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Stiffness matching method for the ball screw feed drive system of machine tools

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Abstract

The static stiffness of machine tools plays an important role in ensuring the performance of machine tools and improving the machining accuracy. In the design stage, stiffness matching provides a theoretical basis for determining the stiffness of each component. This study proposed a stiffness matching design method for machine tools. First, the deformation model of machine tools is established on the basis of the state space model. Through force analysis, the relationships between the deformations and stiffness of each part are determined. Second, the stiffness model of the machine tool is established by combining these relationships with the deformation model. Third, the objective function is determined by performing sensitivity analysis after obtaining the stiffness range. The stiffness matching design results are obtained through multi-objective linear programming. Lastly, the stiffness simulations, theoretical model, and experimental results are analyzed. The maximum errors among the experimental, simulation, and theoretical results (18.8 % and 19.9 %) are within the acceptable range. In conclusion, the proposed method is suitable for designing ball screw feed drive systems that requires rigidity.

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Abbreviations

KjM (j=x,y,z):

Equivalent axial stiffness of the servo motor

Kjc(j=x,y,z):

Equivalent axial stiffness of the coupling

KjB (j=x,y,z):

Axial stiffness of the two end bearings

KjS (j=x,y,z):

Axial stiffness of the ball screw

KjN (j=x,y,z):

Axial contact stiffness of the preloaded nut

Kgnj (j=x,y,z):

Vertical stiffness of the j direction sliders

Kgtj (j=x,y,z):

Horizontal stiffness of the j direction sliders

K sbj :

Contact stiffness of the surface between the spindle and spindle box in the/direction

KSj (j=x,y,z):

Contact stiffness of the surface between the spindle and tool in the j direction

Kwtj (j=x,y,z):

Contact stiffness of the surface between the work-piece and rotation table in j direction

Kwpj (j=x,y,z):

Contact stiffness of the surface between the slider and rotational tables in the j direction

R:

Conversion ratio of the linear-to-rotational motion

η :

Efficiency of the driving mechanism

k :

Characteristic number

[Pk, Qk]T :

Deformation error of characteristic k

Oo :

Reference coordinate system

OFi :

Characteristic coordinate system of characteristic i

Opi :

Part coordinate system of the characteristic i

δi, εj :

Displacement and angle deformation vectors of characteristic, respectively

Δxi, Δyi, Δzi :

Displacement deformation in the x, y, and z directions of characteristic i, respectively

Δαi,Δβi, Δγi :

Angle deformation around the x, y, and z axes of characteristic i, respectively

W i,n :

Deviation transformation matrix

R i,n D i,n :

3 × 3 rotation and translation matrixes, respectively

Xzs, Zzs :

Distance of the X and Z directions from the geometric center of the z-direction slider blocks, respectively

F X-x :

Equivalent force in the X direction caused by the x-direction unit force

M Zzs-x :

Equivalent moment of the z-direction slider block around the Z axis under the effect of the x-direction force

Q zj-xry :

Horizontal force of the jth z-direction slider block bearing under the effect of the equivalent moment MYzs-x

N zj-xrz :

Vertical force of the jth z-direction slider block bearing under the effect of the equivalent moment MZzs-x

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Acknowledgments

This work was supported by the National Natural Science Foundation of China (Grant No. 51675378), National Science and Technology Major Project of China (Grant No. 2015ZX04005001), and Tianjin Natural Science Key Fund (Grant No.18JCZDJC38700).

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Authors and Affiliations

  1. Key Laboratory of Mechanism Theory and Equipment Design of Ministry of Education, School of Mechanical Engineering, Tianjin University, Tianjin, China

    Gaiyun He, Panpan Shi, Dawei Zhang & Guangming Sun

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  1. Gaiyun He
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  2. Panpan Shi
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  4. Guangming Sun
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Correspondence to Gaiyun He.

Additional information

Recommended by Editor Hyung Wook Park

Gaiyun He received her Ph.D. degree from the School of Mechanical Engineering, Tianjin University, Tianjin, China. Her research interests include high-end CNC machine tools and basic manufacturing equipment and online machine monitoring and machining quality control.

Panpan Shi received his M.S. degree from the School of Mechanical Engineering, Tianjin University, Tianjin, China. His research interests include the stiffness matching method of CNC machine tools.

Dawei Zhang received his Ph.D. degree from the School of Mechanical Engineering, Tianjin University, Tianjin, China. His research interests include modern manufacturing equipment and systems.

Guangming Sun is a Ph.D. candidate in the School of Mechanical Engineering, Tianjin University, Tianjin, China. He received his M.S. degree from Henan Polytechnic University. His research interests include error analysis and compensation technology of CNC machine tools.

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He, G., Shi, P., Zhang, D. et al. Stiffness matching method for the ball screw feed drive system of machine tools. J Mech Sci Technol 34, 2985–2995 (2020). https://doi.org/10.1007/s12206-020-0630-5

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  • DOI: https://doi.org/10.1007/s12206-020-0630-5

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