【摘要】：非圓齒輪既有凸輪的優(yōu)點(diǎn)又有圓柱齒輪的優(yōu)點(diǎn),廣泛地應(yīng)用在各種場合。常見的非圓齒輪有橢圓齒輪、Pascal(巴斯噶)蝸線齒輪等,其精密加工一直是研究的熱點(diǎn)。滾齒是一種最為常見的非圓齒輪加工方式,隨著對非圓齒輪精度要求的日益提高,非圓齒輪滾切加工誤差分析顯得尤為重要。對此,論文首先推導(dǎo)非圓齒輪滾切加工運(yùn)動(dòng)模型,獲得機(jī)床運(yùn)動(dòng)軸與誤差源的關(guān)系。在此基礎(chǔ)上,分析工藝誤差對非圓齒輪部分精度指標(biāo)(節(jié)曲線、齒距和根切)的影響,研究插補(bǔ)算法對非圓齒輪滾切加工的影響。根據(jù)數(shù)控伺服進(jìn)給系統(tǒng)模型,以橢圓齒輪節(jié)曲線為例,研究非圓齒輪節(jié)曲線輪廓誤差形成機(jī)理。本文的主要研究工作和獲得的結(jié)論如下： (1)根據(jù)推導(dǎo)出的非圓齒輪滾切加工運(yùn)動(dòng)模型,獲得運(yùn)動(dòng)軸與誤差源的關(guān)系。 (2)根據(jù)非圓齒輪滾切加工運(yùn)動(dòng)模型,分別推導(dǎo)工作臺(tái)轉(zhuǎn)角誤差和中心距誤差作用下非圓齒輪節(jié)曲線誤差矢量表達(dá)式,以及工作臺(tái)轉(zhuǎn)角誤差和齒條水平移動(dòng)量誤差作用下非圓齒輪齒距誤差的表達(dá)式,并進(jìn)行實(shí)例計(jì)算。 根據(jù)齒條與工件間的相對速度和嚙合方程,提出并建立非圓齒輪根切界限函數(shù)。以橢圓齒輪為例,分析非圓齒輪發(fā)生根切的極角位置和工藝誤差、設(shè)計(jì)參數(shù)對橢圓齒輪根切的影響。 (3)根據(jù)推導(dǎo)的非圓齒輪滾切加工運(yùn)動(dòng)模型,獲得非圓齒輪滾切插補(bǔ)算法,從程序段弧長和機(jī)床運(yùn)動(dòng)軸兩方面研究不同插補(bǔ)算法對非圓齒輪滾切加工的加工精度和控制難易程度的影響。為對比程序段弧長的均勻性,提出程序段弧長均勻度的概念。 (4)根據(jù)數(shù)控伺服進(jìn)給系統(tǒng)模型,以橢圓齒輪節(jié)曲線為例,分析一階、二階、高階伺服進(jìn)給系統(tǒng)動(dòng)態(tài)特性對非圓齒輪節(jié)曲線輪廓誤差的影響規(guī)律。借助數(shù)學(xué)推導(dǎo)獲得非圓齒輪節(jié)曲線輪廓誤差的形成機(jī)理。為減小輪廓誤差,提出PID交叉耦合控制方法(cross-coupled control,簡稱CCC方法)。仿真結(jié)果表明交叉耦合控制能改善非圓齒輪節(jié)曲線的輪廓精度。
[Abstract]:Non-circular gears have the advantages of both cam and cylindrical gears, so they are widely used in various situations. The common non-circular gears include elliptical gears Pascal (Basga) cochlear line gears and so on. Hobbing is one of the most common machining methods for non-circular gears. With the increasing demand for the accuracy of non-circular gears, it is particularly important to analyze the machining error of non-circular gears. In order to solve this problem, the paper first deduces the motion model of non-circular gear hobbing, and obtains the relationship between machine tool motion shaft and error source. On this basis, the influence of process error on the accuracy index (pitch curve, pitch and root cut) of non-circular gear is analyzed, and the influence of interpolation algorithm on the machining of non-circular gear is studied. According to the numerical control servo feed system model, taking elliptical gear pitch curve as an example, the forming mechanism of contour error of non-circular gear pitch curve is studied. The main research work and conclusions obtained in this paper are as follows: (1) according to the motion model of non-circular gear rolling machining, the relationship between motion shaft and error source is obtained. (2) according to the motion model of non-circular gear rolling machining, The vector expression of non-circular gear pitch curve error under the action of table angle error and center distance error, and the expression of non-circular gear pitch error under the action of table rotation angle error and rack horizontal movement error are derived respectively. An example is calculated. According to the relative velocity and meshing equation between rack and workpiece, the root tangent limit function of non-circular gear is proposed and established. Taking elliptical gear as an example, this paper analyzes the pole position and technological error of root tangent of non-circular gear, and the influence of design parameters on root cutting of elliptical gear. (3) according to the model of rolling machining of non-circular gear, The non-circular gear cutting interpolation algorithm is obtained. The influence of different interpolation algorithms on the machining accuracy and control difficulty of non-circular gear rolling machining is studied from two aspects: program segment arc length and machine tool motion axis. In order to compare the uniformity of program segment arc length, the concept of program segment arc length uniformity is proposed. (4) according to the numerical control servo feed system model, the elliptical gear pitch curve is taken as an example to analyze the first and second order. The influence of dynamic characteristics of high order servo feed system on the profile error of non-circular gear pitch curve. The forming mechanism of contour error of non-circular gear pitch curve is obtained by mathematical derivation. In order to reduce the contour error, cross-coupled control (CCC method) is proposed for PID cross coupling control. The simulation results show that the cross coupling control can improve the contour accuracy of the non-circular gear pitch curve.
【學(xué)位授予單位】：蘭州理工大學(xué)
【學(xué)位級別】：博士
【學(xué)位授予年份】：2013
【分類號】：TH132.424;TG612
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本文編號：2187078