在工具機的運轉中，各機件的配合度、受熱後的熱誤差、機台的震動…等因素影響加工精度，其中熱誤差即是最重要的關鍵之一，它影響了加工成品最終的精度。但是對於機具內部各組件摩擦與散熱系統所產生的熱傳導、對流與輻射這幾種基本的物理現象，各部件的熱漲冷縮是無可抵抗的，抑制或補償其熱誤差已經成為設計一台工具機的重要關鍵。在舊有文獻中，由於難以在切削時偵測其熱誤差，因此多數都以空負載實驗去量測主軸高速運轉所產生的偏移，進一步了解主軸在各轉速與時間之下形成的熱特性，進而建立主軸行為的模型，預測並且補償其熱誤差。
在本研究中，使用有限元素模擬分析主軸內部熱場分布，建立出主軸暫態與穩態的溫度變化與熱誤差模型。同時採用了舊有文獻的熱誤差量測方式，透過外部量測系統建立數種熱變位模型，包括常見的回歸模型、主成分分析模型和神經網路模型，還有集成學習法，比較各個數學模型的預測能力。更在近年來廣泛被工具機產業所使用的高速同步內藏式主軸內部埋設感測器，包含埋設在前、後軸承與馬達定子的三組熱電偶與另外兩組安裝在主軸冷卻油路系統出口與入口的熱電偶，一個非接觸式位移感測器量測主軸熱誤差，真正監控加工下主軸的狀態。為了量測在加工條件下熱誤差變化，設置螺桿平台帶動工件模擬短時間重負載條件與使用動力計模擬長時間铣削的條件，驗證內部感測器的可靠度與優勢，加強主軸面對外來突發事件的診斷與應變能力。

In the high-precision machining industry, thermal expansion of the high-speed spindle can result in significant displacement errors. As a result, the geometry of the final machined component may deviate significantly from the design values. However, most of the compensation methods do not monitor thermal error of the spindle during machining. This study develops an embedded thermal error measurement system comprising a non-contact displacement sensor mounted at the front of the spindle, and three thermistors installed at the front bearing, rear bearing, and motor stator. Two additional thermocouples are used to measure the inlet and outlet temperatures of the liquid cooling system. The research built several mathematical models based on the relation between the readings of each temperature and the internal displacement sensor, and compared to the output of the external displacement sensor to select the model that gives the best prediction. Both workpiece machining and load simulation used screw and dynamometer to consider the effect of the reverse torque during machining. The experimental results verified that the spindle thermal error is significantly affected by the reaction force from the workpiece. This research also analyzed the structure and thermal aspects by using a finite element model, and was then validated to the experiment results. Overall, the results show that the method will improve the shortcomings of outside sensor cannot use during manufacturing.

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