Research Papers

Determination of Motion Equation of Rivet Head During Shaft Riveting Assembly Process for Wheel Hub Bearing Units

[+] Author and Article Information
Jie Qu

Associate Professor
School of Mechanical & Automotive Engineering,
South China University of Technology, Guangzhou 510640, China
e-mail: qujie@scut.edu.cn

Guojie Zhang

School of Mechanical & Automotive Engineering,
South China University of Technology, Guangzhou 510640, China
e-mail: infinitezgj@163.com

1Corresponding author.

Contributed by the Manufacturing Engineering Division of ASME for publication in the JOURNAL OF MANUFACTURING SCIENCE AND ENGINEERING. Manuscript received February 25, 2015; final manuscript received September 9, 2015; published online October 27, 2015. Editor: Y. Lawrence Yao.

J. Manuf. Sci. Eng 138(4), 041006 (Oct 27, 2015) (9 pages) Paper No: MANU-15-1092; doi: 10.1115/1.4031588 History: Received February 25, 2015; Revised September 09, 2015

The shaft riveting assembly process is a very effective method for assembling lightweight, integrated, and highly reliable automobile wheel hub bearings. This paper proposes a method to determine the motion equation of a rivet head during the shaft riveting process based on a theoretical derivation, on-site test results, and structural equipment parameters. Based on the structure of the riveting machine, the motion equation of the rivet head is deduced through the combined application of a rectangular spatial coordinate system and the Euler angle method. In addition, the axial displacement and axial riveting force of the spindle were measured during the shaft riveting process using a newly developed on-site testing system. The axial velocity of the rivet head is determined using the spline function method based on the measured axial displacement–time curve. Subsequently, the motion equation of velocity and three-axis angular velocity of the rivet head can be obtained based on the deduced motion equation of the rivet head, test data, and structural equipment parameters. Finally, the motion equation of the rivet head is validated by simulating the shaft riveting process using the finite-element (FE) method, and then comparing the simulated axial riveting force and final geometric shape of the riveted hub shaft with the experimental ones. The result shows that the method proposed in this paper lays the foundation for the numerical simulation and optimization of the shaft riveting technology for a wheel hub bearing unit.

Copyright © 2016 by ASME
Your Session has timed out. Please sign back in to continue.


