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.

Dynamic characteristics and research on the dual-drive feed mechanism

2021 ◽  
pp. 095440622098419
Author(s):  
Hong Lu ◽  
Qi Liu ◽  
Xinbao Zhang ◽  
Jingui Yu ◽  
Haoyu Dou ◽  
...  
Keyword(s):  
Dynamic Characteristics ◽  
Contact Stiffness ◽  
Dynamic Performance ◽  
Industrial Robots ◽  
Numerical Control ◽  
Ball Screw ◽  
Axial Stiffness ◽  
Parameter Method ◽  
Feed System ◽  
Moving Parts

The dual-drive feed mechanism (DDFM) based on the drive at the center of gravity (DCG) principle has been widely adopted in computer numerical control (CNC) machines and industrial robots that require high precision and high stability. The friction force affected by feed rates and moving parts positions can change the contact stiffness of kinematic joints, which can further impact on dynamic characteristics of the DDFM and cause dual axes difference. Considering the contact stiffness of kinematic joints, this paper adopts the lumped parameter method to establish the general dynamic model of the DDFM. The equivalent axial stiffness of kinematic joint and feed system transmission stiffness are all derived regarding the influence of feed rates and moving parts positions. The dynamic experiments on the DDFM with different feed rates and moving parts positions are carried out to verify the proposed model. The results suggest that in the motion stage, the DDFM’s natural frequency is greater than that in the static stage, and behaves differently in different feed rates and moving parts positions. The axial contact stiffness value of the ball-screw and nut B can reach 0 when the feed rate increases. When the moving parts are in the middle position of the crossbeam, the DDFM is the most stable and the dynamic performance is the best.

scholarly journals Dynamic Modeling and Experiment Research on Twin Ball Screw Feed System Considering the Joint Stiffness

Symmetry ◽  
2018 ◽  
Vol 10 (12) ◽  
pp. 686 ◽  
Author(s):  
Meng Duan ◽  
Hong Lu ◽  
Xinbao Zhang ◽  
Yongquan Zhang ◽  
Zhangjie Li ◽  
...  
Keyword(s):  
Dynamic Modeling ◽  
Dynamic Characteristics ◽  
Friction Model ◽  
Numerical Control ◽  
Ball Screw ◽  
Cnc Machine Tools ◽  
Axial Stiffness ◽  
Cnc Machine ◽  
Feed System ◽  
Lumped Mass

It is of great significance to study the dynamic characteristics of twin ball screw (TBS) feed system to improve the precision of gantry-type dual-driven computer numerical control (CNC) machine tools. In this paper, an equivalent dynamic model of the TBS feed system is established utilizing lumped mass method considering the stiffness of joints. Equivalent axial stiffness of screw-nut joints and bearing joints are both calculated by Hertz contact theory. Furthermore, a friction model is proposed because the friction force of the screw nut affects the stiffness of the joints. Then, the friction parameters are obtained by using the nonlinear system identification method. Meanwhile, a finite element model (FEM) is developed to assess the dynamic characteristics of TBS feed system under the stiffness of joints. Finally, validation experiments are conducted, and the results show that the positions of the nut and the velocities of worktable greatly affect the dynamic characteristics of the TBS feed system. Compared with the theoretical calculation, FEM and experiments indicate that the dynamic modeling proposed in this article can reach a higher accuracy.

Global load determination in linear guides based on the fusion of local rolling element loads determined from strain sensitive sensor groups

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
David Krampert ◽  
Sebastian Unsleber ◽  
Leonhard Reindl ◽  
Stefan J. Rupitsch
Keyword(s):  
Load Distribution ◽  
Mechanical Load ◽  
Sensor System ◽  
Distribution Model ◽  
Valuable Insight ◽  
Estimation Errors ◽  
Rolling Element ◽  
Rolling Elements ◽  
Load Mode ◽  
Measurement Principle

