Three-dimensional parametric contact analysis of planetary roller screw mechanism and its application in grouping for selective assembly

  • Huilin HE 1 ,
  • Peitang WEI , 1 ,
  • Huaiju LIU 1 ,
  • Xuesong DU 1 ,
  • Rui HU 1 ,
  • Genshen LIU 1 ,
  • Yajun WU 2
Expand
  • 1. State Key Laboratory of Mechanical Transmission for Advanced Equipment, Chongqing University, Chongqing 400044, China
  • 2. Taiyuan Heavy Machinery Group Co., Ltd., Taiyuan 030024, China
peitangwei@cqu.edu.cn

Received date: 12 Jul 2023

Accepted date: 19 Oct 2023

Copyright

2024 Higher Education Press

Abstract

The planetary roller screw mechanism (PRSM) is a novel precision transmission mechanism that realizes the conversion between linear and rotary motions. The contact characteristics of helical surfaces directly determine PRSM’s performance in load-carrying capacity and transmission accuracy. Therefore, studying the contact characteristics of PRSM forms the fundamental basis for enhancing its transmission performance. In this study, a three-dimensional parametric analysis method of contact characteristics is proposed based on the PRSM meshing principle and PyVista (a high-level API to the Visualization Toolkit). The proposed method considers the influence of machining errors among various thread teeth. The effects of key machining errors on contact positions and axial clearance, as well as their sensitivities, are analyzed. With excellent solution accuracy, this method exhibits higher calculation efficiency and stronger robustness than the analytical and numerical meshing models. The influence of nominal diameter and pitch errors of the screw, roller, and nut on the axial clearance follows a linear relationship, whereas flank angle errors have negligible effects on the axial clearance. The corresponding influence coefficients for these three machining errors on the axial clearance are 0.623, 0.341, and 0.036. The variations in contact positions caused by individual errors are axisymmetric. Flank angle errors and roller diameter errors result in linear displacements of the contact points, whereas pitch errors cause the contact points to move along the arc of the roller diameter. Based on the proposed three-dimensional parametric contact characteristics analysis method, the Fuzzy C-Means clustering algorithm considering error sensitivity is utilized to establish a component grouping technique in the selective assembly of critical PRSM components, ensuring the rational and consistent clearances based on the given component’s machining errors. This study provides effective guidance for analyzing contact characteristics and grouping in selective assembly for PRSM components. It also presents the proposed method’s potential applicability to similar calculation problems for contact positions and clearances in other transmission systems.

Cite this article

Huilin HE , Peitang WEI , Huaiju LIU , Xuesong DU , Rui HU , Genshen LIU , Yajun WU . Three-dimensional parametric contact analysis of planetary roller screw mechanism and its application in grouping for selective assembly[J]. Frontiers of Mechanical Engineering, 2024 , 19(1) : 2 . DOI: 10.1007/s11465-023-0775-x

