輪TCA(Tooth Contact Analysis，齒廓接觸分析)方法。 針對非圓齒輪齒廓不能像圓柱齒輪一樣有精確的數(shù)學(xué)公式描述，論文中提出了將所有形式的非圓齒輪用其齒廓離散點為樣條端點的分段三次樣條函數(shù)統(tǒng)一表達(dá)，并且推導(dǎo)出了同一齒廓在旋轉(zhuǎn)運動中的分段三次樣條系數(shù)變換公式。 TCA過程的核心是主動齒輪齒廓與被動齒輪對應(yīng)齒廓傳動的數(shù)值計算。用兩條光滑分段三次樣條來描述主、被動輪齒廓，當(dāng)主動齒轉(zhuǎn)到一個角度，計算被動齒與其滿足齒廓嚙合定律時的角度，從而完成主動齒與被動齒傳動的嚙合計算過程。嚙合計算的本質(zhì)是迭代判斷兩條分段三次樣條在平面中的位置關(guān)系，整個過程分為粗略判斷(幾何法)和精確判斷(解非線性方程組)。為了提高粗略判斷效率，提出了三次樣條外接矩形的概念。同時，考慮到實際齒輪傳動有可能有多對齒同時參與嚙合，由誤差控制準(zhǔn)則，給出了考慮主動輪與被動輪所有齒廓的嚙合傳動計算方法。 由TCA過程計算的嚙合點、轉(zhuǎn)角值、參與嚙合齒對數(shù)、嚙合齒序號等中間數(shù)據(jù)，可以精確得到瞬時重合度、滑動系數(shù)、傳動比、反向間隙值等非圓齒輪齒廓傳動的重要性能參數(shù)，為非圓齒輪副的設(shè)計校驗提供了具體的量化數(shù)據(jù)。這樣可以為非圓齒輪設(shè)計縮短時間，，提高設(shè)計的可靠性，有利于非圓齒輪的進(jìn)一步推廣應(yīng)用。
[Abstract]:With the development of computer technology and NC machining, the design and machining of non-circular gears become more and more easy.However, according to the actual tooth profile of the gear pair, the meshing process is accurately calculated, and the method of evaluating its transmission performance is a blank in the non-circular gear pair transmission.In order to solve this problem, this paper starts with discrete data points of non-circular gear tooth profile, obtains unified mathematical description of non-circular gear tooth profile by curve fitting, and carries out numerical simulation of non-circular gear transmission based on tooth profile meshing principle.A complete method of TCA(Tooth Contact analysis (tooth profile contact analysis) for noncircular gears was constructed.In view of the fact that the tooth profile of a non-circular gear can not be described precisely as a cylindrical gear, a piecewise cubic spline function is proposed in this paper, in which all forms of non-circular gear are expressed as splines with discrete points of tooth profile as spline endpoints.The piecewise cubic spline coefficient transformation formula of the same tooth profile in rotating motion is derived.The core of the TCA process is the numerical calculation of the gear profile corresponding to the passive gear.Two smooth piecewise cubic splines are used to describe the tooth profiles of active and passive gears. When the active teeth turn to an angle, the angle between the passive teeth and the active teeth satisfying the tooth profile meshing law is calculated, thus the meshing calculation process between the active teeth and the passive gear drives is completed.The essence of meshing calculation is to iteratively judge the position relation of two piecewise cubic spline in the plane. The whole process is divided into rough judgment (geometric method) and accurate judgment (solving nonlinear equations).In order to improve the efficiency of rough judgment, the concept of cubic spline external rectangle is proposed.At the same time, considering that the actual gear transmission may have more than one pair of teeth in the meshing at the same time, according to the error control criterion, the calculation method of the meshing transmission considering all the tooth profiles of the active wheel and the passive gear is given.The important performance parameters of non-circular gear profile transmission, such as instantaneous coincidence degree, slip coefficient, transmission ratio, reverse clearance value and so on, can be accurately obtained from the meshing point, rotation angle value, the number of meshing teeth and the number of meshing teeth calculated by the TCA process.The quantitative data are provided for the design check of non-circular gear pair.This method can shorten the design time, improve the reliability of the design, and be beneficial to the further popularization and application of the non-circular gear.
【學(xué)位授予單位】：哈爾濱工業(yè)大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2013
【分類號】：TH132.41

【參考文獻(xiàn)】

相關(guān)期刊論文 前5條

1 高雪強(qiáng);石建玲;崔振勇;;三維環(huán)境下高階橢圓齒輪副的運動仿真[J];工程圖學(xué)學(xué)報;2010年04期

2 唐德威,于紅英,李丹,徐曉俊,李華敏,張光輝;插齒刀加工的非圓齒輪過渡曲線干涉分析[J];哈爾濱工業(yè)大學(xué)學(xué)報;2002年05期

3 李寶妮;張迎春;;非圓齒輪的應(yīng)用及其發(fā)展動向[J];機(jī)床與液壓;2008年04期

4 崔希烈;;非圓齒輪齒廓分析(二)[J];齒輪;1986年01期

5 徐曉俊，唐德威，陳卓如，高業(yè)田，李華敏;非圓齒輪副重合度的精確計算方法[J];機(jī)械傳動;1995年02期

本文編號：1741149