Abstract Measuring the mechanical load on linear guides provides many possibilities regarding predictive maintenance and process monitoring. In this contribution, we provide an in depth evaluation of a Diamond Like Carbon (DLC) based sensor system integrated into the runner block’s raceway that is capable of directly measuring the load on individual rolling elements. An efficient algorithm based on an Extended Kalman Filter (EKF) for local sensor fusion and load estimation is presented and proven to reliably retrieve the load regardless of the rolling element’s position. Afterwards, we compare locally measured loads to results from a theoretical load distribution model, providing valuable insight into modeling parameters and a verification of the sensor measurement principle. In a final step, an algorithm to invert the load distribution model is derived and used for an evaluation of the sensor system, achieving Root-Mean-Square (RMS) estimation errors of equivalently 1.4 kN in the preload range and 2.75 kN overall for one dimensional loads. Load mode distinction was equally successful with a suppression RMS error of 0.7 kN in the preload range and 2.87 kN in total.

scholarly journals A Semi-Analytical Load Distribution Model for Cycloid Drives with Tooth Profile and Longitudinal Modifications

2020 ◽  
Vol 10 (14) ◽  
pp. 4859
Author(s):  
Ting Zhang ◽  
Xuan Li ◽  
Yawen Wang ◽  
Lining Sun
Keyword(s):  
Load Distribution ◽  
Contact Stiffness ◽  
Three Dimensional ◽  
Elastic Half Space ◽  
Distribution Model ◽  
Influence Coefficient ◽  
Hertz Contact ◽  
Tooth Contact Analysis ◽  
Tooth Contact ◽  
Analysis And Design

The current load distribution model for cycloid drives based on the Hertz contact stiffness typically assumes a two-dimensional planar problem without considering the tooth longitudinal modification effects, which fails to comply with the practical situation. In this paper, this issue is clarified by developing a semi-analytical load distribution model based on a three-dimensional and linear elastic solution. Unloaded tooth contact analysis is introduced to determine the instantaneous mesh information. The tooth compliance model considering tooth contact deformation is established by combining the Boussinesq force–displacement relationships in elastic half-space with an influence coefficient method. With this, the loads, contact patterns, and loaded transmission error are calculated by enforcing the compatibility and equilibrium conditions. Comparisons to predictions made with the assumption of Hertz contact stiffness are presented to demonstrate the effectiveness of the proposed model, which shows good agreement. At the end, the effect of tooth longitudinal modifications on load distributions is investigated along with various loading conditions. This study yields an in-depth understanding of the multi-tooth contact characteristics of cycloid drives and provides an effective tool for extensive parameter sensitivity analysis and design optimization studies.

scholarly journals Analysis on Dynamic Contact Characteristics and Dynamic Stiffness Estimating Method of Single Nut Ball Screw Pair Based on the Whole Rolling Elements Model

2020 ◽  
Vol 10 (17) ◽  
pp. 5795
Author(s):  
Ye Chen ◽  
Chunyu Zhao ◽  
Zhenjun Li ◽  
Zechen Lu
Keyword(s):  
Machine Tool ◽  
Mass Production ◽  
Contact Stiffness ◽  
Dynamic Stiffness ◽  
Dynamic Contact ◽  
Ball Screw ◽  
Cnc Machine Tool ◽  
Cnc Machine ◽  
Feed System ◽  
Stiffness Model

The purpose of this paper is investigating the characteristics of dynamic contact and dynamic stiffness of the single nut ball screw pair (SNBSP). Then a new sensorless method is proposed to extract the SNBSP dynamic contact stiffness of a mass production CNC machine tool feed system. First of all, the transformation relationship between each coordinate system of SNBSP is established. Secondly, the dynamic model of all ball–raceway contact pairs is established. Based on this, a dynamic contact stiffness model is established. The dynamic contact parameters are obtained by the numerical method. It is found that the influence of screw speed on screw and nut raceway normal force distribution are opposite. This will affect the variations of dynamic contact stiffness. It is also clear that the effect of axial load on dynamic stiffness is significant. Then, an effective method is proposed to estimate the dynamic contact stiffness of a mass production CNC machine tool feed system without any external sensors. The axial force of feed system is estimated by using torque current of servo motor. Current signals can be obtained through FANUC Open CNC API Specifications (FOCAS) library functions, and then dynamic contact stiffness can be calculated through the stiffness model without external sensors. Finally, a feed system dynamic model is built, and the contact model and sensorless stiffness estimating method are verified by experiments in this dynamic system.

