# Helical compression cylindrical springs

## Helical compression cylindrical springs

The calculation is intended for the purposes of geometric and strength designs of helical compression cylindrical springs made of wires and rods of circular sections, loaded with static or fatigue loading resp. In addition to the design of geometric and strength parameters, the calculation works with CAD systems. The application provides solutions of the following tasks:

1. Automatic design of a spring.

2. Selection of an optimal alternative of spring design in view of strength, geometry and weight.

3. Static and dynamic strength check.

4. Calculation of working forces of a spring of known production and installation dimensions.

5. Calculation of installation dimensions for known loading and production parameters of the spring.

6. The application includes a table of commonly used spring materials according to ISO, EN, ASTM/SAE, DIN, BS, JIS and others.

7. Support of 2D a 3D CAD systems.

The calculation is based on data, procedures, algorithms and data from specialized literature and standards EN 13906-1, DIN 2089-1, DIN 2095, DIN 2096.

User interface.

Purchase, Price list.

## Control, structure and syntax of calculations.

Information on the syntax and control of the calculation can be found in the document "Control, structure and syntax of calculations".

## Information on the project.

Information on the purpose, use and control of the paragraph "Information on the project" can be found in the document  "Information on the project".

## Basic terms.

A compression spring is a helical cylindrical spring with constant spacing of active coils and approximately constant stiffness which is able to receive external forces acting against each other in its axis. In view of spring function, there are four basic states of springs:

 State of the spring Description of states of a spring index free the spring is not loaded 0 preloaded the spring is exposed to minimum operational loading 1 fully loaded the spring is exposed to maximum operational loading 8 limiting the spring is compressed to full contact of coils 9

The above-mentioned indexes are used in the calculation to specify individual parameters of the spring related to the given state of the spring.

## Process of calculation.

The task of spring design cannot be solved directly and allows considerable freedom in options of the design, dimensions or loading of the spring. Many springs of various designs and dimensions may meet requirements of the desired input parameters of the task. Therefore, it is necessary to proceed iteratively and successively evaluate individual designs of the spring. The calculation solves this problem by creation of a table of optimum designs following the chosen qualitative standard. The design procedure is given in the following items.

1. Set operational parameters of the working cycle (manner of loading, temperature and aggressivity of the working environment). [1.1]
2. Select production and installation properties of the spring. [1.5]
3. Select the corresponding mode of loading and set the desired level of safety. [1.12 - 1.13]
4. In case of fatigue loading of the spring, set the mode of fatigue loading, desired service life and level of safety. [1.16 - 1.18]
5. Choose an adequate processing of the spring. [2.1]
6. According to the recommended scope of use [2.3] select the material of the spring. [2.2]
7. Enter the desired parameters of the working cycle (loading, length and stroke of the spring). [3.1]
8. Set the necessary filters and marginal conditions of the spring design. [3.7]
9. Select the manner of classification of results [3.18] and press the button for initiation of the design calculation. [3.19]
10. Select a suitable solution from the table [3.20].
11. Check parameters of the designed spring in chapter. [4]
12. In case you need "fine" tuning of dimensions of the spring, use some of the supplementary calculations [7,8,9] for their modification. After execution of the modifications, transfer the results back to chapter [4] and check again whether the spring meets requirements of all necessary checks. [4.38, 4.43, 4.45]
13. Save the workbook with the designed solution under a new name.

## Selection of load conditions, spring operational and production parameters. [1]

In this paragraph, enter basic input parameters characterizing the manner and mode of loading, design and method of seating the spring and parameters of the working environment.

Two basic methods of loading of springs are available for the purpose of calculation of springs:

Springs loaded statically or with lower variability, i.e. with cyclical changes of loading without mutual contacts of coils, with the requirement of a service life lower than 105 working cycles.
Springs exposed to oscillating (dynamic) loading, i.e. with cyclical changes of loading, with the requirement of a service life from 105 working cycles up.

