【摘要】：螺旋錐齒輪，又稱螺傘錐齒輪，是一種常見空間嚙合齒輪。相對傳統(tǒng)錐齒輪，螺旋錐齒輪具有更大的重疊系數(shù)，更高的負載能力，在航天、艦艇，汽車等高速重載機械中應(yīng)用十分廣泛。傳統(tǒng)螺旋錐齒輪多采用漸開線、圓弧線和外擺線作為齒向線，由于這些曲線無法保證其線上各點螺旋角相等，所以導致了齒輪傳動無法實現(xiàn)最合理嚙合。雖然在加工中可通過調(diào)整機床來加以改善，但也造成了設(shè)備要求高，成本增加等問題。 本課題組采用對數(shù)螺旋線作為齒向線，利用其螺旋角處處相等的特性，解決了普通螺旋錐齒輪由于螺旋角不等帶來的種種問題，不僅實現(xiàn)了理論上的最合理嚙合，獲得了更高的可靠度，傳動更加平穩(wěn)，提高了傳動效率，而且由漸開線和對數(shù)螺旋線構(gòu)成的規(guī)則齒面也使加工過程更加便捷。鑒于以上優(yōu)點很有必要對對數(shù)螺旋錐齒輪展開研究。 齒輪的嚙合理論在齒輪的研究體系中占有重要地位，是齒輪技術(shù)的重要內(nèi)容，無論是傳動形式還是新的加工技術(shù)，都需要掌握齒輪嚙合理論。本課題在之前研究的基礎(chǔ)上研究對數(shù)螺旋錐齒輪的嚙合特性，結(jié)合齒輪嚙合理論和微分幾何原理，進一步完善對數(shù)螺旋錐齒輪的嚙合體系，更全面反映對數(shù)螺旋錐齒輪的嚙合本質(zhì)。本課題主要內(nèi)容如下： 1.建立滑動系數(shù)方程，對齒面的磨損的情況進行定量的分析。齒面的滑動系數(shù)是指：兩共軛齒形相對滑動弧長之比的極限值。在其他條件相同時，滑動系數(shù)的絕對值越大，齒面的磨損就越大。因而是衡量齒面磨損的重要標志。本文采用的趙亞平老師在《點接觸齒面滑動系數(shù)在交錯軸齒輪中的應(yīng)用》一文中提到的方法和思路求解。通過該系數(shù)來反映齒輪在嚙合過程中齒面各點的接觸情況。 2.計算根切界限函數(shù)，所謂的根切界限函數(shù)，就是共軛曲面發(fā)生根切和沒發(fā)生根切的界限，它對于提高傳動系統(tǒng)的壽命和避免干涉均有重要意義。根切界限點和根切界限曲線建模與計算既可為齒輪副在嚙合傳動過程中是否發(fā)生干涉提供理論依據(jù)，也可保證共軛曲面在加工制造過程中不發(fā)生根切�？梢姼薪缦藓瘮�(shù)對于保障齒輪的傳動質(zhì)量和加工質(zhì)量具有重要意義。 3.在根切界限函數(shù)的基礎(chǔ)上完成嚙合界限函數(shù)的計算，一對共軛曲面能保持良好的傳動性能，僅滿足嚙合條件遠遠不夠，還需要討論嚙合界線，這條曲線將齒面分成兩部分即參加嚙合的區(qū)域與不參加嚙合的區(qū)域，根據(jù)嚙合界限函數(shù)的計算結(jié)果，可以改善齒面尺寸，將非嚙合區(qū)域減少，從而是齒輪小型化，輕型化。 4.推導出齒面二次接觸的判別式，對嚙合區(qū)域內(nèi)接觸點的接觸情況判斷，通過判別式，，可以明確各嚙合點哪些是一次接觸，哪些是二次接觸。對于判別式的推導可以通過將嚙合方程變形成三角函數(shù)的形式，利用三角函數(shù)的取值范圍加以判斷各個接觸點的接觸次數(shù)。
[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.
【學位授予單位】：內(nèi)蒙古科技大學
【學位級別】：碩士
【學位授予年份】：2012
【分類號】：TH132.41

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