scholarly journals Study on Gear Contact Stiffness and Backlash of Harmonic Drive Based on Fractal Theory

2021 ◽  
Author(s):  
Tao Zhang ◽  
Zhifeng Liu ◽  
Congbin Yang ◽  
Yang Wang ◽  
Qianqian Liu
Keyword(s):  
Contact Force ◽  
Contact Stiffness ◽  
Fractal Theory ◽  
Roughness Parameter ◽  
Tooth Surface ◽  
Gear Backlash ◽  
Fractal Parameters ◽  
Fractal Roughness ◽  
Gear Contact ◽  
Tooth Pair

Abstract Contact stiffness and backlash model of harmonic reducer is related to robot’s positioning accuracy and vibration characteristics. Harmonic reducer tooth pair height is typically less than 1 mm. Thus, backlash and contact stiffness measurement and modeling are relatively complex. In this paper, contact stiffness and backlash model is proposed by establishing a relationship between fractal parameters and tooth contact load. Non-contact optical profiler and RMS method are combined to obtain fractal roughness parameters of real machined tooth surface. Finally, the effect of rough tooth surface and contact force fractal parameters on contact stiffness and gear backlash is studied. The results indicate that surface topography parameters and contact force have significant effects on contact stiffness and backlash. By increasing the fractal dimension, a decrease of gear backlash and contact stiffness is observed. However, the opposite is true for the fractal roughness parameter. Lastly, an increase in contact force improves the contact stiffness.

scholarly journals Interval estimation for contact stiffness of bolted joint with uncertain parameters

2019 ◽  
Vol 11 (11) ◽  
pp. 168781401988370 ◽  
Author(s):  
Yongsheng Zhao ◽  
Hongchao Wu ◽  
Congbin Yang ◽  
Zhifeng Liu ◽  
Qiang Cheng
Keyword(s):  
Fractal Dimension ◽  
Contact Surface ◽  
Contact Stiffness ◽  
Interval Estimation ◽  
Roughness Parameter ◽  
Normal Pressure ◽  
Bolted Joints ◽  
Uncertain Parameters ◽  
Fractal Parameters ◽  
Fractal Roughness

Bolted joints are elements used to create resistant assemblies in the mechanical system, whose overall performance is greatly affected by joints’ contact stiffness. Most of the researches on contact stiffness are based on certainty theory whereas in real applications the uncertainty characterizes the parameters such as fractal dimension D and fractal roughness parameter G. This article presents an interval estimation theory to obtain the stiffness of bolted joints affected by uncertain parameters. Topography of the contact surface is fractal featured and determined by fractal parameters. Joint stiffness model is built based on the fractal geometry theory and contact mechanics. Topography of the contact surface of bolted joints is measured to obtain the interval of uncertain fractal parameters. Equations with interval parameters are solved to acquire the interval of contact stiffness using the Chebyshev interval method. The relationship between the interval of contact stiffness and the uncertain parameters, that is, fractal dimension D, fractal roughness parameter G, and normal pressure, can be obtained. The presented model can be used to estimate the interval of stiffness for bolted joints in the mechanical systems. The results can provide theoretical reference for the reliability design of bolted joints.

Surface fractal topography-based contact stiffness determination of spindle–toolholder joint

2015 ◽  
Vol 230 (4) ◽  
pp. 602-610 ◽  
Author(s):  
Yongsheng Zhao ◽  
Xiaolei Song ◽  
Ligang Cai ◽  
Zhifeng Liu ◽  
Qiang Cheng
Keyword(s):  
Contact Force ◽  
Contact Area ◽  
High Speed ◽  
Contact Stiffness ◽  
Fractal Theory ◽  
Contact Model ◽  
Real Contact Area ◽  
Real Contact ◽  
Fractal Parameters ◽  
Relationship Of

Accurate modeling of contact stiffness is crucial in predicting the dynamic behavior and chatter vibration of spindle–toolholder system for high-speed machining centers. This paper presents a fractal theory-based contact model of spindle–toolholder joint to obtain the contact stiffness and its real contact area. Topography of the contact surfaces of spindle–toolholder joint is fractal featured and determined by fractal parameters. Asperities in micro-scale are considered as elastic or plastic deformation. Then, the contact stiffness, the real contact area, the elastic contact force, and the plastic contact force of the whole contact surface are calculated by integrating the micro asperities. The relationship of the contact stiffness and the drawbar force follows a power law, in which the power index is determined by the fractal parameters. Experiments are conducted to verify the efficiency of the proposed model. The results from the fractal contact model of spindle–toolholder joint have good agreement with those of experiments.

Experimental Observation of Fractal-Regular Surfaces and a Transformation Scheme for Extracting Fractal Parameters

2005 ◽  
Author(s):  
Shao Wang ◽  
Wai Kin Chan
Keyword(s):  
Silicon Wafer ◽  
Roughness Parameter ◽  
Hard Disk ◽  
Spectral Density Function ◽  
Power Spectral ◽  
Fractal Parameters ◽  
Asperity Contacts ◽  
Fractal Roughness ◽  
Magnetic Hard Disk ◽  
Wafer Surfaces

To account for the effects of asperity contacts at various length scales, it is appropriate to characterize an engineering surface as a fractal-regular surface. In spite of significant theoretical advancement, there is a desperate need for experimental verification of the theory of fractal-regular surfaces and a consistent scheme of obtaining the fractal parameters. In the present study, the existence of a fractal region and a regular-shape region in the power spectral density function for fractal-regular surfaces was confirmed experimentally, for the first time, with data obtained from magnetic hard disk and silicon wafer surfaces. A novel scheme involving a variable transformation was developed to extract fractal parameters. This scheme was validated by accurate recovery of fractal parameters from simulated surfaces. The fractal dimension, the fractal roughness parameter and the fractal domain length were found for magnetic hard disk and silicon wafer surfaces.

