A Contact Stiffness Model of Machined Plane Joint Based on Fractal Theory

2009 ◽  
Vol 132 (1) ◽  
Author(s):  
Shuyun Jiang ◽  
Yunjian Zheng ◽  
Hua Zhu
Keyword(s):  
Contact Stiffness ◽  
Fractal Theory ◽  
Fractal Model ◽  
Experimental Results ◽  
Size Dependent ◽  
Contact Loads ◽  
Proposed Model ◽  
Stiffness Model ◽  
Surface Profiles ◽  
Plane Joint

A general contact stiffness model is proposed in this paper to study the contacts between rough surfaces of machined plane joints. The proposed model uses fractal geometry for surface topography description, elastic-plastic deformation of contacting asperities, and size-dependent contact stiffness of microcontacts, where the contact stiffness is derived from Hertz contact theory. Three cast iron specimens are produced from different machining methods (milling, grinding, and scraping), and their rough surface profiles are extracted. The structure function method was used to calculate each profile’s fractal dimension and scale coefficient. Both theoretical analysis and experimental results of contact stiffness are obtained for these specimens under different contact loads. The comparison between the theoretical contact stiffness and the experimental results at the interface indicates that the present fractal model for the contact stiffness is appropriate and the theoretical contact stiffness is consistent with the experimental data.

Stiffness model of fixed joint considering self-affinity and elastoplasticity of asperities

2019 ◽  
Vol 72 (1) ◽  
pp. 128-135 ◽  
Author(s):  
Hongxu Chen ◽  
Qin Yin ◽  
Guanhua Dong ◽  
Luofeng Xie ◽  
Guofu Yin
Keyword(s):  
Elastic Deformation ◽  
Contact Stiffness ◽  
Roughness Parameter ◽  
Experimental Results ◽  
Content Type ◽  
Elastoplastic Contact ◽  
Proposed Model ◽  
Stiffness Model ◽  
Fractal Roughness ◽  
Deformation Ratio

Purpose The purpose of this paper is to establish a stiffness model of fixed joint considering self-affinity and elastoplasticity of asperities. Design/methodology/approach The proposed model considers that asperities of different scales are interrelated rather than independent. For elastoplastic contact, a spring-damper model and an elastic deformation ratio function were proposed to calculate the contact stiffness of asperities. Findings A revised fractal asperity model was proposed to calculate the contact stiffness of fixed joint, the impacts of the fractal dimension, the fractal roughness parameter and the Meyer index on the contact stiffness were discussed, and the present experimental results and the Jiang’s experimental results showed that the stiffness can be well predicted by proposed model. Originality/value The contradiction between the Majumdar and Bhushan model and the Morag and Etsion model can be well explained by considering the interaction among asperities of different scales. For elastoplastic contact, elastic deformation ratio should be considered, and the stiffness of asperities increases first and then decreases with the increasing of interference.

A normal contact stiffness model of machined joint surfaces considering elastic, elasto-plastic and plastic factors

2019 ◽  
Vol 234 (7) ◽  
pp. 1007-1016 ◽  
Author(s):  
Yongquan Zhang ◽  
Hong Lu ◽  
Xinbao Zhang ◽  
He Ling ◽  
Wei Fan ◽  
...  
Keyword(s):  
Surface Topography ◽  
Contact Stiffness ◽  
Fractal Theory ◽  
Fractal Model ◽  
Single Pair ◽  
Machined Surface ◽  
Normal Contact ◽  
Joint Surfaces ◽  
Stiffness Model ◽  
Normal Contact Stiffness

Considering the rough surface as a fractal model makes the research of contact parameters more practical. In the fractal model of the machined surface, the parameters describing the surface topography are independent of the measurement resolution. Based on the elastic, elasto-plastic and plastic deformations of a single pair of contact asperities, a normal contact stiffness model using the fractal model for surface topography description is proposed in this paper. The specimens machined by milling and grinding methods are used to verify the proposed contact stiffness model based on the fractal theory. The experimental and theoretical results indicate that the proposed contact stiffness model is appropriate for the machined joint surfaces.

Normal Contact Stiffness Fractal Geometric Model Based on the Gamma Distribution of Rough Joint Surface

2013 ◽  
Vol 760-762 ◽  
pp. 2064-2067 ◽  
Author(s):  
Jing Fang Shen ◽  
Ke Xiang Wu ◽  
Fei Yang
Keyword(s):  
Convex Body ◽  
Gamma Distribution ◽  
Contact Stiffness ◽  
Geometric Model ◽  
Fractal Theory ◽  
Fractal Model ◽  
Joint Surface ◽  
Engineering Practice ◽  
Normal Contact ◽  
Normal Contact Stiffness

In this article, according to WenShuHua and Zhangxueniang fractal model, we point out the deficiency. Based on the fractal theory and Zhang, Wens contact stiffness fractal model, this paper puts forward Gamma distribution of rough joint surface normal contact stiffness. This paper considers micro convex body for ellipsoid, contact area for elliptic. This is slightly convex body for sphere hypothesis is more close to the actual situation. At the same time by using statistics theory, considering the contact ellipse long, short axis a and b are greater than zero, the assumption of a and b to two-dimensional Gamma distribution, it is more suitable for engineering practice.

