General Case of Elastic Contact | Online Calculator

Contact Interaction Calculators

General Case of Elastic Contact

In this calculation, the contact of two bodies of arbitrary curvature is considered. When performing calculations, the following should be taken into account:

  • At the point of contact of the two bodies, the maximum R and minimum r radiuses of curvature for both bodies are determined;
  • In this calculation, if the radius of curvature forms a male face, it is set by a positive value;
  • If the radius of curvature forms a female face, it is set by a negative value;
  • The planes containing the lines of maximum and minimum curvature are mutually perpendicular;
  • In the general case, the planes containing the maximum curvature lines of both bodies are turned through an angle α relative to each other (for example, if perpendicular cylinders are in contact α = 90°).

For the calculation, the elastic moduli E and Poisson's ratios ν of the contacting bodies should be specified.

As a result of these calculations, the contact stresses σ in the contact zone, the dimensions of the contact zone A × B and the joint total deformations of the bodies Y in the direction of the load action are determined.

General Case of the Two Bodies in Contact
General Case of Two Any Bodies in Contact

INITIAL DATA

R1 - Maximum radius of curvarure of the first body in contact point;

r1 - Minimum radius of curvarure of the first body in contact point;

Е1 - Young's modulus of the first body;

ν1 - Poisson's ratio of the first body;

R2 - Maximum radius of curvarure of the second body in contact point;

r2 - Minimum radius of curvarure of the second body in contact point;

Е2 - Young's modulus of the second body;

ν2 - Poisson's ratio of the second body;

α - angle between planes, contained curvature 1/R1 and curvature 1/R2;

F - Load.

RESULTS DATA

σ - Stress at contact area ;

Y - Total deformation of cylinders;

A - Length of contact area.

B - Width of contact area;

Maximum radius (R1)

Minimum radius (r1)

Young's modulus (Е1)

Poisson's ratio (ν1)

Maximum radius (R2)

Minimum radius (r2)

Young's modulus (Е2)

Poisson's ratio (ν2)

Angle (α)

Load (F)

Stress at contact area (σ)

Total deformation (Y)

Length of contact area (A)

Width of contact area (B)

BASIC FORMULAS

Length of contact area:

A = K1(F*C*[1.5/(1/R1 + 1/r1 + 1/R2 + 1/r2)])1/3;

Width of contact area:

B = K2(F*C*[1.5/(1/R1 + 1/r1 + 1/R2 + 1/r2)])1/3;

Stress at contact area:

σ = 1.5F / π*A*B;

Total deformation:

Y = K3(F2C2 / [1.5/(1/R1 + 1/r1 + 1/R2 + 1/r2)])1/3;

K1, K2, K3 - coefficients depending on ratio D1/D2;

C - coefficient depending on Young's modulus and Poisson's ratio of the materials.

INITIAL DATA

R1 - Maximum radius of curvarure of the first body in contact point;

r1 - Minimum radius of curvarure of the first body in contact point;

Е1 - Young's modulus of the first body;

ν1 - Poisson's ratio of the first body;

R2 - Maximum radius of curvarure of the second body in contact point;

r2 - Minimum radius of curvarure of the second body in contact point;

Е2 - Young's modulus of the second body;

ν2 - Poisson's ratio of the second body;

α - angle between planes, contained curvature 1/R1 and curvature 1/R2;

F - Load.

RESULTS DATA

σ - Stress at contact area ;

Y - Total deformation of cylinders;

A - Length of contact area.

B - Width of contact area;

MATERIALS PROPERTIES

Material

Young’s modulus

Pa (psi)

Poisson’s ratio

Steel

1.86÷2.1×1011 (2.7÷3.05×107)

0.25÷0.33

Cast iron

0.78÷1.47×1011 (1.1÷2.1×107)

0.23÷0.27

Copper

1.0÷1.3×1011 (1.45÷1.9×107)

0.34

Tin bronze

0.74÷1.22×1011 (1.1÷1.8×107)

0.32÷0.35

Brass

0.98÷1.08×1011 (1.4÷1.6×107)

0.32÷0.34

Aluminum alloy

0.7×1011 (1.0×107)

0.33

Magnesium alloy

0.4÷0.44×1011 (5.8÷6.4×106)

0.34

Nickel

2.5×1011 (3.6×107)

0.33

Titanium

1.16×1011 (1.7×107)

0.32

Lead

0.15÷0.2×1011 (2.2÷2.9×106)

0.42

Zinc

0.78×1011 (1.1×107)

0.27

Glass

4.9÷5.9×1010 (7.1÷8.5×106)

0.24÷0.27

Concrete

1.48÷2.25×1010 (2.1÷3.3×106)

0.16÷0.18

Wood (along the grain)

8.8÷15.7×1010 (12.8÷22.8×106)

-

Wood (across the grain)

3.9÷9.8×1010 (5.7÷14.2×106)

-

Nylon

1.03×1010 (1.5×106)

-

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