### 1.3 Working temperature.

Temperature of the working environment affects the spring relaxation, i.e. decrease in the force from the spring with its deformation to a constant length, depending on time. It is advisable to take this fact into account when designing the spring, and increase the level of safety during strength checks of the spring in case of temperatures over 80 °C. It is necessary to respect the working temperature also with selection of the spring material.

### 1.4 Working environment.

The service life of springs decreases significantly due to corrosion effects. Corrosion has very powerful effects particularly on springs exposed to fatigue loading. It is advisable to take this fact into account when designing the spring, and increase the level of safety during strength checks of the spring in case of a corrosion-aggressive environment. It is also necessary to consider corrosion effects with selection of the spring material.

### 1.6 Seating of the spring.

In case of compression springs, it is always necessary to check its safety against side deflection. In addition to the size of the maximum working deformation (compression) of the spring, the manner of seating of the spring also considerably affects possible side deflection.

A spring which cannot be designed to prevent side deflection is usually supported using a centre pin or a sleeve. If there is a danger of damage to the spring due to friction with the pin or sleeve, the spring can be divided into several shorter springs arranged in series.

Select the type of seating in the list according to the illustration.

A) Fixed - free ends

B) Pinned - pinned ends

C) Clamped - clamped ends with lateral restraint

D) Clamped - pinned ends

E) Clamped - clamped ends without lateral restraint

F) Guided seating: the spring is guided inside a sleeve or on a pin

### 1.7 Design of spring ends.

In case of compression springs, several various designs of spring ends are used. These differ in numbers of ends and machined coils and designs of supporting surfaces of the springs. Select the design in the list according to the illustration.

G) Open ends not ground: the edge coil is not bent to the next one, the supporting surface is unmachined

H) Open ends ground: the edge coil is not bent to the next one, the supporting surface is machined to a flat end perpendicular to the spring axis

I) Closed ends not ground: the edge coil is bent to the next one (it usually adjoins its free end), the supporting surface is unmachined

J) Closed ends ground: the edge coil is bent to the next one, the supporting surface of the spring is machined

### 1.8 Surface treatment of the spring.

Shot peening of the spring increases the fatigue limit in torsion by approx. 10 to 15%. In case of springs with shot peening exposed to fatigue loading, this allows users to reduce the consumption of material for production of the spring, reduce its dimensions and installation space, increase the working stroke or increase protection of the spring against fatigue breaks. Therefore, it is advisable to apply the technical requirement of shot peening to all springs exposed to oscillating loading. Due to technological reasons, only springs with diameters of wire over 1 mm are shot peened.

### 1.9 Direction of coil winding.

Right-hand winding of springs is preferred (dextrorsal helix); left-hand winding is used only if necessary due to technical reasons.

### 1.10 Number of end / ground coils.

End coils

End coils are edge coils of the spring, co-axial with the active coils, whose angle pitch does not change during functional deformation of the spring. End coils create a supporting surface for the spring and with compression springs, one end coil is usually used at both ends of the spring.

Gound coils

Edge coils of the spring, machined to a flat surface perpendicular to the spring axis. Usually machined from three-fourths of half of the end coil up to its free end. Machined coils are commonly used only with springs with diameters of wires d > 1 mm.

Select the manner of loading which best meets the requirements of the entered specifications.

1. Light service.
Continuous loading without shocks, with a course according to the sinusoid, loading with small deformations or low frequency, not much or rarely loaded springs with service life up to 1000 cycles. For example, springs used in measuring instruments, safety and locking devices, etc.
2. Medium duty service.
Continuous loading with low or medium uniformity, loading with normal frequency of deformations and service life up to 105 cycles. Commonly used springs in machine tools, machine products or electrical components.
3. Heavy duty service.
Loading with strong shocks, loading with high frequency of deformations or sudden deformations over longer time periods, springs with a requirement for long service life, springs where coils hitting each other occur or may occur due to inertia effects. For example, springs used in pneumatic hammers, hydraulic machines, valves, etc.