The Stiffness Analysis and Modeling Simulation of Ball Screw Feed System

2010 ◽  
Vol 97-101 ◽  
pp. 2914-2920 ◽  
Author(s):  
Qin Wu ◽  
Zhi Yuan Rui ◽  
Jian Jun Yang
Keyword(s):  
Machine Tool ◽  
Control Strategy ◽  
Feedforward Control ◽  
Dynamic Performance ◽  
Numerical Control ◽  
Ball Screw ◽  
Axial Stiffness ◽  
Cnc Machine Tool ◽  
Cnc Machine ◽  
Feed System

The computer numerical control (CNC) machine tool was investigated and the dynamics model for the servo feed system was established. Based on the fixing constraint of the ball screw, the mathematical models of axial stiffness and torsion stiffness are constructed. According to the effects of stiffness on the dynamic performance, the simulation model for CNC machine tool feed system with stiffness considered was set up by the dynamic simulation tool Simulink, and a curve representing the performance of the system was obtained. To reduce the effect of stiffness on the system, the feedforward control strategy is used for stiffness compensation. The simulation results show that the stability and response performances of the system are improved and the steady-state error of the system is reduced by the control strategy.

Low Order Static Load Distribution Model for Ball Screw Mechanisms Including Effects of Lateral Deformation and Geometric Errors

2017 ◽  
Vol 140 (2) ◽  
Author(s):  
Bo Lin ◽  
Chinedum E. Okwudire ◽  
Jason S. Wou
Keyword(s):  
Load Distribution ◽  
Static Load ◽  
High Order ◽  
Contact Model ◽  
Ball Screw ◽  
Distribution Model ◽  
Computational Time ◽  
Geometric Errors ◽  
Lateral Deformation ◽  
Low Order

Accurate modeling of static load distribution of balls is very useful for proper design and sizing of ball screw mechanisms (BSMs); it is also a starting point in modeling the dynamics, e.g., friction behavior, of BSMs. Often, it is preferable to determine load distribution using low order models, as opposed to computationally unwieldy high order finite element (FE) models. However, existing low order static load distribution models for BSMs are inaccurate because they ignore the lateral (bending) deformations of screw/nut and do not adequately consider geometric errors, both of which significantly influence load distribution. This paper presents a low order static load distribution model for BSMs that incorporates lateral deformation and geometric error effects. The ball and groove surfaces of BSMs, including geometric errors, are described mathematically and used to establish a ball-to-groove contact model based on Hertzian contact theory. Effects of axial, torsional, and lateral deformations are incorporated into the contact model by representing the nut as a rigid body and the screw as beam FEs connected by a newly derived ball stiffness matrix which considers geometric errors. Benchmarked against a high order FE model in case studies, the proposed model is shown to be accurate in predicting static load distribution, while requiring much less computational time. Its ease-of-use and versatility for evaluating effects of sundry geometric errors, e.g., pitch errors and ball diameter variation, on static load distribution are also demonstrated. It is thus suitable for parametric studies and optimal design of BSMs.

The Vibration Characteristic Analysis of Feed System of CNC Machine Tool

2013 ◽  
Vol 482 ◽  
pp. 169-173
Author(s):  
Qin Wu ◽  
Jian Jun Yang
Keyword(s):  
Machine Tool ◽  
Lagrange Equation ◽  
Contact Stiffness ◽  
Ball Screw ◽  
Cnc Machine Tool ◽  
Test Bed ◽  
Cnc Machine ◽  
Characteristic Analysis ◽  
Feed System ◽  
Vibration Displacement

The mathematical model of feed system of CNC machine tool was established base of Lagrange Equation and energy principle, then uses the Runge-Kutta method to solve the equation, and analyzes the influence that the parameters to the vibration displacement of ball screw. According to the result of orthogonal test, it is concluded that the most important three factors which influence ballscrew vibration displacement were the ball screw's lead h, the table quality m and the longitudinal contact stiffness kn in the connection of workbench and ballscrew. On the feed system test-bed, the longitudinal amplitude, torsional amplitude and horizontal amplitude of ball screw were measured, the results show the larger the ball screw's lead and the quality of workbench, the greater the amplitude of ball screw, the bigger the longitudinal contact stiffness kn, and the smaller the amplitude of screw.

