Kinematic Model of Planetary Roller Screw Mechanism With Run-Out and Position Errors

2018 ◽  
Vol 140 (3) ◽  
Author(s):  
Xiaojun Fu ◽  
Geng Liu ◽  
Shangjun Ma ◽  
Ruiting Tong ◽  
Teik C. Lim
Keyword(s):  
Rigid Body ◽  
Body Movement ◽  
Kinematic Model ◽  
Rotation Period ◽  
Fundamental Property ◽  
Transmission Error ◽  
Position Errors ◽  
Proposed Model ◽  
Roller Screw ◽  
Screw Mechanism

A kinematic model of the planetary roller screw mechanism (PRSM) is proposed, which accounts for the run-out errors of the screw, roller, nut, ring gear, and carrier, and the position errors of the nut and the pinhole in the carrier. The roller floating region, which contains all the possible positions of the roller inside the pinhole, is obtained by analyzing the axial clearances between mating thread surfaces and the radial clearance between the roller and carrier. The proposed model is based on the constraint that the set of roller floating region is not empty. Then, the additional rigid-body movement on the nut is derived and the path of motion transfer from the screw to the nut is obtained. According to the fundamental property of rigid-body kinematics, the axial velocity of the nut is derived and the transmission error of the PRSM is calculated. The proposed model is verified by comparing the calculated transmission error with experimental one. The results show that the transmission error of the PRSM with run-out and position errors is cyclic with a period corresponding to the rotation period of the screw and the magnitude of the transmission error can be much larger than the lead error of the screw. Besides, due to the run-out and position errors, the roller can move radially or transversally inside the pinhole of the carrier when the elements in the PRSM are regarded as rigid bodies.

A Comprehensive Contact Analysis of Planetary Roller Screw Mechanism

2016 ◽  
Vol 139 (1) ◽  
Author(s):  
Xiaojun Fu ◽  
Geng Liu ◽  
Shangjun Ma ◽  
Ruiting Tong ◽  
Teik C. Lim
Keyword(s):  
Design Process ◽  
Three Dimensional ◽  
Contact Analysis ◽  
Analysis Model ◽  
Transformation Matrices ◽  
Proposed Model ◽  
Roller Screw ◽  
Screw Mechanism

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.

scholarly journals Relative position and attitude coordinated control based on unit dual quaternion

2018 ◽  
Vol 10 (12) ◽  
pp. 168781401881897
Author(s):  
Jing Li
Keyword(s):  
Rigid Body ◽  
Sliding Mode ◽  
Kinematic Model ◽  
Coordinated Control ◽  
Control Law ◽  
Dual Quaternion ◽  
Control Laws ◽  
Proposed Model ◽  
Relative Pose ◽  
Theory Framework

In traditional algorithms, relative pose controls of a leader–follower rigid body consider the position and attitude as two subsystems in designing control laws. Since relative pose of a leader–follower rigid body is coupled, having a pose coupling control is a smarter choice. For deficiencies in decentralized control of relative pose, this article establishes a coupled dynamic and kinematic model of a leader–follower rigid body based on the dual-number and dual-quaternion theory framework. Furthermore, based on the proposed model, the sliding mode control theory is used to conduct coordinated control for relative pose of a leader–follower rigid body. The coupled algorithm does not need to design two sets of control laws for relative pose of a leader–follower rigid body; therefore, the complexity of the control system is reduced. Simulation results show that this algorithm does not only demonstrate the coupled control law of the relative pose but also show good tracking control performance.

Kinematics of Roller Migration in the Planetary Roller Screw Mechanism

2012 ◽  
Vol 134 (6) ◽  
Author(s):  
Matthew H. Jones ◽  
Steven A. Velinsky
Keyword(s):  
Slip Velocity ◽  
Kinematic Model ◽  
Helical Gear ◽  
Orbital Mechanics ◽  
Ring Gear ◽  
Manufacturing Errors ◽  
Roller Screw ◽  
Screw Mechanism ◽  
The Given