### 1.13 Desired level of safety of a spring exposed to static loading.

Minimum permissible ratio between the permissible limit stress in torsion of the selected spring material and the actual maximum working stress t8in the spring coils. For a non-corrosive atmosphere and working temperature of the immediate vicinity of the spring up to 80 °C, and with regards to the course and mode of loading, it is advisable to choose a level of safety of compression springs in the interval from 1.05 to 1.3. Springs working at higher temperatures or in an aggressive environment should be designed with higher levels of safety.

### 1.14 Method of stress curvature correction.

With helical springs, the stress appearing in the spring coil at a given loading is calculated for simple torsion. Additional bending stress appears in the coil due to its rounding. Therefore, the stress is corrected in the calculation using a correction coefficient. As several different coefficients are commonly used, select in the list the correction coefficient which meets your local usage or recommendations of standards.

###### Hint: With springs exposed to static loading, corrections are usually not executed.

Select the loading mode which best meets the requirements of the entered specifications.

Continuous loading without shocks, with a course according to the sinusoid, without coils hitting each other.
Loading with lower or medium non-uniformity, without mutual hitting of coils, if the course of loading varies according to a curve substantially different from the sinusoid.
Springs exposed to heavy shocks, with discontinuous course of loading, springs with sudden deformations over longer or irregular time intervals, springs where coils hitting each other occurs or may occur due to inertia effects.

### 1.17 Desired service life of the spring.

Two fields of fatigue loading of springs can be distinguished with springs exposed to fatigue loading. In the first field, with limited service life of springs (lower than approx. 107 working cycles, the fatigue strength of the spring decreases with an increasing number of working cycles. In the field of unlimited service life (the desired service life of the spring is higher than 107 working cycles), the fatigue limit of the material and thus the strength of the spring remains approximately constant.

### 1.18 Desired level of safety of a spring exposed to fatigue loading.

The level of safety gives the minimum permissible ratio between the fatigue strength in torsion of the spring and the actual maximum working stress t8in spring coils. For a non-corrosive atmosphere and working temperature of the immediate vicinity of the spring up to 80 °C, and with regards to the course and mode of loading, it is advisable to choose a level of safety of compression springs in the interval from 1.05 .. 1.25. When determining the level of safety, it is also necessary to consider suitability of the selected material for fatigue loading. With materials unsuitable for fatigue loading, it is advisable to increase the desired level of safety by up to 20%. Springs working at higher temperatures or in a corrosive environment should be designed with higher levels of safety. Particularly corrosion significantly decreases the service life of a spring exposed to fatigue loading.

### 1.19 Method of stress curvature correction.

With helical springs, the stress appearing in the spring coil at a given loading is calculated for simple torsion. Additional bending stress appears in the coil due to its rounding. Therefore, the stress is corrected in the calculation using a correction coefficient. As several different coefficients are commonly used, select in the list the correction coefficient which meets your local usage or recommendations of standards.

## Option of spring material. [2]

This paragraph can be used for selection of the spring material. Immediately after selection of material in the list, all information necessary for the design and calculation of the spring is displayed. If you need more detailed information on the selected material, or define or modify your own material, switch over to the material sheet "Material".

### 2.1 Production method.

From the selection list choose the required processing of the spring. The cold winding shall be used for springs of ordinary sizes with a diameter of the wire up to 16 mm. Hot forming shall be used for the production of heavily loaded springs of greater sizes with a diameter of the over10 mm.

### 2.2 Spring material.

Select the spring material from the list. In addition to 5 user's materials, the list includes selected materials of one standard. If you wish to use materials from another standard, select the respective standard in the sheet "Material".

### 2.3 Field of use of the selected material.

This paragraph includes information on recommended use of the selected material. The spring material should be designed with regards to the manner of loading of the spring and operational conditions. If you must use a less suitable material, this fact should be reflected in an increased level of safety in the design of the spring (see row [1.13] or [1.18] resp.).