Elastic Contact Model Accounting for Both Asperity and Substrate Compliance With Application to Patterned Media

2007 ◽  
Author(s):  
Chang-Dong Yeo ◽  
Andreas A. Polycarpou
Keyword(s):  
Bulk Material ◽  
Contact Stiffness ◽  
Contact Model ◽  
Elastic Contact ◽  
Element Analysis ◽  
Patterned Media ◽  
Single Asperity ◽  
Proposed Model ◽  
Stiffness Model ◽  
Bulk Substrate

An improved elastic contact stiffness model for a single asperity system is proposed to account for the effects of both bulk substrate and asperity deformations between two contacting surfaces. Depending upon the applied load, as well as the geometrical and physical properties of the asperity and bulk material, the bulk substrate can have a considerable contribution to the overall contact stiffness. Finite element analysis is performed to verify the proposed analytical model. The single asperity model is extended to rough surfaces in contact. The contact stiffness values from the proposed model are compared to those from the GW model. The proposed contact model can be directly relevant to analyze the contact behavior of modern patterned media.

Torsional Stiffness Model of an Industrial Robotic Joint Using Fractal Theory

2019 ◽  
Author(s):  
Jingjing Xu ◽  
Zhifeng Liu ◽  
Yongsheng Zhao ◽  
Qiang Cheng ◽  
Yanhu Pei ◽  
...  
Keyword(s):  
Prediction Accuracy ◽  
Fractal Theory ◽  
Great Influence ◽  
Joint Stiffness ◽  
Equilibrium Analysis ◽  
Torsional Stiffness ◽  
Tangential Stiffness ◽  
Proposed Model ◽  
Stiffness Model ◽  
Rv Reducer

Abstract It is known that mechanical connections have great influence on the dynamic characteristic of the assembly. In existing methods, the torsional stiffness of the robotic joint is calculated only considering the stiffness of components of the system, which largely reduces the prediction accuracy of the joint stiffness. In the paper, to predict the joint stiffness more accurately, a model is proposed considering influences of the stiffness of all connections existed in a joint system. The normal and tangential stiffness of the contact surface of each connection are calculated by combining the equilibrium analysis of the force and the fractal theory. Then the total stiffness of one robotic joint can be modelled by putting the torsional stiffness of all connections and that of the RV reducer and gear pair in parallel. To verify the proposed model, its simulation result is compared to the stiffness based on the previous technique without considering the influence of connections. The comparison result shows that the proposed model can improve the stiffness-prediction accuracy. This study can be extended to the stiffness modeling of other joint systems and provides a theoretical basis for the dynamic analysis of the robotic system.

scholarly journals The Effect of Grinding Wheel Contact Stiffness on Plunge Grinding Cycle

Inventions ◽  
2020 ◽  
Vol 5 (4) ◽  
pp. 62
Author(s):  
Fukuo Hashimoto ◽  
Hiroto Iwashita
Keyword(s):  
Normal Load ◽  
Contact Stiffness ◽  
Critical Parameters ◽  
Grinding Wheel ◽  
Plunge Grinding ◽  
Contact Loads ◽  
Proposed Model ◽  
Machine Stiffness ◽  
Centerless Grinding ◽  
Grinding Operations

This paper presents the effect of grinding wheel contact stiffness on the plunge grinding cycle. First, it proposes a novel model of the generalized plunge grinding system. The model is applicable to all plunge grinding operations including cylindrical, centerless, shoe-centerless, internal, and shoe-internal grinding. The analysis of the model explicitly describes transient behaviors during the ramp infeed and the spark-out in the plunge grinding cycle. Clarification is provided regarding the premise that the system stiffness is composed of machine stiffness and wheel contact stiffness, and these stiffnesses significantly affect productivity and grinding accuracy. The elastic deflection of the grinding wheel is accurately measured and formulas for representing the deflection nature under various contact loads are derived. The deflection model allows us to find the non-linear contact stiffness with respect to the normal load. The contact stiffnesses of four kinds of grinding wheels with different grades and bond materials are presented. Both cylindrical grinding and centerless grinding tests are carried out, and it is experimentally revealed that the time constant at ramp infeed and spark-out is significantly prolonged by reducing the grinding force. It is verified that a simulation of the grinding tests using the proposed model can accurately predict critical parameters like forces and machine deflection during plunge grinding operations. Finally, this paper provides a guideline for grinding cycle design in order to achieve the required productivity and grinding accuracy.