Evaluation of Friction Damping in Dovetail Root Joints Based on Dissipation Energy on Contact Surfaces

2009 ◽  
Author(s):  
Kunio Asai ◽  
Shigeo Sakurai ◽  
Takeshi Kudo ◽  
Norihiko Ozawa ◽  
Taizo Ikeda
Keyword(s):  
Contact Force ◽  
Contact Stiffness ◽  
Relative Displacement ◽  
Contact Angles ◽  
Forced Response ◽  
Contact Forces ◽  
Friction Damping ◽  
Normal Contact ◽  
Tangential Contact ◽  
Contact Surfaces

It is necessary to increase and estimate friction damping at contact interfaces to reduce vibratory stresses in turbines. The hysteresis behavior between tangential contact force and relative displacement should be precisely estimated to improve the accuracy of fiction-damping estimates. There is a difficulty in establishing a general model of hysteresis because tangential contact stiffness depends on many parameters, such as normal contact force, contact geometry, surface roughness, and wear status. We discuss a procedure to empirically calculate friction damping in dovetail root joints using the tangential contact stiffness estimated from measured natural frequencies and the micro-slip model whose coefficients were experimentally obtained from special fretting tests. Instead of the multi-harmonic balance methods, we calculated the friction damping on the basis of the energy dissipation at contact surfaces to discuss the effects of the tangential contact stiffness on several physical values, i.e., tangential and normal contact forces, natural frequency, and micro-slip. In our model, the linear forced response analysis was conducted by taking into consideration the non-linearity between the tangential contact force and the relative displacement by defining the actual and imaginary tangential contact stiffness. We confirmed that the numerically calculated damping ratios are quantitatively in very good agreement with the measured ones under different contact angles, input gravity levels, and contact forces. This indicates that if the tangential contact stiffness is accurately estimated, friction damping with our method can be precisely estimated under different test conditions. We also showed that the estimated tangential contact stiffness for dovetail root joints are smaller than those obtained by the fretting tests at high input gravity. This is probably because the contact interface partially separates during a cyclic loading in the former case; this results in the decrease of the contact area and contact stiffness.

Modeling of axial contact stiffness of a double-nut with preloads

2016 ◽  
Vol 232 (4) ◽  
pp. 629-638 ◽  
Author(s):  
Tiemin Li ◽  
Fuhua Li ◽  
Yao Jiang ◽  
Haitong Wang ◽  
Yunsong Du
Keyword(s):  
Theoretical Model ◽  
Axial Load ◽  
Contact Stiffness ◽  
Ball Screw ◽  
Axial Stiffness ◽  
Axial Deformation ◽  
Displacement Sensors ◽  
Ball Screw Drive ◽  
Improved Model ◽  
Ball Screw Drives

Ball screw drives are commonly used to provide linear motion in machine tools. And stiffness is one of the most important performance indexes. However, stiffness of nuts with different preloads is difficult to be calculated precisely because of complex structures. In order to improve the calculating accuracy, a new model is proposed with the consideration of geometry errors of grooves and balls based on the existing theoretical model. The influence of geometry errors on axial deformation of double-nut is analyzed and modeled. Meanwhile, a preload-adjustable ball screw drive is constructed on the basis of a modified double-nut mechanism. A novel loading mechanism is designed to apply axial load on the working table and test the force in real time. Two laser displacement sensors are adopted to test axial deformation of the double-nut. The axial stiffness of the double-nut is analyzed based on the axial load and the axial deformation. Stiffness simulations of the new improved model, the theoretical model, and the empirical model are also analyzed. The contrastive analysis shows that the experimental results agree much better with the axial stiffness calculated by the new improved model. This study provides a more accurate model to calculate the stiffness of the double-nut with preloads for preloaded ball screw drives.

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