本研究以有限元素法建立中空圓環於感應加熱下之電磁場、溫度場與固體 力學耦合模型，探討非均勻溫度場所引起之熱膨脹、熱應力及雙環界面接觸行 為。首先 以單環模型比較 均勻升溫下之自由膨脹 、 施加 外表面徑向約束、給 定內 、 外 表面 溫差 及 感應加熱等條件，以釐清溫度梯度及機械約束對熱應力形 成之影響；並進一步分析比熱容、熱傳導率與導電率之溫度相依性，以及相對 磁導率對磁場穿透、焦耳熱源分布與升溫歷程之 影響 。其後，將模型延伸至灰 鑄鐵內環與氧化鋯外環組成之雙環結構，探討初始干涉量、熱膨脹係數、楊氏 模數及不同約束條件對界面接觸壓力、接觸範圍與法向間隙的影響。
分析結果顯示， 圓環在 均勻升溫且可自由變形時 不會產生明顯熱應力； 當存在徑向溫度梯度或機械約束時，則會因 熱膨脹受到限制或變形不相容而形 成熱應力 。感應加熱所產生之焦耳熱主要集中於靠近線圈的工件外表面， 使圓 環形成 外側溫度較高、內側溫度較低 的溫度分布，其熱應力主要受到溫度梯度 與約束條件控制。雙環接觸壓力則由初始干涉量及內、外環相對熱膨脹共同決 定，其中熱膨脹係數會同時影響接觸壓力與接觸範圍，楊氏模數主要影響接觸 壓力大小，而外環徑向約束的影響最為顯著。此外，界面傳熱會使氧化鋯外環 產生徑向溫度梯度及端部熱彎曲，造成上下端部形成局部間隙，使接觸壓力集 中於軸向中段。本研究結果可作為感應加熱雙環結構之材料選配、干涉量設計 及約束條件設定之參考。

This study develops a finite element model to investigate thermal expansion, thermal stress, and interfacial contact in hollow rings under induction heating. A single-ring model is first used to examine how temperature gradients, mechanical constraints, temperature-dependent properties, and relative magnetic permeability affect heating and thermal stress. The model is then extended to a double-ring structure consisting of a gray cast iron inner ring and a zirconia outer ring.
The results show that free uniform expansion produces negligible thermal stress, whereas temperature gradients and mechanical constraints cause significant stress. Induction heating concentrates Joule heat near the outer surface facing the coil, creating a nonuniform radial temperature field. In the double-ring structure, contact pressure is governed by initial interference and relative thermal expansion. The thermal expansion coefficient affects both contact pressure and contact range, while Young’s modulus mainly affects pressure magnitude. Radial constraint on the outer ring has the greatest influence. Furthermore, thermal bending of the zirconia outer ring causes end separation and concentrates contact pressure near the axial midsection.

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