本文選題：螺旋錐齒輪 + 產(chǎn)形線切齒法　； 參考：《吉林大學(xué)》2014年博士論文

【摘要】：螺旋錐齒輪用于傳遞相交軸的運(yùn)動(dòng)與動(dòng)力，相比于直齒錐齒輪，螺旋錐齒輪具有重合度大、承載能力高、傳動(dòng)平穩(wěn)、強(qiáng)度高，對(duì)安裝誤差的敏感性小等優(yōu)點(diǎn)，廣泛應(yīng)用于艦船、航空和國防技術(shù)裝備以及汽車，機(jī)床、工程機(jī)械和礦山機(jī)械等各種機(jī)械產(chǎn)品中。螺旋錐齒輪的加工技術(shù)一直受到廣泛的關(guān)注。成立于1865年的美國格里森公司，是國際上錐齒輪加工機(jī)床和技術(shù)的主要領(lǐng)跑者，它所生產(chǎn)的螺旋錐齒輪是目前應(yīng)用最廣泛的一種錐齒輪。由于格里森公司固有的加工原理，使得機(jī)床結(jié)構(gòu)非常復(fù)雜，加工調(diào)整計(jì)算十分繁雜、困難，是最難以操作使用的機(jī)床之一。另一方面，格里森的“近似替代”和“局部共軛”原理導(dǎo)致加工的兩齒面往往不能正確嚙合，出現(xiàn)接觸區(qū)不良、噪音增大、強(qiáng)度下降等弊端。為了改善齒輪的嚙合狀態(tài)，獲得較好的接觸區(qū)，需要對(duì)機(jī)床和刀具進(jìn)行復(fù)雜的調(diào)整和反復(fù)的試切、檢驗(yàn)，增加了制造成本，加工一對(duì)齒輪的生產(chǎn)周期長，且齒輪需要配對(duì)使用。這樣加工出來的齒輪不是球面漸開線齒形，因而也就不具備互換性、瞬時(shí)傳動(dòng)比恒定等優(yōu)良特性。 本文的研究基于產(chǎn)形線切齒法原理，利用產(chǎn)形線切齒原理可以獲得具有球面漸開線齒廓的螺旋錐齒輪。球面漸開線是錐齒輪的理論齒廓，具有漸開線齒廓的一切優(yōu)良特性。產(chǎn)形線切齒法原理提供了球面漸開線螺旋錐齒輪的切齒方法和切齒裝備的設(shè)計(jì)制造方案。本文在上述研究工作的基礎(chǔ)上，從空間嚙合原理出發(fā)，對(duì)這種新型球面漸開線螺旋錐齒輪的接觸和嚙合狀態(tài)進(jìn)行了分析和研究。螺旋錐齒輪的嚙合特性和接觸分析對(duì)傳動(dòng)性能有很大影響，直接影響齒輪的使用和加工，因此有必要對(duì)其開展深入的研究。本文的研究?jī)?nèi)容主要包括以下幾個(gè)方面： （1）系統(tǒng)研究了球面漸開線螺旋錐齒輪的齒面生成運(yùn)動(dòng)過程，闡述了左旋、右旋以及凸、凹齒面形成的切齒運(yùn)動(dòng)關(guān)系。在此基礎(chǔ)上，運(yùn)用坐標(biāo)變換原理推導(dǎo)了齒面的數(shù)學(xué)模型，從嚙合原理的角度對(duì)所推導(dǎo)的右旋凹齒面方程進(jìn)行了分析，給出了嚙合方程、接觸線方程和與之共軛的左旋凸齒面方程的表達(dá)式。并對(duì)接觸線方程與產(chǎn)形線方程的同一性進(jìn)行了對(duì)比分析。這部分研究?jī)?nèi)容從理論上為產(chǎn)形線切齒法原理提供了支持，同時(shí)也是開展齒面研究和接觸分析的基礎(chǔ)。 （2）對(duì)所推導(dǎo)的左、右旋凸、凹齒面的嚙合特性進(jìn)行了研究，計(jì)算了各自曲面的法曲率，主曲率、確定了主方向，計(jì)算了理論上線接觸的螺旋錐齒輪齒面的誘導(dǎo)法曲率，推導(dǎo)了曲面的曲率干涉界限線和嚙合界限線的表達(dá)式。為進(jìn)一步研究齒面接觸區(qū)的調(diào)整提供依據(jù)。 （3）對(duì)于理論上線接觸共軛的球面漸開線螺旋錐齒輪提出了通過改變產(chǎn)形線半徑將線接觸轉(zhuǎn)化為點(diǎn)接觸的接觸區(qū)調(diào)整方法。分析并推導(dǎo)了產(chǎn)形線半徑的計(jì)算公式，對(duì)調(diào)整后的點(diǎn)接觸共軛齒面的誘導(dǎo)法曲率計(jì)算公式進(jìn)行了推導(dǎo)，為輪齒接觸分析奠定了基礎(chǔ)。 （4）采用輪齒接觸分析（TCA）方法對(duì)調(diào)整后的點(diǎn)接觸共軛齒輪副的接觸區(qū)進(jìn)行了模擬。首先將兩齒面方程及法向量方程轉(zhuǎn)化至同一坐標(biāo)系中，建立由矢量方程表示的接觸方程。其次將矢量方程表示的接觸方程轉(zhuǎn)化為數(shù)量方程并運(yùn)用MATLAB軟件進(jìn)行非線性方程組的求解，求解的方法是迭代法，為此需要確定合理的迭代初值，文中分析了迭代初值的選擇方法。最后將非線性方程組的求解結(jié)果以圖形的形式進(jìn)行表達(dá)，獲得了接觸跡線，為了獲得更直觀的接觸區(qū)，計(jì)算了以瞬時(shí)接觸點(diǎn)為中心的接觸橢圓的各項(xiàng)參數(shù)，并繪制了由接觸橢圓長軸所組成的接觸區(qū)。