scholarly journals Dynamic Model of Planetary Roller Screw Mechanism with Considering Torsional Degree of Freedom

2020 ◽  
Vol 306 ◽  
pp. 01003
Author(s):  
Linping Wu ◽  
Shangjun Ma ◽  
Qi Wan ◽  
Geng Liu
Keyword(s):  
Dynamic Model ◽  
Mechanical Design ◽  
Relative Displacement ◽  
Hertzian Contact ◽  
Torsional Stiffness ◽  
Roller Screw ◽  
Mode Characteristics ◽  
Screw Mechanism ◽  
The Relationship ◽  
Hertzian Contact Theory

To predict accurately the dynamics performance of planetary roller screw mechanism, it is necessary to establish its streamline and engineering-compliant dynamic model, which is the basis of mechanical design and precision control of the system. In this paper, the relative displacement between roller and ring gear along the line of action is deduced and the relationship between nature frequencies and the number of rollers is discussed. Considering the torsional stiffness of all components and the thread mesh stiffness based on the Hertzian contact theory, the purely torsional model for planetary roller screw mechanism is presented to reveal the natural frequencies and vibration mode characteristics of the system. The results show that the natural properties of undamped system in planetary roller screw mechanism are mainly reflected by two typical vibration modes: rotational mode and roller mode.

A nonlinear six degrees of freedom dynamic model of planetary roller screw mechanism

2018 ◽  
Vol 119 ◽  
pp. 22-36 ◽  
Author(s):  
Xiaojun Fu ◽  
Geng Liu ◽  
Ruiting Tong ◽  
Shangjun Ma ◽  
Teik C. Lim
Keyword(s):  
Dynamic Model ◽  
Degrees Of Freedom ◽  
Six Degrees Of Freedom ◽  
Roller Screw ◽  
Screw Mechanism

Contact Stress Analysis in Ball Screw Mechanism Using the Tubular Medial Axis Representation of Contacting Surfaces

1997 ◽  
Vol 119 (1) ◽  
pp. 8-14 ◽  
Author(s):  
Hual-Te T. Huang ◽  
B. Ravani
Keyword(s):  
Mechanical Design ◽  
Medial Axis ◽  
Hertzian Contact ◽  
Ball Screw ◽  
Simple Method ◽  
Curvature Analysis ◽  
Screw Mechanism ◽  
Tubular Surfaces ◽  
Curvature Information ◽  
Helical Grooves

A simple method is presented for analysis of contact stresses and deformation conditions between the bearing balls, screw, and nut of the ball screw mechanism. The method is based on representation of contact geometry and curvature analysis of contacting surfaces using a generalization of the medial axis transform (MAT) to tubular surfaces. Simplified Hertzian contact solutions are obtained using the curvature information. The results are approximate but do include the effect of complex thread profiles as a result of the helical grooves and are suitable for mechanical design purposes.

scholarly journals Thread Modification Method for Load Balance on Planetary Roller Screw Mechanism

2018 ◽  
Vol 36 (4) ◽  
pp. 685-692
Author(s):  
Hui Guo ◽  
Ruiting Tong ◽  
Geng Liu ◽  
Wenjie Zhang ◽  
Shangjun Ma
Keyword(s):  
Load Balancing ◽  
Load Balance ◽  
Load Distribution ◽  
Load Capacity ◽  
Optimal Value ◽  
Modification Method ◽  
The Future ◽  
Roller Screw ◽  
Screw Mechanism ◽  
The Relationship

Based on the relationship between the load distribution and the load deformation of the thread of the planetary roller screw mechanism (PRSM), a modification method of the roller thread is proposed. The nut side and the screw side of the roller thread are modified by different amount of modification, and the modified thread load distribution is calculated and analyzed. The results show that the effects of roller thread modification on the load distribution are significant, and the sensitivity of the load capacity of the nut and screw to the modification is different. Through the study of the influence of roller thread modification on thread load distribution, the optimal value of the roller thread modification on the nut side and the screw side is obtained under the PRSM parameters given in this paper, which provides a theoretical guidance for the future PRSM load balancing design.

