Open Design Optimization Platform (ODOP) - Coil spring design app; mechanical springs; compression spring, extension spring, torsion spring

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Torsion Spring Design Type

Torsion spring image

The Torsion Spring design type is a full-featured mathematical model enabling the engineering design of round wire helical coil torsion springs.

This section presents material unique to the Torsion Spring design type. The more general material available at Spring Design Topics provides important supplemental information.

On this page:


Torsion spring variable names on Moment-Deflection diagram

             |                / 
     M_2 ----|---------------/  
             |              /:
       M     |             / :
             |            /  :        ODOP:Spring
       O     |           /   :          Names
             |          /    :  
       M     |         /     :          Torsion
             |        /      :          spring
       E     |       /       :  
             |      /        :  
    M_1 -----|-----/         :  
             |    /:         :  
       N     |   / :<------->:------- Stroke
             |  /  :         :  
       T     | /   :         :  
        L_Free     :         :  
                  L_1       L_2
             Deflect_1     Deflect_2
             D E F L E C T I O N


Torsion spring Moment-Deflection point names

The torsion spring moment-deflection points and associated names are:

  moment (torque) deflection length outside diameter inside diameter
free: L_Body OD_Free ID_Free
point 1: M_1 Deflect_1 L_1
point 2: M_2 Deflect_2 L_2
max safe:
  stress factor of safety
point 1: Stress_1
point 2: Stress_2 FS_2
max safe:

point 1 = minimum operating load     point 2 = maximum operating load


Torsion spring dimensions

The following diagram may be of some assistance in interpreting the names associated with various dimensions of a torsion spring.

Torsion Spring Names


Independent Variable names:

Name   Description
Wire_Dia wire diameter
OD_Free outside diameter in the free condition
Coils_T total number of coils, including inactive coils
M_1 load (moment) at point 1 (minimum operating load)
M_2 load (moment) at point 2 (maximum operating load)
Coil_Spacing extra space between each coil


Dependent Variable names:

Name   Description
Mean_Dia mean diameter of spring coil in free condition;   (OD_free + ID_Free)/2
ID_Free inside diameter in free condition
Coils_A number of active coils (turns; includes arm deflection)
Rate spring constant - moment per unit deflection
Deflect_1 deflection caused by M_1
Deflect_2 deflection caused by M_2
L_Body length of body in free condition (without ends)
L_1 spring body length at minimum operating load (M_1)
L_2 spring body length at maximum operating load (M_2)
End_Angle_Free relative angle between arms in free condition
Stroke angular displacement from point 1 to point 2
Weight weight of spring;   wire density * wire volume
Spring_Index spring index; the ratio: Mean_Dia/Wire_Dia
End_Deflect_All End deflection allowance (equivalent coils); calculated from L_End_1 + L_End_2
Stress_1 bending stress at point 1
Stress_2 bending stress at point 2
FS_2 static factor of safety at point 2;   The ratio of allowable stress at point 2 to the calculated stress induced by the load at point 2 (Stress_Lim_Bnd_Stat/Stress_2).
FS_Cycle_Life factor of safety based on the Soderberg endurance limit calculation.   This figure uses the allowable endurance stress (Stress_Lim_Bnd_Endur) to include fatigue considerations.   Refer to additional discussion in the Cycle_Life topic.
Cycle_Life expected cycle life based on a calculation using the "modified Goodman method". This value is approximate. Refer to additional discussion in the Cycle_Life topic.
%_Safe_Deflect the percentage of available deflection consumed at load point 2
Force_Arm_2 Force produced at distance of Arm_2;   See: Torsion spring dimensions
Energy change in elastic potential energy between point 1 and point 2

  For additional information: Cycle_Life


Calculation Input names

Name   Description
Spring_Type character string used only as a label
Prop_Calc_Method Property Calculation Method controls how material properties and allowable stresses are determined. See also: Materials.
  1 - indicates values come from materials table; allowable stresses will be calculated as a function of Wire_Dia.
  2 - indicates tensile and allowable % are supplied by the user; allowable stresses are calculated.
  3 - indicates allowable stresses are supplied directly by the user.
Material_Type selects an entry in the material table. Is used to determine allowable stresses when Prop_Calc_Method is 1. Otherwise is ignored.
ASTM/Fed-Spec character string used only as a label to further identify the origin of material property data
Process character string used to identify the manufacturing process. It is normally controlled by the material selected from the material table. Values are usually Cold_Coiled or Hot_Wound. See also: Hot_Factor_Kh (below).
Heat_Treat Selects heat treatment process. Controls use of Kb - stress correction factor
Life_Category This value reflects the user's input about shot peening and required cycle life. It is input to the calculation of FS_CycleLife. See also: Cycle_Life
Density wire density; weight per unit volume
Elastic_Modulus Modulus of Elasticity modulus (E) (a.k.a. Young's Modulus)
Hot_Factor_Kh empirical correction factor applied to hot wound modulus
Tensile tensile strength
%_Ten_Bnd_Endur allowable fraction of tensile strength for bending endurance (cyclic load); See also: Cycle_Life
%_Ten_Bnd_Stat allowable fraction of tensile strength for bending static load
Stress_Lim_Bnd_Endur allowable stress limit; cyclic application (bending)
Stress_Lim_Bnd_Stat allowable stress limit; static application (bending)
End_Type This selection indicates end configuration: Tangent ends versus User Specified ends.. See also: Torsion spring end types
Arm_1, etc. See: Torsion spring end types


For additional information:


Values in reports

Other values calculated and displayed in the Reports include:

Name   Description
Wire Length total length of wire required to manufacture the spring, not including any waste
Safe Load The load supported by the spring at maximum allowable stress (Stress_Lim_Bnd_Stat).
Pitch distance between the wire centers of adjacent coils, measured in the free state (Wire_Dia + Coil_Spacing)
Weight/1000 weight of 1,000 springs
Stress Ratio ratio of minimum stress to maximum stress (Stress_1/Stress_2)
Kb stress correction factor; (see: Heat_Treat above)
Helix Angle angle, in degrees, of the spring helix relative to a perpendicular to the spring axis


End Types

For torsion springs, the Calculation Input End_Type has the following possible values:

1    Tangent
2    User_Specified

In the current version of ODOP:Spring, no calculations depend on these End_Type settings. They are for display only.

Separately, the values of Arm_1, Arm_2, L_End_1, L_End_2, XLen_1 and XLen_2 are available to describe end conditions. This diagram may be helpful.

Torsion Spring Names

Related topics