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Contact Interaction Calculators







Sphere and Cylindrical Socket Contact

In this calculation, the contact of a sphere with a diameter D2 and cylindrical socket with a diameter D1 is considered. Sphere is under load F, which is transferred to socket through the contact zone. For the calculation, the elastic moduli E1, E2 and Poisson's ratios ν1, ν2 of the contacting bodies should be specified.

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

Sphere and Cylindrical Socket Contact
Calculation of Sphere and Cylindrical Socket Contact

INITIAL DATA

D1 - Cylindrical socket diameter;


Е1 - Young's modulus of the socket;


ν1 - Poisson's ratio of the socket;


D2 - Cylinder diameter;


Е2 - Young's modulus of the cylinder;


ν2 - Poisson's ratio of the cylinder;


F - Load.

RESULTS DATA

σ - Stress at contact area ;


A - Length of contact area;


B - Width of contact area;


Y - Tolal deformation of two bodies.

Socket diameter (D1)

Young's modulus (Е1)

Poisson's ratio (ν1)

Sphere diameter (D2)

Young's modulus (Е2)

Poisson's ratio (ν2)

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 + 2/R2)])1/3;

Width of contact area:

B = K2(F*C*[1.5/(1/R1 + 2/R2)])1/3;

Stress at contact area:

σ = 1.5F / π*A*B;

Total deformation:

Y = K3(F2C2 / [1,5/(1/R1 + 2/R2)])1/3;

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

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

INITIAL DATA

D1 - Cylindrical socket diameter;


Е1 - Young's modulus of the socket;


ν1 - Poisson's ratio of the socket;


D2 - Cylinder diameter;


Е2 - Young's modulus of the cylinder;


ν2 - Poisson's ratio of the cylinder;


F - Load.

RESULTS DATA

σ - Stress at contact area ;


A - Width of contact area;


B - Length of contact area;


Y - Tolal deformation of two bodies.

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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