Contact Interaction Calculators

Two Spheres Contact

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

Following the calculations, the contact stresses σ in the contact zone, the diameter d of the contact zone, and the total deformations of the bodies Y in the direction of the load action are determined.

Two spheres contact calculation

Two spheres contact calculation

INITIAL DATA

D₁ - First sphere diameter;

Е₁ - Young's modulus of the first sphere;

ν₁ - Poisson's ratio of the first sphere;

D₂ - Second sphere diameter;

Е₂ - Young's modulus of the second sphere;

ν₂ - Poisson's ratio of the second sphere;

F - Load.

RESULTS DATA

σ - Stress at contact area ;

d - Diameter of contact area;

Y - Tolal deformation of two bodies.

Metric Imperial

Sphere 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)

Diameter of contact area (d)

Tolal deformalion (Y)

BASIC FORMULAS

Stress at contact area:

σ = 0.6[FE² / [(D₁D₂)/(D₁ + D₂)]²]^1/3;

Diameter of contact area:

d = 1.8(F[(D₁D₂)/(D₁ + D₂)] / E)^1/3;

Tolal deformalion:

Y = 1.6[F² / [(D₁D₂)/(D₁ + D₂)]E²]^1/3.

*The above formulas are valid for equal material with ν = 0.3.

INITIAL DATA

D₁ - First sphere diameter;

Е₁ - Young's modulus of the first sphere;

ν₁ - Poisson's ratio of the first sphere;

D₂ - Second sphere diameter;

Е₂ - Young's modulus of the second sphere;

ν₂ - Poisson's ratio of the second sphere;

F - Load.

RESULTS DATA

σ - Stress at contact area ;

d - Diameter 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)	-

OTHER CALCULATORS

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BEAM CALCULATORS

TORSION OF BARS

CIRCULAR FLAT PLATES

BUCKLING

ELASTIC CONTACT

IMPACT LOADS

NATURAL FREQUENCIES

PRESSURED SHELLS

FLUID DYNAMIC

COMPOSITES

SPRINGS

THREAD CONNECTIONS

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DRIVES

FATIGUE

HEAT TRANSFER