A comprehensive adaptive approach to calculating the envelope surface of the digital models in CNC machining

Abstract The digital models are the fundamental elements used in the virtual simulation of CNC machining for process planning, result prediction, analysis, etc. The essential work to build the digital models of machined parts is the calculation of the envelope surface generated by moving a cutter surface relative to workpieces. This calculation is usually complicated, and the requirements in different cases are also varied. Hence, it is very beneficial to develop an effective approach for different requirements. In this work, a comprehensive envelope approach is established, and it adaptively choose 1) the elimination parameter among two cutter surface parameters, 2) the representation form of envelope surface, and 3) the discretization way, so it is robust to satisfy different requirements. The elimination parameter and representation form are adaptively chosen to improve the calculation efficiency by obtaining the closed-form representation of the envelope surface prior to the implicit one. The discretization way is further adaptively chosen to obtain approximately even point distribution to the applications of 3D and FEA modeling. Finally, comprehensive algorithms are proposed to effectively implement this adaptive envelope approach for different applications. The examples are given to the manufacturing of spiral bevel gears and five-axis CNC milling.

[1]  Cai-chao Zhu,et al.  Investigation on the influence of work holding equipment errors on contact characteristics of face-hobbed hypoid gear , 2019, Mechanism and Machine Theory.

[2]  Sanjeev Bedi,et al.  Surface swept by a toroidal cutter during 5-axis machining , 2001, Comput. Aided Des..

[3]  Yuansheng Zhou,et al.  An innovative approach to NC programming for accurate five-axis flank milling of spiral bevel or hypoid gears , 2017, Comput. Aided Des..

[4]  Karim Abdel-Malek,et al.  Multiple sweeping using the Denavit-Hartenberg representation method , 1999, Comput. Aided Des..

[5]  Yuansheng Zhou,et al.  A new closed-form calculation of envelope surface for modeling face gears , 2019, Mechanism and Machine Theory.

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

[7]  Jie Sun,et al.  A novel approach to determination of wheel position and orientation for five-axis CNC flute grinding of end mills , 2016 .

[8]  Yuansheng Zhou,et al.  An accurate, efficient envelope approach to modeling the geometric deviation of the machined surface for a specific five-axis CNC machine tool , 2015 .

[9]  Chih-Hsing Chu,et al.  Five-axis flank machining of ruled surfaces with developable surface approximation , 2005, Ninth International Conference on Computer Aided Design and Computer Graphics (CAD-CG'05).

[10]  Chih-Hsing Chu,et al.  Machining accuracy improvement in five-axis flank milling of ruled surfaces , 2008 .

[11]  Zhenyu Zhou,et al.  A hybrid modification approach of machine-tool setting considering high tooth contact performance in spiral bevel and hypoid gears , 2016 .

[12]  Zhenyu Zhou,et al.  An advanced CAD/CAE integration method for the generative design of face gears , 2018, Adv. Eng. Softw..

[13]  Sanjeev Bedi,et al.  Generalization of the imprint method to general surfaces of revolution for NC machining , 2002, Comput. Aided Des..

[14]  Liming Wang,et al.  A New and Accurate Mathematical Model for Computer Numerically Controlled Programming of 4Y1 Wheels in 2½-Axis Flute Grinding of Cylindrical End-Mills , 2013 .

[15]  Ning Wang,et al.  Analytical calculation of the envelope surface for generic milling tools directly from CL-data based on the moving frame method , 2009, Comput. Aided Des..

[16]  Antoniadis Aristomenis,et al.  CAD-Based Calculation of Cutting Force Components in Gear Hobbing , 2012 .

[17]  Faydor L. Litvin,et al.  Design and Geometry of Face-Gear Drives , 1992 .

[18]  Ben Richard Hughes,et al.  The development of modelling tools to improve energy efficiency in manufacturing processes and systems , 2019, Journal of Manufacturing Systems.

[19]  Chih-Hsing Chu,et al.  Tool path planning for 5-axis flank milling of ruled surfaces considering CNC linear interpolation , 2012, J. Intell. Manuf..

