Static load distribution and axial static contact stiffness of a preloaded double-nut ball screw considering geometric errors

2022 ◽  
Vol 167 ◽  
pp. 104460
Author(s):  
Jun Liu ◽  
Hutian Feng ◽  
Changguang Zhou
Keyword(s):  
Load Distribution ◽  
Static Load ◽  
Contact Stiffness ◽  
Ball Screw ◽  
Geometric Errors ◽  
Static Contact

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.

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 Dynamic axial contact stiffness analysis of position preloaded ball screw mechanism

2019 ◽  
Vol 11 (1) ◽  
pp. 168781401881928 ◽  
Author(s):  
Jun Liu ◽  
Yi Ou
Keyword(s):  
Axial Load ◽  
Contact Stiffness ◽  
Dynamic Contact ◽  
Ball Screw ◽  
Coupling Relationship ◽  
Stiffness Model ◽  
Static Contact ◽  
Variation Range ◽  
Screw Mechanism ◽  
Feed Drive System

This article establishes an axial contact stiffness model of position preloaded ball screw mechanism based on Hertz contact theory. The analysis of dynamic axial contact stiffness is one of the foundations of the research on the dynamic characteristic of the ball screw feed drive system. The model takes into account the coupling relationship between the contact angle and the normal contact force, as well as the coupling relationship between the elastic deformation and the contact deformation coefficient. The static and dynamic axial contact stiffness characteristics of the preloaded ball screw mechanism are studied. The numerical analysis result shows that the static contact stiffness of the preloaded ball screw mechanism increases with the increase in the preload and decreases with the increase in the axial load. The dynamic contact stiffness of the preloaded ball screw mechanism increases with the increase in the screw’s rotational speed. The variation range of dynamic contact stiffness increases with the increase in axial load under the same preload. And the variation range of dynamic contact stiffness decreases with the increase in preload under the same axial load. The axial contact stiffness model established in this article can be used to analyze either static or dynamic contact stiffness of position preloaded ball screw mechanism.

Analysis of Bouncing Vibrations of a 2-DOF Tripad Contact Slider Model With Air Bearing Pads Over a Harmonic Wavy Disk Surface

1999 ◽  
Vol 121 (4) ◽  
pp. 939-947 ◽  
Author(s):  
Kyosuke Ono ◽  
Kan Takahashi
Keyword(s):  
Contact Stiffness ◽  
Disk Surface ◽  
Design Parameters ◽  
Air Bearing ◽  
Static Contact ◽  
Tracking Ability ◽  
The Coefficient Of Friction ◽  
Bearing Stiffness ◽  
Perfect Contact ◽  
Contact Slider

In this study, the authors numerically analyzed the bouncing vibrations of a two-degree-of-freedom (2-DOF) model of a tripad contact slider with air bearing pads over a harmonic wavy disk surface. The general features of bouncing vibrations were elucidated in regard to the modal characteristics of a 2-DOF vibration system and design parameters such as contact stiffness, contact damping, air hearing stiffness, the rear to front air bearing stiffness ratio, static contact force and the coefficient of friction. The design of a contact slider was discussed in terms of tracking ability and wear durability. In addition, two sample designs of a perfect contact slider with sufficient wear durability were also presented.

scholarly journals Comparison of Numerical Analyses with a Static Load Test of a Continuous Flight Auger Pile

2014 ◽  
Vol 22 (4) ◽  
pp. 1-10 ◽  
Author(s):  
Michal Hoľko ◽  
Jakub Stacho
Keyword(s):  
Load Distribution ◽  
Static Load ◽  
Numerical Models ◽  
Load Test ◽  
Numerical Analyses ◽  
Static Load Test ◽  
Material Models ◽  
The Common ◽  
Constitutive Material ◽  
The Impact

Abstract The article deals with numerical analyses of a Continuous Flight Auger (CFA) pile. The analyses include a comparison of calculated and measured load-settlement curves as well as a comparison of the load distribution over a pile's length. The numerical analyses were executed using two types of software, i.e., Ansys and Plaxis, which are based on FEM calculations. Both types of software are different from each other in the way they create numerical models, model the interface between the pile and soil, and use constitutive material models. The analyses have been prepared in the form of a parametric study, where the method of modelling the interface and the material models of the soil are compared and analysed. Our analyses show that both types of software permit the modelling of pile foundations. The Plaxis software uses advanced material models as well as the modelling of the impact of groundwater or overconsolidation. The load-settlement curve calculated using Plaxis is equal to the results of a static load test with a more than 95 % degree of accuracy. In comparison, the load-settlement curve calculated using Ansys allows for the obtaining of only an approximate estimate, but the software allows for the common modelling of large structure systems together with a foundation system.

Static load distribution analysis of ball screws with nut position variation

2020 ◽  
Vol 151 ◽  
pp. 103893 ◽  
Author(s):  
Chang Liu ◽  
Chunyu Zhao ◽  
Xianli Meng ◽  
Bangchun Wen
Keyword(s):  
Load Distribution ◽  
Static Load ◽  
Distribution Analysis

Investigation of load distribution and deformations for ball screws with the effects of turning torque and geometric errors

2019 ◽  
Vol 141 ◽  
pp. 95-116 ◽  
Author(s):  
Jiajia Zhao ◽  
Mingxing Lin ◽  
Xianchun Song ◽  
Qizhen Guo
Keyword(s):  
Load Distribution ◽  
Geometric Errors

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.

A novel approach to predict the precision sustainability of ball screw under multidirectional load states

2020 ◽  
pp. 095440622094323
Author(s):  
Jiajia Zhao ◽  
Mingxing Lin ◽  
Xianchun Song ◽  
Yanfeng Zhao ◽  
Nan Wei
Keyword(s):  
Elastic Deformation ◽  
Load Distribution ◽  
Contact Load ◽  
Ball Screw ◽  
Deformation Model ◽  
Load Model ◽  
Novel Approach ◽  
Position Precision ◽  
The Relationship ◽  
Load State

The accurate model of the load state for all balls under multidirectional load is very helpful for the design process of ball screws. The contact deformation model of the ball screw without consideration of the stress difference of all balls is inaccurate. In this paper, a novel contact load model of the ball screw is established by considering coupled axial, radial load to study the elastic deformation displacement and position accuracy. The deviation and variation of axial elastic deformation with the dimension errors of all balls are investigated to obtain the influence of load state on the precision sustainability of the ball screw. The position precision including travel deviation and variation by considering load distribution of all balls is studied under the different load conditions. In addition, a new working bench is designed to study the position precision of the ball screw. The experimental study is carried out to obtain the relationship between the position precision and the contact load state of all balls, which is a reference to compensate for the precision loss of the ball screw.

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.

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