Analysis of Two Ball’s Surface Contact Stress Based on Fractal Theory

2011 ◽  
Vol 675-677 ◽  
pp. 619-627 ◽  
Author(s):  
Han Zhao ◽  
Qi Chen ◽  
Kang Huang

In order to deeply investigate the contact stress state of two balls, a new fractal contact model of two ball’s surfaces is set up on the basic of traditional contact theory and new fractal contact model theory. It is proved to be true through the predicting result and the contact example respectively by using the traditional Hertz theory and the fractal theory. This model can generally reflect the infections of contact stress by the micro-factors and macro-factors of two balls, so it can ensure veracity and certainness of stress analysis. The establishment of the model supplies a basis and theory foundation for further practical application (such as contact stress calculation of rolling bearing and sliding bearing) and experimental research.

2010 ◽  
Vol 43 ◽  
pp. 414-419
Author(s):  
Kang Huang ◽  
Song Bo Han ◽  
Rong De Yang ◽  
Shun Xu

Aiming at the problem that it is difficult to solve contact strength calculation of double circular arc gear with the method of traditional the Hertz contact theory and FEM, methods of fractal theory had been used to establish the contact model of double arc gear based on fractal theory, and an example of calculation was given away. This article results that it is feasible to calculate contact strength with fractal theory in the driving of concave convex meshing gear and this contact model of double circular arc gear based on fractal theory would provide a new way of the research of contact strength calculation of double circular arc gear.


2020 ◽  
Vol 13 (2) ◽  
pp. 141-155
Author(s):  
Lili Zhu ◽  
Guangxin Wang ◽  
Wenjie He ◽  
Wenzhong Fan

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.


2013 ◽  
Vol 712-715 ◽  
pp. 399-402
Author(s):  
Rong Yan Chen ◽  
Gao Liang Peng ◽  
Xin Li

The aim of this paper is to present a method to predict the leakage of the seal dynamically. The surface of the seal in the sealing area is modeled based on fractal theory. In order to simulate the change of the surface topography during the working process, a meso-scale contact model is set up. The simulation is accomplished with the distinct element software, PFC2D. This will be helpful to predict the lifetime of O-ring in mechanical application.


Author(s):  
Michael A. Mason ◽  
Charles P. Cartin ◽  
Parham Shahidi ◽  
John E. Speich ◽  
James Hargraves

The connection between bearing raceway condition and fatigue in tapered roller bearings utilized in the railroad environment is of interest. Roller bearings for railroad applications are typically precision ground to exact dimensions with crowned contact geometries for optimal loading of components. This normally results in completely elastic Hertzian contact stresses under standard railcar loads with original equipment manufacturer raceway contact geometries. However, with extremely uneven bogie load distributions, impact damage, corrosion and spall repair, imperfect stress distributions can occur on bearing raceways utilized in the railroad environment. Railroad bearing applications in North America have the added complexity that the life of the product is not defined in the same way as in other industries. For example, the definition of spalling remains consistent across all industries and is outlined in the Association of American Railroads (AAR) Manual of Standards and Recommended Practices. However, an inconsistency compared to other industries is that the fatigue life of the product in the rail industry is not always considered complete at the first evidence of fatigue spalling. Although some other industries allow for the remanufacture and restoration of bearing assemblies, the aggressive raceway fatigue regrinding practices allowed by the AAR are not commonly permissible in other industries. These remanufacturing practices adversely influence subsurface stress magnitudes below the raceway surface, as they reduce the effective length of the raceway and can create stress risers. Engineering tools like the novel modeling method presented in this paper can be used by bearing designers to evaluate the impact of surface discontinuities, at the center or edge of the raceway, on the overall stress state of bearing raceways. For the various types of raceway conditions detailed above, a new tool was developed using finite element methods to simulate the stress state of the bearing under complex raceway contact geometries or adverse load conditions. The finite element contact stress tool was successfully validated using proven Hertzian contact theory. Peak maximum shear and von Mises subsurface stress predictions between the finite element model and conventional contact theory agreed within .001 inches, with regards to peak stress depth below the surface, and 10,000 psi, with regards to peak stress magnitude. This newly developed methodology will be used in future studies to analyze other load conditions and raceway contact geometries that cannot be analyzed with basic Hertzian contact theory, in order to illustrate practical application of the tool. Specifically, overload conditions are analyzed in the work presented. Furthermore, a proposed methodology for future work related to the examination of the stress state created by current AAR bearing reconditioning acceptance standards related to raceway impact damage and spall repair will be introduced.