Morita, K. , 2001, “ Trends of Production Engineering for Bearings and Unit Products,” KOYO Eng. J., Engl. Ed., 159, pp. 31–36.
Ishida, H. , and Kaneko, T. , 2001, “ Development of Hub Unit Bearings With Swaging,” NSK Tech. Motion Control, 10, pp. 9–14.
Park, H. S. , and Dang, X. P. , 2015, “ Multiobjective Optimization of the Heating Process for Forging Automotive Crankshaft,” ASME J. Manuf. Sci. Eng., 137(3), p. 031011. [CrossRef]
Abdelal, G. F. , Georgiou, G. , Cooper, J. , Robotham, A. , Levers, A. , and Lunt, P. , 2015, “ Numerical and Experimental Investigation of Aircraft Panel Deformations During Riveting Process,” ASME J. Manuf. Sci. Eng., 137(1), p. 011009. [CrossRef]
Toda, K. , Ishii, T. , and Kashiwagi, S. , 2001, “ Development of Hub Units With Shaft Clinching for Automotive Wheel Bearings,” KOYO Eng. J., Engl. Ed., 158, pp. 26–30.
Kajihara, K. , 2005, “ Improvement of Simulation Technology for Analysis of Hub Unit Bearing,” KOYO Eng. J., Engl. Ed., 167, pp. 35–39.
Moon, H. K. , Lee, M. C. , and Joun, M. S. , 2007, “ An Approximate Efficient Finite Element Approach to Simulating a Rotary Forming Process and Its Application to a Wheel-Bearing Assembly,” Finite Elem. Anal. Des., 44(1–2), pp. 17–23. [CrossRef]
Han, X. H. , Hua, L. , Zhuang, W. H. , and Zhang, X. Ch. , 2014, “ Process Design and Control in Cold Rotary Forging of Non-Rotary Gear Parts,” J. Mater. Process. Technol., 214(11), pp. 2402–2416. [CrossRef]
Jian, L. , Sun, H. X. , Wang, L. M. , and Tao, M. H. , 2014, “ Large-Size Wheel Rotary Forging Process Research,” Appl. Mech. Mater., 456, pp. 282–285.
Aksenov, L. B. , and Kunkin, S. N. , 2015, “ Rotary Forging of Hollow Components With Flanges,” Lecture Notes in Control and Information Sciences, Vol. 22, Springer, Germany, pp. 1–5.
Zhang, M. , and Hu, Y. M. , 1998, Rotary Forging Technology, China Machine Press, Beijing, China.
Liu, X. L. , and Liu, X. H. , 1998, “ Plain Motion of Hypocycloid,” J. Changsha Railw. Univ., 16, pp. 75–79 (in Chinese).
Mei, Y. , 2012, “ Design Analysis on the Plum Blossom Type Radial Riveting Machine,” Manuf. Technol. Mach. Tool, 9, pp. 53–56 (in Chinese).
Xiao, Y. Y. , Zhou, Zh. X. , Li, W. , and Meng, G. F. , 2013, “ Axial Force Test and Analysis in Riveting Assembly of Automotive Hub Bearing Unit,” Appl. Mech. Mater., 268, pp. 1058–1062.
Nam, C. H. , Lee, M. C. , and Eom, J. G. , 2014, “ Finite Element Analysis Model of Rotary Forging for Assembling Wheel Hub Bearing Assembly,” Procedia Eng., 81, pp. 2475–2480. [CrossRef]
Dong, L. Y. , Han, X. H. , Hua, L. , Lan, J. , and Zhuang, W. H. , 2015, “ Effects of the Rotation Speed Ratio of Double Eccentricity Bushings on Rocking Tool Path in a Cold Rotary Forging Press,” J. Mech. Sci. Technol., 29(4), pp. 1619–1628. [CrossRef]
Jin, Sh. N. , and Ma, Y. L. , 2002, Theoretical Mechanics, 2nd ed., Higher Education Press, Beijing, China (in Chinese).
Boor, C. D. , 2001, A Practical Guide to Splines, Springer-Verlag, New York.
Nmata, T. , 2005, “ Latest Technical Trends Regarding Hub Unit Bearings,” KOYO Eng. J., Engl. Ed., 168, pp. 9–13.
Cho, H. , Kim, N. , and Altan, T. , 2014, “ Simulation of Orbital Forming Process Using 3D FEM and Inverse Analysis for Determination of Reliable Flow Stress,” http://nsmwww.eng.ohio-state.edu/519.pdf
Munshi, M. , Shah, K. , and Cho, H. , 2014, “ Finite Element Analysis of Orbital Forming Used in Spindle Inner Ring Assembly,” http://nsmwww.eng.ohio-state.edu/557.pdf


Grahic Jump Location
Fig. 5

Relationship between precession angle φ and revolution angle ψ of external gear

Grahic Jump Location
Fig. 4

Schematic diagram of spatial movement of rivet head

Grahic Jump Location
Fig. 3

Analysis of point M motion due to engagement of external and internal gear

Grahic Jump Location
Fig. 2

Structural schematic diagram of riveting machine

Grahic Jump Location
Fig. 1

Principle of shaft riveting assembly

Grahic Jump Location
Fig. 6

Data testing system and testing site during shaft riveting process: (a) schematic diagram of on-site testing system and (b) testing site of shaft riveting process

Grahic Jump Location
Fig. 7

Experimental axial displacement–time and axial load–time curves

Grahic Jump Location
Fig. 8

(a) Smoothed axial displacement–time curves and (b) calculated axial velocity–time curves

Grahic Jump Location
Fig. 9

Upper end point velocities of rivet's central axis–time curves during riveting process: (a) upper end point velocities of rivet's central axis at deforming phase, (b) upper end point velocities of rivet's central axis at reshaping phase, and (c) upper end point velocities of rivet's central axis at tool retracting phase

Grahic Jump Location
Fig. 10

Rotational angular velocities of rivet head–time curves around X and Y axes

Grahic Jump Location
Fig. 11

Simulated axial riveting force–time curve

Grahic Jump Location
Fig. 12

Comparison of simulated (a) and experimental (b) ultimate deformed shapes of wheel hub shaft



Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In