對(duì)輪齒接觸分析的結(jié)果進(jìn)行實(shí)驗(yàn)驗(yàn)證。將所加工的螺旋錐齒輪模型進(jìn)行傳動(dòng)實(shí)驗(yàn)，獲得實(shí)際的接觸區(qū)，并對(duì)模擬和實(shí)驗(yàn)的結(jié)果進(jìn)行分析說明。 （5）為了揭示外在因素對(duì)齒輪接觸區(qū)的影響，，本文分析了齒輪副安裝誤差對(duì)接觸區(qū)的影響規(guī)律。通過建立包含安裝誤差的接觸方程并對(duì)其進(jìn)行求解的方法，分別對(duì)小輪安裝距誤差H、大輪安裝距誤差J、齒輪副軸間距偏差V和軸交角偏差對(duì)接觸跡線的位置和形態(tài)的影響進(jìn)行了研究并得到了相關(guān)結(jié)論。在此基礎(chǔ)上，進(jìn)一步對(duì)各項(xiàng)誤差對(duì)接觸跡線的綜合影響進(jìn)行了分析，得出了對(duì)齒輪安裝有指導(dǎo)意義的調(diào)整規(guī)律。
[Abstract]:Spiral bevel gear is used to transfer the motion and power of intersecting axis. Compared with straight tooth bevel gear, spiral bevel gear has many advantages, such as large coincidence degree, high bearing capacity, smooth transmission, high strength and low sensitivity to installation error. It is widely used in ships, aviation and defense technology and automobiles, machine tools, engineering machinery and mining machinery. In mechanical products, the machining technology of spiral bevel gear has been widely concerned. The United States Gleason Corp, founded in 1865, is the main leader of the bevel gear processing machine and technology in the world. Its spiral bevel gear is the most widely used bevel gear. Because of the inherent processing principle of Gleason Corp, it is a kind of bevel gear. The machine tool structure is very complex, and the machining adjustment calculation is very complicated and difficult. It is one of the most difficult to operate machine tools. On the other hand, Gleason's "approximate substitution" and "local conjugation" principle cause the two tooth surfaces to be not properly meshed, bad contact area, noise increase, strength decline and so on. To get a better contact area and get a better contact area, it is necessary to make complex adjustment and trial cutting of the machine tools and tools, and the manufacturing cost is increased. The production cycle of a pair of gears is long and the gear needs to be paired. So the machined gear is not a spherical involute tooth shape, so it is not interchangeable and instantaneous transmission Better than constant.
