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.

Deterministic Contact Model of a Rough Surface Against a Flat-Layered Surface

2004 ◽  
Author(s):  
H. R. Pasaribu ◽  
D. J. Schipper
Keyword(s):  
Mechanical Properties ◽  
Rough Surface ◽  
Contact Area ◽  
Indentation Depth ◽  
Normal Load ◽  
Contact Model ◽  
Real Contact Area ◽  
Single Asperity ◽  
Real Contact ◽  
Effective Mechanical Properties

The effective mechanical properties of a layered surface vary as a function of indentation depth and the values of these properties range between the value of the layer itself and of the substrate. In this paper, a layered surface is modelled like a solid that has effective mechanical properties as a function of indentation depth by assuming that the layer is perfectly bounded to the substrate. The normal load as a function of indentation depth of sphere pressed against a flat layered surface is calculated using this model and is in agreement with the experimental results published by El-Sherbiney (1975), El-Shafei et al. (1983), Tang & Arnell (1999) and Michler & Blank (2001). A deterministic contact model of a rough surface against a flat layered surface is developed by representing a rough surface as an array of spherically shaped asperities with different radii and heights (not necessarily Gaussian distributed). Once the data of radius and height of every single asperity is obtained, one can calculate the number of asperities in contact, the real contact area and the load carried by the asperities as a function of the separation.

Study on Identification of Contact Stiffness Considering Surface Roughness

2014 ◽  
Vol 1017 ◽  
pp. 441-446 ◽  
Author(s):  
Kyoko Nakamura ◽  
Haruhisa Sakamoto
Keyword(s):  
Surface Roughness ◽  
Contact Area ◽  
Quantitative Measurement ◽  
Experimental Approach ◽  
Contact Stiffness ◽  
Real Contact Area ◽  
Special Device ◽  
Real Contact ◽  
Dominant Configuration ◽  
Simplified Calculation

In previous study, the quantitative measurement method of contact stiffness of the joint considering real contact area is developed by experimental approach. However, the measurement of contact stiffness needs special device and skillful measuring technique. Therefore, in this paper, simplified calculation method with material properties and profile data of surface roughness obtained by profilometer is considered. As a result, real contact area, contact stiffness and contact spring stiffness calculated from specific wavelength of rough surface are near agreement with experimental value. Hence, it is revealed that there is dominant configuration in surface roughness.

A Fractal Theory of the Interfacial Temperature Distribution in the Slow Sliding Regime: Part II—Multiple Domains, Elastoplastic Contacts and Applications

1994 ◽  
Vol 116 (4) ◽  
pp. 824-832 ◽  
Author(s):  
S. Wang ◽  
K. Komvopoulos
Keyword(s):  
Temperature Distribution ◽  
Contact Area ◽  
Temperature Rise ◽  
Frictional Heating ◽  
Fractal Theory ◽  
Cumulative Distribution ◽  
Maximum Temperature ◽  
Real Contact Area ◽  
Fractal Structures ◽  
Real Contact

The limitation of the fractal theory as applied to real surfaces is interpreted, and engineering surfaces are considered as a superimposition of fractal structures on macroscopic regular shapes by introducing the concepts of fractal-regular surfaces and multiple fractal domains. The effects of frictional heating at neighboring microcontacts are analyzed, and a simple solution of the temperature distribution is obtained for contact regions that are appreciably larger than a fractal domain. It is shown that the temperature rise at an elastoplastic microcontact does not differ significantly from that at an elastic microcontact of a similar geometry under the same load. The fractional real contact area subjected to temperature rises greater than any given value is represented by a complementary cumulative distribution function. The analysis yields that the average value and standard deviation of the temperature rise at the real contact area are 0.4 and 0.24 times the maximum temperature rise, respectively. The implications of the theory in boundary lubrication are demonstrated in light of results for ceramic materials.

Unloading Process in Elastic-Plastic Contact of a Rough Surface With a Flat

2008 ◽  
Author(s):  
A. Sepehri ◽  
K. Farhang
Keyword(s):  
Finite Element ◽  
Rough Surface ◽  
Contact Force ◽  
Contact Area ◽  
Three Dimensional ◽  
Integral Form ◽  
Real Contact Area ◽  
Elastic Plastic ◽  
Real Contact ◽  
Approximate Equations

Three dimensional elastic-plastic contact of a nominally flat rough surface and a flat is considered. The asperity level Finite Element based constitutive equations relating contact force and real contact area to the interference is used. The statistical summation of asperity interaction during unloading phase is derived in integral form. Approximate equations are found that describe in closed form contact load as a function of mean plane separation during unloading. The approximate equations provide accuracy to within 6 percent for the unload phase of the contact force.

