耦合几何与材料误差的柔性装配偏差统计分析

Statistical variation analysis of compliant assembly coupling geometrical and material error

飞机结构中包含大量的弱刚性柔性零件,柔性零件在装配中的受力变形,是影响飞机尺寸质量的重要因素。针对仅考虑零件几何误差进行装配偏差建模的不足,结合一阶摄动理论和有限元方法,提出了耦合柔性零件几何和材料误差的装配偏差统计分析(SVA_G&M)方法。该方法运用影响系数法建立零件几何、弹性模量和泊松比误差与装配偏差的关系,在此基础上利用泰勒公式推导了装配偏差的均值和协方差方程。结合薄板、某飞机平尾前缘组件两个装配实例,将该方法与基于ANSYS的有限元装配过程仿真法进行了实验对比。结果表明,两种方法计算得到的装配偏差均值和标准差非常吻合,但在计算时间上前者只用了30s,而后者用了250min,前者算法效率远高于后者。实验还表明材料误差对装配偏差具有明显影响,其中弹性模量的影响大于泊松比,与仅考虑几何误差的装配偏差分析方法相比,该方法对装配偏差的预测更加真实准确。

Compliant part is widely used in aircraft structure. Its deformation subjected to assembly forces is an important issue in assembly dimensional management for aircraft. To compensate for the deficiencies of assembly variation model concerning merely geometrical error of part, a method of statistical variation analysis for compliant assembly coupling the geometrical and material error （SVA_G＆M） is proposed based on the first-order perturbation theory and the finite element method. In the SVA_G ＆ M method, the method of influence coefficients is adopted to deduce the assembly variation regarding the source errors of part geometrical shape, material elastic modulus and Poisson＇s ratio, and the mean and standard deviation equations of assembly variation are formulated. Two experiments, simple sheet metals assembly and leading edge assembly of aircraft horizontal tail, are illustrated to verify the proposed method, and it is compared to the assembly process simulation of ANSYS finite element method （FEM）. The result shows that the mean and standard by the SVA_G ＆ M method has a good agreement with the FEM simulation. Meanwhile, the computing time is 30 s and 250 min respectively, which indicates that the SVA_G ＆ M method is much more efficient than the FEM simulation. The experiments also show that material error has a considerable effect on assembly variation, in which elastic modulus plays a more important role than Poisson;s ratio. Compared to assembly variation model concerning merely geometrical error, the SVA_G ＆ M method can make more accurate and practical variation prediction of compliant assembly.