球面渐开线螺旋锥齿轮接触区调整方法研究

发布时间：2018-05-02 20:19

本文选题：螺旋锥齿轮 + 产形线切齿法　；参考：《吉林大学》2014年博士论文

【摘要】：螺旋锥齿轮用于传递相交轴的运动与动力，相比于直齿锥齿轮，螺旋锥齿轮具有重合度大、承载能力高、传动平稳、强度高，对安装误差的敏感性小等优点，广泛应用于舰船、航空和国防技术装备以及汽车，机床、工程机械和矿山机械等各种机械产品中。螺旋锥齿轮的加工技术一直受到广泛的关注。成立于1865年的美国格里森公司，是国际上锥齿轮加工机床和技术的主要领跑者，它所生产的螺旋锥齿轮是目前应用最广泛的一种锥齿轮。由于格里森公司固有的加工原理，使得机床结构非常复杂，加工调整计算十分繁杂、困难，是最难以操作使用的机床之一。另一方面，格里森的“近似替代”和“局部共轭”原理导致加工的两齿面往往不能正确啮合，出现接触区不良、噪音增大、强度下降等弊端。为了改善齿轮的啮合状态，获得较好的接触区，需要对机床和刀具进行复杂的调整和反复的试切、检验，增加了制造成本，加工一对齿轮的生产周期长，且齿轮需要配对使用。这样加工出来的齿轮不是球面渐开线齿形，因而也就不具备互换性、瞬时传动比恒定等优良特性。本文的研究基于产形线切齿法原理，利用产形线切齿原理可以获得具有球面渐开线齿廓的螺旋锥齿轮。球面渐开线是锥齿轮的理论齿廓，具有渐开线齿廓的一切优良特性。产形线切齿法原理提供了球面渐开线螺旋锥齿轮的切齿方法和切齿装备的设计制造方案。本文在上述研究工作的基础上，从空间啮合原理出发，对这种新型球面渐开线螺旋锥齿轮的接触和啮合状态进行了分析和研究。螺旋锥齿轮的啮合特性和接触分析对传动性能有很大影响，直接影响齿轮的使用和加工，因此有必要对其开展深入的研究。本文的研究内容主要包括以下几个方面：（1）系统研究了球面渐开线螺旋锥齿轮的齿面生成运动过程，阐述了左旋、右旋以及凸、凹齿面形成的切齿运动关系。在此基础上，运用坐标变换原理推导了齿面的数学模型，从啮合原理的角度对所推导的右旋凹齿面方程进行了分析，给出了啮合方程、接触线方程和与之共轭的左旋凸齿面方程的表达式。并对接触线方程与产形线方程的同一性进行了对比分析。这部分研究内容从理论上为产形线切齿法原理提供了支持，同时也是开展齿面研究和接触分析的基础。（2）对所推导的左、右旋凸、凹齿面的啮合特性进行了研究，计算了各自曲面的法曲率，主曲率、确定了主方向，计算了理论上线接触的螺旋锥齿轮齿面的诱导法曲率，推导了曲面的曲率干涉界限线和啮合界限线的表达式。为进一步研究齿面接触区的调整提供依据。（3）对于理论上线接触共轭的球面渐开线螺旋锥齿轮提出了通过改变产形线半径将线接触转化为点接触的接触区调整方法。分析并推导了产形线半径的计算公式，对调整后的点接触共轭齿面的诱导法曲率计算公式进行了推导，为轮齿接触分析奠定了基础。（4）采用轮齿接触分析（TCA）方法对调整后的点接触共轭齿轮副的接触区进行了模拟。首先将两齿面方程及法向量方程转化至同一坐标系中，建立由矢量方程表示的接触方程。其次将矢量方程表示的接触方程转化为数量方程并运用MATLAB软件进行非线性方程组的求解，求解的方法是迭代法，为此需要确定合理的迭代初值，文中分析了迭代初值的选择方法。最后将非线性方程组的求解结果以图形的形式进行表达，获得了接触迹线，为了获得更直观的接触区，计算了以瞬时接触点为中心的接触椭圆的各项参数，并绘制了由接触椭圆长轴所组成的接触区。对轮齿接触分析的结果进行实验验证。将所加工的螺旋锥齿轮模型进行传动实验，获得实际的接触区，并对模拟和实验的结果进行分析说明。（5）为了揭示外在因素对齿轮接触区的影响，，本文分析了齿轮副安装误差对接触区的影响规律。通过建立包含安装误差的接触方程并对其进行求解的方法，分别对小轮安装距误差H、大轮安装距误差J、齿轮副轴间距偏差V和轴交角偏差对接触迹线的位置和形态的影响进行了研究并得到了相关结论。在此基础上，进一步对各项误差对接触迹线的综合影响进行了分析，得出了对齿轮安装有指导意义的调整规律。
[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.

【学位授予单位】：吉林大学
【学位级别】：博士
【学位授予年份】：2014
【分类号】：TH132.422

【参考文献】