Analysis of Contact Strength for Nutation Transmission with Conical Movable Teeth by Fractal Theory

2020 ◽  
Vol 13 (2) ◽  
pp. 141-155
Author(s):  
Lili Zhu ◽  
Guangxin Wang ◽  
Wenjie He ◽  
Wenzhong Fan
Keyword(s):  
Contact Area ◽  
Fractal Theory ◽  
Planetary Gear ◽  
Contact Model ◽  
Contact Theory ◽  
Tooth Surface ◽  
Real Contact Area ◽  
Contact Strength ◽  
Present Solution ◽  
The Relationship

Background: Nutation transmission with conical movable teeth is a patent about a new type of spacial movable tooth drive that was developed based on the bevel planetary gear drive with a difference in the number of small teeth. Objective: The aim of this study was to establish the fractal contact model and calculate the contact strength of the center gear in the nutation transmission with conical movable teeth based on the M-B fractal contact theory and also to demonstrate the validity of the present solution by comparing it with the FEM results and the Hertz contact results. Methods: Based on the fractal theory, the relationship between the loads and the area for the tapered roller teeth in contact with the center disk was obtained, and the four basic parameters were simulated to analyze the effect of the fractal contact model in MATLAB. Results: The accuracy of the fractal contact model was verified using numerical simulation and analysis of the relationship diagram for the real contact area and load and the contact area ratio chart with different parameters. Conclusion: Based on the FEM theory, the Hertz elastic contact theory, and the fractal theory, the tooth surface contact strength of the center disk was compared and analyzed, which enabled us to demonstrate the validity of the present solution, and measures were taken to optimize and improve the followup design of the nutation drive.

Contact stiffness of mating surfaces of parts under dynamic loading

2020 ◽  
pp. 57-60
Author(s):  
M.M. Matlin ◽  
V.A. Kazankin ◽  
E.N. Kazankina ◽  
A.I. Mozgunova
Keyword(s):  
Dynamic Loading ◽  
Contact Area ◽  
Contact Stiffness ◽  
Dynamic Contact ◽  
Real Contact Area ◽  
Contact Loading ◽  
The Real ◽  
Real Contact ◽  
Nominal Pressure ◽  
Plastic Hardness

The dependences of the relative real contact area of the flat contacting surfaces of steel parts on the nominal pressure under dynamic contact loading are studied. It is determined, that the real contact area under dynamic loading is less than under static one. Keywords dynamic plastic hardness, contact approach, real contact area, contact stiffness. [email protected]

Three-Dimensional Contact Analysis of Elastic-Plastic Layered Media With Fractal Surface Topographies

2000 ◽  
Vol 123 (3) ◽  
pp. 632-640 ◽  
Author(s):  
K. Komvopoulos ◽  
N. Ye
Keyword(s):  
Contact Area ◽  
Three Dimensional ◽  
Homogeneous Medium ◽  
Real Contact Area ◽  
Rigid Sphere ◽  
Real Surface ◽  
Elastic Plastic ◽  
Real Contact ◽  
Fractal Parameters ◽  
Surface Topographies

Three-dimensional rough surfaces were generated using a modified two-variable Weierstrass-Mandelbrot function with fractal parameters determined from real surface images. The number and size of truncated asperities were assumed to follow power-law relations. A finite element model of a rigid sphere in normal contact with a semi-infinite elastic-plastic homogeneous medium was used to obtain a constitutive relation between the mean contact pressure, real contact area, and corresponding representative strain. The contact model was extended to layered media by modifying the constitutive equation of the homogeneous medium to include the effects of the mechanical properties of the layer and substrate materials and the layer thickness. Finite element simulations of an elastic-plastic layered medium indented by a rigid sphere validated the correctness of the modified contact model. Numerical results for the contact load and real contact area are presented for real surface topographies resembling those of magnetic recording heads and smooth rigid disks. The model yields insight into the evolution of elastic, elastic-plastic, and fully plastic deformation at the contact interface in terms of the maximum local surface interference. The dependence of the contact load and real contact area on the fractal parameters and the carbon overcoat thickness is interpreted in light of simulation results obtained for a tri-pad picoslider in contact with a smooth thin-film hard disk.

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