Kinematic Analysis of the Ball Screw Mechanism Considering Variable Contact Angles and Elastic Deformations

2003 ◽  
Vol 125 (4) ◽  
pp. 717-733 ◽  
Author(s):  
Chin Chung Wei ◽  
Jen Fin Lin
Keyword(s):  
Present Model ◽  
Ball Bearing ◽  
Normal Force ◽  
Mechanical Efficiency ◽  
Contact Angles ◽  
Ball Screw ◽  
Elastic Deformations ◽  
Contact Areas ◽  
Screw Mechanism ◽  
Theoretical Analyses

The theoretical analyses developed by Lin et al. 6 for the kinematics of the ball screw mechanism have been partly adapted for the present study. In order to better understand the sliding behavior arising at two contact areas, the analyses of a ball bearing, while accounting for elastic deformation, are modified through coordinate transformations prior to their applications to the analyses for the ball screw mechanism. The influence of differing the parameters such as friction coefficient, normal force acting on the ball, and contact angle on a ball-screw’s mechanism at two contact areas are evaluated. The results of the ball-screw’s mechanical efficiency achieved by the present model are displayed to compare with those evaluated based on the model of Lin et al. Substantial differences exist in the results evaluated by these two models, especially those created at high screw rotational speeds.

scholarly journals A new method to calculate the friction coefficient of ball screws based on the thermal equilibrium

2019 ◽  
Vol 11 (1) ◽  
pp. 168781401882073
Author(s):  
Lu-Chao Zhang ◽  
Li Zu
Keyword(s):  
Friction Coefficient ◽  
Temperature Rise ◽  
Thermal Equilibrium ◽  
Heat Dissipation ◽  
Mechanical Efficiency ◽  
New Method ◽  
Measuring System ◽  
Ball Screw ◽  
Heat Absorption ◽  
Screw Mechanism

Based on the theory of thermal transmission, this article provides a new method to acquire the friction coefficient in ball screw mechanism. While the screw is in thermal equilibrium, the heat absorption is equal to the heat dissipation. The heat absorption is able to be achieved by calculating the heat energy due to the friction at the contact area and the heat dissipation can be calculated by the law of thermodynamics. When the temperature rise is determined, the heat dissipation can be obtained and the friction coefficient in ball screw mechanism can be calculated further. In order to confirm the validity of this method, a measuring system is constructed to obtain the temperature rise of ball screws. The experimental results show that the temperature rise has the same tendency with the theoretical values depending on this model. Therefore, it can be exploited to predict the temperature rise of ball screws in the rated life cycle when the ball screw is under the condition of thermal equilibrium. Furthermore, this model can be used to evaluate the mechanical efficiency, which is an important parameter for the performance of the ball screw.

Determination of contact stiffness in ball screws considering variable contact angles

2014 ◽  
Vol 228 (12) ◽  
pp. 2193-2203 ◽  
Author(s):  
Yongjiang Chen ◽  
Wencheng Tang
Keyword(s):  
Contact Angle ◽  
Contact Stiffness ◽  
Position Angle ◽  
Contact Angles ◽  
Ball Screw ◽  
Design Parameters ◽  
Operation Condition ◽  
Normal Forces ◽  
Screw Mechanism

The contact angles formed at the position of each ball in ball screws are conventionally assumed to be a constant value in determination of contact stiffness. In this study, instead of being treated as pre-assumed constants, the contact angle is formulated as functions of the position angle of balls to reflect their distribution dependent on the operation condition and design parameters. After establishing a proper transformed coordinate system according to the ball screw mechanism, the variable contact angles and normal forces of the ball screw are predicted. Then the contact stiffness obtained by numerical calculations is validated by experiment and several characteristics arising from the variable contact angle will be discussed.

Precision loss of ball screw mechanism under sliding-rolling mixed motion behavior

2021 ◽  
Vol 28 (5) ◽  
pp. 1357-1376
Author(s):  
Bao-bao Qi ◽  
Qiang Cheng ◽  
Shun-lei Li ◽  
Zhi-feng Liu ◽  
Cong-bin Yang
Keyword(s):  
Ball Screw ◽  
Screw Mechanism ◽  
Motion Behavior

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.