A stiffness model for bolted joints considering asperity interactions of rough surface contact

2021 ◽  
pp. 1-20
Author(s):  
Hua Zhou ◽  
Xinhua Long ◽  
Guang Meng ◽  
Xianbo Liu
Keyword(s):  
Contact Stiffness ◽  
Classical Model ◽  
Surface Profile ◽  
Bolted Joints ◽  
Normal Stiffness ◽  
Proposed Model ◽  
Stiffness Model ◽  
Fractal Roughness ◽  
Rough Surface Contact ◽  
Stiffness Loss

Abstract A revised fractal contact model considering asperity interactions is proposed. The displacement of mean of asperity heights is used to represent the effects of the asperity interactions. Then the critical contact area will be dependent on the contact load and the contact stiffness will be an integral whose integrand is an implicit expression. The fractal dimension and the fractal roughness are obtained by the measurement of surface profile to calculate the theoretical contact stiffness. The measurement of deformation is conducted to obtain the actual contact stiffness for verification, the results show that the proposed model is closer to the experimental results than other models without considering asperity interactions. Once the contact stiffness is determined, a new total normal stiffness model for bolted joints considering the contact of two rough surfaces is also proposed. Since the contact stiffness is dependent on the clamped force, the total normal stiffness for bolted joints is calculated iteratively at given initial preload and external separating force. Different from the classical model, the total normal stiffness for bolted joint decreases with the external separating force increases, and this stiffness loss will become larger with initial preload decreases. In this sense, the proposed total normal stiffness model is a way to determine the suitable initial preload for different sizes of bolts when the stiffness loss is restricted to a certain range.

An improved stiffness model for line contact elastohydrodynamic lubrication and its application in gear pairs

2020 ◽  
Vol 72 (5) ◽  
pp. 703-708 ◽  
Author(s):  
Jiaxing Pei ◽  
Xu Han ◽  
Yourui Tao
Keyword(s):  
External Load ◽  
Contact Stiffness ◽  
Elastohydrodynamic Lubrication ◽  
Line Contact ◽  
Content Type ◽  
Meshing Stiffness ◽  
Proposed Model ◽  
Stiffness Model ◽  
Film Stiffness ◽  
Ehl Contact

Purpose The purpose of this paper is to propose an simple and efficient stiffness model for line contact under elastohydrodynamic lubrication (EHL) and to investigate the gear meshing stiffness by the proposed model. Design/methodology/approach The method combines the surface contact stiffness and film stiffness as EHL contact stiffness. The EHL contact stiffness can be calculated by the external load and displacement of the load action point. The displacement is the sum of deformation of the film and contact surface and is equal to the distance of the mutual approach of two contact bodies. Findings The conclusion is drawn that the contact stiffness calculated by the proposed model is smaller than that by the minimum film model and larger than that by the mean film model. It is also concluded that the gear meshing stiffness under EHL is slightly smaller than that under dry contact. Originality/value The EHL contact stiffness can be obtained by the increment of external load and mutual approach directly. The calculation of oil film stiffness and surface contact stiffness separately is avoided. Peer review The peer review history for this article is available at: https://publons.com/publon/10.1108/ILT-11-2019-0465

Fractal analysis of permeability near the wall in porous media

2014 ◽  
Vol 25 (07) ◽  
pp. 1450021 ◽  
Author(s):  
Mingchao Liang ◽  
Boming Yu ◽  
Li Li ◽  
Shanshan Yang ◽  
Mingqing Zou
Keyword(s):  
Porous Media ◽  
Pore Size ◽  
Pore Space ◽  
Fractal Theory ◽  
Particle Diameter ◽  
Fractal Dimensions ◽  
Fractal Model ◽  
Proposed Model ◽  
Medium Porosity ◽  
The Relationship

In this paper, a fractal model for permeability of porous media is proposed based on Tamayol and Bahrami's method and the fractal theory for porous media. The proposed model is expressed as a function of the mean particle diameter, the length along the macroscopic pressure drop in the medium, porosity, fractal dimensions for pore space and tortuous capillaries, and the ratio of the minimum pore size to the maximum pore size. The relationship between the permeability near the wall and the dimensionless distance from the wall under different conditions is discussed in detail. The predictions by the present fractal model are in good agreement with available experimental data. The present results indicate that the present model may have the potential in comprehensively understanding the mechanisms of flow near the wall in porous media.

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