Nomenclature

Abbreviations
CNCComputer numerical control
FCMFuzzy C-Means
OBBOriented bounding box
PRSMPlanetary roller screw mechanism
VTKVisualization toolkit
Variables
AiBi (i = S, R, N)Thread root arc segment in the axial thread profile of screw, roller, or nut
axesThree coordinate axis vectors of the meshing model’s OBB
BiEi (i = S, R, N)Contact profile segment in the axial thread profile of screw, roller, or nut
ci (i = S, R, N)Half thread tooth thickness of screw, roller, or nut
cciCluster center of the ith group of samples
Ci (i = 1,2,...,K)ith group group of samples
cVertex coordinates matrix of the meshing model’s OBB
celli (i = 1,2,...,n)Cell of the meshing model’s OBB
di (i = S, R, N)Nominal diameter of screw, roller, or nut
dijwWeighted Euclidean distance between cluster center cci and the jth sample xj
Δdi (i = S, R, N)Nominal diameter error of screw, roller, or nut
ennth sample
EsamSample set
EEij (i = 1,2,...,9; j = 1,2,...,Nsam)Axial clearance variation resulting from consecutive runs in which only the ith error xij of the jth sample is changed to (xij + Δ)
KNumber of clusters
LintOverlapping region between the meshing model and v
LmProjection ranges of the meshing model along the axes
LvProjection ranges of v along the axes
ni (i = S, R, N)Number of starts of screw, roller, or nut
Nj (j = 1,2,...,K)Total number of samples in the jth group
NsamNumber of samples in Esam
ni (i = 1,2,3)Normal vectors of meshing model cell
pi (i = S, R, N)Pitch of screw, roller, or nut
Δpi (i = S, R, N)Pitch error of screw, roller, or nut
PClustering center
Pi (i = S, R, N)Point sets for the screw, roller, or nut thread profiles
pi1, pi2, pi3 (i = 1,2,...,n)Three vertices of meshing model cell
pintIntersection point between celli and v
pintNIntersection points between v and the nut
pintRNIntersection points between v and the roller on nut side
pintRSIntersection points between v and the roller on screw side
pintSIntersection points between v and the screw
rNmNut contact radius
rroot_i (i = S, R, N)Root arc radius of screw, roller, or nut
rRarRoller arc radius
rRmNRoller contact radius on the nut‒roller side
rRmSRoller contact radius on the screw‒roller side
rSa, rRa, rNfMajor diameters of the screw, roller, and nut, respectively
rSmScrew contact radius
R1, R2Random numbers within the range [0, 1]
SerrorWeighting coefficients of errors
SclearanceWeighting coefficients of axial clearance
si (i = 1,2,...,9)Sensitivity coefficient of 9 errors
sk (k = 1,2,...,10)Weight coefficient of the kth sample attribute
SSESum of square errors
tIntersection coefficient between celli and v
TIteration times
uij (i = 1,2,...,K)Membership of the jth sample to the ith group Ci
UMembership matrix
v = b1b2Ray vector and its starting point vector and ending point vector
xn1, xn2, …, xn9Sampling values of 9 errors in en
ZNiU, ZNiB, ZRNiU, ZRNiB (i = 1,2,...,n)z-coordinate of the intersection point between v and the upper and lower contact surfaces of the ith pair of meshing threads on the nut‒roller side, corresponding to the minimum axial distance
ZSiU, ZSiB, ZRSiU, ZRSiB (i = 1,2,...,n)z-coordinate of the intersection point between v and the upper and lower contact surfaces of the ith pair of meshing threads on the screw‒roller side, corresponding to the minimum axial distance
αSignificance level of hypothesis testing
βi (i = S, R, N)Flank angle of screw, roller, or nut
Δβi (i = S, R, N)Flank angle error of screw, roller, or nut
ΓUi, ΓBi (i = S, R, N)Upper and lower profile curves of the screw, roller, or nut, respectively
ΓSRU, ΓSRB, ΓNRU, ΓNRBContact pairs on the upper and lower sides of the roller threads
δgOverall global axial clearance of PRSM
δij, δj (i = 1,2,...,Nj;  j = 1,2,...,K)Clearance values of sample within the group and their mean value
δnAxial clearance value with 9 errors in en
δNRiU, δNRiB (i = 1,2,...,n)Axial clearances between the upper and lower contact surfaces of the ith pair of meshing threads on the nut‒roller side, respectively
δRmNAxial clearances on the nut‒roller side
δRmSAxial clearances on the screw‒roller side
δSRiU, δSRiB  (i = 1,2,...,n)Axial clearances between the upper and lower contact surfaces of the ith pair of meshing threads on the screw‒roller side, respectively
εIterative threshold
λi (i = S, R, N)Helix angle of screw, roller, or nut
μLocation parameter of errors distribution
μi (i = 1, 2,..., 10)Sensitivity factor of each error
σScale parameter of errors distribution
φNmNut contact angle
φRmNRoller contact angle on the nut‒roller side
φRmSRoller contact angle on the screw‒roller side
φSmScrew contact angle

Acknowledgement

The work was supported by the National Key R&D Program of China (Grant No. 2023YFB3406404).

Conflict of Interest

The authors declare that they have no conflict of interest.
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