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Dynamic model on thermally induced characteristics of ball screw systems

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Abstract

Ball screws used for high-speed feed systems generate friction heat, which affects the preload and supporting system stiffness, and further, the dynamic characteristics of the screw system are modified and negative effects on the positioning accuracy are produced. Therefore, a thermal dynamic model for investigating dynamic performance variation with temperature is needed. First, a new dynamic temperature model of a hollow cylinder with varied heat flow was proposed based on the heat transfer theory. By using the thermocouples to read the real-time surface temperatures of heat sources, this model can be used to obtain the real-time temperature field of the supporting bearings and nut, and by using the FOCAS function to read the real-time position of nut, a finite difference heat transfer model with real-time moving heat sources was established. Based on this model, the dynamic thermally induced preload and stiffness models of the system were obtained. Second, a real-time thermal dynamic model of the ball screw system was achieved. Finally, an inverse identification method of the heat excitation was proposed. Through measuring dynamic characteristics of the feed system in machine tools, the real-time thermal dynamic models of the screw system were validated. It provided the theoretical and practical foundation for real-time monitoring and controlling of dynamic characteristics of preloaded ball screw systems.

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Abbreviations

k b :

Axial stiffness of the support bearing

F0 :

Initial tensile preload of the screw

ΔF0 :

Lessened tensile preload of the temperature increasing

ΔT(x, t):

Temperature increment

S S :

Section area of the screw

E:

Modulus of elasticity

α S :

Expansion coefficient of the screw shaft

L:

Length of the screw

x :

Position of the table in the screw

k e :

Axial equivalent stiffness for the supporting bearings and the screw

d s :

Diameter of the screw

F n0 :

Initial compressive preload between the screw and the nut

k n :

Screw-nut stiffness

F a0 :

Compressive preload of the moving nut

k s :

Axial stiffness for the screw

K :

Rate stiffness of the screw-nut

ε :

Constant of the load

C a :

Rate equivalent dynamic load of the screw

F ap :

Axial load applied on the working table

δ b0 :

Elastic axial deformation of the fastened supporting bearing

F b0 :

Compressive preload of the fastened supporting bearing

d b :

Diameter of balls of the supporting bearing

β b :

Contact angle of the supporting bearing

Q :

Axial load of each ball of the supporting bearing

[M]:

System mass matrices

[C]:

System damping matrices

[K]:

System stiffness matrices

[F]:

Excitation force vector

[X]:

Displacement vector

T(x, t):

Temperature distribution of the screw, dependent on time and distance

k :

Thermal conductivity of the screw

ρ :

Screw density

c :

Heat capacity

h :

Convective coefficient

T air(t):

Temperature of the ambient air

T cb1(t):

Key point temperature of the screw connecting with the bearing 1

T cb2(t):

Key point temperature of the screw connecting with the bearing 2

T cn(t):

Key point temperature of the screw connecting with the moving-nut

P :

Perimeter of the screw

Ac:

Cross-sectional area of the screw

S:

Feed stroke

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Funding

This work was supported by the National Natural Science Foundation of China under Grants 51775085 and U1708254.

Author information

Authors and Affiliations

  1. Department of Mechanical Engineering, Shenyang University of Chemical Technology, Shenyang, 110142, China

    Tie-jun Li

  2. Key Laboratory for Precision and Non-traditional Machining Technology of Ministry of Education, Dalian University of Technology, Dalian, 116024, China

    Kuo Liu

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  1. Tie-jun Li
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  2. Kuo Liu
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Correspondence to Tie-jun Li.

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Li, Tj., Liu, K. Dynamic model on thermally induced characteristics of ball screw systems . Int J Adv Manuf Technol 103, 3703–3715 (2019). https://doi.org/10.1007/s00170-019-03760-9

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  • DOI: https://doi.org/10.1007/s00170-019-03760-9

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