This paper develops a kinematic model to predict the axial migration of the rollers relative to the nut in the planetary roller screw mechanism (PRSM). This axial migration is an undesirable phenomenon that can cause binding and eventually lead to the destruction of the mechanism. It is shown that this migration is due to slip at the nut–roller interface, which is caused by a pitch mismatch between the spur-ring gear and the effective nut– roller helical gear pairs. This pitch circle mismatch can be due to manufacturing errors, deformations of the mechanism due to loading, and uncertainty in the radii of contact between the components. This paper derives the angle through which slip occurs and the subsequent axial migration of the roller. It is shown that this roller migration does not affect the overall lead of the PRSM. In addition, the general orbital mechanics, in-plane slip velocity at the nut–roller interface, and the axial slip velocities at the nut–roller and the screw–roller interfaces are also derived. Finally, an example problem is developed using a range of pitch mismatch values for the given roller screw dimensions, and the axial migration and slip velocities are determined.

Load distribution over threads of planetary roller screw mechanism with pitch deviation

2018 ◽  
Vol 233 (13) ◽  
pp. 4653-4666 ◽  
Author(s):  
Wenjie Zhang ◽  
Geng Liu ◽  
Shangjun Ma ◽  
Ruiting Tong
Keyword(s):  
Load Distribution ◽  
Machining Error ◽  
Experimental Conditions ◽  
Load Distributions ◽  
Machining Errors ◽  
Proposed Model ◽  
Roller Screw ◽  
Multiple Threads ◽  
Screw Mechanism ◽  
Pitch Deviation

A model is proposed to calculate load distribution over threads of planetary roller screw mechanism (PRSM) with pitch deviation. Firstly, four kinds of machining errors of threads including pitch deviation, deviation of thread angle, division error of multiple threads and deviation of pitch diameter are analyzed, and the relationships among them are investigated. After analyzing the relationships among the errors, pitch deviation is chosen to be the main machining error to investigate because it can reflect the effects of other machining errors, and is the most influential machining error on the contact condition and deformation compatibility relationship, i.e. the load distribution of PRSM. Based on the proposed model, the effects of pitch deviation on the load distribution of PRSM are studied through numerical analyses, and load distributions under different machining precisions are analyzed. In order to experimentally verify the investigation, two PRSM samples are measured and tested under the same experimental conditions. The experimental results show that load distributions over threads will fluctuate because of the existence of pitch deviations. The pitch deviations, load distributions over threads and wear depths of threads in the samples show obvious accordance, which indirectly demonstrates the effects of pitch deviation on load distribution.

scholarly journals Rigid-Body Dynamic Analysis of Multi-Stage Planetary Roller Screw Mechanism

2020 ◽  
Vol 38 (5) ◽  
pp. 1001-1009
Author(s):  
Xin Li ◽  
Geng Liu ◽  
Chunyu Song ◽  
Xiaojun Fu ◽  
Shangjun Ma ◽  
...  
Keyword(s):  
Rigid Body ◽  
Structural Characteristics ◽  
Great Influence ◽  
Body Motion ◽  
Motion Equations ◽  
Rigid Body Dynamic ◽  
Multi Stage ◽  
Roller Screw ◽  
Screw Mechanism ◽  
Body Dynamic

Based on the structural characteristics of the multi-stage Planetary Roller Screw Mechanism (PRSM), the motion and force among the different stages are analyzed. In terms of the Newton's second law, the rigid-body motion equations of the multi-stage PRSM without considering the manufacturing and assembly errors are derived. Then, the method for solving the motion equations is given. The forces acting on the parts in the multi-stage PRSM and the motion of the mechanism can be obtained from the present rigid-body dynamic model. The influence of the friction coefficients among the different stages on the dynamic characteristics of the multi-stage PRSM is discussed. The results show that the forces acting on the first-stage PRSM are larger than that acting on the second-stage PRSM, although the nominal radius of the screw in the first-stage PRSM is smaller. The friction coefficient between the nut and the screw in the different stages has the great influence on the efficiency of multi-stages PRSM with small helix angles, while that among the screws in the different stages has the slight effect on the efficiency.

