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Research Papers: Design of Mechanisms and Robotic Systems

A Comprehensive Contact Analysis of Planetary Roller Screw Mechanism

[+] Author and Article Information
Xiaojun Fu, Shangjun Ma, Ruiting Tong

Shaanxi Engineering Laboratory for
Transmissions and Controls,
Northwestern Polytechnical University,
Xi'an 710072, China

Geng Liu

Shaanxi Engineering Laboratory for
Transmissions and Controls,
Northwestern Polytechnical University,
Xi'an 710072, China
e-mail: npuliug@nwpu.edu.cn

Teik C. Lim

College of Engineering and Applied Science,
University of Cincinnati,
Cincinnati, OH 45221

1Corresponding author.

Contributed by the Mechanisms and Robotics Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received April 29, 2016; final manuscript received August 9, 2016; published online October 14, 2016. Assoc. Editor: Ettore Pennestri.

J. Mech. Des 139(1), 012302 (Oct 14, 2016) (11 pages) Paper No: MD-16-1326; doi: 10.1115/1.4034580 History: Received April 29, 2016; Revised August 09, 2016

A comprehensive contact analysis model to determine the contact positions and clearances of mating thread surfaces in the planetary roller screw mechanism (PRSM) is proposed in this paper. By introducing a three-dimensional clearance vector, the modified conditions of continuous tangency of mating surfaces are established, in which the clearances along all the directions and contact positions of an arbitrary pair of mating surfaces can be calculated. The deviations of the screw, roller, and nut from their nominal positions are considered in the transformation matrices, which describe the position relations of the screw, roller, and nut. Then, the equations of thread surfaces with deviations are derived. Using the modified conditions and the equations of surfaces, the meshing equations at the screw–roller and nut–roller interfaces are derived to compute the clearances along all the directions and contact positions of mating thread surfaces on each pair of thread teeth in the imperfect PRSM. The effectiveness of the proposed model is verified by comparing the contact positions at the screw–roller interface with those from the previously published model. Then, the effect of the direction of clearance vector on the clearances and contact positions is analyzed and discussed. Because of the roller deviation, the clearances between multiple pairs of thread teeth are no longer identical, and the contact positions of a pair of mating thread surfaces on different pairs of thread teeth are different. Also, the parameters of a PRSM without clearances can be obtained from the proposed model in the design process.

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Figures

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Fig. 1

Structure of the planetary roller screw mechanism (PRSM)

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Fig. 2

Partial enlarged view of the threads of the screw, nut, and roller #q

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Fig. 3

Movement directions of the surface ΠqB at the screw–roller #q interface: (a) radial, (b) transversal, and (c) axial

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Fig. 4

Clearance vector between mating surfaces

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Fig. 5

Three initial states of mating surfaces: (a) clearance, (b) contact, and (c) overlap

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Fig. 6

Positions of the screw, nut, and rollers in the global coordinate system O-XYZ and local coordinate system oPq-xPqyPqzPq in the idealized PRSM

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Fig. 7

Positions of the screw, nut, and roller #q in the globalcoordinate system O-XYZ and local coordinate system oPq-xPqyPqzPq with deviations

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Fig. 8

Cross-sectional slices of the PRSM

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Fig. 9

Positions of the contact points at the screw–roller #q interface in coordinate systems fixed to (a) the screw and (b) the roller

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Fig. 10

Positions of the contact points at the nut–roller #q interface in coordinate systems fixed to (a) the nut and (b) the roller

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Fig. 11

Movement directions of the surface ΠqU at the nut–roller #q interface: (a) radial, (b) transversal, and (c) axial

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Fig. 12

Contact positions of the mating thread surfaces ΠSU–Π1B along the axial direction of the PRSM without deviations with different pitches

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Fig. 13

Clearances between mating thread surfaces ΠSU–Π1B and ΠNB1U when eS1P1 is [0, 0, −1]T or 1/3⋅[−1, 1, 1]T and eN1P1 is [0, 0, 1]T or 1/3⋅[1,−1, 1]T without deviations

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Fig. 14

Contact positions of the mating thread surfaces ΠSU–Π1B when eS1P1 is [0, 0, −1]T or 1/3⋅[−1, 1, 1]T without deviations

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Fig. 15

Dimensional tolerances and the accuracy of spur-ring gear pairs in the PRSM (unit: mm)

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Fig. 16

Deviation of the roller #1

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Fig. 17

Clearances between the mating thread surfaces ΠSU–Π1B on each pair of thread teeth along the axial direction when ε1 = [10 μm, 10 μm, 7 μm]T, φ1 = 1.5 arc min, and ψ1 = −1.5 arc min

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Fig. 18

Contact positions of the mating thread surfaces ΠSU–Π1B on each pair of thread teeth along axial direction when ε1 = [10 μm, 10 μm, 7 μm]T, φ1 = 1.5 arc min, and ψ1=−1.5 arc min

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