Contact Interaction Calculators

Sphere and Spherical Socket Contact

In this calculation, the contact of a sphere with a diameter D₂ and spherical 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 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 - Spherical socket diameter;

Е₁ - Young's modulus of the socket;

ν₁ - Poisson's ratio of the socket;

D₂ - Sphere diameter;

Е₂ - Young's modulus of the sphere;

ν₂ - Poisson's ratio of the sphere;

F - Load.

RESULTS DATA

σ - Stress at contact area ;

d - Diameter of contact area;

Y - Tolal deformation of two bodies.

Metric Imperial

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)

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 - Spherical socket diameter;

Е₁ - Young's modulus of the socket;

ν₁ - Poisson's ratio of the socket;

D₂ - Sphere diameter;

Е₂ - Young's modulus of the sphere;

ν₂ - Poisson's ratio of the 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

AREA MOMENTS OF INERTIA

BEAM CALCULATORS

TORSION OF BARS

CIRCULAR FLAT PLATES

BUCKLING

ELASTIC CONTACT

IMPACT LOADS

NATURAL FREQUENCIES

PRESSURED SHELLS

FLUID DYNAMIC

COMPOSITES

SPRINGS

THREAD CONNECTIONS

SHAFT CONNECTIONS

BEARINGS

DRIVES

FATIGUE

HEAT TRANSFER