In the first part of this twopart series has Gutekunst feathers about the Basics of spring design informed. In this second part you will find the specific calculation data for the design of Compression springs , Tension springs and Leg springs (Torsion springs). This is also available to you for individual calculation Gutekunst spring calculation program WinFSB to disposal.
The aim of the spring design of a compression spring, tension spring or leg spring is to find the most economical spring for the given task, taking into account all the circumstances, which also fits into the available space and which is required lifespan reached. In addition to these manufacturing and material requirements, there is also the right one Spring design particular importance to.
The designer should put together the following requirements:
1. Load type (static or dynamic)
2. lifespan
4. Ambient medium
5. Necessary forces and spring travel
6th Existing installation space
7th Tolerances
8th. Installation situation (Buckling, lateral suspension)
Every spring design consists of two stages:
 Proof of function : Checking the spring rate, the forces and the spring travel, the vibration behavior, etc.
 Proof of strength : Check for compliance with the permissible stresses or proof of fatigue strength.
This requires an iterative approach.
The Proof of strength is based on the decision whether the spring is loaded statically, quasistatically or dynamically. The following criteria should be used for delimitation:
 Static or quasistatic stress : Timeconstant (resting) load or timevariable load with less than 10,000 strokes in total.
 Dynamic stress : timevarying loads with more than 10,000 strokes. The spring is usually pretensioned and subjected to periodic swell loads with a sinusoidal curve that occur randomly (stochastically), for example in vehicle suspensions. In some cases sudden changes in force occur.
When dimensioning the springs, stress limits are to be specified which are based on the Strength values of the materials and take into account the type of stress. A safety factor is included to determine the permissible voltage. After a comparison with the actual tension, the spring dimensioning must be revised using an iterative procedure. The following applies:
Nominal voltage ≤ permissible voltage
Calculation of compression springs
General
Cold formed cylindrical compression springs with constant incline are most commonly used in practice. The wire is cold formed by being wound around a mandrel. Depending on the advance of the pitch pin, the coil spacing and the position of the spring are regulated. After winding, tempering takes place in order to reduce internal stresses in the spring and to increase the shear elasticity limit. So the Setting amount . The tempering temperatures and times depend on the material; cooling takes place in air at normal room temperature.
Other important work steps in spring production are grinding and setting. The spring ends are usually ground from a wire thickness of 0.5 mm in order to guarantee a planeparallel mounting of the spring as well as an optimal introduction of force.
Exceeds when the spring is loaded Shear stress the permissible value, a permanent deformation occurs, which manifests itself in the reduction of the unstressed length. This process is called “setting” in spring technology, which is associated with the terms “creeping” and “ relaxation “From materials engineering is to be equated. To counteract this, the compression springs are wound longer by the expected amount of setting and later compressed to block length. This setting enables a better material utilization and allows a higher load in later use.
Calculation formulas cylindrical compression spring
The calculation of the Compression spring based on the calculation equations from DIN EN 139061:
Image: Theoretical compression spring diagram
Proof of function of compression springs
The following applies to cylindrical compression springs made of wire with a circular crosssection:
Spring rate:
from R = F / s follows:
Spring force:
such as:
Suspension travel:
Proof of strength compression spring
After the spring dimensions have been determined, the strength must be verified. To do this, the existing shear stress is determined:
Tension from power:
Tension out of way:
While the shear stress τ is to be used for the design of statically or quasistatically loaded springs, the following applies corrected shear stress τ_{ k} for dynamically stressed springs. The distribution of shear stress in the wire crosssection of a spring is uneven, the highest stress occurs on the inside diameter of the spring. With the tension correction factor k, which depends on the winding ratio (ratio of mean diameter to wire thickness) of the spring, the highest tension can be approximately determined. For dynamically stressed compression springs the result is:
Corrected shear stress:
where for k applies (according to Bergsträsser):
Now the comparison is made with the permissible voltage. This is defined as follows:
Allowable voltage:
and
The values for the Minimum tensile strength R_{ m} are dependent on the wire thickness and can be found in the standards of the corresponding materials.
As a rule, it must be possible to compress compression springs up to the block length, which is why the permissible stress at block length is t_{ czul} to consider.
In the case of dynamic loads Low and high tension (t_{ k} 1 and t_{ k} 2) of the corresponding stroke can be determined. The difference is the stroke voltage. Both the upper tension and the stroke tension must not exceed the corresponding permissible values. These can be found in the fatigue strength diagrams in EN 139061: 2002. If the stresses withstand this comparison, the spring is fatigueresistant with a limit load cycle of 10^{ 7th} .
Geometric relationships in compression springs
Spring size  Calculation equation 
Total number of turns  n_{ t} = n + 2 
Block length of the ground spring  L._{ c} = n_{ t} d_{ Max} 
Block length of the unpolished nib  L._{ c} = (n_{ t} + 1.5) d_{ Max} 
Smallest usable length  L._{ n} = L_{ c} + S_{ a} 
Unstrained length  L._{ 0} = L_{ n} + s_{ n} 
Sum of the minimum distances between the turns 

Enlargement of the outside diameter under load
pitch 
(ground) (unpolished)

