Time-Varying Characteristics of Bending Deformation of Work-Piece in the Turning Process

Abstract:

Based on the geometrical description of work-pieces cutting process, the time-varying differential equations of deflection curve under two different conditions were obtained using the singular function: one with thimble and one without thimble constraint. Using the Mathcad software, we have solved the time-varying differential equations analytically and have studied the deflection changing of work piece with the position of turning tool and given the distribution characteristic for the time-varying deflection of each section. The results indicate that (1) the deflection of an arbitrary section is time-varying due to the time-varying position of the turning tool and the time-varying inertia moment; (2) for the shaft with thimble constraint, the position of the maximal deflection is not at the section with turning tool; (3) for the shaft without thimble constraint, when the turning tool is at the free end, the deflection at each section of the work-piece is the maximal compared with the other positions of turning tool.

• Periodical: Advanced Materials Research (Volume 337)
• Pages: 203-208
• DOI: https://doi.org/10.4028/www.scientific.net/AMR.337.203
• Online since: September 2011
• Authors: Shun Cai Li, Hua Meng
• Keywords: Deflection, Singular Function Method, Turning Machining, Variable Boundaries Systems

References

[1] SUN M., TANG P., Chen Z.: Expectation on dynamic system with variable boundary. Journal of Changde Teachers University (Natural Science Edition), 15(2), 12-15(2003) (in Chinese)

[2] Naunov, V. E.: Mechanics of growing deformable solids: A review. Journal of Engineering Mechanics, 120(2), 207-220(1994)

[3] Huang Z.: Continuum model for growth and deformation of materials: equilibrium equations and boundary conditions. Chinese Quarterly of Mechanics, 24(4), 494-499(2003) (in Chinese)

[4] Zhou G.，Huang Z.: Continuum model for growth and deformation of materials constitutive equations based on first-order gradient theory. Chinese Quarterly of Mechanics, 25(2), 163-167(2004) (in Chinese)

[5] Cao Z.: Construction mechanics and time-varying mechanics in civil engineering. Journal of China Civil Engineering, 34(3), 41-46(2001) (in Chinese)

[6] Zeng Q., Guo X.: Vibration analyses of time-varying system of train-bridge and its application. Beijing: China railway publishing House (1999).

[7] Yang F., Yu J.: Zhang H.: On-line control of cutting vibrations. Journal of Jiling University of Technology, 24(2), 27-33(1994) (in Chinese).

[8] Li Y.，TANG P., LI T.: Analysis on shaft lathe coupled vibration by dynamics of systems with variable boundaries. Journal of Hunan Institute of Engineering, 16(2), 24-27(2006) (in Chinese).

[9] Yang F., Yu J., Zhang H.: A study on stability of tool working orthogonal rake system with time-variation [J]. Journal of Vibration Engineering, 7(1), 80-85(1994) (in Chinese)

[10] Bao S., Yang F., Wang H., Qiao S.: Theoretical analysis and experimental verification of suppressing chatter by time-varying feed rate. Journal of Vibration Engineering, 8(4):293-301(1995) (in Chinese)

[11] Zhang Q: Cutting force modeling and analysis in axial contour CNC turning. Jiling University, Jiling (2007) (in Chinese)

[12] Ren C.: Modal analysis of work-piece in turning operation. Mechanical Research & Application, 4(19), 32-33(2006) (in Chinese).

[13] Wang X.: Singular functions and their application in mechanics. Beijing：Science publishing house (1993)