[20]  Yuansheng Zhou,et al.  A novel method to generate the tooth surface model of face-milled generated spiral bevel gears , 2019 .

[21]  Zeng-Jia Hu,et al.  Swept volumes generated by the natural quadric surfaces , 1996, Comput. Graph..

[22]  Panagiotis Stavropoulos,et al.  Indirect online tool wear monitoring and model-based identification of process-related signal , 2020 .

[23]  F. Litvin,et al.  Gear geometry and applied theory , 1994 .

[24]  Eyyup Aras,et al.  Generating cutter swept envelopes in five-axis milling by two-parameter families of spheres , 2009, Comput. Aided Des..

[25]  Yuansheng Zhou,et al.  An adaptive geometric meshing theory for the face-milled generated spiral bevel gears , 2019 .

[26]  M. Sortino,et al.  An innovative approach for automatic generation, verification and optimization of part programs in turning , 2015 .

[27]  Ming C. Leu,et al.  Analysis and modelling of deformed swept volumes , 1994, Comput. Aided Des..

[28]  Panagiotis Stavropoulos,et al.  Prediction of surface roughness magnitude in computer numerical controlled end milling processes using neural networks, by considering a set of influence parameters: An aluminium alloy 5083 case study , 2014 .

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

[30]  Q. Fan,et al.  Ease-Off and Application in Tooth Contact Analysis for Face-Milled and Face-Hobbed Spiral Bevel and Hypoid Gears , 2016 .

[31]  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 .

[32]  Nikolaos Tapoglou.  Calculation of non-deformed chip and gear geometry in power skiving using a CAD-based simulation , 2019 .

[33]  Zezhong C. Chen,et al.  An Efficient, Accurate Approach to Representing Cutter-Swept Envelopes and Its Applications to Three-Axis Virtual Milling of Sculptured Surfaces , 2008 .

[34]  Yuansheng Zhou,et al.  A new geometric meshing theory for a closed-form vector representation of the face-milled generated gear tooth surface and its curvature analysis , 2015 .

[35]  Berend Denkena,et al.  Virtual process systems for part machining operations , 2014 .

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

[37]  Jinyuan Tang,et al.  A new worm grinding method of face gears based on the optimization of dressing wheel profile , 2019 .

[38]  K. K. Wang,et al.  Geometric Modeling for Swept Volume of Moving Solids , 1986, IEEE Computer Graphics and Applications.

[39]  Zezhong C. Chen,et al.  A Generic and Efficient Approach to Determining Locations and Orientations of Complex Standard and Worn Wheels for Cutter Flute Grinding Using Characteristics of Virtual Grinding Curves , 2017 .

[40]  Ming C. Leu,et al.  The sweep-envelope differential equation algorithm and its application to NC machining verification , 1997, Comput. Aided Des..

[41]  Yuansheng Zhou,et al.  A New Method of Designing the Tooth Surfaces of Spiral Bevel Gears With Ruled Surface for Their Accurate Five-Axis Flank Milling , 2017 .

[42]  Byoung Kyu Choi,et al.  Modeling the surface swept by a generalized cutter for NC verification , 1998, Comput. Aided Des..

[43]  Yuan-Shin Lee,et al.  Swept surface determination for five-axis numerical control machining , 2002 .

[44]  Karim Abdel-Malek,et al.  Geometric representation of the swept volume using Jacobian rank-deficiency conditions , 1997, Comput. Aided Des..

[45]  Liming Wang,et al.  CNC milling of face gears with a novel geometric analysis , 2019 .

[46]  Behrooz Arezoo,et al.  Virtual machining considering dimensional, geometrical and tool deflection errors in three-axis CNC milling machines , 2014 .

[47]  Han Ding,et al.  An accurate model of high-performance manufacturing spiral bevel and hypoid gears based on machine setting modification , 2016 .

[48]  Klaus Weinert,et al.  Formulating swept profiles for five-axis tool motions , 2005 .