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.

scholarly journals Research on effect of damping variation on vibration response of defective bearings

2019 ◽  
Vol 11 (3) ◽  
pp. 168781401982773 ◽  
Author(s):  
Fanzhao Kong ◽  
Wentao Huang ◽  
Yunchuan Jiang ◽  
Weijie Wang ◽  
Xuezeng Zhao
Keyword(s):  
Dynamic Model ◽  
Vibration Signal ◽  
Vibration Response ◽  
Hertzian Contact ◽  
Contact Theory ◽  
Viscous Damping ◽  
Lubricating Grease ◽  
Rolling Element ◽  
Different Types ◽  
Hertzian Contact Theory

This article presents a dynamic model of ball bearings with a localised defect on the outer raceway to analyse the effect of damping variation on the vibration response of defective bearings. First, a dynamic model is built based on the Hertzian contact theory, the interaction between the bearing inner ring, outer ring, and rolling element; the effect of damping and stiffness is considered; and the vibration equation of the bearing system is solved by the fourth-order Runge–Kutta algorithm. Then, the damping ratios of the experimental bearings using different types of viscosity lubricating grease are measured and compared with the damping ratios of the dynamic model; in addition, the viscous damping coefficient of the experimental bearings are calculated. Finally, the numerical analysis and experimental results show that the grease with a different level of viscosity affects the vibration signal of the defective bearing.

Contact Stress Analysis in Ball Screw Mechanism Using the Tubular Medial Axis Representation of Contacting Surfaces

1995 ◽  
Author(s):  
Huai-Te T. Huang ◽  
Bahram Ravani
Keyword(s):  
Mechanical Design ◽  
Medial Axis ◽  
Hertzian Contact ◽  
Ball Screw ◽  
Medial Axis Transform ◽  
Simple Method ◽  
Curvature Analysis ◽  
Screw Mechanism ◽  
Tubular Surfaces ◽  
Helical Grooves

Abstract A simple method is presented for analysis of contact stresses and deformation conditions between the bearing balls, screw, and nut of the Ball Screw Mechanism. The method is based on representation of contact geometry and curvature analysis of contacting surfaces using a generalization of Medial Axis Transform (MAT) to tubular surfaces developed in this paper. Simplified Hertzian contact solutions are obtained using the curvature relationship in MAT. The results are approximate but do include the effect of complex thread profiles as a result of the helical grooves and are suitable for mechanical design purposes.

A New Method to Analyze Three-Dimensional Non-Repetitive Run-Out (3D-NRRO) of Angular Contact Ball Bearings

2011 ◽  
Author(s):  
Zhaohui Yang ◽  
Jun Hong ◽  
Jinhua Zhang ◽  
Micheal Yu Wang ◽  
Baotong Li
Keyword(s):  
Three Dimensional ◽  
Hertzian Contact ◽  
Contact Theory ◽  
Ball Bearings ◽  
Angular Contact Ball Bearing ◽  
Geometrical Errors ◽  
Ultra Precision ◽  
The Relationship ◽  
Hertzian Contact Theory

As ultra-precision index of high-precision ball bearings, the value of three-dimensional non-repetitive run-out (3D-NRRO) directly influences the rotation accuracy in complex mechanical system. Reducing 3D-NRRO contributes to improve the quality of manufacturing in machining tools. This paper develops five-freedom model to analyze the 3D-NRRO of an angular contact ball bearing caused by geometrical errors of the rings raceways and the balls. In the model, the variation of contact angle caused by centrifugal force of balls is taken into consideration, and the geometrical errors of rings raceway and balls are described by Fourier series. Meanwhile, based on Hertzian contact theory and the solution method of dimensional chains, the 3D-NRRO analytical program has been developed, the value of 3D-NRRO analysis is shown. From the results, the relationship between the 3D-NRRO and the geometrical errors of rings raceway and balls are analyzed quantitatively. Findings of this paper provide theoretical supports to reduce or control the 3D-NRRO by optimizing manufacturing process of bearing components.

