Optimizing tool size and tool path of five-axis flank milling with bounded constraints via normal mapping

This article presents an approach to generate optimal couples of tool size and tool path for flank milling ruled surface with a conical cutter based on normal mapping, while at the same time keeping this couples within the given bounded constraints. For given initial pairs of taper tool and tool path, tool envelope surface is calculated. Then, the tool axis trajectory surface is related to envelope surface through the normal mapping. On this basis, the correspondence between the surface pair “design ruled surface–envelope surface–tool axis trajectory surface” is established, and it is used to obtain the signed flank milling error. By using this signed error, tool size and tool path optimization for flank milling is formulated as an optimization model subjected to bounds, and the trust-region-reflective least-squares method is used to solve this problem. Numerical example is given to confirm the validity of the proposed method.

[1]  Walter Rubio,et al.  Five-axis NC milling of ruled surfaces: Optimal geometry of a conical tool , 2002 .

[2]  Han Ding,et al.  Global optimization of tool path for five-axis flank milling with a cylindrical cutter , 2009 .

[3]  Stephen P. Radzevich.  Kinematic geometry of surface machining , 2007 .

[4]  Li-Min Zhu,et al.  Envelope Surface Modeling and Tool Path Optimization for Five-Axis Flank Milling Considering Cutter Runout , 2014 .

[5]  Han Ding,et al.  Simultaneous optimization of tool path and shape for five-axis flank milling , 2012, Comput. Aided Des..

[6]  Claire Lartigue,et al.  Tool path deformation in 5-axis flank milling using envelope surface , 2003, Comput. Aided Des..

[7]  H. Ding,et al.  A Distance Function Based Approach for Localization and Profile Error Evaluation of Complex Surface , 2004 .

[8]  Michael Barton,et al.  Towards efficient 5-axis flank CNC machining of free-form surfaces via fitting envelopes of surfaces of revolution , 2016, Comput. Aided Des..

[9]  Alain Bernard,et al.  5-axis flank milling: A state-of-the-art review , 2013, Comput. Aided Des..

[10]  Li-Min Zhu,et al.  Cutter size optimisation and interference-free tool path generation for five-axis flank milling of centrifugal impellers , 2012 .

[11]  Walter Rubio,et al.  Calculation of tool paths for a torus mill on free-form surfaces on five-axis machines with detection and elimination of interference , 1998 .

[12]  Behzad Fatahi,et al.  Numerical optimization applying trust-region reflective least squares algorithm with constraints to optimize the non-linear creep parameters of soft soil , 2017 .

[13]  John C. J. Chiou,et al.  Accurate tool position for five-axis ruled surface machining by swept envelope approach , 2004, Comput. Aided Des..

[14]  Bo Zhao,et al.  Tool path optimization for five-axis flank milling with cutter runout effect using the theory of envelope surface based on CL data for general tools , 2016 .

[15]  Han Ding,et al.  Analytical Expression of the Swept Surface of a Rotary Cutter Using the Envelope Theory of Sphere Congruence , 2009 .

[16]  Han Ding,et al.  Global optimization of tool path for five-axis flank milling with a cylindrical cutter , 2009, Comput. Aided Des..

[17]  Liang Yu,et al.  Envelope surface formed by cutting edge under runout error in five-axis flank milling , 2013 .

[18]  Han Ding,et al.  Geometry of Signed Point-to-Surface Distance Function and Its Application to Surface Approximation , 2010, J. Comput. Inf. Sci. Eng..

[19]  L. Piegl,et al.  The NURBS Book , 1995, Monographs in Visual Communications.

[20]  J. Paulo Davim,et al.  Machining of Complex Sculptured Surfaces , 2012 .

[21]  Jian Liu,et al.  Improved positioning of cylindrical cutter for flank milling ruled surfaces , 2005, Comput. Aided Des..

[22]  Han Ding,et al.  Formulating the swept envelope of rotary cutter undergoing general spatial motion for multi-axis NC machining , 2009 .

[23]  Ning Wang,et al.  Optimize tool paths of flank milling with generic cutters based on approximation using the tool envelope surface , 2009, Comput. Aided Des..

[24]  Johanna Senatore,et al.  Analysis of improved positioning in five-axis ruled surface milling using envelope surface , 2005, Comput. Aided Des..

[25]  Li-Min Zhu,et al.  Five-axis flank milling of impellers: Optimal geometry of a conical tool considering stiffness and geometric constraints , 2016 .

[26]  Der Min Tsay,et al.  Accurate 5-Axis Machining of Twisted Ruled Surfaces , 2001 .

[27]  Walter Rubio,et al.  Side milling of ruled surfaces: Optimum positioning of the milling cutter and calculation of interference , 1998 .

[28]  Sanjeev Bedi,et al.  Flank milling with flat end milling cutters , 2003, Comput. Aided Des..

[29]  David H. Eberly,et al.  Geometric Tools for Computer Graphics , 2002 .

[30]  Walter Rubio,et al.  Comparative study of interference caused by different position settings of a conical milling cutter on a ruled surface , 2001 .

[31]  Thomas F. Coleman,et al.  An Interior Trust Region Approach for Nonlinear Minimization Subject to Bounds , 1993, SIAM J. Optim..