Dynamics of a Two-DOF Parallel Pointing Mechanism

2005 ◽  
Author(s):  
Alessandro Cammarata ◽  
Rosario Sinatra
Keyword(s):  
Numerical Simulation ◽  
Parallel Mechanism ◽  
Inverse Dynamics ◽  
Kinematic Model ◽  
Degree Of Freedom ◽  
Numerical Examples ◽  
Proposed Model ◽  
Dynamic Analyses ◽  
Moving Platform ◽  
Two Degree Of Freedom

This paper presents kinematic and dynamic analyses of a two-degree-of-freedom pointing parallel mechanism. The mechanism consists of a moving platform, connected to a fixed platform by two legs of type PUS (prismatic-universal-spherical). At first a simplified kinematic model of the pointing mechanism is introduced. Based on this proposed model, the dynamics equations of the system using the Natural Orthogonal Complement method are developed. Numerical examples of the inverse dynamics results are presented by numerical simulation.

A Three-Dimensional Load Sharing Model of Planetary Gear Sets Having Manufacturing Errors

2015 ◽  
Author(s):  
Nicholas D. Leque ◽  
Ahmet Kahraman
Keyword(s):  
Three Dimensional ◽  
Planetary Gear ◽  
Load Sharing ◽  
Distribution Model ◽  
Gear Mesh ◽  
Position Errors ◽  
Proposed Model ◽  
Manufacturing Errors ◽  
Manufacturing Tolerancing ◽  
Planetary Gear Sets

Planet-to-planet load sharing is a major design and manufacturing tolerancing issue in planetary gear sets. Planetary gear sets are advantageous over their countershaft alternatives in many aspects, provided that each planet branch carries a reasonable, preferably equal, share of the torque transmitted. In practice, the load shared among the planets is typically not equal due to the presence of various manufacturing errors. This study aims at enhancing the models for planet load sharing through a three-dimensional formulation of N-planet helical planetary gear sets. Apart from previous models, the proposed model employs a gear mesh load distribution model to capture load and time dependency of the gear meshes iteratively. It includes all three types of manufacturing errors, namely constant errors such as planet pinhole position errors and pinhole diameter errors, constant but assembly dependent errors such as nominal planet tooth thickness errors, planet bore diameter errors, and rotation and assembly dependent errors such as gear eccentricities and run-outs. At the end, the model is used to show combined influence of these errors on planet load sharing to aid designers on how to account for manufacturing tolerances in the design of the gears of a planetary gear set.

Dynamic Modeling of the Double-Nut Planetary Roller Screw Mechanism Considering Elastic Deformations

2021 ◽  
Author(s):  
Xiaojun Fu ◽  
Geng Liu ◽  
Xin Li ◽  
Ma Shangjun ◽  
Qiao Guan
Keyword(s):  
External Force ◽  
Load Distribution ◽  
Equations Of Motion ◽  
Great Influence ◽  
Compressive Force ◽  
Mass System ◽  
Elastic Deformations ◽  
Roller Screw ◽  
Screw Mechanism ◽  
Nonlinear Equations Of Motion

Abstract With the rising application of double-nut Planetary Roller Screw Mechanism (PRSM) into industry, increasing comprehensive studies are required to identify the interactions among motion, forces and deformations of the mechanism. A dynamic model of the double-nut PRSM with considering elastic deformations is proposed in this paper. As preloads, inertial forces and elastic deformations have a great influence on the load distribution among threads, the double-nut PRSM is discretized into a spring-mass system. An adjacency matrix is introduced, which relates the elastic displacements of nodes and the deformations of elements in the spring-mass system. Then, the compressive force acting on the spacer is derived and the equations of load distribution are given. Considering both the equilibrium of forces and the compatibility of deformations, nonlinear equations of motion for the double-nut PRSM are developed. The effectiveness of the proposed model is verified by comparing dynamic characteristics and the load distribution among threads with those from the previously published models. Then, the dynamic analysis of a double-nut PRSM is carried out, when the rotational speed of the screw and the external force acting on the nut #2 are changed periodically. The results show that if the external force is increased, the preload of the nut #1 is decreased and that of the nut #2 is increased. Although the nominal radii of rollers are the same, the maximum contact force acting on the roller #2 is much larger than that of the roller #1.

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