In this paper, based on the principle of shape cutting tooth method, the spiral bevel gear with spherical involute tooth profile can be obtained by using the principle of shape cutting tooth. The spherical involute is the theoretical tooth profile of the bevel gear and has all the excellent characteristics of the involute tooth profile. The principle of the shape cutting tooth method provides the tooth cutting method of the spherical involute spiral bevel gear and the method of cutting the tooth. On the basis of the above research work, the contact and meshing state of this new type of spherical involute spiral bevel gear is analyzed and studied on the basis of the principle of space meshing. The meshing characteristics and contact analysis of the spiral bevel gear have great influence on the transmission performance, which directly affects the use of the gear. Therefore, it is necessary to conduct in-depth research on it.
(1) the tooth surface movement process of the spherical involute spiral bevel gear is systematically studied, and the relationship between the left rotation, the right spin and the convex and concave tooth surface is expounded. On this basis, the mathematical model of the tooth surface is derived by using the coordinate transformation principle, and the derived right spin concave tooth surface equation is analyzed from the angle of meshing principle, and the equation of the derived right rotation concave tooth surface is analyzed. The meshing equation, the contact line equation and the expression of the conjugate convex tooth surface equation are expressed. The same character of the contact line equation and the shape line equation is compared and analyzed. This part of the study provides the support to the principle of the tooth cutting tooth method in theory, and is also the basis of the tooth surface research and the contact analysis.
(2) the meshing characteristics of the left, dextral convex and concave tooth surface are studied. The normal curvature of the surface, the main curvature and the main direction are calculated. The induced normal curvature of the spiral bevel gear tooth surface is calculated, and the expression of the boundary line of the curvature interference and the line of the meshing boundary is derived. The adjustment of the contact area provides the basis.
(3) for the spherical involute spiral bevel gear with conjugate spherical involute spiral bevel gear, the contact area adjustment method is put forward to transform the line contact into point contact by changing the radius of the production line. The calculation formula of the radius of the shape line is analyzed and derived, and the calculation formula of the induced normal curvature of the adjusted point contact tooth surface is deduced, which is the wheel tooth. The contact analysis laid the foundation.
(4) the gear contact analysis (TCA) method is used to simulate the contact area of the adjusted contact conjugate gear pair. First, the two tooth surface equation and the normal vector equation are transformed into the same coordinate system, and the contact equation expressed by the vector equation is established. Secondly, the contact equation expressed by the vector equation is converted into the quantity equation and the soft MATLAB is used. The method of solving the nonlinear equations is to solve the nonlinear equations. The solution is iterative method. Therefore, we need to determine the reasonable initial value of the iteration. In this paper, the selection method of the initial iteration value is analyzed. Finally, the solution results of the nonlinear equations are expressed in the form of graphics, and the contact trace is obtained. In order to obtain a more intuitive contact area, the instantaneous connection is calculated. The contact ellipse is the center of the contact ellipse, and the contact area composed of the long axis of the contact ellipse is drawn. The result of the tooth contact analysis is verified experimentally. The machined spiral bevel gear model is carried out to get the actual contact area, and the results of the simulation and the test are analyzed and explained.
(5) in order to reveal the influence of external factors on gear contact area, this paper analyzes the influence rule of gear pair installation error on contact area. By establishing contact equation including installation error and solving it, the error H of small wheel installation distance, error J of large wheel installation distance, V of gear shaft spacing deviation V and axis angle deviation are respectively butted. The influence of the position and shape of the trace is studied and the related conclusions are obtained. On the basis of this, the comprehensive influence of the contact trace of the error butt contact is further analyzed, and the regulation law of the guiding significance for the gear installation is obtained.

【學(xué)位授予單位】：吉林大學(xué)
【學(xué)位級(jí)別】：博士
【學(xué)位授予年份】：2014
【分類號(hào)】：TH132.422

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