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Research Papers: Applications

Averaging Effect on Pitch Errors in Hydrostatic Lead Screws With Continuous Helical Recesses

[+] Author and Article Information
Yongtao Zhang, Wei Pan, Shujiang Chen, Zichao Liu

School of Mechanical Engineering;Key Laboratory of High-Efficiency and
Clean Mechanical Manufacture,
Shandong University,
Ministry of Education,
Jinan 250061, China

Changhou Lu

School of Mechanical Engineering;Key Laboratory of High-Efficiency and
Clean Mechanical Manufacture,
Shandong University,
Ministry of Education,
Jinan 250061, China
e-mail: luchh@sdu.edu.cn

1Corresponding author.

Contributed by the Tribology Division of ASME for publication in the JOURNAL OF TRIBOLOGY. Manuscript received March 7, 2015; final manuscript received June 14, 2015; published online October 29, 2015. Assoc. Editor: Sinan Muftu.

J. Tribol 138(2), 021103 (Oct 29, 2015) (8 pages) Paper No: TRIB-15-1069; doi: 10.1115/1.4031463 History: Received March 07, 2015; Revised June 14, 2015

The motion errors of hydrostatic lead screws can be smaller than the pitch errors due to the averaging effect of oil films, which is the so-called averaging effect on the pitch errors (AEPE). This paper investigates the factors influencing AEPE under low speeds and a constant external load. An equivalent model of hydrostatic lead screws with continuous helical recesses is established, and the axial motion errors of the nut are obtained by combining the dichotomy and finite difference methods. The results show that (a) the motion errors caused by the pitch errors of the lead screw have additivity, and the pitch errors of the nut have little influence on the motion errors, (b) when the lead screw only has cumulative pitch errors, the motion errors are equal to the average value of the cumulative pitch errors located on the two flank surfaces of the lead screw, and (c) when the lead screw only has periodic pitch errors, the number of nut threads with helical recesses n and the period of the pitch errors of the lead screw T are the main influencing factors on AEPE.

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Figures

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Fig. 5

Geometrical dimension of the top surface (or bottom surface) of the slide block

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Fig. 2

Unfolded drawing of helices

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Fig. 1

Hydrostatic lead screw system with continuous helical recesses

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Fig. 6

The grid point in the xnk and ynk direction

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Fig. 4

(a) Cross section perpendicular to the thread ridge and (b) equivalent model

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Fig. 3

Cross section of the thread ridge

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Fig. 8

Comparison of transfer functions K(ω)

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Fig. 9

Nut's axial displacements Δz for different components of pitch errors of the lead screw

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Fig. 10

Averaging coefficient curves for the nut with and without pitch error

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Fig. 11

Averaging coefficient curves for different external static loads W and amplitudes El

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Fig. 12

Averaging coefficient curves for different numbers of nut threads without helical recesses on each side of the nut m

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Fig. 13

Oil film pressure distribution on the top surface of the slide block (when W = 0, El = 2.5 μm, φl = 0, λl = Le, m = 1, n = 4, and X = 0)

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Fig. 14

(a) Averaging coefficient curves for different numbers of nut threads with helical recesses n and (b) zoomed view

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