The Precision Synthesis Of Three-axis Vertical Machining Based On Jacobian-torsor And Homogeneous Coordinate Transformation

Modeling of CNC machine most focus on the influence of component error for the machine tool error.But,how the part error affect the component error and how to describe it quantitatively is still unsolved although this makes great sense to precision design.The tolerance chain model is the main method to analyze the assembly tolerance,it is hard to solve the 3D tolerance analysis and to describe shape and geometric tolerance.The Jacobian-Torsor model based on Small Displacement Torsor and Jacobian matrix was introduced in this thesis,it helps establish the model of part error and transfer these errors.The research of the sensitivity of each error source provide theory for manufacturing and assembly.(1)Jacobian-Torsor model based on Small Displacement TorsorThis thesis first introduced Jacobian-Torsor model to research the assembly of machine tool.It used Small Displacement Torsor to express the error of each part and the assembly process.Solve the constraint equation and achieve error ranges,then establish the Jacobian matrix based on the relationship between different coordinate system.It solved how to build SDT of some error source under parallel constraint.(2)Synthesis error model of AxisBefore,Jacobian-Torsor model was used on gear pump assembly and engine assembly,this thesis applied it to three-axis machining center.Analyze the structure of machine tool and judge the error sources.Establish SDT of each part and the assembly process,use Jacobian matrix to transfer and accumulate error,thus to build the synthesis error model of axis.(3)Error synthesis and sensitivity analysis based on Monte Carlo methodAfter modeling of axis,use Monte Carlo method to generate random number of each torsor to simulate the error model.Calculate the extreme value and the value in confidence interval of 99.45% of synthesis error.Using control variable method to analyze the sensitivity of each torsor to the synthesis error.As a result,this provides theory for precision control in manufacturing and assembly.(4)Error synthesis and analysis of Three-Axis vertical machining centerBased on the above theoretical research,in view of the characteristics of each axis,establish the synthesis error model of each axis,complete the error accumulation from parts to component.Because of the manufacturing precision of three-axis machining center depends on the location relationship between workplace and cutter,research error transfer path of workplace and error transfer path of cutter.Get the SDT expression of workplace and cutter,then build the error ellipsoid of them,the manufacturing precision of machining center can be described as the distance between two points in different error ellipsoid.