Conical Helical Spring | Online Calculator

Springs Calculators







Conical Helical Spring

In this calculation, a conical helical spring with the average diameters D1, D2 and wire diameter d is considered. The number of active coils is n, with clearance between coils m.

The spring is under a load F, parallel to the spring axis. As a result of calculations, the spring deflection Y under load, length of the unloaded and fully compressed spring L, Lc are determined.

One of the parameters that determine the minimum length of the spring is the distance C1 between the coils of the spring in a fully compressed state, which can take on the values from 0 to d (look at figure).

Also, the calculations of the maximum shear stress in the coils τ and stiffness C, wich depend on the load value in addition to the dimensions of the spring, are performed. For the calculation, the elastic modulus E of the spring should be specified.

Conical helical spring
spring calculation

INITIAL DATA

D1 - Mean diameter of the smaller coil;


D2 - Mean diameter of the larger coil;


d - Wire diameter;


n - Number of active coils;


m - Clearance between coils;


C1 - Distance between coils of fully compressed spring. It can take values from 0 to d;


E - Young's modulus;


F - Spring load.

RESULTS DATA

C - Spring stiffness;


Y - Tolal deflection of the spring under load F;


L - Free length of the spring;


Lc - Minimum length of the fully compressed spring;


τ - Maximum shear stress under load F.

Diameter (D1)

Diameter (D2)

Diameter (d)

Number of active coils (n)

Clearance (m)

Young's modulus (Е)

Spring load (F)

Distance (С1)

Stiffness (C)

Deflection (Y)

Free length (L)

Length (Lc)

Shear stress (τ)

BASIC FORMULAS

Coil ratio:

i = D2 / d;

Stress concentration factor:

k = (4i - 1) / (4i - 4) + 0,615 / i;

Stiffness:

C = G*d4 / [2n(D1 + D2)(D12 + D22)];

Deflection:

Y = F / C;

Maximum shear stress:

τ = k*(8F*D1 / π*d3).

These formulas apply in the absence of fully compressed spring coils. The program algorithm changes spring stiffness dynamically, according to sequential compression of the coils.

INITIAL DATA

D1 - Mean diameter of the smaller coil;


D2 - Mean diameter of the larger coil;


d - Wire diameter;


n - Number of active coils;


m - Clearance between coils;


C1 - Distance between coils of fully compressed spring. It can take values from 0 to d;


E - Young's modulus;


F - Spring load.

RESULTS DATA

C - Spring stiffness;


Y - Tolal deflection of the spring under load F;


L - Free length of the spring;


Lc - Minimum length of the fully compressed spring;


τ - Maximum shear stress under load F.

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)

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