臺灣博碩士論文加值系統

齒輪及其傳動裝置是機械工業中一重要的基礎件，其應用範圍相當廣泛。而一般傳統之漸開線齒輪，其具有漸開線齒廓之幾何外形、製造容易，且對中心距之組裝誤差不敏感等特性。但漸開線齒廓之齒輪對為線接觸型的傳動運轉方式，具有軸組裝誤差敏感與齒面邊緣接觸，因而導致齒面運轉時振動噪音及接觸應力的提高等傳動問題。
根據齒輪原理和微分幾何，本研究提出一個新型面滾式雙刀盤創成法之數學模式，以及新型的製造方式，即利用二組刀盤以面滾式切削法模擬成假想齒條刀創成齒輪，此切削法創成之齒輪齒面具有導程弧形修整之特性，可有效解決組裝誤差敏感與邊緣接觸的問題。本文所提之面滾式切齒法的過程為連續分度及連續切齒，所以切齒之效率將大幅提高。而在創成過程中，雙刀盤組之旋轉角速度與齒胚之旋轉角速度二者存在一定速比轉動關係，雙刀盤組再由齒胚左側起點創成至右側，即完成工件加工。此外二組刀盤之角速度切削刃口由齒面之一端隨著導程方向切削至齒面另一端，故其痕跡在導程方向為平滑之圓弧切削痕跡，且因為切削痕跡與齒面嚙合接觸方向垂直，因此在齒形方向之表面粗糙度也就是切削痕跡之高度可透過刀盤座旋轉角速度與齒胚創成速度之間的速比關係來控制與改善。此切齒法之數學模式可模擬成三種不同之型式，分別為由雙刀盤內刀刃加工之雙凸型齒輪、雙刀盤外刀刃加工之雙凹型齒輪、以及由雙刀盤退化成單刀盤內外刃加工之凸凹型齒輪三種型式，我們通稱為弧齒線圓柱齒輪。因此其齒輪對組成可有雙凸齒輪對、凸平齒輪對、凸凹齒輪對三種，其齒面承載能力及組裝公差都較一般業界常用的漸開線齒輪來的大且傳動平穩。
本文依據雙刀盤創成法來建立具有弧形修整之螺旋齒輪數學模式，以Litvin教授所提之方法探討齒面的過切問題與接觸性能分析，並提出避免過切的方法。此數學模式能模擬齒輪對在無負載條件下，具有水平軸、垂直軸、以及中心距上下與左右組裝偏差時，其齒面接觸齒印的位置、形狀、變化情形和其運動誤差曲線。此切削法創成之齒輪齒面具有弧形修整之特性，因此其傳動運轉方式為點接觸之嚙合情況。因此一方面可避免齒輪對邊緣接觸的情形發生，另一方面可藉由低敏感度之組裝誤差來降低齒輪對運轉時所產生的振動噪音及增加齒輪嚙合的接觸強度。

Of the gear pairs and transmissions that play an important role in many industrial applications—including vehicles and machine and power tools—involute helical gears are among the most common because of their simple geometry, easy manufacturing, and low sensitivity to center distance. However, the conventional helical gear pair meshes in line contact, is very sensitive to assembly errors, and is prone to edge contact problems. Therefore, based on the theory of gearing and differential geometry, this investigation proposes a novel face-hobbing method to generate a helical gear with lengthwise crowning. In this method, two head cutters form an imaginary generating rack with lengthwise cycloidal tooth traces that generate cylindrical helical or spur gears with longitudinal cycloidal traces.
The proposed cutting method, in which the cutter blade travels longitudinally from one side face to the other to create smoother longitudinal cutting marks, is particularly efficient for continuous indexing cutting. In gear generation, this method relies on the ratio between the cutter rotation speed and the generating roll speed. When the head cutters move from the left start-of-generation position to the right end-of-generation position, tooth flank generation is complete. In addition, because the cutting marks in this proposed method are perpendicular to the contact path between the mating gears, the height of the cutting mark can be reduced by decreasing the rolling ratio of the cutter rotation speed to the generating roll speed.
In addition, this mathematical model of a cutting system can simulate three different modules. First, the procedure uses all inside cutter blades mounted on the head cutter and all outside cutter blades for a double-concave gear. Because all inside and outside cutter blades are mounted on the same head cutter, it is easy to simulate a cutting system for a convex-concave helical gear using one head cutter. The three possible contact arrangements between the racks’ meshing tooth traces depend on the arrangement of each head cutter, whether convex to convex, convex to straight, or convex to concave. It should also be noted that the contact load capacity of the proposed longitudinal cycloidal gear drive is larger than that of an involute gear drive.
Drawing on a dual face-hobbing method, we develop a mathematical model with lengthwise crowning and analyze the tooth undercutting and sensitivity of the tooth contact pattern using the techniques proposed by Litvin. Applying the mathematical model of tooth contact analysis also allows evaluation of meshing and contact characteristics without load when assembly errors and axes misalignment can occur. Because the proposed helical gear has longitudinal cycloidal traces, the gear pair meshes in point contact, a condition that not only eliminates tooth edge contact but decreases the gear vibration and noise from axial misalignment and increases the bearing strength of the contact gears.

摘 要
ABSTRACT
致 謝
TABLE OF CONTENTS
LIST OF FIGURES
LIST OF TABLES
NOMENCLATURE
CHAPTER 1 INTRODUCTION
1.1 Background and Motivation
1.2 Literature Reviews
1.3 Dissertation Outlines
CHAPTER 2 MATHEMATICAL MODEL OF THE CYCLOIDAL CROWNING OF SPUR GEARS GENERATED BY A DUAL FACE-HOBBING METHOD
2.1 Introduction
2.2 Generating Concept
2.3 Mathematical Model of the Cutting Blades
2.4 Machine Settings for the Head Cutter
2.5 Mathematical Model of generated the Cycloidal Crowning of Spur Gears
2.6 Numerical Examples and Discussions
2.7 Concluding Remarks
CHAPTER 3 Mathematical Model of Longitudinal Cycloidal Cylindrical Gears with Circular Arc Teeth Generated by the Dual Face-Hobbing Method
3.1 Introduction
3.2 Mathematical Model for the circular arc cutting blades
3.3 Mathematical Model of generated the Cycloidal Crowning of Helical Gears
3.4 Numerical Examples and Discussions
CHAPTER 4 ANALYSIS OF TOOTH UNDERCUTTING
4.1 Introduction
4.2 Conditions of Tooth Undercutting
4.3 Numerical Examples of Tooth Undercutting
4.4 Concluding Remarks
CHAPTER 5 SIMULATION OF THE CONDITION OF MESHING AND CONTACT
5.1 Introduction
5.2 Tooth Contact Analysis
5.3 Contact Ellipses
5.4 Numerical Examples and Discussions
5.5 Concluding Remarks
CHAPTER 6 CONCLUSIONS AND FURTHER RESEARCH
6.1 Conclusions
6.2 Further Research
REFERENCES
PUBLICATION LIST
作者簡介

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