Contact Interaction Calculators

Cylinder and Flat Plate Contact

In this calculation, a contact of a cylinder with a diameter D, length L and a flat plate is considered. For the calculation, the elastic moduli E₁, E₂ and Poisson's ratios ν₁, ν₂ of the contacting bodies should be specified. The cylinder is under load F, which is transmitted to a flat surface through the contact zone.

Following the calculations, the contact stresses σ in the contact zone and width A of the contact zone are determined.

Cylinder and plate contact

Cylinder and flat plate contact

INITIAL DATA

Е₁ - Young's modulus of the flat plate;

ν₁ - Poisson's ratio of the flat plate;

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.

Metric Imperial

Young's modulus (Е₁)

Poisson's ratio (ν₁)

Cylinder diameter(D₂)

Young's modulus (Е₂)

Poisson's ratio (ν₂)

Cylinder length (L)

Load (F)

Stress at contact area (σ)

Width of contact area (A)

BASIC FORMULAS

Stress at contact area:

σ = 0.6[FE / D₂]^1/2;

Width of contact area:

A = 2.2[FD₂ / E]^1/2;

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

INITIAL DATA

Е₁ - Young's modulus of the flat plate;

ν₁ - Poisson's ratio of the flat plate;

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.

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