Analysis of contact problems in elastic – plastic metal seals/Tampriųjų metalinių sandariklių kontaktinės sąveikos tyrimas

Abstract

One of the most important problems in the design of seal joints is the optimisation of their shape and the material properties. This paper presents the results of the numerical simulation of conical and cantilever seal joints contact problems by using the finite element system ANSYS 5.0A. The temperature and friction have been taken into account.
The sealing principle of conical seals, which are usually used as flange joints in networks of pipes, is based on large plastic deformations of seal edges and maintaining the highly elastic property of the whole construction of the seal. Fig 1 presents the scheme of the conical seal used as a base for numerical simulations.
The relation between the contact force and displacement in conical seals with various material hardening shows that the contact force is not proportional to the displacement. The latter statement is demonstrated by Fig 2, presenting the results of the numerical simulations, where the curves 1, 2, 3 correspond to the following numerical values of material properties curve 1- E = 2,1.10⁵ MPa, σ_y = 280 MPa, E_κ1 = 7000 MPa (ε ≤ 0,0125), E_&kappa2 = 2500 MPa (0,0125 < ε ≤ 0,0125), E_κ3 = 600 MPa (0,1 < ε ≤ 0,3), E_κ4 = 1000 MPa (ε > 0,3), curve 2—E=2,1.10⁵ MPa, σ_y = 200 MPa, E_κ = 5.10³ MPa; curve 3—E = 2,1.10⁵ MPa, σ_y = 500 MPa, E_κ = 3.10³ MPa.
Under displacement 0,7—1,3 mm, the cone seal usually loses stability by exhibiting the second form of instability. Such a sealing joint is not suitable for the practical application as it is not hermetic. Fig 3 shows the deformed shape and contours of the equivalent plastic strains of the above-mentioned conical seal (RAD1=0,153 m, RAD2=0,159 m, h=0,001 m, A=0,0007m, α = 60°, β=0°, ϕ = 10°, γ = 45°, E = 2,1.10⁵ MPa, σ_y=280 MPa, E_κ1 =7000 MPa (ε ≤ 0,0125), E_κ2 =2500 MPa (0,0125 < ε ≤ 0,0125), E_κ3 = 1600 MPa (0,1 < ε ≤ 0,3), E_κ4 = 1000 MPa (ε > 0,3), ν = 0,3) in one of the loading steps of the solution process.
Numerous numerical simulations have shown that the second form of instability is caused by unfavourable loading and boundary conditions for the first instability form. Such numeric results correspond exactly to the experiments.
Under high pressure of the working medium (over 40 MPa), such seals collapse by exhibiting the first form of instability. The contact force increases only by 10%, and the collapse occurs when the seal is loaded more than 1,4 mm.
V—and λ—form (cantilever) seals may recover from static and 0,1–0,4 mm dynamic displacements due to their high elasticity. Usually such seals possess soft metallic or polymeric coats. The process of the seal deformation is very complex because the contact surface slides and rolls upon the basic surface.
In this paper the problem has been solved be using the submodelling techniques of ANSYS. The submodelling involves analysing a coarse model and by subsequently creating the finely meshed “submodel” of the region of interest. The coarse model displacements are applied as constraints on the cut boundary of submodel. In this problem, we will use the region of the whole cantilever seal as the coarse model. The region of interest is the contact zone, so we create the submodel of this region. Due to symmetry, only half a seal needs to be modelled (Fig 4), where RADX = 3 mm,S1 = 5 mm, H1 = 1,7 mm, H2 = 0,5 mm,S2 = 0,5 mm,3 = 2,8 mm, S3=5,5 mm, RAD1 = RAD2 = RAD3 = 1 mm, RADY = 4mm, RADC=30 mm, DD=0,1 mm, δ=0,12 mm, E= 2,1.10⁵ MPa, ν = 0,3.
After numerous numerical simulations, the base relations were defined. The maximum stress intensity dependence against the parameters of the arms of the cantilever spring seal elastic zone (Fig 6); ratio of relative seal radius against maximal stress intensity σ_I, pressure force F and contact pressure q₁ (Fig 7). The analysis enabled to obtain the optimised construction of the seal. 
The elastic-plastic deformation analysis of the coating has been performed. When the loads are small, the stress and strain contours are characteristic of classic Hertzian [1] contact theory. With higher loads, the picture changes significantly. After increasing the contact area width, the plastic zone grows and develops through to the boundaries of the interacting region.
By summarising the simulation results were obtained: the relations between the contact width, the approach of the contact surfaces δ, relative contact force F_k and ratio q/σ_y, when coating thickness is 0,14 mm and radius of the indenter 0,5 mm. The relation q/σ_y in this case is constant, approximately equal to 16. With the increase of the indenter radius, the ratio q/σ_y is not constant and increases with an increase of the contact force.
The numerical simulations of various seals allow to arrive to the following conclusions:
For cone seals the geometric instability (usually in the second form) is exhibited even at computatively small loads. When the loading exceeds 1,2 mm, the elastic structure may acquire an unaxisymmetric form. In the usage of such seals, the following points should be taken into account:

1. 
   
   
   
   • it is necessary to match the materials properly. Best suitable materials have higher yield point and higher stiffness hardening;
   
   
   • try to keep axisymmetric form of a seal even under the collapse. For this reason it is necessary to keep high requirements;
   
   
   • good results are obtained by covering the seals with soft coatings, thus reducing the force. In such way only the coating is subjected to the plastic deformation, while the whole structure remains elastic.
   
   
   
   


2. Cantilever seals have good elastic properties and do not loose stability. After summarising the numerical simulations results, the suggestions for the rational geometric shape of the cantilever seal have been made.


3. In the design of coated seals it is necessary to take into account that the equivalent plastic strains in the coat layers close to the indenter increase with increasing contact force, decreasing the indenter radius and the coat thickness.

Article in Lithuanian.

First Published Online: 26 Jul 2012

Keyword : -