中文摘要：

为使数控机床主轴系统热模型更为准确，混合响应面模型和多目标遗传算法，提出一种多参数、多目标热模型修正方法。该修正方法根据热平衡试验所获得的数控机床主轴系统热态特性（温升、热变形等）数据，采用中心复合设计的试验设计方法，在设计空间抽取样本点进行数值模拟，建立了由多个有限元热模型设计参数所决定的主轴系统热态特性的二阶响应面模型，利用多目标遗传算法对响应面模型进行循环逼近优化，取得Pareto最优解集，提高原有限元热模型的准确度。最后，以某精密数控双磨头磨床主轴系统为例进行分析，结合热平衡试验的温升和热变形数据，并以此为目标对其有限元热模型的4个主要参数（1个热流密度，3个换热系数）进行了修正研究。结果表明：提出的基于近似模型的多参数、多目标修正方法，适用于机床主轴系统等复杂结构的模型修正，可以有效地利用试验数据，通过有限次的数值模拟计算获得需修正参数的最优解，减少了模型分析的计算误差，使得修正后的模型结果更为接近实际。

英文摘要：

For thermal model of machine tool spindle system, a multi-parameter and multi-objective correction method is presented, which is hybrid response surface model and multi-objective genetic algorithm （MOGA）. Based on the thermal characteristic （ temperature and thermal deformation ） datum of spindle system from thermal equilibrium test, the central composite experiment design method and surface response method are combined to establish the second-order surface models of thermal characteristic for the multi-parameter finite element thermal model of spindle system. Then these surface models are optimized by employing the approximation loop technique of MOGA, and a distributed Pareto solution set is obtained. Finally, the accuracy of initial thermal model is improved. Taking a double spindle system of one precision CNC grinder as an example, the thermal model which included four input parameters and two output parameters is corrected with temperature and thermal deformation from thermal equilibrium test. It is shown that the model correction method can use the test datum effectively, and obtain the optimal solution for corrected parameters by limited simulation. The method is suitable for multi-parameter and multi-objective correction of complex model, which can reduce the model calculation error and make the correction model analysis results more realistic.