Parallel Mechanism Structure Optimization Design Based On The Whole Machine Stiffness Characteristics

After years of research,the basic theory of parallel mechanism has been gradually perfect.Due to its unique quality,parallel mechanism can make up many shortcomings of serial mechanism.The advantages of parallel mechanism products has been found in all areas.But after years of applications,many problems appear and need to be solved.High stiffness is one of the important factors to ensure the precision of product.The parallel mechanism has been used in many areas,especially in the field of machine tool due to its high stiffness.The prototype experiments show that the machining precision of parallel machine tool is not as good as that of traditional serial machine tool and its insufficient stiffness restricted the further development in the field of machine tool.Because of the complexity and non-additivity of the stiffness of the parallel mechanism,the present analysis of the stiffness can not take all factors into account.But by only considering some main influence factors,the optimal design of the parallel mechanism can be achieved.The 3-TPT parallel mechanism was studied in this thesis.The influence of active joints and passive joints and bars on the whole stiffness were analyzed for steady state,and the structure sizes of the parallel mechanism were optimized.The main research contents were as follow:Firstly,the basic problems for 3-TPT parallel mechanism were analyzed.The configuration of 3-TPT parallel mechanism was analyzed,and the degree of freedom was calculated.It was determined that the working point could move along three axes.The kinematics of the mechanism was analyzed for obtaining the positive and inverse solution expression of the position and the velocity Jacobian matrix.The work space of the parallel mechanism was calculated,and the workspace simulation diagrams were established by using Matlab software.Secondly,the stiffness characteristics of 3-TPT parallel mechanism were analyzed.According to the principle of virtual work,the Jacobian matrix could be solved.The axial stiffness of branch chain was solved,and the influence of the components stiffness on the branch chain was analyzed.Based on the analytical model,the static stiffness characteristic of the parallel mechanism was analyzed,and the whole stiffness matrix was obtained.The stiffness matrices of some points on the work space of the parallel mechanism was solved,and their variations were analyzed.Thirdly,the performance evaluation index of the 3-TPT parallel mechanism was analyzed.By using the minimum eigenvalue method and static stiffness performance quotient method,the stiffness of the 3-TPT parallel mechanism was simulated.The advantages and disadvantages of these two methods were discussed.The minimum eigenvalue method was more suitable for optimization,and the static stiffness performance method was more suitable for verifying the optimized results.The work space performance of the parallel mechanism was analyzed,and the length range of the branch chain was obtained,which guaranteed that the structure optimization was performed within allowance.Finally,the structure sizes of the 3-TPT parallel mechanism were optimized.According to the smallest eigenvalue method,the influences of the main structure sizes on the whole machine stiffness were analyzed.An optimization model was established in order to increase stiffness in the work space,the minimum eigenvalue of the boundary point was the optimization objective,the work space was the constraint conditions,and the main structure sizes were the design variables.Then the sizes of the parallel mechanism were optimized.By using the minimum eigenvalue method and the static stiffness performance evaluation method,the comparison of the stiffness for the optimized and unoptimized parallel mechanisms was made to validate the effectiveness of the proposed optimization method.In this thesis,the stiffness of 3-TPT parallel mechanism was analyzed and optimized,and the working space performance for the optimized parallel mechanism was guaranteed.The proposed optimization method provided a good foundation for the further optimal design of parallel mechanism.