对数螺旋锥齿轮的逆向设计研究

发布时间：2018-05-16 05:05

本文选题：对数螺旋锥齿轮 + 齿面重构　；参考：《内蒙古科技大学》2012年硕士论文

【摘要】：螺旋锥齿轮的设计与制造在机械行业中已占有相当重要的地位，螺旋锥齿轮在传动过程中，只是在齿轮中部啮合处的螺旋角为设计的标准螺旋角，而在其它部位均为近似值，严格的说，从原理上无法保证最合理的啮合。因此，解决螺旋锥齿轮传动中存在的不同啮合点处的螺旋角不相等问题就显得很重要。而对数螺旋锥齿轮作为一种新型的齿轮传动形式，比传统螺旋锥齿轮有更多的优势。但由于对数螺旋锥齿轮其本身复杂的曲面形状，导致了其加工过程比一般的锥齿轮要更加困难。根据展成法加工出的对数螺旋锥齿轮在加工过程中，要先根据展成原理调整机床的加工参数，加工出大轮，再根据齿轮的共轭原理切制出小轮。这样，，实际加工出的对数螺旋锥齿轮齿面与理论齿面有一定的加工误差，即齿面偏差。为了减小齿面偏差,最经济适用的方法就是采用激光扫描设备采集齿面离散数据点，从而获得齿面网格点的法向偏差，并通过数值分析对齿面误差进行修正。本课题是针对已有的对数螺旋锥齿轮实物，采用逆向工程技术对对数螺旋锥齿轮做进一步的研究，不断完善了对数螺旋锥齿轮的啮合理论。 1.对数螺旋锥齿轮的齿面重构。通过3D扫描设备对已有的对数螺旋锥齿轮进行扫描，将获取到的齿面离散点的坐标数据运用NURBS插值算法进行计算，先得到齿面上的三次B样条插值曲线，由插值曲线最终会重构出对数螺旋锥齿轮的齿面。 2.对数螺旋锥齿轮的构造齿面与理论齿面的误差分析。在建立起来的对数螺旋锥齿轮真实数学模型的基础上，最终目的是要将构造的对数螺旋锥齿轮齿面与理论齿面相比较，从而计算它们之间的误差。因此，根据得出的对数螺旋锥齿轮的真实齿面方程计算出一系列的离散数据点，将离散数据点带到对数螺旋齿轮的理论方程里，会得到一组相应理论数据点的坐标。根据理论齿面的数据点坐标和真实齿面的数据点坐标最终会计算出齿面的齿向偏差，利用差曲面分析工具，建立差曲面方程并修正齿面误差。
[Abstract]:The design and manufacture of spiral bevel gears have played a very important role in the mechanical industry. In the course of transmission, the helical angle of spiral bevel gears is only the standard spiral angle in the middle of the gear meshing, but it is approximate in other parts. Strictly speaking, there is no guarantee of the most reasonable engagement in principle. Therefore, it is very important to solve the problem of helical angle inequality at different meshing points in spiral bevel gear transmission. As a new type of gear transmission, logarithmic spiral bevel gear has more advantages than traditional spiral bevel gear. However, the machining process of logarithmic spiral bevel gear is more difficult than that of conventional bevel gear due to its complex curved surface shape. According to the logarithmic spiral bevel gear machined by generating method, the machining parameters of machine tool should be adjusted according to the principle of generating first, the large wheel should be machined, and then the small wheel should be cut according to the conjugate principle of gear. In this way, the tooth surface of the logarithmic spiral bevel gear actually machined has certain machining error with the theoretical tooth surface, that is, the tooth surface deviation. In order to reduce the tooth surface deviation, the most economical and applicable method is to collect the discrete data points of the tooth surface by using laser scanning equipment, so as to obtain the normal deviation of the tooth surface grid point, and to correct the tooth surface error by numerical analysis. Aiming at the existing logarithmic spiral bevel gear, the reverse engineering technology is used to further study the logarithmic spiral bevel gear, and the meshing theory of logarithmic spiral bevel gear is improved. 1. Tooth surface reconstruction of logarithmic spiral bevel gear. The existing logarithmic spiral bevel gears were scanned by 3D scanning equipment. The coordinate data of the discrete points of tooth surface were calculated by NURBS interpolation algorithm, and the cubic B-spline interpolation curve on the tooth surface was obtained first. The tooth surface of logarithmic spiral bevel gear will be reconstructed from interpolation curve. 2. Error analysis of the structural and theoretical tooth surfaces of logarithmic spiral bevel gears. On the basis of the real mathematical model of logarithmic spiral bevel gear, the final aim is to compare the tooth surface of the constructed logarithmic spiral bevel gear with the theoretical tooth surface and to calculate the error between them. Therefore, a series of discrete data points are calculated according to the real tooth surface equation of logarithmic spiral bevel gear. The discrete data points are brought into the theoretical equation of logarithmic spiral gear, and the coordinates of corresponding theoretical data points are obtained. According to the data point coordinates of the theoretical tooth surface and the real tooth surface data point coordinate, the tooth deviation of the tooth surface is calculated finally, and the differential surface equation is established and the tooth surface error is corrected by using the difference surface analysis tool.
【学位授予单位】：内蒙古科技大学
【学位级别】：硕士
【学位授予年份】：2012
【分类号】：TH132.41

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