Properties of the selected material described in rows [2.4, 2.6] are evaluated in five degrees (excellent, very good, good, poor, insufficient), the relative strength in row [2.5] in three degrees (high, medium, low).

### 2.9 Mechanical and physical properties of the material.

This part gives all parameters necessary for calculation, independent of the diameter of the used wire.

### 2.13 Strength characteristics of the material.

This chapter includes strength characteristics of the selected material which are necessary for the design and calculation of the spring. The data characterizing strength of the material may be different for the same material depending on the diameter of the used wire. Therefore, the values given here depend on the diameter of the wire as given in row [4.8].

### 2.16 Ultimate fatigue strength in torsion.

Maximum permissible stress of the spring material for infinite life and zero-to-maximum stress fluctuation.

## Spring design. [3]

This paragraph can be used for the design of the spring. The task of designing the spring often has many various suitable solutions for the given input conditions. The application, therefore, proceeds iteratively with the spring design and for the given input conditions, it passes through individual designs of the spring and a set of most advantageous solutions is selected following the chosen qualitative standard. The selected solutions are then offered in the form of a sorted table in which you can select a suitable design. The data on the selected spring are then displayed immediately in the chapter of results.

### 3.1 Desired parameters of the working cycle.

This part can be used for entering input data describing the basic parameters of the working cycle which have to be met by the designed spring. The first input column displays the desired value of the given parameter of the spring; the second column gives the permissible deviation from the desired value in the range 0-99%. If the designed spring has to meet the desired value of the given parameter, a zero deviation must be entered.

### 3.7 Filters of the designed solution.

In this part it is necessary to specify various filters and marginal conditions of the design calculation. Their setting may significantly affect the course of the spring design and determine the speed, accuracy and quality of the design, the scope and number of suitable solutions and a qualitative standard for evaluation of the best designs.

### 3.8 Maximum permissible outer spring diameter.

If it is necessary to limit the outer diameter of the spring in its design (for example, if the spring has to be led in a sleeve), enable the check box at the beginning of the row and enter the maximum permissible value of the outer diameter of the spring in the input field.

### 3.9 Minimum permissible inner spring diameter.

If it is necessary to limit the inner diameter of the spring in its design (for example, if the spring has to be led on a pin), enable the check box at the beginning of the row and enter the minimum permissible value of the inner diameter of the spring in the input field.

### 3.10 Permissible division of the number of active coils.

Active coils of the spring are those coils whose pitch angle varies during functional deformation of the spring. When setting a fine division, the design calculation tests a higher number of different designs of the spring and is able to give a more accurate and higher quality solution. On the other hand, this naturally slows down the design calculation of the spring.

### 3.11 Permissible exceeding of spring limit dimensions.

When designing the spring, it is not possible to proceed without certain dimensional limitations. Some dimensions or ratios of individual dimensions of the spring are limited by the recommended values specified by the respective standards and producers. This creates a file of marginal conditions which must be taken into account in the spring design.

Strictly following these marginal conditions may cause elimination of some advantageous solutions from the resulting design, which may exceed some of the specified limits, however, despite this, they may be acceptable. Due to this reason, it is possible to set a filter of the design calculation in this row. Such filter specifies the percentage of exceeding the limit dimensions of the spring. This brings more suitable solutions, however, on the other hand it is then necessary to visually check the selected solution in the chapter of results and consider acceptability of possible exceeding of the limit dimensions of the springs. Exceeding limit dimensions is indicated by a change in color of the parameter value to red in the chapter of results.

### 3.12 Perform check of buckling.

This row decides whether the spring will be checked regarding side deflection in the course of the design calculations. If the check is enabled, the resulting design eliminates all solutions which do not meet the requirement of stability of the spring shape. The manner of seating of the spring very considerably affects any possible side deflection (see row [1.6]). If the spring has to be installed with a guide, the check need not be performed.

