Dynamics of the Planetary Roller Screw Mechanism

2015 ◽  
Vol 8 (1) ◽  
Author(s):  
Matthew H. Jones ◽  
Steven A. Velinsky ◽  
Ty A. Lasky
Keyword(s):  
Steady State ◽  
Slip Velocity ◽  
Equations Of Motion ◽  
Viscous Friction ◽  
Contact Angles ◽  
Dynamic Equations ◽  
Roller Screw ◽  
Angular Velocities ◽  
Screw Mechanism ◽  
Lagrange’S Method

This paper develops the dynamic equations of motion for the planetary roller screw mechanism (PRSM) accounting for the screw, rollers, and nut bodies. First, the linear and angular velocities and accelerations of the components are derived. Then, their angular momentums are presented. Next, the slip velocities at the contacts are derived in order to determine the direction of the forces of friction. The equations of motion are derived through the use of Lagrange's Method with viscous friction. The steady-state angular velocities and screw/roller slip velocities are also derived. An example demonstrates the magnitude of the slip velocity of the PRSM as a function of both the screw lead and the screw and nut contact angles. By allowing full dynamic simulation, the developed analysis can be used for much improved PRSM system design.

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.

Bond graph-based dynamic model of planetary roller screw mechanism with consideration of axial clearance and friction

2017 ◽  
Vol 232 (16) ◽  
pp. 2899-2911
Author(s):  
Shangjun Ma ◽  
Tao Zhang ◽  
Geng Liu ◽  
Jipeng He
Keyword(s):  
Dynamic Model ◽  
Dynamic Characteristics ◽  
Graph Model ◽  
Bond Graph ◽  
Graph Models ◽  
Axial Acceleration ◽  
Roller Screw ◽  
Angular Velocities ◽  
Screw Mechanism ◽  
Axial Clearance

To reveal the dynamic characteristics of planetary roller screw mechanism, a dynamic model of planetary roller screw mechanism is developed in this study, which is based on the bond graph theory that accounts for friction, axial clearance, and screw stiffness. First, the bond graph models of friction, axial clearance, and load distribution are presented. Then, a bond graph model of the entire planetary roller screw mechanism for the dynamic analysis is established using the 20-sim software package, and the dynamic equations are solved using the Runge–Kutta–Fehlberg algorithm. Finally, the axial speed, axial acceleration, and contact force of the components are derived under different axial loads and with different axial clearances. Furthermore, the dynamic friction characteristics at different angular velocities of the screw and the dynamic stiffnesses for different axial clearances are also obtained. The results can provide a theoretical basis for planetary roller screw mechanism design with consideration of dynamic characteristics.

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.

The Anchor-Last Deployment Problem for Inextensible Mooring Lines

1975 ◽  
Vol 97 (3) ◽  
pp. 1046-1052 ◽  
Author(s):  
Robert C. Rupe ◽  
Robert W. Thresher
Keyword(s):  
Numerical Model ◽  
Equations Of Motion ◽  
Simultaneous Equations ◽  
Mooring Line ◽  
Integration Scheme ◽  
Lumped Mass ◽  
Mooring Lines ◽  
Concentrated Masses ◽  
Predictor Corrector ◽  
Lagrange’S Method

A lumped mass numerical model was developed which predicts the dynamic response of an inextensible mooring line during anchor-last deployment. The mooring line was modeled as a series of concentrated masses connected by massless inextensible links. A set of angles was used for displacement coordinates, and Lagrange’s Method was used to derive the equations of motion. The resulting formulation exhibited inertia coupling, which, for the predictor-corrector integration scheme used, required the solution of a set of linear simultaneous equations to determine the acceleration of each lumped mass. For the selected cases studied the results show that the maximum tension in the cable during deployment will not exceed twice the weight of the cable and anchor in water.

