惯性张量平移和旋转复合变换的一般形式及其应用

The General Formula of Composite Translation and Rotation Transformations of Inertial Tensor and Its Application

在汽车等工业领域中包含多个复杂子系统,需要将不同子系统的惯量进行合成。基于实物测量的方法对测量设备要求较高、周期长、成本高,基于CAD测量的方法对模型完整度要求高、实时性差,基于现有的理论变换方法难以求解同时包含平移和旋转的复合变换。为此,从惯性张量和位置矢量的坐标变换关系出发,采用矩阵变换推导出了惯性张量分量矩阵平移和旋转复合变换的一般形式,进一步完善了理论变换方法,同时解决了惯性矩和惯性积的坐标变换问题,给出了变换关系中各项的物理意义,讨论了在不同简化条件下的理论结果。为验证推导的理论方法的有效性,分别采用该理论方法和CAD软件测量方法对包含三个组件的某系统的惯性矩、惯性积进行了合成,算例结果表明理论方法与CAD软件的测量结果一致,充分验证了推导的理论方法的有效性,相关结果可实现工程中多组件复杂系统惯量的快速合成,具有一定理论意义和工程使用价值。

In the fields of automobile and other industries,there are many complex subsys-tems,which need to synthesize the inertia of different subsystems.The physical-measurement-based method has strict requirements for measuring equipment,long cycle and high cost.The CAD-measurement-based method has high requirements for model integrity and poor real-time performance.The theoretical-transformation-based methods are difficult to solve the composite transformation.Therefore,starting from the coordinate transformation of the position vector,the general form of the composite transformation of the translation and rotation of the inertial tensor component matrix is derived by using the matrix transformation,which further improves the theoretical transformation method.At the same time,the coordinate transformation prob-lem of the inertial moment and inertial product is solved,the physical meaning of each item in the transformation relationship is given,and the theoretical results under different simplified conditions are discussed.The results of the typical example show that the theoretical method is consistent with the measurement results of CAD software,which verifies the effectiveness of the derived theoretical method.The relevant results can realize the rapid synthesis of inertia of multi component complex systems in engineering.Thus,the proposed method has certain theoretical significance and engineering application value.