Improved Dimension Reduction Method Based Reliability Algorithms And Applications To Heavy Duty Forging Manipulator

The heavy duty forging manipulator, with the heavy load, large inertia and multi-degree-of freedom, has the capacity of multi-dimensional control of forces and positions, which could greatly improve the capacity and precision of manufacture, production efficiency, material utilization and reduce the energy consumption working together with the heavy duty hydraulic. The key issues for the heavy duty forging manipulator design focus on how to guarantee the operating performance of the forging manipulator, the capacities of strength and stiffness of the components, the interface characteristics between the key components under the extreme conditions. With the support of the973Program "the mechanical properties and interface characteristics of the heavy load manipulator under discontinuous load cases"(No.2006CB705403),this paper introduces the uncertainty analysis and optimization thoughts into the heavy duty equipment concentrates on the reliability algorithm based on the Univariate Dimension Reduction Method(UDRM,DRM) and the correlated random variable for the reliability algorithm, and discusses the key issues, such as the mechanical properties of the key component of the forging manipulator, reliability analysis and the structural optimization design.Related studies of this paper are listed as follows:1. The Normalized Moment Based Quadrature Rule (NMBQR) is proposed. The numerical instability of the Moment Based Quadrature Rule (MBQR) in the DRM could occur in the condition of the great mean value or the small coefficient of variation of the input parameters. The NMBQR could effectively improve the numerical instability of singular coefficient matrix by normalizing the parameters when solving the linear equations.2. The reliability algorithm based on the Improved Dimension Reduction Method is proposed by combining the Improved DRM and Maximum Entropy Method (MEM) which is used to calculate the probability density function (PDF) of the response. The results of the numerical examples show that the reliability algorithm based on the Improved DRM has the great advantages, such as no need of the derivative of the response function and the iterative procedure for the Most Probable failure Point (MPP), resulting in high computational efficiency.3. The Improved DRM based reliability algorithm for the correlated random variables is proposed. The Nataf transformations and Winterstein approximations could normalize the correlated random variables with arbitrary distributions. The independent random variables could be obtained by the Cholesky factorization and the reliability can be calculated by the improve DRM. Compared to JC method for the correlated variables, the Nataf transformations give the equivalent probability transformations on all domain of the design space. As for the correlation coefficient in the Nataf transformations, the two-dimensional Gauss-Hermite quadrature is carried out instead of the empirical formula. The correlation coefficient is obtained by the polynomial equation for the Winterstein approximations, which has the closed-form solution with high computational efficiency.4. The reliability analysis for the wall frame of the forging manipulator based on the surrogate model is carried out. The uncertainty factors include the thickness of the ribs, the thickness of the side wall and the load. The explicit function of the structural response with respect to the input parameters can be achieved by the Design of Experiment (DOE) and Response Surface Method (RSM).The reliability of the wall frame of the forging manipulator is calculated by the proposed method considering the strong correlated relationship between the loads.5. The structural optimization for the wall frame of the forging manipulator is performed and a new type of wall frame structure of the forging manipulator is proposed. The mechanical properties of the new type wall frame structure are improved with the less material consumption. Due to the lack of the effective utilization of the materials and the less contribution to the side stiffness of the original design of the wall frame, the topology optimization for the maximum structural stiffness is given. The results of the topology optimization is introduced to the distribution of the ribs of the wall frame and the new finite element model (FEM) is built. Then the optimal designs are obtained by the sizing optimization based on the surrogate model, which show that the stiffness and strength are improved with the reduction of the materials.