对数螺旋锥齿轮啮合特性研究
发布时间：2018-07-28 12:06
【摘要】：螺旋锥齿轮，又称螺伞锥齿轮，是一种常见空间啮合齿轮。相对传统锥齿轮，螺旋锥齿轮具有更大的重叠系数，更高的负载能力，在航天、舰艇，汽车等高速重载机械中应用十分广泛。传统螺旋锥齿轮多采用渐开线、圆弧线和外摆线作为齿向线，由于这些曲线无法保证其线上各点螺旋角相等，所以导致了齿轮传动无法实现最合理啮合。虽然在加工中可通过调整机床来加以改善，但也造成了设备要求高，成本增加等问题。 本课题组采用对数螺旋线作为齿向线，利用其螺旋角处处相等的特性，解决了普通螺旋锥齿轮由于螺旋角不等带来的种种问题，不仅实现了理论上的最合理啮合，获得了更高的可靠度，传动更加平稳，提高了传动效率，而且由渐开线和对数螺旋线构成的规则齿面也使加工过程更加便捷。鉴于以上优点很有必要对对数螺旋锥齿轮展开研究。 齿轮的啮合理论在齿轮的研究体系中占有重要地位，是齿轮技术的重要内容，无论是传动形式还是新的加工技术，都需要掌握齿轮啮合理论。本课题在之前研究的基础上研究对数螺旋锥齿轮的啮合特性，结合齿轮啮合理论和微分几何原理，进一步完善对数螺旋锥齿轮的啮合体系，更全面反映对数螺旋锥齿轮的啮合本质。本课题主要内容如下： 1.建立滑动系数方程，对齿面的磨损的情况进行定量的分析。齿面的滑动系数是指：两共轭齿形相对滑动弧长之比的极限值。在其他条件相同时，滑动系数的绝对值越大，齿面的磨损就越大。因而是衡量齿面磨损的重要标志。本文采用的赵亚平老师在《点接触齿面滑动系数在交错轴齿轮中的应用》一文中提到的方法和思路求解。通过该系数来反映齿轮在啮合过程中齿面各点的接触情况。 2.计算根切界限函数，所谓的根切界限函数，就是共轭曲面发生根切和没发生根切的界限，它对于提高传动系统的寿命和避免干涉均有重要意义。根切界限点和根切界限曲线建模与计算既可为齿轮副在啮合传动过程中是否发生干涉提供理论依据，也可保证共轭曲面在加工制造过程中不发生根切。可见根切界限函数对于保障齿轮的传动质量和加工质量具有重要意义。 3.在根切界限函数的基础上完成啮合界限函数的计算，一对共轭曲面能保持良好的传动性能，仅满足啮合条件远远不够，还需要讨论啮合界线，这条曲线将齿面分成两部分即参加啮合的区域与不参加啮合的区域，根据啮合界限函数的计算结果，可以改善齿面尺寸，将非啮合区域减少，从而是齿轮小型化，轻型化。 4.推导出齿面二次接触的判别式，对啮合区域内接触点的接触情况判断，通过判别式，，可以明确各啮合点哪些是一次接触，哪些是二次接触。对于判别式的推导可以通过将啮合方程变形成三角函数的形式，利用三角函数的取值范围加以判断各个接触点的接触次数。
[Abstract]:Spiral bevel gear, also called spiral umbrella bevel gear, is a common space meshing gear. Compared with traditional bevel gears, spiral bevel gears have higher overlap coefficient and higher load capacity. They are widely used in aerospace, naval vessels, automobiles and other high-speed heavy load machinery. The traditional spiral bevel gears usually use involute, arc and epicycloid as tooth direction, because these curves can not guarantee the equal helical angle of each point on the line, so the gear transmission can not realize the most reasonable meshing. Although it can be improved by adjusting machine tools in machining, it also causes problems such as high equipment requirements and increased costs. Using the logarithmic helix as the tooth direction and the characteristic of equal helical angle everywhere, the problem of common spiral bevel gear caused by different helical angles is solved, which not only realizes the most reasonable meshing in theory. Higher reliability, more stable transmission and higher transmission efficiency are obtained, and the regular tooth surface composed of involute and logarithmic helix also makes the machining process more convenient. In view of the above advantages, it is necessary to study logarithmic spiral bevel gears. The meshing theory of gear plays an important role in the research system of gear, and is an important content of gear technology. It is necessary to master the theory of gear meshing, both in the form of transmission and in the new machining technology. In this paper, the meshing characteristics of logarithmic spiral bevel gears are studied on the basis of previous studies, and the meshing system of logarithmic spiral bevel gears is further improved by combining the theory of gear meshing and differential geometry. More fully reflects the meshing nature of logarithmic spiral bevel gears. The main contents of this topic are as follows: 1. The sliding coefficient equation is established and the wear of tooth surface is analyzed quantitatively. The slip coefficient of tooth surface is the limit value of the ratio of two conjugate tooth shapes to sliding arc length. Under the same other conditions, the greater the absolute value of the slip coefficient, the greater the wear of the tooth surface. Therefore, it is an important mark to measure tooth surface wear. The method and train of thought mentioned in the paper "Application of sliding coefficient of Point contact Tooth Surface in staggered Shaft Gear" is used in this paper. Through the coefficient to reflect the gear in the meshing process of tooth surface contact. 2. The calculation of the radical tangent limit function, the so-called radical tangent limit function, is the limit of the conjugate surface with and without the root tangent, which is of great significance for increasing the life of the transmission system and avoiding interference. The modeling and calculation of the root cutting boundary point and the root cutting boundary curve can not only provide a theoretical basis for the interference of the gear pair in the course of meshing transmission, but also ensure that the conjugate surface does not take place in the process of machining and manufacturing. It can be seen that the root tangent boundary function is of great significance for ensuring the transmission quality and machining quality of gears. On the basis of the root tangent boundary function, the meshing boundary function is calculated. A pair of conjugate surfaces can maintain good transmission performance. It is far from enough to satisfy the meshing condition only. The meshing boundary also needs to be discussed. This curve divides the tooth surface into two parts, that is, the engaged region and the non-meshing region. According to the calculation results of the meshing boundary function, the tooth surface size can be improved and the non-meshing area can be reduced, thus the gear is miniaturized. Lightness. 4. The discriminant of secondary contact of tooth surface is derived, and the contact condition of contact point in meshing area is judged. By discriminating formula, it is clear which contact point is primary contact and which contact is secondary contact. For the derivation of the discriminant, the contact number of each contact point can be judged by transforming the meshing equation into a trigonometric function and using the value range of the trigonometric function.
