臺灣博碩士論文加值系統

擺線齒輪泵用於將機械能轉換為液壓能，其缺點為流量脈動大且會產生困油
現象。非圓形節曲線使用於外轉子內齒輪齒形，使齒頂、工作區與齒根為一圓滑
曲線，並使用此節曲線建立刨齒刀刀具面方程式，運用齒輪原理配合刨齒刀加工
內轉子外齒輪加工機構，以解析法來推導內轉子外齒輪齒形數學模式。並利用所
推得之內、外轉子齒輪齒形數學模式及數值解法，建立非圓形型內齒輪泵之各種
特性分析所需要模型。
齒輪組嚙合傳動精度會受到外力、環境溫度及工作溫度影響，使齒面產生應
力集中及齒面變形。將建立外轉子內齒輪及內轉子外齒輪齒面模型輸入有限元素
分析軟體進行靜力分析，來求得在馬達轉動力矩帶動下接觸齒面之接觸應力及接
觸應變分析的探討，並以一齒差與兩齒差以及一齒差三點接觸液壓泵做為比較的
依據。
而當非圓形型內齒輪液壓泵在高速運轉時，其內、外轉子在運轉狀態下將會
產生溫升現象，而導致轉子幾何外型發生變化。在本論文中利用求得轉子齒形之
數學模式，建立有限元素熱變形分析所需要之轉子齒形幾何模型，來進行齒輪泵
加壓時升溫產生熱膨脹分析，同時依據有限元素法分析軟體ANSYS 模擬後的結
果，未來進行內齒輪液壓泵參數設計修正，以達到減少膨脹變形之目的。
最後希望本研究所創成非圓形型內齒輪模組以及特性研究結果，能對此型液
壓泵設計以及未來研究能有所幫助。
關鍵字: 非圓形型內齒輪泵、非圓形節曲線、有限元素法

Gerotor pump is used to transfer mechanical energy into hydrautic energy. Its
disadvantage is larger pumping oil fluctuatation and has phenomenon of trapped oil.
Tooth profiles of an outer rotor have a smooth cuve when its top land, work section,
and fillet describe by a mathematical model of a noncircular pitch curve. Tool profiles
of a shaper cutter are determined by that of a noncircular pitch curve. Based on the
theory of gearing and a manufacturing mechanism between shaper cutter and inner
rotor, the tooth profile mathematical model of an inner rotor is derived by analytic
method. Tooth profiles of outer and inner rotors are computed by numerical method
with the deived mathematical models, and those tooth profiles are established to
investigate various characteristics required for the analysis models.
When transmission precision of a gear set is affected by external force,
enviromental temperture, and working temperature, gear tooth profiles have stress
concentration and tooth deformation. The obtained tooth profile models are inputed to
finite element analysis program to study static analysis, and contact stress and
deformation of contact teeth compared with one tooth difference, two teeth difference
and one tooth difference with three contact teeth are computed by a driving torque of
a motor.
When a noncircular type gerotor pump runs at high speed, the operating state of
phenomenon of rising temperature causes changes in the geometric shape of inner and
outer rotors. Therefore, based on the mathematical models of rotors in this paper, rotor
geometry models are built up with thermal deformation of finite element analysis
module to study thermal expansion of outer and inner rotors under rising temperture
of pumping oil. Thus, design parameter values are corrected by means of the obtained
results of the simulation software ANSYS in order to achieve the purpose of reducing
the swelling deformation in future.

目錄
中文摘要 …………………………………………………………………………… I
英文摘要 ………………………………………………………………………… II
致謝 ……………………………………………………………………………… IV
目錄 ……………………………………………………………………………… V
表目錄 …………………………………………………………………………… VI
圖目錄 …………………………………………………………………………… VII
第一章 緒論 ……………………………………………………………………… 1
1.1 簡介 …………………………………………………………………………… 1
1.2 文獻回顧 ……………………………………………………………………… 1
1.3 研究方向 ……………………………………………………………………… 4
第二章 非圓形型內齒輪數學模型 ……………………………………………… 5
2.1 前言 …………………………………………………………………………… 5
2.2 以節曲線為基本線型之轉子外型數學模型 ………………………………… 5
2.3 範例 …………………………………………………………………………… 8
第三章 轉子之接觸分析 ………………………………………………………… 19
3.1 前言 …………………………………………………………………………… 19
3.2 接觸應力分析 ………………………………………………………………… 19
3.3 分析結果 ……………………………………………………………………… 25
第四章 非圓形型內齒輪幫浦熱效應分析 ……………………………………… 45
4.1 前言 …………………………………………………………………………… 45
4.2 轉子之熱膨脹分析 …………………………………………………………… 45
4.3 分析結果 ……………………………………………………………………… 46
第五章 結論與展望 ……………………………………………………………… 62
5.1 結論 …………………………………………………………………………… 62
5.2 未來展望 ……………………………………………………………………… 62
參考文獻 …………………………………………………………………………… 64
作者簡介 …………………………………………………………………………… 64
VI
表目錄 頁次
表 3.1 不鏽鋼材 AISI 304 之機械性質表 ....……………………………..…... 24
表 3.2 一齒差內轉子接觸端面變形量(N= 6，

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