Belleville Spring | Online Calculator

Springs Calculators

Belleville Spring

In this calculation, a belleville spring with an inner diameter D1, outer diameter D2 and height H is considered. The spring is made of a material with thickness t.

Belleville springs deflected in the axial direction by the value of Y and assembled in stacks with sequential (I) and parallel (II) mutual arrangement. As a result of calculations, the stiffness C of the spring stack, force F required for achieving the specified deflection, and equivalent stresses σ are determined.

For the calculation, the elastic modulus E and Poisson's ratio ν of the spring should be specified.

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INITIAL DATA

D1 - Spring inner diameter;

D2 - Spring outer diameter;

n - Number of springs in assembly;

t - Spring thickness;

H - Height of one spring;

E - Young's modulus;

ν - Poisson's ratio;

Y - Total deflection of springs assembly.

RESULTS DATA

CI - Stiffness of springs assembly (in sequential arrangement);

FI - Spring load at deflection Y (in sequential arrangement);

σI - Maximum equivalent stress in the spring at deflection Y (in sequential arrangement);

CII - Stiffness of springs assembly (in parallel arrangement);

FII - Spring load at deflection Y (in parallel arrangement);

σII - Maximum equivalent stress in the spring at deflection Y (in parallel arrangement).

Diameter (D1)

Diameter (D2)

Steel thickness (t)

Spring height (H)

Number of springs (n)

Young's modulus (Е)

Poisson's ratio (ν)

Deflection (Y)

SEQUENTIAL ARRANGEMENT (I)

Stiffness (CI)

Spring load (FI)

Equivalent stress (σI)

PARALLEL ARRANGEMENT (II)

Stiffness (CII)

Spring load (FII)

Equivalent stress (σII)

BASIC FORMULAS

Spring load at sequential arrangement:

FI = [(2E*Y / n) / ((1-ν2)*(k1*D22))] * [(H - Y / n)*(H - Y / 2n)*T + T3];

Equivalent stress at sequential arrangement:

σI = [(E*Y / 2n) / ((1 - ν2)*(k1*D22))] * [k2*(H - Y/4n) + k3*T];

Spring Stiffness at sequential arrangement:

CI = FI / YI .

Spring load at parallel arrangement:

FII = 2n*[(E*Y)/((1-ν2)*(k1*D22))] * [(H - Y)*(H - Y / 2)*T + T3];

Equivalent stress at parallel arrangement:

σII = [(E*Y / 2)/((1 - ν2)*(k1*D22))] * [k2*(H - Y/4) + k3*T];

Spring Stiffness at parallel arrangement:

CII = FII / YII

k1, k2, k3 - coefficients depending on the inner and outer diameters of spring.

INITIAL DATA

D1 - Spring inner diameter;

D2 - Spring outer diameter;

n - Number of springs in assembly;

t - Spring thickness;

H - Height of one spring;

E - Young's modulus;

ν - Poisson's ratio;

Y - Total deflection of springs assembly.

RESULTS DATA

KI - Stiffness of springs assembly (in sequential arrangement);

FI - Spring load at deflection Y (in sequential arrangement);

σI - Maximum equivalent stress in the spring at deflection Y (in sequential arrangement);

CII - Stiffness of springs assembly (in parallel arrangement);

FII - Spring load at deflection Y (in parallel arrangement);

σII - Maximum equivalent stress in the spring at deflection Y (in parallel arrangement).

MATERIAL PROPERTIES

Steel

Tensile strength, depending on tempering temperature

MPa (psi)

Yield strength, depending on tempering temperature

MPa (psi)

1050

738÷979 (107*103÷142*103)

469÷724 (68*103÷105*103)

1080

889÷1310 (129*103÷190*103)

600÷979 (87*103÷142*103)

4150

958÷1931 (139*103÷280*103)

841÷1724 (122*103÷250*103)

5160

896÷2220 (130*103÷322*103)

800÷1793 (116*103÷260*103)

6150

945÷1931 (137*103÷280*103)

841÷1689 (122*103÷245*103)

9255

993÷2103 (144*103÷305*103)

814÷2048 (118*103÷297*103)

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