Low-Order Contact Load Distribution Model for Ball Nut Assemblies

2016 ◽  
Vol 9 (2) ◽  
pp. 535-540 ◽  
Author(s):  
Bo Lin ◽  
Chinedum E. Okwudire
Keyword(s):  
Load Distribution ◽  
Contact Load ◽  
Distribution Model ◽  
Order Contact ◽  
Low Order

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.

scholarly journals The Cold Rolling Load Distribution of the Nuclear Power Zirconium Alloy Based on the Self-adaptive Particle Swarm Optimization Algorithm

2021 ◽  
Author(s):  
Cao Yuan ◽  
Jianguo Cao ◽  
Wang Tao ◽  
Wang Leilei ◽  
Li Fang ◽  
...  
Keyword(s):  
Particle Swarm Optimization ◽  
Cold Rolling ◽  
Optimization Algorithm ◽  
Load Distribution ◽  
Zirconium Alloy ◽  
Particle Swarm Optimization Algorithm ◽  
Particle Swarm ◽  
Rolling Process ◽  
Distribution Model ◽  
Swarm Optimization

Abstract Aiming at the problem of load distribution during multi-pass cold rolling of nuclear zirconium alloy strip, the load distribution model with good shape is established by the self-adaptive particle swarm optimization algorithm (SAPSO), considering the main constraint conditions including rolling force, reduction and torque in cold rolling process. Based on the penalty function method transforming the constraint problem into the unconstrained problem, the particle swarm optimization algorithm with adaptive inertia weight factor optimized the load distribution model is developed to improve the local search ability of the particle swarm optimization algorithm. Compared with the existing nuclear zirconium alloy industrial schedule, the simulation results of load distribution based on the SAPSO can keep good shape in multi-pass cold rolling process with the high prediction accuracy. The industrial experiments demonstrate that the proportional crown difference value is consistent, the plate shape flatness is good.

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.

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 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.

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