**Prof. (Dr.) Veera P. Darji** Professor and Head Department of Mechanical Engineering C. U. Shah College of Engineering and Technology C. U. Shah University Wadhwan City, Gujarat (India)

**Section 1**

**Contact Mechanics**

**Section 1**

**Contact Mechanics**

**Chapter 1**

Provisional chapter

**Contact Mechanics of Rough Surfaces in Hermetic**

DOI: 10.5772/intechopen.72196

It is indicated that the sealing capacity depends on the contact characteristics—the relative contact area and the gap density in the joint. To determine the contact characteristics, a discrete roughness model is used in the form of a set of spherical segments, the distribution of which in height is related to the bearing curve described by the regularized beta function. The contact of a single asperity is considered with taking into account the influence of the remaining contacting asperities. The equations for determining the relative contact area and gap density in the joint depending on the dimensionless force

Keywords: contact mechanics, hermetic sealing studies, rough surface, spherical asperity, discrete model, elastic contact, elastic-plastic contact, hardening power law,

Tightness is the property of the joints to provide an acceptable leakage value, determined from the conditions of normal operation of various systems and equipment, human safety, and environmental protection. To quantify the tightness, the leakage rate is used, that is, the mass or volume of the medium per unit time per unit length along the SJ's perimeter. By 'sealing

The SJ's tightness is provided by loading with a compressive load (the contact sealing pressures), which is largely determined by the stress-strain state in the contact area and depends on the contact interaction of the rough surfaces. The main contact characteristics ensuring SJ's tightness are the approaching of rough surfaces, the relative contact area, the density of gaps in the joint, and the degree of fusion of contact spots of single asperities. Depending on the

> © The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and eproduction in any medium, provided the original work is properly cited.

distribution, and reproduction in any medium, provided the original work is properly cited.

© 2018 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use,

joint' (SJ), we mean a set of details that form a structure to ensure tightness.

Contact Mechanics of Rough Surfaces in Hermetic

**Sealing Studies**

Sealing Studies

Denis Gorokhov

Denis Gorokhov

Abstract

1. Introduction

Peter Ogar, Sergey Belokobylsky and

Peter Ogar, Sergey Belokobylsky and

http://dx.doi.org/10.5772/intechopen.72196

Additional information is available at the end of the chapter

Additional information is available at the end of the chapter

parameters for elastic and elastic-plastic contacts are provided.

relative contact area, gaps density, sealing joint, tightness

#### **Contact Mechanics of Rough Surfaces in Hermetic Sealing Studies** Contact Mechanics of Rough Surfaces in Hermetic Sealing Studies

DOI: 10.5772/intechopen.72196

Peter Ogar, Sergey Belokobylsky and Denis Gorokhov Peter Ogar, Sergey Belokobylsky and Denis Gorokhov

Additional information is available at the end of the chapter Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/intechopen.72196

#### Abstract

It is indicated that the sealing capacity depends on the contact characteristics—the relative contact area and the gap density in the joint. To determine the contact characteristics, a discrete roughness model is used in the form of a set of spherical segments, the distribution of which in height is related to the bearing curve described by the regularized beta function. The contact of a single asperity is considered with taking into account the influence of the remaining contacting asperities. The equations for determining the relative contact area and gap density in the joint depending on the dimensionless force parameters for elastic and elastic-plastic contacts are provided.

Keywords: contact mechanics, hermetic sealing studies, rough surface, spherical asperity, discrete model, elastic contact, elastic-plastic contact, hardening power law, relative contact area, gaps density, sealing joint, tightness

## 1. Introduction

Tightness is the property of the joints to provide an acceptable leakage value, determined from the conditions of normal operation of various systems and equipment, human safety, and environmental protection. To quantify the tightness, the leakage rate is used, that is, the mass or volume of the medium per unit time per unit length along the SJ's perimeter. By 'sealing joint' (SJ), we mean a set of details that form a structure to ensure tightness.