An Assessment of the Value of Theory in Predicting Gas-Bearing Performance

1961 ◽  
Vol 83 (2) ◽  
pp. 195-200 ◽  
Author(s):  
S. Cooper
Keyword(s):  
Steady State ◽  
Slip Velocity ◽  
Reynolds Equation ◽  
Energy Equation ◽  
Experimental Methods ◽  
Experimental Results ◽  
Theoretical Investigations ◽  
Gas Bearing ◽  
Theoretical Results

The object of the paper is to indicate the value of theoretical investigations of hydrodynamic finite bearings under steady-state conditions. Methods of solution of Reynolds equation by both desk and digital computing, and methods of stabilizing the processes of solution, are described. The nondimensional data available from the solutions are stated. The outcome of an attempted solution of the energy equation is discussed. A comparison between some theoretical and experimental results is shown. Experimental methods employed and some difficulties encountered are discussed. Some theoretical results are given to indicate the effects of the inclusion of slip velocity, stabilizing slots, and a simple case of whirl.

scholarly journals The formation of vortices from a surface of discontinuity

1931 ◽  
Vol 134 (823) ◽  
pp. 170-192 ◽  
Keyword(s):  
Steady State ◽  
Plane Surface ◽  
Equations Of Motion ◽  
Steady Motion ◽  
Small Oscillations ◽  
Approximate Form ◽  
History Of ◽  
State Increase ◽  
Liquid Surfaces

Helmholtz was the first to remark on the instability of those “liquid surfaces” which separate portions of fluid moving with different velocities, and Kelvin, in investigating the influence of wind on waves in water, supposed frictionless, has discussed the conditions under which a plane surface of water becomes unstable. Adopting Kelvin’s method, Rayleigh investigated the instability of a surface of discontinuity. A clear and easily accessible rendering of the discussion is given by Lamb. The above investigations are conducted upon the well-known principle of “small oscillations”—there is a basic steady motion, upon which is superposed a flow, the squares of whose components of velocity can be neglected. This method has the advantage of making the equations of motion linear. If by this method the flow is found to be stable, the equations of motion give the subsequent history of the system, for the small oscillations about the steady state always remain “small.” If, however, the method indicates that the system is unstable, that is, if the deviations from the steady state increase exponentially with the time, the assumption of small motions cannot, after an appropriate interval of time, be applied to the case under consideration, and the equations of motion, in their approximate form, no longer give a picture of the flow. For this reason, which is well known, the investigations of Rayleigh only prove the existence of instability during the initial stages of the motion. It is the object of this note to investigate the form assumed by the surface of discontinuity when the displacements and velocities are no longer small.

Effect of payloads contact upon the coupled dynamic response of two cooperating robots

Robotica ◽  
1996 ◽  
Vol 14 (6) ◽  
pp. 659-665
Author(s):  
G. Shagal ◽  
S.A. Meguid
Keyword(s):  
Dynamic Response ◽  
Function Method ◽  
Search Algorithm ◽  
Contact Region ◽  
Dynamic Equations ◽  
Penalty Function Method ◽  
The Finite Element Method ◽  
Contact Search ◽  
Cooperating Robots ◽  
Lagrange’S Method

The coupled dynamic response of two cooperating robots handling two flexible payloads is treated using a new algorithm. In this algorithm, the dynamic equations describing the system are obtained using Lagrange's method for the rigid robot links and the finite element method for the flexible payloads. The contact between the flexible payloads is modelled using the penalty function method and a contact search algorithm is employed to identify the contact region.

Sensitivity Analysis for the Steady-State Response of Damped Linear Elastodynamic Systems Subject to Periodic Loads

1990 ◽  
Author(s):  
Daniel A. Tortorelli
Keyword(s):  
Steady State ◽  
Vibration Amplitude ◽  
Equations Of Motion ◽  
Steady State Response ◽  
Analysis Techniques ◽  
Direct Differentiation ◽  
State Response ◽  
Need To Evaluate ◽  
The Time Domain ◽  
General Response

Abstract Adjoint and direct differentiation methods are used to formulate design sensitivities for the steady-state response of damped linear elastodynamic systems that are subject to periodic loads. Variations of a general response functional are expressed in explicit form with respect to design field perturbations. Modal analysis techniques which uncouple the equations of motion are used to perform the analyses. In this way, it is possible to obtain closed form relations for the sensitivity expressions. This eliminates the need to evaluate the adjoint response and psuedo response (these responses are associated with the adjoint and direct differentiation sensitivity problems) over the time domain. The sensitivities need not be numerically integrated over time, thus they are quickly computed. The methodology is valid for problems with proportional as well as non-proportional damping. In an example problem, sensitivities of steady-state vibration amplitude of a crankshaft subject to engine firing loads are evaluated with respect to the stiffness, inertial, and damping parameters which define the shaft. Both the adjoint and direct differentiation methods are used to compute the sensitivities. Finite difference sensitivity approximations are also calculated to validate the explicit sensitivity results.

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