2018 ◽  
Vol 31 (1) ◽  
Author(s):  
Shi-Hua Li ◽  
Xue-Yan Han ◽  
Jun-Qi Wang ◽  
Jing Sun ◽  
Fu-Juan Li

2015 ◽  
Vol 25 (3) ◽  
pp. 489-495 ◽  
Author(s):  
Hongyun Guo ◽  
Xiangyang Lei ◽  
Yumei Zhang ◽  
Guoxing Yang ◽  
Zhang Niu

2013 ◽  
Vol 457-458 ◽  
pp. 257-261
Author(s):  
Li Gang Cai ◽  
Teng Yun Xu ◽  
Yong Sheng Zhao

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.


2021 ◽  
Author(s):  
Weiwei Zhang ◽  
Jian Weng ◽  
Kejia Zhuang ◽  
Cheng Hu ◽  
Xing Dai ◽  
...  

Abstract Cutting tools with round edge can enhance the performance of machining difficult-to-machine materials, while the complex contact mechanism related to micro cutting edge limits the deeper understanding of cutting mechanics. Material separation, which is associate to plough mechanism with formation of dead metal zone (DMZ), also requires the analysis of contact behavior. This study develops a contact model along the round edge together with the illustration of DMZ, with three contact feature points defined to explain the contact situation between workpiece and cutting edge. Among these feature points, two separation points related to DMZ classify the sliding and sticking region considering the dual-zone approach. The stagnation point is the zero shear stress point where a sudden change in shear stress direction happens. Besides, the parabolic stress model obtained from finite element simulations is established to define the normal contact distribution along the round edge. In this basis, the tool-based frictional forces are determined and two contact force components are classified for different contact regions. The proposed contact feature points and contact stress are validated through illustration with finite element simulations. Besides, orthogonal cutting tests ensure the practicality and accuracy of the proposed contact model and predicted cutting forces.


2009 ◽  
Vol 25 (01) ◽  
pp. 1-6
Author(s):  
Zhou Bo ◽  
Liu Yujun ◽  
Ji Zhuoshang

The lifting padeyes are widely used in the construction of offshore structures and ships. Because of the lack of more accurate information, heavily conservative simplified approaches have to be applied to strength analysis and structure design. Therefore, the calculated stress results contain a lot of discrepancies with the actual stress. In the paper, a robust stress check formula is derived using the theory of frictionless cylindrical contact. The influences of padeye thickness and clearance ratio on contact stress are analyzed. It is shown that the new expressions account for a better representation of the real stress value and distribution. By applying the strength check formula presented in the paper, the safe reliability of structure design can be improved significantly.


2011 ◽  
Vol 308-310 ◽  
pp. 1571-1576 ◽  
Author(s):  
Xiu Feng ◽  
Feng Lu ◽  
Guo Liang Shen

Metallic gasket seals are widely used in pressure vessels and piping. The failure of sealing systems is mostly caused not by the strength of flanges or bolts but by the leakage of the connections. The contact area of sealing surface has a major influence on the leakage of the bolted flange connections. The contact model of sealing surfaces of the flange and the metallic gasket was established on the basis of the modified M-B model, and the relationship between the contact area and the compressive stress is obtained. It’s found that the bigger the compressive stress, the bigger the contact area. When the compressive stresses are identical, the bigger fractal dimension and the less scale coefficient, the bigger the contact area. These can be used in the evaluation of sealing behavior of metallic gaskets.


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