The SJ's tightness is provided by loading with a compressive load (the contact sealing pressures), which is largely determined by the stress-strain state in the contact area and depends on the contact interaction of the rough surfaces. The main contact characteristics ensuring SJ's tightness are the approaching of rough surfaces, the relative contact area, the density of gaps in the joint, and the degree of fusion of contact spots of single asperities. Depending on the

© The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons © 2018 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and eproduction in any medium, provided the original work is properly cited.

materials' properties and microgeometry parameters, there are elastic, viscoelastic, elastic-plastic, and rigid-plastic contacts.

At present, to solve the tribology problems, we need to use the roughness models and the rough surfaces contacting theory developed by the authors [1, 2] and their followers. However, the use of such models to solve the problems in hermetic sealing studies leads to significant errors, which is explained by the following:


Therefore, to describe the SJ, a rough surface model is required that adequately describes the real surface and corresponds to the whole bearing curve, and not just its initial part. In addition, in order to improve the accuracy of the calculation of the contact characteristics, the discrete model of a rough surface must be taken into account, the real distribution of dimensions of microasperities and the mutual influence. The criterion of plasticity must take into account the general stress-strain state when contacting of a rough surface and not just of a single asperity. In most cases, the contact of metallic rough surfaces is elastic-plastic, therefore, to determine the contact characteristics, it is necessary to take into account the parameters of material hardening.

To estimate the SJ's sealing property, in [3, 4], the nondimensional permeability functional is used

$$\mathcal{C}\_{u} = \frac{\Lambda^{3} \nu\_{k}}{4\left(1 - \eta\right)^{2}}\tag{1}$$

2. Discrete model of the rough surface

We consider that the initial data for the model representation of a rough surface are parameters of roughness according to ISO 4287–1997, ISO 4287/1–1997: maximum roughness depth Rmax, arithmetic mean deviation of the profile Ra, root-mean-square deviation of the profile Rq, mean height of the profile elements Rp, mean width of the profile elements Sm, bearing profile curve tp, and bearing profile curve on the midline tm. Thus, the standard parameters of the roughness for the developed model must coincide with the corresponding parameters of the real surface.

To describe the entire rough surface, it is required to know one of two functions:

Au Ac

or φnð Þ¼ u

where Au is the material cross-sectional area at a relative level ε ¼ h=Rmax; Ac is the contour area; nu is the number of asperities whose peaks are located above the level u; nc ¼ Ac=Aci is

According to ISO 4287–1997, parameters of roughness are determined from profilograms and the functions describing the distribution for the profile tp and the surface ηu(ε), but it is not fulfilled for the peaks and valleys asperities distribution functions of the profile φnl(ul) and the

Let us assume that the function ηuð Þε is monotonic and twice differentiable. A rough surface (Figure 1) is a set of asperities in the form of spherical segments of radius r and height ωRmax,

distribution of the material in the rough layer corresponds to the bearing surface curve.

where u is the relative distance from the peaks level to the peak of the i-th asperity.

dnr ¼ ncφ<sup>0</sup>

nu nc

Aci=<sup>π</sup> <sup>p</sup> . It is necessary to find such a function <sup>φ</sup>nð Þ <sup>u</sup> for which the

Ari ¼ 2πrRmaxð Þ ε � u , (3)

<sup>n</sup>ð Þ u du: (4)

, (2)

Contact Mechanics of Rough Surfaces in Hermetic Sealing Studies

http://dx.doi.org/10.5772/intechopen.72196

5

ηuð Þ¼ ε

the total number of asperities; and Aci is the area due to a single asperity.

surface φn(u), then the model is based on the bearing profile curve.

The number of peaks in the layer du and at a distance u is equal to

The cross-section of the i-th asperity at the level ε is

Figure 1. The scheme and the bearing curve of a rough surface.

and base radius ac <sup>¼</sup> ffiffiffiffiffiffiffiffiffiffiffiffi

where Λ is the gaps density in the joint; η is the relative contact area; υ<sup>k</sup> is the probability of a medium flowing, which depends on the single contact spots fusion.

All the parameters that appear in Eq. (1) depend on the parameters of microgeometry and dimensionless force parameters f <sup>q</sup> or qσ, the determination of which is given in the following sections.

The purpose of the given research is to develop methods for calculating the contact characteristics that ensure the given tightness of the immobile joints with taking into account the complex of functional parameters of the sealing surfaces and mutual influence of asperities.