If the check is not performed during the design, the calculations are faster and more suitable solutions are obtained. On the other hand, there is the need to perform the check by the user himself, by visual matching of the data in row [4.44]. If the spring design is unsuitable, it is necessary to select another designed solution or change the manner of spring seating. A spring which cannot be secured against side deflection is usually guided on a pin or inside a sleeve.

### 3.13 Perform a check of the limit working length.

If this check is enabled, the resulting design eliminates all solutions which include a length of the fully loaded spring shorter than the minimum limit test length. If this check is disabled, it is advisable to perform a visual check of the designed solution by matching rows [4.24] and [4.30].

### 3.14 Keep to the desired level of safety with the strength check.

If this filter of solutions is set to "Yes", the resulting design eliminates all solutions with calculated levels of safety ss lower than the desired level of safety given in row [1.13]. In case of springs exposed to fatigue loading, this filter also eliminates solutions with calculated levels of safety sf lower than the desired level of safety given in row [1.18].

If the filter is disabled, the resulting design includes all solutions with calculated levels of safety higher or equal to 1. Due to the fact that the desired levels of safety are usually more or less accurate estimations and only rarely reflect the accurately determined value, whose exceeding could lead to damage to the spring, experienced users can disable this filter during execution of the design and consider the level of safety of the designed spring directly in the table of the design or in the chapter of results in row [4.42] or [4.49] resp.

### 3.15 Quality criterion.

This row sets the criterion of evaluation of the quality of individual suitable solutions of spring design. The best solutions are then offered to the user in the table. The standard of quality can be chosen from the list according to the following formula:

1. Deviation from desired dimensions: Use of this criterion provides a solution for parameters of the working cycle as close to the desired input parameters entered in paragraph [3.1] as possible. It is advisable to use this criterion in cases when you wish to keep to the desired parameters of the working cycle as far as possible.
2. Minimum spring weight: This criterion selects suitable solutions with the lowest weight of spring.
3. Deviation from desired level of safety: Use of this criterion provides a solution for the calculated level of safety given in row [1.13] with a spring exposed to static loading, so it is as close as possible to the desired level of safety or to the level of safety given in row [1.18] in case of a spring exposed to fatigue loading. It is advantageous to use this criterion particularly if you wish to find the most optimal solution in view of strength check of the spring.
4. Combined: Combination of all previous standards of quality.

### 3.16 Number of design iterations.

The design calculation of the spring works on the iteration principle. This row can be used for setting of the number of iterations in the calculation and it affects the speed, accuracy and quality of the design. Generally, the more iterations, the slower the calculation and the more accurate the solution. However, it is also advisable to take into account other aspects when setting this row.

The speed of the design is affected by the capacity of the computer and the type of design more than by the chosen number of iterations. At the same time, setting a high number of iterations need not always bring more accurate solutions for certain types designs. Generally speaking, it is usually sufficient to set a low or medium number of iterations for common designs. Use of a high number of iterations is more important for very free designs, where all or the majority of parameters of the working cycle in paragraph [3.1] entered with a considerable permissible deviation, and the desired diameter of the spring, is not limited by filters in rows [3.8, 3.9].

### 3.17 Options of solutions.

This part can be used to initiate the design calculation and then to choose a suitable spring in the table of designed solutions. With regards to the complexity of the spring design, it is not possible to perform the design calculation automatically always with a change to one of the input parameters, as can be done with other calculations on the sheet. The design calculation is initiated once when pressing the button in row [3.19]. Information on the progress of the calculation is displayed in the dialogue.

After completion of the calculation, a table of designed solutions is filled in and sorted and values of the best (chosen) solution are transferred automatically to the chapter of results. The table is sorted according to the criterion set in row [3.18]. The table of designed solutions can be re-sorted whenever using another sorting criterion.

