scholarly journals The effect of the lead error on the load distribution and no-load drag torque in a double-nut ball screw

2021 ◽  
Author(s):  
Lu-Chao Zhang ◽  
Yi Ou ◽  
Hu-Tian Feng
Keyword(s):  
Load Distribution ◽  
Mechanical Analysis ◽  
Contact Angles ◽  
Ball Screw ◽  
Contact Theory ◽  
Drag Torque ◽  
Hertz Contact ◽  
Relative Errors ◽  
Lead Error ◽  
Key Parameter

Abstract In a ball screw mechanism, the lead error is not only the key parameter to evaluate the precision, but also an important parameter to determine the load distribution. In this paper, a model is proposed to predict the load distribution related to the lead errors. The mechanical analysis of a double-nut ball screw is conducted to investigate the effect of the lead errors on the balls’ contact deformations and contact angles. Based on the Hertz contact theory, the equations to predict the preload and no-load drag torque are established, and the amplitude of the preload is obtained when the rotational speed is low. To verify the model, various experiments are conducted to measure the lead errors and the no-load drag torques of the ball screw by changing the screws with different accuracy levels. The experimental results show that the preload and no-load drag torque rise when the lead error increases in a double-nut ball screw. Besides, the relative errors between the experimental value and the theoretical value are less than 10%. This proves that the model can predict the preload and the no-load drag torque influenced by the lead error well, which is beneficial to the design of the double-nut ball screw for a certain preload.

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.

Model of Precision Loss for the Precision Ball Screw

2013 ◽  
Vol 753-755 ◽  
pp. 1680-1685 ◽  
Author(s):  
Guang Yuan Xu ◽  
Wei Jun Tao ◽  
Hu Tian Feng
Keyword(s):  
Dynamic Characteristics ◽  
Classical Mechanics ◽  
Load Condition ◽  
Ball Screw ◽  
Contact Theory ◽  
Hertz Contact ◽  
External Interference ◽  
Characteristics Analysis ◽  
The Impact ◽  
Dynamic Characteristics Analysis

Aiming at the precision retaining ability problems of the precision ball screw, the modeling on the motion precision loss process under load condition is studied. The mechanics and deformation of the interface of ball and groove under load condition is analyzed by using the classical mechanics and Hertz contact theory, also a precision loss model for precision ball screw is established based on the dynamic characteristics analysis of the ball screw. Regardless of the external interference, the impact of various factors on the precision loss is analyzed and calculated.

Study on Leakage Rate of Rubber Sealing Structures Based on Percolation Theory

2016 ◽  
Author(s):  
Xiaoming Huang ◽  
Guoliang Xu
Keyword(s):  
Percolation Theory ◽  
Great Influence ◽  
Mechanical Analysis ◽  
Leakage Rate ◽  
Operating Conditions ◽  
Contact Theory ◽  
Hertz Contact ◽  
Mechanism Model ◽  
Sealing Performance ◽  
Theoretical Mechanism

To enhance the containment integration for nuclear safety, sealing performance of those numerous penetrations has to be concerned. Surface roughness of the sealing pairs contact ends has great influence on the leakage characteristics. Following the essence of leakage phenomena, a theoretical mechanism model of leakage rate for rubber sealing structure was built based on percolation theory, where rough contact interface was treated as an aperture region. Deformation behavior of the roughness was solved by using Hertz contact theory. The mechanism model can realize the conversion of leakage rate between different operating conditions, which is important to leakage rate prediction. And the model can be easily combined with macro mechanical analysis of the sealing structure, which is helpful for their optimum design. Validation and convenience of this model is verified through two concrete examples.

Study on the Influence of the Installation Error of Ball Screw Feed System

2014 ◽  
Vol 945-949 ◽  
pp. 826-830
Author(s):  
Wei Wei Zhang ◽  
Hua Ling Chen ◽  
Shu Hai Jia ◽  
Yong Quan Wang
Keyword(s):  
Contact Angle ◽  
Theoretical Analysis ◽  
Quantitative Research ◽  
Ball Screw ◽  
Contact Theory ◽  
Machining Accuracy ◽  
Hertz Contact ◽  
Feed System ◽  
Theoretical Analyses ◽  
Screw Feed

Focusing on the quantitative research on feed system with installation errors, a theoretical analyses model is developed to analyze the influence of parallelism error and coaxiality error of the system. The change law of stress, deformation and contact angle is discussed based on the analysis with hertz contact theory. The theoretical analysis is verified by the simulation with FEM software. The result shows that bias load, deformation of guide and compress variation of the ball decrease as the deviation from bearing for the coaxiality error, while these changes remain small for the first half stroke and dramatically increase later for the parallelism error. The analysis above may be helpful for the installing of the ball screw and for improving the machining accuracy.

scholarly journals Investigation on indentation rolling resistance of belt conveyor based on Hertz contact theory compared with one-dimensional Winkler foundation

2018 ◽  
Vol 10 (7) ◽  
pp. 168781401878393 ◽  
Author(s):  
Lu Yan
Keyword(s):  
Rolling Resistance ◽  
Contact Theory ◽  
Theoretical Formula ◽  
Winkler Foundation ◽  
Hertz Contact ◽  
Belt Conveyor ◽  
One Dimensional ◽  
Hertz Contact Theory ◽  
Viscoelastic Theory ◽  
Indentation Rolling Resistance

Based on Hertz contact theory and one-dimensional Winkler foundation combination with viscoelastic theory, the author derived theoretical formulas of indentation rolling resistance, respectively. Using the laboratorial apparatus of indentation rolling resistance, the author mainly concentrates on the error analysis about two kinds of theoretical formula which bear on indentation rolling resistance compared with experimental result. The reason why author employs Hertz contact theory to discuss indentation rolling resistance is that indentation rolling resistance is a sort of contact resistance. As a result, Hertz contact theory is generally applicable to study it. On the other hand, because conveyor belt has viscoelastic property, it is appropriate to use viscoelastic theory by the aid of three-parameter Maxwell viscoelastic model combination with one-dimensional Winkler foundation. Ultimately, this article infers that theoretical formula based on the Hertz contact is brief and clear compared with one-dimensional Winkler foundation in principle. However, it is noticeable that when the belt is at high speed, the reliability of formula based on Hertz theory has decreased obviously. This conclusion can give a beneficial reference for the energy saving of belt conveyor.

