Contact of surfaces and contact characteristics of offset surfaces

Abstract

Based on differential geometry, the contact problems of two surfaces are discussed in this paper. The relationship between the contact status of two surfaces and that of offset surfaces are also analyzed. For a 5-axis NC machining, some research such as optimization of cutter location and calculation of the geometrical cusp height are important. The research results indicate that the relative normal curvature is an important geometrical invariant for describing the contact state of two surfaces. For point contact two surfaces, the calculation equation for the second order remained error is given. For line contact two surfaces, the condition of the second order line contact is that the principal directions and curvatures of the two surfaces are the same along the contact curve. If two surfaces keep the second order line contact, their two offset surfaces will also keep the second order line contact, and their third order remained errors are also uniform with that of the two offset surfaces.

References

1. Sasaki S DifferentialGeometryTokyoKyoritsu Press 1956 (in Japanese)
2. Wu D R DifferentialGeometryBeijingThe People's Education Press 1981 (inChinese)
3. Baxter M L Second-ordersurface generationJ Indus Math 1973 23(2)85106
4. Litvin F L Chen N X Chen J S Computerized determination of curvature relations and contactellipse for conjugate surfacesComputerMethods in Applied Mechanics and Engineering 1995 125151170. doi:10.1016/0045‐7825(95)00799‐7
5. Yan Hongsen Cheng Wenteng Curvature analysis of spatialcam-follower mechanismsMechanism and MachineTheory 1999 34319339. doi:10.1016/S0094‐114X(98)00038‐X
6. Wang X C Li Y et al.A new approach for machiningsculptured surfaces by curvature catering methodChinese Journal of Mechanical Engineering 1992 5(3)221230
7. Cao L X Wu H J Liu J The geometrical theory of machining free form surface bycylindrical cutter in 5-Axis NC Machine ToolsInternationalConference of Manufacture Automation. HongKong 2002