Envelope to a Two-Parameter Family of Point Vectors Method for Surface Swept by Form Wheel

Abstract:

The form wheel generating curve is always a composited curve which is composed of lines and arcs, and the calculation of the envelope surface is more complex than conventional rotary cutter. Therefore, a method of envelope to a two-parametric family of point vectors is proposed, which defines the point and its normal vector on the wheel generating curve as a point vector. Each point vector corresponds to a virtual ball uniquely. The rotation of point vector forms latitude circle and the valid envelopment movement forms sectional circle. The intersection of latitude circle and sectional circle is grazing point; The analytical calculation model is established, in which the geometry parameters of virtual ball can be directly calculated from point vector; An example is presented to demonstrate the effectiveness of the method which can be used for form grinding geometry simulation, accuracy evaluation and optimization of the wheel path.

• Periodical: Applied Mechanics and Materials (Volumes 494-495)
• Pages: 563-568
• DOI: https://doi.org/10.4028/www.scientific.net/AMM.494-495.563
• Online since: February 2014
• Authors: Yuan Zhi Peng, Kun He*, Guo Long Li, Wei Zhang
• Keywords: Family of Point Vectors, Form Grinding, Grinding Wheels, Swept Envelope, Two-Parameter Movement

References

[1] LI GUO-LONG, LI XIAN-GUANG, LIU FEI, et al. Method of Profile Optimization of a Form Grinding Wheel for grinding with Additional Radial Motion of Topologically Modified Gear[J]. Chinese Journal of Mechanical Engineering，2011, 47(11): 155—162. In Chinese.

DOI: 10.3901/jme.2011.11.155

[2] SHIH Y P, CHEN S D. A flank correction methodology for a five-axis CNC gear profile grinding machine[J]. Mechanism and Machine Theory, 2012, 47: 31—45.

DOI: 10.1016/j.mechmachtheory.2011.08.009

[3] LIU FENG-LIN, QIN DA-TONG, XU XIAO-GANG et al. Accurate mathematical models for relief grinding of gear hob cutters[J]. Journal of Chongqing University, 2009, 32(12): 1374-1380. In Chinese.

[4] DING HAN, ZHU LI-MING. Geometric theories and methods for digital manufacturing of complex surfaces[M]. Beijing: Science Press, 2011. In Chinese.

[5] CHIOU C J, LEE Y S. Swept surface determination for five-axis numerical control machining[J]. International Journal of Machine Tools and Manufacture, 2002, 42(14): 1497—1507.

DOI: 10.1016/s0890-6955(02)00110-4

[6] DU SHANG-JAN, SURMANN T, WEBBER O, et al. Formulating swept profiles for five-axis tool motions[J]. International Journal of Machine Tools and Manufacture, 2005, 45(7-8): 849—861.

DOI: 10.1016/j.ijmachtools.2004.11.006

[7] GONG HU, WANG NING. Analytical calculation of the envelope surface for generic milling tools directly from CL-data based on the moving frame method[J]. Computer-Aided Design, 2009, 41(1): 848—855.

DOI: 10.1016/j.cad.2009.05.004

[8] ARAS E. Generating cutter swept envelopes in five-axis milling by two-parameter families of spheres[J]. Computer-Aided Design, 2009, 41(2): 95—105.

DOI: 10.1016/j.cad.2009.01.004

[9] ZHU LI-MING, ZHENG GANG, DING HAN. Formulating the swept envelope of rotary cutter undergoing general spatial motion for multi-axis NC machining[J]. International Journal of Machine Tools and Manufacture, 2009, 49(2): 199—202.

DOI: 10.1016/j.ijmachtools.2008.10.004

[10] MEEK D S, WALTON D J. Approximation of discrete data by G1 arc splines[J]. Computer-Aided Design, 1992, 24(6): 301-306.

DOI: 10.1016/0010-4485(92)90047-e

[11] LI GUO-LONG, SUN MENG-HUI, LI XIAN-GUANG, LIU FEI. Method of Discreting Cusp Vectors of Helicoid and its Application in Minimization of the Relief Grinding of Double Circular-arc Gear Hob[J]. Chinese Journal of Mechanical Engineering，2011, 47(17): 187—192. In Chinese.

DOI: 10.3901/jme.2011.17.187