Research On Controlling Method Of NURBS Curve Interpolation Based On S Curve Acceleration And Deceleration Method

For complex parts CNC machining,how to realize tool path smooth interpolation control is very important.A NURBS curve interpolation method based on S curve acceleration and deceleration is developed in the paper.The NURBS curve length is calculated with the compound Simpson quadrature formula;The tool path curve feed speed is firstly planned within the limitation of the maximum permissible centripetal acceleration and the maximum permissible contour error.Then the NURBS curve is interpolated with the second-order Taylor expansion,and the feed speed is secondly planned within the limitation of the acceleration.The simulation machining results show that the introduced method can realize smooth motion control,and obtain satisfied machining precision.The main research contents are as follows:(1)In terms of interpolation algorithm,An detailed introduction is made about process of the NURBS method being proposed.The three equivalent definitions of NURBS curves and the nature of it are introduced as well as its three related parameters(the control point,node vector,weight factor).Then the advantages and disadvantages of the NURBS method are discussed.Finally,the calculation method of NURBS basis function and its derivatives are proposed.(2)In the aspect of controlling the NURBS interpolation speed,By analysis of the advantages and disadvantages of various acceleration and deceleration method,using S curve acceleration and deceleration mode.It is characterized by the continuous acceleration curve,it can effectively reduce impact,so it is widely used in high speed machining.(3)The location parameter of the interpolation point is calculated with the second-order Taylor expansion.Within the limitation of the maximum permissible centripetal acceleration.the maximum permissible contour error and the maximum permissible acceleration,adjusting speed to finish realtime interpolation.(4)In order to verify the correctness of the algorithm,a interpolation simulation test based on MATLAB on NURBS curve which is generated by seven control vertex is proposed,including the analysis of velocity profile,the analysis of curvature of curve.the analysis of centripetal acceleration profile,the analysis of contour error and the analysis of the fluctuation of acceleration.