J. Tobin's Monetary Dynamic Model and the Analysis of Russian Economy

2009 ◽  
pp. 70-93
Author(s):  
V. Manevich
Keyword(s):  
Dynamic Model ◽  
Economic Thought ◽  
Financial Policies ◽  
Russian Economy ◽  
Q Theory ◽  
Keynesian Economic ◽  
The Relationship ◽  
Monetary Assets

The paper considers the monetary dynamic model developed by J. Tobin, the leader of Keynesian economic thought in 1970-1990. Particularly, the author examines q-theory of investment proposed by Tobin which allows to expose the relationship between supply of monetary assets and investment in real capital. Application of various tools of monetary and financial policies is also considered in its different forms. The author aspires to use Tobin's model for the analysis of processes existing in the Russian economy and to test theoretical propositions and relationships elaborated by Tobin on Russian statistics.

A realistic model for transverse shear stiffness prediction of composite corrugated-core sandwich structure with bonding effect

2021 ◽  
pp. 109963622199386
Author(s):  
Tianshu Wang ◽  
Licheng Guo
Keyword(s):  
Present Model ◽  
Shear Stiffness ◽  
Realistic Model ◽  
Torsional Stiffness ◽  
Fem Model ◽  
The Core ◽  
Bonding Effect ◽  
Stiffness Model ◽  
Bonding Area ◽  
The Relationship

In this paper, a shear stiffness model for corrugated-core sandwich structures is proposed. The bonding area is discussed independently. The core is thought to be hinged on the skins with torsional stiffness. The analytical model was verified by FEM solution. Compared with the previous studies, the new model can predict the valley point of the shear stiffness at which the relationship between the shear stiffness and the angle of the core changes from negative correlation to positive correlation. The valley point increases when the core becomes stronger. For the structure with a angle of the core smaller than counterpart for the valley point, the existing analytical formulations may significantly underestimate the shear stiffness of the structure with strong skins. The results obtained by some previous models may be only 10 persent of that of the present model, which is supported by the FEM model.

scholarly journals Analysis of Dynamic Response of a Two Degrees of Freedom (2-DOF) Ball Bearing Nonlinear Model

2021 ◽  
Vol 11 (2) ◽  
pp. 787
Author(s):  
Bartłomiej Ambrożkiewicz ◽  
Grzegorz Litak ◽  
Anthimos Georgiadis ◽  
Nicolas Meier ◽  
Alexander Gassner
Keyword(s):  
Mathematical Model ◽  
Degrees Of Freedom ◽  
Ball Bearing ◽  
Hertzian Contact ◽  
Two Degrees Of Freedom ◽  
Wide Range ◽  
Shape Errors ◽  
Nonlinear Features ◽  
Fourier Transform Phase ◽  
Hertzian Contact Theory

Often the input values used in mathematical models for rolling bearings are in a wide range, i.e., very small values of deformation and damping are confronted with big values of stiffness in the governing equations, which leads to miscalculations. This paper presents a two degrees of freedom (2-DOF) dimensionless mathematical model for ball bearings describing a procedure, which helps to scale the problem and reveal the relationships between dimensionless terms and their influence on the system’s response. The derived mathematical model considers nonlinear features as stiffness, damping, and radial internal clearance referring to the Hertzian contact theory. Further, important features are also taken into account including an external load, the eccentricity of the shaft-bearing system, and shape errors on the raceway investigating variable dynamics of the ball bearing. Analysis of obtained responses with Fast Fourier Transform, phase plots, orbit plots, and recurrences provide a rich source of information about the dynamics of the system and it helped to find the transition between the periodic and chaotic response and how it affects the topology of RPs and recurrence quantificators.

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