Buckling spring travel (valid for various Support coefficients n, see EN 139061: 2002) 
All dynamically stressed springs with one wire size> 1mm should shot peened will. This increases the fatigue strength. After both the functional verification and the strength verification have been carried out, various geometry calculations must be carried out and taken into account in order to achieve the Feather fitting to be able to insert into the construction of the component. The block length can not be undercut, because the turns are tight against each other, the smallest usable length should not be undercut because then a linear force curve as well as dynamic resilience are no longer guaranteed. In addition, the permissible tolerances according to DIN 2095 must be taken into account.
Calculation of tension springs
General
Tension springs are wound around a mandrel just like compression springs, but with no distance between the windings and with different Eyelet shapes / Spring ends to attach the spring. The turns are pressed tightly against one another in terms of manufacturing technology. This inner Preload F_{ 0} depends on the winding ratio and cannot be manufactured to any desired height. The provides reference values for the amount of preload Calculation software WinFSB of Gutekunst feathers after entering the respective spring data.
Image: Common eyelet shapes: a.) half German eyelet; b.) whole German loop; c.) hook eye; d.) English eyelet; e.) curled hook; f.) screwin piece
The advantage of tension springs is that Freedom from kinks Disadvantages are the larger installation space and the complete interruption of the flow of force when the spring breaks.
Calculation formulas cylindrical tension spring
According to the calculation equations for compression springs, but taking the preload force into account, the following relationships apply to cylindrical tension springs made of round wire (see also Figure 1.8):
Image: Theoretical tension spring diagram
Proof of function of the tension spring
The following applies to cylindrical tension springs made of wire with a circular crosssection:
Spring rate:
from R = F / s follows:
Spring force:
such as:
Suspension travel:
Proof of strength of tension springs
As with compression spring calculations, the existing shear stress must be determined.
Shear stress:
The corrected stroke tension must also be calculated for dynamic loads.
Corrected shear stress:
Allowable voltage:
The existing maximum voltage t_{ n} for the greatest travel s_{ n} is set equal to the permissible voltage. To however Relaxation To avoid this, only 80% of this spring travel should be used in practice.
For dynamic loads, no generally applicable Fatigue strength values must be specified, as the Bending points of the eyelets additional stresses occur, some of which can exceed the permissible stresses. Tension springs should therefore only be subjected to static loads if possible. If dynamic stress cannot be avoided, one should Eliminate curved eyelets and rolled or screwedin end pieces insert e. A life test under later operating conditions makes sense. A surface consolidation through Shot peening is not feasible because of the tight turns.
Geometric relationships in tension springs
Spring size  Calculation equation 
body length  L._{ K} = (n_{ t} + 1) d 
Unstrained length  L._{ 0} = L_{ K} + 2 L_{ H} 
Eyelet height half German eyelet  L._{ H} = 0.55D_{ i} up to 0.80D_{ i} 
Eyelet height whole German eyelet  L._{ H} = 0.80D_{ i} to 1.10D_{ i} 
Eye height hook eye  L._{ H}> 1.10D_{ i} 
Eyelet height English eyelet  L._{ H} = 1.10D_{ i} 
The permissible manufacturing tolerances according to DIN 2097 must be taken into account.
Calculation of torsion springs (torsion springs)
General
Spiral cylindrical Leg springs (Torsion springs) have essentially the same shape as cylindrical ones pressure – and Tension springs , but with the exception of the spring ends. These are bent in a leg shape in order to allow the spring body to rotate around the spring axis. This means that there are very many different areas of application, for example as return or hinge springs. The torsion spring should be mounted on a guide mandrel and the load should only be applied in the winding direction. The inside diameter is reduced here. The springs are usually coiled with no pitch. However, if friction is absolutely undesirable, torsion springs can also be manufactured with a coil spacing. In the case of dynamic loading, it must be ensured that there are no sharpedged bends at the spring ends in order to avoid unpredictable stress peaks.
Calculation formulas for cylindrical torsion springs (Torsion springs)
The calculation is based on the guidelines of EN 139063: 2001:
Image: Theoretical torsion spring / torsion spring diagram
Proof of function of torsion springs (torsion springs)
Spring torque rate:
Spring torque:
Rotation angle:
Proof of strength of torsion springs (torsion springs)
The existing bending stress is determined and compared with the permissible stress. In the case of dynamic loading, the corrected stress must again be used for comparison.
Bending stress:
Corrected bending stress:
where for q applies:
Permissible bending stress:
In the case of dynamic loading, the lower and upper stress (t_{ k} 1 and t_{ k} 2) of the corresponding stroke can be determined. The difference is the stroke voltage. Both the upper tension and the stroke tension must not exceed the corresponding permissible values. For spring steel wire, these can be found in the fatigue strength diagrams in EN 139063: 2001. If the stresses withstand this comparison, the spring is fatigueresistant with a limit load cycle of 10^{ 7th} .
Geometric relationships in torsion springs (torsion springs)
Spring size  Calculation equation 
Reduction of the inside diameter at maximum load 

Unloaded body length  
Body length in the maximally loaded condition  
Suspension travel 
In addition, the manufacturing tolerances according to DIN 2194 must be taken into account.
A summary of the article “Design of a metal spring”, consisting of Part 1 “Basics” and Part 2 “Calculation” can also be downloaded from the Gutekunst springs 1×1 .
Should you need one individual spring design just email us the key data for the metal spring you need technik@gutekunstco.com , contact our technology department by phone at (+49) 035 877 22711 or use at https://www.federnshop.com the Gutekunst spring calculation program WinFSB for free calculation of compression springs, tension springs and torsion springs.
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