If the design calculation was unsuccessful and no suitable solution was found, this fact is indicated by a warning message and the table of solutions remains in its original state. The following text gives some particular problems which may appear, and their possible remedies:

• Incorrectly entered parameters of the working cycle or limit diameters of the spring resp.: Some input data in paragraph [3.1] or rows [3.8, 3.9] are entered incorrectly. Incorrect entering is indicated by a change in color of the parameter value to red.
• Incorrectly set limit dimensions of the spring: Some data in chapter [3.0] in the sheet "Options" are entered incorrectly. Incorrect entering is indicated by a change in color of the parameter value to red.
• The desired diameters of the spring do not correspond with its the limit dimensions: Some of the desired diameters in rows [3.8, 3.9] are out of the marginal conditions given in chapter [3.0] in the sheet "Options".
• For the chosen wire and desired diameters of the spring, no suitable solution can be found: This problem can probably be resolved by selection of another wire material which is delivered in different diameters (see row [2.8]) or less strict limitation of the spring diameter in rows [3.8, 3.9] if possible. The problem may also be caused due to too limiting a setting of marginal conditions in rows [3.1, 3.2] in the sheet "Options".
• For the chosen wire and desired parameters of the working cycle or diameters of the spring resp., no suitable solution can be found: The problem probably has similar causes and solution as the previous problem. Another possible cause can be found in low strength of the material with regards to the desired value of the maximum working loading in row [3.2]. The solution can be found in a material with higher strength or possibly disabling of the control of the desired level of safety in row [3.14].
• For the given entry data, no suitable solution was found: In this case, it is very difficult to determine the source of the problem. It is advisable to use several common procedures to localize and resolve the problem. One of the options of how to find causes of the problem is to initiate a design with differently set filters of solution in rows [3.8 .. 3.14]. A greater permissible deviation from the desired parameters of the working cycle in paragraph [3.1] is another option. The last option is to choose a material with higher strength or wider range of delivered diameters of wire. If even these procedures do not bring any suitable solutions, the problem can probably be found in a too high loading of the designed spring and the problem could be solved by using several springs arranged in parallel.
• For the given entry data no solution could be found which meets requirements of the strength check in view of dynamic loading: In this case, the application can find springs sufficient for static loading, however, in view of fatigue strength, no spring is suitable. The solution could be found in a material with higher fatigue strength or by trying to disable the check of the desired level of safety in row [3.14] or by trying to reduce the difference between the maximum and minimum working loading.

### 3.20 Table of designed solutions

Meaning of parameters in the table:

## Summarized list of designed spring parameters. [4]

All necessary parameters describing the designed spring are shown in this paragraph for the given loading and dimensions of the spring. Entry data are transferred to the calculation from the table of solutions [3.20] of the chosen design of the spring or from some of the supplementary calculations [7,8,9]. For easier evaluation and check of values of individual parameters of the spring, some data are completed with their recommended limit values (shown in green fields in the listing). Exceeding of the recommended values is indicated by a change in color of the parameter to red. Critical values which might cause non-functionality or damage to the spring are indicated by a change in color of the whole field to red.

Parameters of the spring are divided in the listing into paragraphs according to the spring status; results of the performed strength checks of the spring are given at the end of the chapter. Meanings of individual dimensional parameters of the spring can be seen in the illustration.

If there is a need to tune some parameters of the designed spring (e.g. rounding of the designed dimensions), use some of the supplementary calculations [7,8,9] for this purpose

### 4.1 Refresh results from the selected spring design.

Pressing the button in this row refreshes values in the listing of parameters of the spring with the data from the design of the spring chosen in the table of solutions [3.20].

### 4.10 Spring index

This parameter gives the ratio D/d between the mean diameter of the spring and the diameter of the used wire.

### 4.29 Sum of min. permissible spaces between active coils.

Theoretically determined limit value characterizing the maximum permissible deformation (squeezing) of a compression spring. This can be used to determine the minimum permissible test length of the spring [4.30].

### 4.30 Minimum spring limit length.

If the spring is compressed to a length shorter than the limit length, the actual stiffness of the spring increases significantly above the theoretically determined stiffness valid in the field of compression to this length. At the same time, the critical speed decreases (see [4.34]) and this also increases the risk of mutual hitting of coils in operation. Due to these reasons, a compression spring (even during a test or installation) should not be squeezed to a smaller length. This results in the condition for the design of the spring that the length of the spring in a fully loaded condition [4.22] is greater than this limit length.

