Loading–unloading contact analysis of a fractal rough surface with functional gradation

The present paper deals with a finite-element-based static loading–unloading analysis of a functionally graded rough surface contact with fractal characteristics. Two different gradation models, namely elastic and plastic gradations, are adopted. In these models, one out of yield strength and Young's modulus is varied spatially according to exponential functions, while the other is kept constant. In both these material models, separate inhomogeneity parameters control the variation of material properties. The gradation is such that throughout the top of the rough surface properties remain constant with variations in the depth direction being controlled by the above-mentioned parameters. Different fractal surfaces with different levels of roughness (governed by the values of fractal dimension and fractal roughness) have been analysed. The influence of the gradation parameters on the contact properties, viz. contact force, contact area, contact stress, etc., are investigated for both loading and unloading phases. It was found that for most of the loading phase, higher elastic, as well as plastic gradation parameter, causes higher contact force and contact area. However, in the case of the unloading of elastically graded surfaces, this trend is not maintained throughout. For the cases, where a substantial amount of yielding takes place during loading near the contact surface, the resulting contact area is found to be higher for the unloading phase in comparison with the same during the loading phase. The trend of plastic yielding at the vicinity of the contact surface is studied for varying gradation parameters. It is observed that the higher volume of yielded material is obtained for the higher value of elastic gradation parameter. On the other hand, the higher value of plastic gradation parameter causes more yielding to take place at the vicinity of the contact surface. Additionally, the effect of gradation on the energy dissipation due to plasticity after complete unloading is explored in detail.

Mechanics Analysis of Rough Surface Based on Shoulder-Shoulder Contact

Proper methods and models for mechanical analysis of rough surface can improve the theory of surface contact. When the topography parameters of two rough surfaces are similar, the contact should be considered shoulder-shoulder rather than top-top. Based on shoulder-shoulder contact and fractal characteristics, the geometric model for asperity and contact mechanics model for rough surfaces are established, and the deformation of asperity, the real contact area and contact load of sealing surface are discussed. The effects of contact pressure p and topography parameters (fractal dimension D and fractal roughness G) on the variation of porosity and contact area ratio Ar/A0 are achieved. Results show that with the increase of p, larger D and smaller G corresponds to larger initial porosity but faster and larger decrease of porosity; with the increment of D, porosity increases first and then decreases, and smaller G corresponds to larger porosity reduction; as G becomes bigger, porosity increases, and larger D corresponds to larger porosity difference and change. With the addition of p, Ar/A0 increases, and the variation of Ar/A0 is closer to linearity and less at smaller D and larger G; with the increase of D, Ar/A0 increases gradually, and the growth rate is bigger at smaller G and bigger p; as G becomes bigger, Ar/A0 declines, and it declines more gently at smaller D and p. The influence of D on Ar/A0 is greater than that of G. The results can provide the theoretical basis for the design of sealing surfaces and the research of sealing or lubrication technologies of rough surfaces.

Contact analysis of measured surfaces based on modified interacting and coalescing Hertzian asperities (ICHA) model with oblique contact asperities

The contact mechanism for joint surfaces is important for predicting the loading process and dynamic properties of precision machinery products. A multiasperity model considering the lateral interaction and coalescence of contact regions with oblique asperity contact, the interacting and coalescing Hertzian asperities (ICHA) model, is introduced in this work. Contact angle [Formula: see text] and radius of curvature [Formula: see text] are vital parameters that are directly calculated based on grid points measured from the milling and grinding surfaces. Numerical simulations of [Formula: see text] and [Formula: see text] were analysed. The results show that the proposed model is more effective at improving the contact area versus force relationship than various asperity models for low and middle contact forces. [Formula: see text] and [Formula: see text] follow a Gaussian distribution. Because of the existence of coalescence, they decrease with increasing contact force. Furthermore, the [Formula: see text] and [Formula: see text] in the startup phase are crucial data that can be used to judge the effects of oblique asperity contact. They are greatly influenced by fractal dimension [Formula: see text] and fractal roughness G. From the comparisons with the surfaces generated by Weierstrass-Mandelbrot function, it is suggested that to obtain an accurate contact prediction in the loading process, oblique contact is as important as lateral interaction and coalescence.

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

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.

Numerical Calculation Method of Meshing Stiffness for the Beveloid Gear considering the Effect of Surface Topography

The tooth surfaces of beveloid gears have different topography features due to machining methods, manufacturing accuracies, and surface wear, which will affect the contact state of the tooth surface, thereby affecting time-varying mesh stiffness between mating gear pairs. Therefore, a slice grouping method was proposed in this paper on the basis of potential energy to calculate the total meshing stiffness of beveloid gears with the surface topography. The method in this paper was verified by finite element method (FEM). Compared with the calculation results of this paper, the relative error is 5.9%, which demonstrated the feasibility and accuracy of the method in this paper. Then, the influence of parameters such as pressure angle, helix angle, pitch angle, tooth width, fractal dimension, and fractal roughness on meshing stiffness was investigated, of which results show that pressure angle, pitch angle, tooth width, and fractal dimension have an incremental impact on the mean value of mesh stiffness. However, the fluctuating value of mesh stiffness has also increased as the pressure angle, tooth width, and pitch cone angle increase. Both the helix angle and the fractal roughness have a depressive impact on the total stiffness. But the difference is that, with the increase of the helix angle, the fluctuation of meshing stiffness has been decreased. Conversely, with the increase of the fractal roughness, the fluctuation of meshing stiffness has been increased.

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

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.