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Optimization design of structural parameters of single-row four-point contact ball slewing bearing

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Abstract

The single-row four-point contact ball slewing bearing has a large structure and is subjected to heavy load, which requires extremely high carrying capacity. The structural parameters of the ball diameter and the number of balls are optimized with the fixed size of the inner and outer rings of the slewing bearing. Numerical methods based on static bearing capacity and fatigue life are used to optimize the structural parameters of the slewing bearing. The finite element model and the local finite element model of the slewing bearing are established to analyze the carrying capacity of different structural parameters. The Hertz contact theory and the experiment are used to compare the theoretically calculated load distribution, contact stress, contact area and deformation. Optimization of structural parameters of the slewing bearing is beneficial to improve the carrying capacity and service life, which provides an important reference for designers.

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Abbreviations

\(\alpha\) (o):

Contact angle

\(a\) (mm):

Contact ellipse long half-axis length

\(a^{*}\) :

Function related to \(F\left( \rho \right)\)

\(b\) (mm):

Contact ellipse short half-axis length

\(b^{*}\) :

Function related to \(F\left( \rho \right)\)

\(C_{\text{a}}\) (N):

Axial basic dynamic load rating

\(D_{\text{L}}\) (mm):

Raceway center diameter

\(D_{\text{i}}\) (mm):

Outer ring inner diameter

\(D_{\text{O}}\) (mm):

Outer ring outer diameter

\(D_{\text{w}}\) (mm):

Ball diameter

\(d_{\text{i}}\) (mm):

Inner ring inner diameter

\(d_{\text{o}}\) (mm):

Inner ring outer diameter

\(E_{1}\) (MPa):

Ball elastic modulus

\(E_{2}\) (MPa):

Raceway elastic modulus

f cm :

Variable

\(f\) :

Groove radius coefficient

\(F_{\text{a}}\) (N):

Axial load

\(F_{\text{r}}\) (N):

Radial load

\(F\left( \rho \right)\) :

Principal curvature difference function

\(H\) (mm):

Outer ring height

\(H_{1}\) (mm):

Total height

\(i\) :

Rolling element row

\(h\) (mm):

Inner ring height

\(K\) :

Value related to the cage

\(K_{\text{c}}\) :

Ball stiffness

\(L\) (106 r/min):

Fatigue life

\(M\) (N mm):

Overturning moment

\(P_{\text{ea}}\) (N):

Dynamic equivalent axial load rating

\(P_{\text{a}}\) (N):

Single load of axial force

\(P_{\text{M}}\) (N):

Single load of overturning moment

\(Q\) (N):

Contact load

\(Q_{\hbox{max} }\) (N):

Maximum contact load

\(r_{{1{\rm I}}}\) (mm):

Radius of the plane 1 of the object 1

\(r_{1\coprod }\) (mm):

Radius of the plane 2 of the object 1

\(r_{{2{\rm I}}}\) (mm):

Radius of the plane 1 of the object 2

\(r_{2\coprod }\) (mm):

Radius of the plane 2 of the object 2

\(Z\) :

Ball number

\(\delta\) (mm):

Deformation

\(\mu_{1}\) :

Ball Poisson ratio

\(\mu_{2}\) :

Raceway Poisson ratio

\(\sigma_{\hbox{max} }\) (MPa):

Maximum contact stress

\(\sum \rho\) :

Sum of curvature

\(\rho_{{1{\rm I}}}\) :

Curvature of plane 1 of object 1

\(\rho_{1\coprod }\) :

Curvature of plane 2 of object 1

\(\rho_{{2{\rm I}}}\) :

Curvature of plane 1 of object 2

\(\rho_{2\coprod }\) :

Curvature of the plane 2 of the object 2

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Acknowledgements

The authors gratefully acknowledge the support provided by the National Natural Science Foundation of China (Nos. 51575245, 51679112, 51805225, and 51875273) and Jiangsu Province Key Research and Development Program (BE2016161).

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Authors and Affiliations

  1. School of Mechanical Engineering, Jiangsu University, Zhenjiang, 212013, Jiangsu, China

    Peiyu He, Yun Wang, Hong Liu & Erkuo Guo

  2. School of Mechanical and Power Engineering, Nanjing Technology University, Nanjing, 211816, China

    Hua Wang

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  1. Peiyu He
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  2. Yun Wang
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  3. Hong Liu
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  4. Erkuo Guo
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  5. Hua Wang
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Correspondence to Yun Wang.

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Technical Editor: João Marciano Laredo dos Reis.

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He, P., Wang, Y., Liu, H. et al. Optimization design of structural parameters of single-row four-point contact ball slewing bearing. J Braz. Soc. Mech. Sci. Eng. 42, 291 (2020). https://doi.org/10.1007/s40430-020-02391-6

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