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Influence of thermal effect on dynamic behavior of high-speed dry hobbing motorized spindle system

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Abstract

This paper is devoted to investigating the influence of thermal effect on the dynamic behavior of a motorized spindle system in high-speed dry hobbing machine tool. First, the thermal induced preloads of combined bearings were calculated by characterizing the uneven temperature rise under operational condition. Subsequently, the influence relationship of thermal induced preload on the stiffness of combined bearings was studied. The change rules of the dynamic behavior of motorized spindle system with respect to the temperature rise were analyzed by coupling bearing stiffness and spindle dynamic models. Finally, experimental measurements on bearing temperature rise and spindle dynamic behavior were implemented for validation. The results indicate that thermal effects have a significant impact on the stiffness of combined bearings and hence the operating stability of high-speed dry hobbing motorized spindle system. This study can provide a reference for thermal dynamic optimization of motorized spindle system for high performance high-speed dry hobbing.

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Abbreviations

B :

Total curvature of bearing

C s :

Static rated load of bearing

D b :

Ball diameter

D h :

Bearing housing outer diameter

D i :

Inner raceway groove diameter

D o :

Outer raceway groove diameter

d m :

Pitch diameter of bearing

F a :

Total axial preload

F a,i :

Initial preload

F a,T :

Thermal induced preload

F cj :

Centrifugal force induced by the jth ball rotation

F L :

Axial preload of a bearing on the left

F mL :

Total axial force of bearings on the left

F mR :

Total axial force of bearings on the right

F R :

Axial preload of a bearing on the right

f i :

Curvature of bearing inner groove raceway

f o :

Curvature of bearing outer groove raceway

H b :

Friction heat distributed to bearing balls

H cf :

Friction heat generation in bearing contact zone

H fi :

Heat generation by friction between the balls and inner raceway

H fo :

Heat generation by friction between the balls and outer raceway

H i :

Friction heat distributed to bearing inner ring

H o :

Friction heat distributed to bearing outer ring

H spin :

Friction heat generation induced by ball spinning

K L :

Stiffness matrix of a single bearing on the left

K R :

Stiffness matrix of a single bearing on the right

K tot :

Total stiffness of the (m, n) combined bearings

k T :

Radial elastic constant of the bearing

M gj :

Gyroscopic moment induced by the jth ball rotation

M ij :

Friction moment between the jth ball and inner raceway

M oj :

Friction moment between the jth ball and outer raceway

Q ij :

Contact force between the jth ball and inner raceway

Q oj :

Contact force between the jth ball and outer raceway

R i :

Radius of the inner raceway groove curvature center

T i :

Transfer matrix between the station i and i+1

x b :

Center distance between left and right bearings

Z:

Number of bearing balls

Z i :

State vector of the spindle at station i

α b :

Thermal expansion coefficient of bearing ball

aα i :

Contact angle between ball and inner ring

α h :

Thermal expansion coefficient of housing material

α o :

Contact angle between ball and outer ring

α s :

Thermal expansion coefficient of spindle material

σ :

Ratio of bearing ball diameter to pitch diameter

δ L :

Axial displacement of bearing on the left

δ R :

Axial displacement of bearing on the right

ε a :

Axial thermal displacement of a bearing

ε b :

Thermal expansion of bearing ball

ε r :

Radial thermal displacement of a bearing

ψ j :

Angular position of the jth rolling ball

ω :

Angular speed of spindle

ω b :

Ball spinning speed

ω i :

Inner ring rotation speed

ω m :

Ball orbit rotation speed

ω roll,i :

Angular speed of ball related to the inner raceway

ω roll,o :

Angular speed of ball related to the outer raceway

ΔT b :

Temperature rise of bearing ball

ΔT i :

Temperature rise of bearing inner ring

ΔT o :

Temperature rise of bearing outer ring

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Acknowledgments

This work was supported by the National Natural Science Foundation (52105533, 51905144), China; the National Engineering Research Center for Oil & Gas Drilling Equipment (BOMCO-JHTKY-016-2021), China; the Natural Science Foundation of Chongqing (cstc2019jcyj-msxmX0205), China; and the Science and Technology Research Program of Chongqing Municipal Education Commission (KJQN201800839), China. The authors gratefully acknowledge the reviewers and editors for their insightful comments.

Author information

Authors and Affiliations

  1. School of Mechatronic Engineering, Southwest Petroleum University, Chengdu, 610500, China

    Benjie Li

  2. School of Mechanotronics and Vehicle Engineering, Chongqing Jiaotong University, Chongqing, 400074, China

    Yongpeng Chen

  3. Chongqing Key Laboratory of Manufacturing Equipment Mechanism Design and Control, Chongqing Technology and Business University, Chongqing, 400067, China

    Xiao Yang

  4. School of Mechanical Engineering, Hefei University of Technology, Hefei, 230009, China

    Libin Zhu

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  1. Benjie Li
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  2. Yongpeng Chen
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Corresponding author

Correspondence to Benjie Li.

Additional information

Benjie Li is a Post-doctor of the School of Mechatronic Engineering, Southwest Petroleum University, China. He received his Ph.D. in Mechanical Engineering from Chongqing University. His research interests mainly include machine tool dynamics and high-speed dry gear machining technology.

Yongpeng Chen is an Associate Professor of the School of Mechatronics and Vehicle Engineering, Chongqing Jiaotong University, Chongqing, China. His research interests include high-efficient and green gear machining technology.

Xiao Yang is an Associate Professor of Mechanical Engineering, Chongqing Technology and Business University, Chongqing, China. His research interests include sustainable manufacturing and high-speed dry gear machining technology.

Libin Zhu is a lecturer in Mechanical Engineering, Hefei University of Technology. He received his Ph.D. in Mechanical Engineering from Chongqing University. His research interests include dry machining and minimum quantity lubrication.

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Li, B., Chen, Y., Yang, X. et al. Influence of thermal effect on dynamic behavior of high-speed dry hobbing motorized spindle system. J Mech Sci Technol 36, 2521–2531 (2022). https://doi.org/10.1007/s12206-022-0434-x

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  • DOI: https://doi.org/10.1007/s12206-022-0434-x

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