Analysis of load distribution and contact stiffness of the single-nut ball screw based on the whole rolling elements model

2019 ◽  
Vol 43 (3) ◽  
pp. 344-365 ◽  
Author(s):  
Ye Chen ◽  
Chun-yu Zhao ◽  
Si-yu Zhang ◽  
Xian-li Meng
Keyword(s):  
Load Distribution ◽  
Contact Stiffness ◽  
Structural Parameters ◽  
Contact Angles ◽  
Ball Screw ◽  
Distribution Model ◽  
Axial Stiffness ◽  
Feed System ◽  
Normal Contact ◽  
Rolling Elements

This paper aims to investigate the load distribution and contact stiffness characteristics of the single-nut ball screw pair (SNBSP). First, the transformed relationship of coordinate systems is established. Then, the whole rolling elements load distribution model of the SNBSP is presented. Based on this, the whole rolling elements contact stiffness model is obtained. Applying the Newton–Raphson iterative method to solve the model, the normal force of rolling elements and the contact angles between balls and raceway surface are determined. The calculation results are reasonably consistent with those of the half pitch model. Then, the local contact stiffness and global contact stiffness are obtained. Furthermore, the effects of axial load and structural parameters of the SNBSP on the normal contact force, contact angle, and local and global contact stiffness are discussed using numeric analysis. Finally, a dynamic model of the z-axis feed system with time-varying axial stiffness is established, and the accuracy of the model is verified by experiments.

scholarly journals Kinematic analysis and simulation of a new type of differential micro-feed mechanism with friction

2019 ◽  
Vol 103 (1) ◽  
pp. 003685041987566
Author(s):  
Hanwen Yu ◽  
Xianying Feng ◽  
Qun Sun
Keyword(s):  
Mechanical Efficiency ◽  
System Structure ◽  
Advanced Technology ◽  
Ball Screw ◽  
National Defense ◽  
Integrated Electronics ◽  
Contact Points ◽  
Feed Control ◽  
Potential Applications ◽  
New Type

This article presents a new micro-feed mechanism, whose main transmission component is the nut–rotary ball screw pair. The screw and nut are driven by two motors, and they rotate in the same direction, with their movements enabling micro-feeding. The main contribution of the micro-feed mechanism is to avoid the inevitable low-speed nonlinear creeping phenomenon caused by the inherent properties of traditional electromechanical servo system structure, thus realizing high precision micro-feed. In this study, the motion state of the working ball is analyzed using the principle of differential geometry, the friction at the contact points is calculated, the balance equation for force and moment is established, the influences of the screw and nut on the kinematic parameters of the ball at different velocities and the differences in the motion states of the ball in different drive modes are studied, and the mechanical efficiency of the dual-driven ball screw mechanism is calculated. The potential applications of the new micro-feed mechanism and the results of numerical analysis can be applied to advanced technology fields such as robotics, suspensions, powertrain, national defense, integrated electronics, optoelectronics, medicine, and genetic engineering, so that the new system can have a lower stable speed limit and achieve precise micro-feed control.

Wear Prediction of Ball Screw Based on Adhesive Wear

2014 ◽  
Vol 635-637 ◽  
pp. 261-265
Author(s):  
Xiang Hong Xu ◽  
Yan Hui Wang ◽  
Dong Xu
Keyword(s):  
Adhesive Wear ◽  
Wear Behavior ◽  
Mechanical Efficiency ◽  
Test System ◽  
Ball Screw ◽  
Analysis Model ◽  
Wear Model ◽  
Systematic Analysis ◽  
Mechanics Model ◽  
Stabilization Condition

This paper aims to develop a new systematic analysis model to predict the wear of ball screw in stabilization condition. In order to investigate the wear behavior between the ball and raceway, a proper contact mechanics model should be established. Then, the wear model of ball screw based on Archard will be proposed and calculated by substituting the ball screw parameters. It has been proved that the effectiveness of the wear model on ball screw is verified through experiments in a specialized test system, which provides the theory basis of reasonably reducing the wear and improving the mechanical efficiency of a ball screw.

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.

scholarly journals Developing a Novel Miniature 3D-Printed TLBS with High Mechanical Efficiency and Better Controllability

Micromachines ◽  
2020 ◽  
Vol 11 (7) ◽  
pp. 662
Author(s):  
Chung-Wei Lee ◽  
Jung-Hua Chou
Keyword(s):  
Mechanical Efficiency ◽  
Ball Screw ◽  
Maximum Efficiency ◽  
Design Parameters ◽  
Affecting Factors ◽  
Lead Screw ◽  
Torque Loss ◽  
3D Printed ◽  
Novel Model ◽  
Better Than

This paper focuses on the development of a 3D-printed threadless ball screw (TLBS) for the applications that require miniaturization, customization, and accuracy controllability. To enhance the efficiency of the TLBS, a novel model of the TLBS for analyzing the mechanical efficiency is presented to obtain the key affecting factors. From these factors, the design parameters for fabrication are determined. For miniaturization, a novel 3D-printed one-piece preloaded structure of light weight of 0.9 g is implemented as the TLBS nut part. Experimental results show that the measured mechanical efficiency of TLBS is close to that predicted by the theoretical model with a normalized root mean square error of 3.16%. In addition, the mechanical efficiency of the present TLBS (maximum efficiency close to 90%) is better than that of the lead screw and close to the ball screw. The unique characteristic of the present TLBS is that its total torque loss is a weak function of the load, a phenomenon not observed in either the ball screw or the lead screw. This characteristic is advantageous in enhancing the controllability of accuracy at different loads.

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