Virtual Material Model of Joint Interfaces Considering Elastic-Plastic Deformation of Asperities

2013 ◽  
Vol 457-458 ◽  
pp. 257-261
Author(s):  
Li Gang Cai ◽  
Teng Yun Xu ◽  
Yong Sheng Zhao
Keyword(s):  
Plastic Deformation ◽  
Elastic Modulus ◽  
Fractal Theory ◽  
Material Model ◽  
Contact Theory ◽  
Hertz Contact ◽  
Calculation Methods ◽  
Elastic Plastic ◽  
Element Simulation ◽  
Simulation Results

A virtual material model of joint interfaces was established based on the Hertz contact theory and fractal theory, this model was improved by considering the influence of the elastic-plastic deformation of asperities and ameliorating the calculation methods of the elastic modulus. The simulation results of elastic-plastic considered and elastic-plastic unconsidered were compared, moreover, the finite element simulation results and experimental results were compared to fully explain the necessity of considering the influence of the elastic-plastic deformation and the the correctness of the method to calculate the elastic modulus. The research suggested that under a same load the elastic modulus of the model considering the influence of the elastic-plastic deformation was slightly larger than the un considering one, which means it could describe the characteristics of joint interfaces more accurately.

scholarly journals Экспериментальное и теоретическое исследование осциллятора с соударениями

2020 ◽  
Vol 90 (10) ◽  
pp. 1672
Author(s):  
В.В. Нарожнов
Keyword(s):  
Theoretical Model ◽  
Equations Of Motion ◽  
Spectral Characteristics ◽  
Contact Theory ◽  
Hertz Contact ◽  
Mechanical Oscillator ◽  
Impact Oscillator ◽  
Fourier Filtering ◽  
Nonlinear Mechanical ◽  
The Impact

The results of a study of a nonlinear mechanical oscillator with elastic impacts are presented. The experiment was carried out using an electromechanical impact oscillator. The theoretical model is based on the equations of motion, taking into account the elastic force, which is calculated under the Hertz contact theory. It is shown that bifurcations and attractors of the “stable focus” and “limit cycle” types can occur for the impact oscillator. Fourier filtering was used to analyze the spectral characteristics of the signals.

Comparative Study of Surface Energies of Native Oxides of Si(100) and Si(111) via Three Liquid Contact Angle Analysis

MRS Advances ◽  
2018 ◽  
Vol 3 (57-58) ◽  
pp. 3379-3390 ◽  
Author(s):  
Saaketh R. Narayan ◽  
Jack M. Day ◽  
Harshini L. Thinakaran ◽  
Nicole Herbots ◽  
Michelle E. Bertram ◽  
...  
Keyword(s):  
Contact Angle ◽  
Surface Energy ◽  
Sessile Drop ◽  
Surface Composition ◽  
Ion Beam ◽  
Contact Angles ◽  
Van Der Waals Interactions ◽  
Native Oxides ◽  
Relative Errors ◽  
Contact Angle Analysis

ABSTRACTThe effects of crystal orientation and doping on the surface energy, γT, of native oxides of Si(100) and Si(111) are measured via Three Liquid Contact Angle Analysis (3LCAA) to extract γT, while Ion Beam Analysis (IBA) is used to detect Oxygen. During 3LCAA, contact angles for three liquids are measured with photographs via the “Drop and Reflection Operative Program (DROP™). DROP™ removes subjectivity in image analysis, and yields reproducible contact angles within < ±1°. Unlike to the Sessile Drop Method, DROP can yield relative errors < 3% on sets of 20-30 drops. Native oxides on 5 x 1013 B/cm3 p- doped Si(100) wafers, as received in sealed, 25 wafer teflon boats continuously stored in Class 100/ISO 5 conditions at 24.5°C in 25% controlled humidity, are found to be hydrophilic. Their γT, 52.5 ± 1.5 mJ/m2, is reproducible between four boats from three sources, and 9% greater than γT of native oxides on n- doped Si(111), which averages 48.1 ± 1.6 mJ/m2 on four 4” Si(111) wafers. IBA combining 16O nuclear resonance with channeling detects 30% more oxygen on native oxides of Si(111) than Si(100). While γT should increase on thinner, more defective oxides, Lifshitz-Van der Waals interactions γLW on native oxides of Si(100) remain at 36 ± 0.4 mJ/m2, equal to γLW on Si(111), 36 ± 0.6 mJ/m2, since γLW arises from the same SiO2 molecules. Native oxides on 4.5 x 1018 B/cm3 p+ doped Si(100) yield a γT of 39 ± 1 mJ/m2, as they are thicker per IBA. In summary, 3LCAA and IBA can detect reproducibly and accurately, within a few %, changes in the surface energy of native oxides due to thickness and surface composition arising from doping or crystal structure, if conducted in well controlled clean room conditions for measurements and storage.

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.

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