【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
本文编号：2150081
[Abstract]:Spiral bevel gear, also called spiral umbrella bevel gear, is a common space meshing gear. Compared with traditional bevel gears, spiral bevel gears have higher overlap coefficient and higher load capacity. They are widely used in aerospace, naval vessels, automobiles and other high-speed heavy load machinery. The traditional spiral bevel gears usually use involute, arc and epicycloid as tooth direction, because these curves can not guarantee the equal helical angle of each point on the line, so the gear transmission can not realize the most reasonable meshing. Although it can be improved by adjusting machine tools in machining, it also causes problems such as high equipment requirements and increased costs. Using the logarithmic helix as the tooth direction and the characteristic of equal helical angle everywhere, the problem of common spiral bevel gear caused by different helical angles is solved, which not only realizes the most reasonable meshing in theory. Higher reliability, more stable transmission and higher transmission efficiency are obtained, and the regular tooth surface composed of involute and logarithmic helix also makes the machining process more convenient. In view of the above advantages, it is necessary to study logarithmic spiral bevel gears. The meshing theory of gear plays an important role in the research system of gear, and is an important content of gear technology. It is necessary to master the theory of gear meshing, both in the form of transmission and in the new machining technology. In this paper, the meshing characteristics of logarithmic spiral bevel gears are studied on the basis of previous studies, and the meshing system of logarithmic spiral bevel gears is further improved by combining the theory of gear meshing and differential geometry. More fully reflects the meshing nature of logarithmic spiral bevel gears. The main contents of this topic are as follows: 1. The sliding coefficient equation is established and the wear of tooth surface is analyzed quantitatively. The slip coefficient of tooth surface is the limit value of the ratio of two conjugate tooth shapes to sliding arc length. Under the same other conditions, the greater the absolute value of the slip coefficient, the greater the wear of the tooth surface. Therefore, it is an important mark to measure tooth surface wear. The method and train of thought mentioned in the paper "Application of sliding coefficient of Point contact Tooth Surface in staggered Shaft Gear" is used in this paper. Through the coefficient to reflect the gear in the meshing process of tooth surface contact. 2. The calculation of the radical tangent limit function, the so-called radical tangent limit function, is the limit of the conjugate surface with and without the root tangent, which is of great significance for increasing the life of the transmission system and avoiding interference. The modeling and calculation of the root cutting boundary point and the root cutting boundary curve can not only provide a theoretical basis for the interference of the gear pair in the course of meshing transmission, but also ensure that the conjugate surface does not take place in the process of machining and manufacturing. It can be seen that the root tangent boundary function is of great significance for ensuring the transmission quality and machining quality of gears. On the basis of the root tangent boundary function, the meshing boundary function is calculated. A pair of conjugate surfaces can maintain good transmission performance. It is far from enough to satisfy the meshing condition only. The meshing boundary also needs to be discussed. This curve divides the tooth surface into two parts, that is, the engaged region and the non-meshing region. According to the calculation results of the meshing boundary function, the tooth surface size can be improved and the non-meshing area can be reduced, thus the gear is miniaturized. Lightness. 4. The discriminant of secondary contact of tooth surface is derived, and the contact condition of contact point in meshing area is judged. By discriminating formula, it is clear which contact point is primary contact and which contact is secondary contact. For the derivation of the discriminant, the contact number of each contact point can be judged by transforming the meshing equation into a trigonometric function and using the value range of the trigonometric function.
【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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