三維螺旋傘齒輪動態接觸衝擊分析

Three-Dimensional Dynamic Contact and Impact Analysis of Spiral Bevel Gear

范斯淇(Sih-Ci Fan)

指導教授 ： 王培郁

國立虎尾科技大學/工程學院/機械與機電工程研究所/碩士(2010年)

摘要

齒輪是機械構件中最常見的傳動零組件，背負著傳遞動力、改變運動速度和方向的重要任務。由於傳統的螺旋傘齒輪強度計算(美國齒輪製造協會，AGMA)中幾乎沒有考慮到齒輪材料彈性變形、動態嚙入及嚙出衝擊、及熱處理的滲碳深度對一齒輪對齒面接觸應力及等效應力的影響。本論文建立一套螺旋傘齒輪三維動態接觸/衝擊分析模組，以C++視窗程式計算出螺旋傘齒輪真實齒面藉以匯入Pro/E軟體建構三維模型，再將三維模型匯入HyperMesh前處理器進行有限元素模型網格劃分、材料性質設定、碰撞接觸模式的選擇、速度載荷設定、沙漏控制設定與輸出條件控制等，最後藉由LS-DYNA顯式動力學軟體進行分析求解運算。考慮齒輪材料為一彈性體在不同轉速、扭矩、大小齒輪各別滲碳深度及硬度等參數影響下對傳動誤差曲線之影響。分析齒輪對在動態接觸/衝擊負載下其齒面接觸應力、等效應力、暫態及穩態響應，並與AGMA計算結果作一比對，提供齒輪設計者在轉速、扭矩、硬度及其滲碳深度一建議值。

關鍵字

螺旋傘齒輪 ； 動態接觸/衝擊 ； LS-DYNA ； 動態嚙入及嚙出衝擊

並列摘要

Gears are the most important components of the transmission systems that support power carrying out and motion characteristics changing. Many researchers had applied AGMA standards to evaluate the strength of spiral bevel gear, presently. However, the elastic deformation of gear materials, dynamic meshing-in and meshing-out impact, and the surface hardening depth did not considered in AGMA standard. A great portion of research efforts on spiral bevel gear transmission errors is focused on contact stress and V/H values, while only a few investigate into the relations between transmission errors and rotational speeds. In this research, an approach for 3D dynamic contact and impact analysis of spiral bevel gear drives is addressed. The HyperMesh /LS-DYNA software is utilized to calculate the transmission errors, surface contact stresses and root bending stresses of a spiral bevel gear pair. The vibration behavior of actual gear set under dynamic loading conditions has been simulated in the dynamic model. The dynamic responses of the spiral bevel gear drives are obtained under the conditions of initial speed with driver and the resistance with driven. The stiffness and elastic deformation of the gear teeth are calculated by using the finite element method with actual geometry and positions of the gears. The influences of the transmission errors, initial speed, and the surface hardening depth on impact characteristics of the meshing teeth are analyzed. After the impact analysis, the numerical results of transmission errors, contact pressure, and effective stress involve with the transient and steady states that difference AGMA standards.

並列關鍵字

Spiral bevel gear ； dynamic ； impact ； LS-DYNA ； meshing-in and meshing-out

參考文獻

[1] Vilmos Simon, FEM stress analysis in hypoid gears, Mechanism and Machine Theory 35 (2000) 1197-1220.

[2] Jesper Brauer, A general finite element model of involute gears, Finite Elements in Analysis and Design 40 (2004) 1857-1872.

[3] K.Mao, Gear tooth contact analysis and its application in the reduction of fatigue wear, Wear 262 (2007) 1281-1288.

[4] V. Abousleiman, P. Velex, A hybrid 3D finite element/lumped parameter modle for quasi-static and dynamic analyses of planetary/epicyclic gear sets, Mechanism and Machine Theory 41 (2006) 725-748.

[5] Yi-Cheng Chen, Chung-Biau Tsay, Stress analysis of a helical gear set with localized bearing contact, Finite Element in Analysis and Design 38 (2002) 707-723.