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 multi-scale stiffness fractal model of joint interfaces

2021 ◽  
pp. 81-95
Author(s):  
Jingfang Shen ◽  
◽  
Sijie Cheng ◽  
Siyan Wang ◽  
Wenwei Liu ◽  
...  
Keyword(s):  
Contact Mechanics ◽  
Normal Load ◽  
Contact Stiffness ◽  
Roughness Parameter ◽  
Numerical Control ◽  
Joint Interface ◽  
Normal Contact ◽  
Multi Scale ◽  
Stiffness Model ◽  
Fractal Roughness

Stiffness characterization of mechanical interfaces is quite crucial for the analysis of several tribological behaviors. The stiffness of different machine tools varies greatly, particularly for computer numerical control machine. Therefore, this research aims at providing an assessment of influence factors for stiffness of joint interfaces theoretically. Based on fractal roughness parameters independent of scale and contact mechanics theory, the contact area of joint interface is studied, and the multi-scale normal contact stiffness model and multi-scale tangential contact stiffness model are proposed. Meanwhile, the problem of the deformation of any contact asperity is considered as three separate regimes. The laws of area-displacement and force-displacement under elastic-plastic regime are established. The transition which is in the deformation mechanism of asperity from elastic to plastic is consistent with classical contact mechanics. The analysis of numerical calculation results indicates the approximate linear relation among dimensionless normal load and key parameters. Moreover, these key parameters have been divided into two main categories for the multiscale model of joint interfaces, one is fractal parameters such as fractal dimension D and fractal roughness parameter G, and the other is interfacial parameters. In addition, tangential load and friction factor are two important factors to the tangential stiffness.

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.

A stress sensitivity model for the permeability of porous media based on bi-dispersed fractal theory

2018 ◽  
Vol 29 (02) ◽  
pp. 1850019 ◽  
Author(s):  
X.-H. Tan ◽  
C.-Y. Liu ◽  
X.-P. Li ◽  
H.-Q. Wang ◽  
H. Deng
Keyword(s):  
Porous Media ◽  
Fractal Dimension ◽  
Fractal Theory ◽  
Stress Sensitivity ◽  
Maximum Diameter ◽  
Proposed Model ◽  
Fractal Parameters ◽  
Stress Changes ◽  
Capillary Bundle ◽  
Definition Of

A stress sensitivity model for the permeability of porous media based on bidispersed fractal theory is established, considering the change of the flow path, the fractal geometry approach and the mechanics of porous media. It is noted that the two fractal parameters of the porous media construction perform differently when the stress changes. The tortuosity fractal dimension of solid cluster [Formula: see text] become bigger with an increase of stress. However, the pore fractal dimension of solid cluster [Formula: see text] and capillary bundle [Formula: see text] remains the same with an increase of stress. The definition of normalized permeability is introduced for the analyzation of the impacts of stress sensitivity on permeability. The normalized permeability is related to solid cluster tortuosity dimension, pore fractal dimension, solid cluster maximum diameter, Young’s modulus and Poisson’s ratio. Every parameter has clear physical meaning without the use of empirical constants. Predictions of permeability of the model is accordant with the obtained experimental data. Thus, the proposed model can precisely depict the flow of fluid in porous media under stress.

Finite Element Analysis for Gear Contact Based on UG and ABAQUS

2013 ◽  
Vol 442 ◽  
pp. 229-232 ◽  
Author(s):  
Li Mei Wu ◽  
Fei Yang
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Contact Stress ◽  
Three Dimensional ◽  
Element Model ◽  
Tooth Surface ◽  
Element Analysis ◽  
Tooth Width ◽  
Gear Contact ◽  
Maximum Contact

According to the cutting theory of involute tooth profile, established an exact three-dimensional parametric model by UG. Used ABAQUS to crate finite element model for gear meshing. After simulated the meshing process, discussed the periodicity of the tooth surface contact stress. Based on the result of finite element analysis, made a comparison of the maximum contact stress between finite element solution and Hertz theoretical solution, analyzed the contact stress distribution on tooth width, and researched the effect of friction factor on contact stress. All that provided some theoretical basis for gear contact strength design.

Coupling fractal model for fretting wear on rough contact surfaces

2020 ◽  
pp. 1-32
Author(s):  
Yi Wang ◽  
Gang Liang ◽  
Shuo LIU ◽  
Yi Cui
Keyword(s):  
Contact Surface ◽  
Fractal Theory ◽  
Three Dimensional ◽  
Parameter Analysis ◽  
Fretting Wear ◽  
Wear Depth ◽  
Contact Parameter ◽  
Wear Process ◽  
Actual Surface ◽  
Fractal Parameters

Abstract In this paper, a fretting damage model based on fractal theory is proposed. The Weierstrass-Mandelbrot function of fractal theory is used to represent the rough contact surface, and a corresponding contact parameter analysis method is also established. Based on neural network algorithm, the values of fractal parameters are fitted, and the fitting accuracy has been greatly improved compared with traditional methods. According to the fractal parameters of the actual surface, the fretting wear process of the rough contact surface is analyzed based on theory of adhesive and three body abrasive wear. A generic program for the analysis of three-dimensional fretting wear problems is also proposed. Compared with material tests, the prediction error of fretting wear simulation model is 13.4% for wear depth and 16.7% and 3.9% for width and length of wear scar in stable wear stage. The prediction results show that the model can be applied to the prediction of the actual three-dimensional fretting wear model.

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