運行條件（包括運行速度和環境溫度）不僅會影響整個機床的熱變形特性，還會影響主軸的熱變形特性。雖然已知熱致誤差會在環境溫度變化時顯著影響機床和主軸的精度，但過去熱誤差未得到適當補償。因此，需要熱誤差模型來補償和減少機床和主軸運行期間的誤差。在這項工作中，實驗研究了操作速度和環境溫度的變化對主軸熱變形特性的影響。此外，通過結合模糊C均值聚類，Pearson相關，多項式回歸分析建立熱誤差模型。通過熱誤差模型，建立了熱變形與溫升之間的關係。結果表明，利用三個溫度敏感點，熱誤差模型可以準確計算環境溫度和速度變化條件下的熱誤差。 Operating conditions (including operational speed and ambient temperature) significantly affect the thermal deformation characteristics of not only the entire machine tool but also the spindle. Although thermally induced errors were known to significantly affect the accuracy of machine tools and spindles when the ambient temperature changed, thermal errors were not properly compensated in the past. A thermal error model is therefore needed to compensate and reduce error during the operation of a machine tool and spindle. In this work, the effects of the changes in the operational speed and ambient temperature on the thermal deformation characteristics of a spindle are investigated experimentally. In addition, a thermal error model is established by combining the fuzzy C-mean clustering, Pearson correlation, multinomial regression analysis. Through the thermal error model, relationship between thermal deformation and temperature rise is established. Results show that using three temperature sensitive points, the thermal error model can accurately calculate the thermal errors under conditions of changing ambient temperature and speed.