Contact Interaction Calculators

Two Perpendicular Cylinders Contact

In this calculation, the contact of two perpendicular cylinders with diameters D₁ and D₂ is considered. Cylinder D₂ is under load F, which is transferred to cylinder D₁ 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 cylinders Y in the direction of the load action are determined.

Two perpendicular cylinders contact

Two perpendicular cylinders contact calculation

INITIAL DATA

D₁ - First cylinder diameter;

Е₁ - Young's modulus of the first cylinder;

ν₁ - Poisson's ratio of the first cylinder;

D₂ - Second cylinder diameter;

Е₂ - Young's modulus of the second cylinder;

ν₂ - Poisson's ratio of the second cylinder;

F - Load.

RESULTS DATA

σ - Stress at contact area ;

Y - Total deformation of cylinders;

A - Length of contact area;

B - Width of contact area.

Metric Imperial

Cylinder diameter (D₁)

Young's modulus (Е₁)

Poisson's ratio (ν₁)

Cylinder 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*[(D₁D₂)/(D₁ + D₂)])^1/3;

Width of contact area:

B = K₂(F*C*[(D₁D₂)/(D₁ + D₂)])^1/3;

Stress at contact area:

σ = 1.5F / π*A*B;

Total deformation:

Y = K₃(F²C² / [(D₁D₂)/(D₁ + D₂)])^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

D₁ - First cylinder diameter;

Е₁ - Young's modulus of the first cylinder;

ν₁ - Poisson's ratio of the first cylinder;

D₂ - Second cylinder diameter;

Е₂ - Young's modulus of the second cylinder;

ν₂ - Poisson's ratio of the second cylinder;

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)	-

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