### 4.34 Critical spring speed.

In case of compression springs with maximum speed of shifts of the moving end of the spring when loading or releasing is higher than their critical speed of squeezing, the inertia effects cause mutual hitting of coils. This leads to an increase in the actual stress in the spring coils by contact stress. This fact usually very adversely affects the service life of the spring and it is necessary to take it into account in designs of compression springs.

### 4.35 Natural spring frequency.

Resonance effects occur with compression springs exposed to fatigue loading. To eliminate these effects, it is necessary to load the spring at an excitation frequency different from the characteristic frequency of the spring (by approx. 15%).

### 4.38 Spring strength check.

The strength check of a compression spring is performed by comparison of the limit permissible stress in torsion of the chosen material [4.41] with the corrected stress of the spring in a fully loaded condition [4.40]. If the designed spring has to meet the strength check in the full extent, the resulting level of safety [4.42] must be higher or equal to the desired level of safety [1.13].

### 4.39 Curvature correction factor.

The stress in the spring coil is calculated for simple torsion and its calculated value is a theoretical value. In fact, the stress in the coil is higher because the curving of the coil causes an additional bending stress. Therefore, the stress is corrected using a corrective coefficient (see row [1.14]) for the purpose of a strength check.

### 4.43 Check of buckling.

In case of compression springs, it is always necessary to check its protection against side deflection. The check is performed by comparison of the maximum working deformation of the spring (expressed as a percentage of the free length of the spring) with the permitted deformation. The value of the permitted deformation is determined empirically for the given slenderness ratio of the spring L0/D and the type of seating of the spring. Generally, the risk of possible side deflection increases with an increasing value of the slenderness ratio and increasing value of the working compression of the spring. The manner of seating of the spring (see row [1.6]) has a significant effect on its possible side deflection.

A spring which cannot be designed as secured against side deflection is usually installed on a pin or inside a sleeve. If there is a danger of damage of the spring due to friction, the spring can be divided into several shorter springs arranged in series.

##### Curves of permitted deformation according to the type of seating of the spring

The strength check of a spring exposed to fatigue loading is performed by comparison of the maximum fatigue strength of the material determined for the given course of loading [4.48] with the corrected stress of the spring in a fully loaded state [4.47]. If the designed spring has to meet the strength check in the full extent, the resulting level of safety [4.49] must be higher or equal to the desired level of safety [1.18]. Naturally, even with a spring exposed to fatigue loading the condition of "static" strength check [4.38] must be met as well.

### 4.46 Curvature correction factor.

The stress in the spring coil is calculated for simple torsion and its calculated value is a theoretical value. In fact, the stress in the coil is higher because the curving of the coil causes an additional bending stress. Therefore, the stress is corrected using a corrective coefficient (see row [1.19]) for the purpose of a strength check.

Determination of the maximum fatigue strength of the spring is based on the ultimate fatigue strength of the chosen material and the given course of loading of the spring using a Goodman's fatigue diagram.

## Parameters of designed spring for specific working load or spring length. [5]

This paragraph can be used for calculation of parameters of a spring (designed in paragraph [4]) which is in a specific working condition. The paragraph [5.1] is designed for calculation of the length Lx of the spring, compressed by the given working force Fx. Paragraph [5.6] enables users to find the working force which is needed to squeeze the spring to the given length Lx.

This paragraph gives parameters of a strength check of a spring exposed to fatigue loading. The strength check of a spring exposed to fatigue loading is performed by comparison of the maximum fatigue strength of the material determined for the given course of loading [6.8] with the corrected stress of the spring in a fully loaded state [6.3]. If the designed spring has to meet the strength check in the full extent, the resulting level of safety [6.9] must be higher or equal to the desired level of safety [1.18].

### 6.1 Curvature correction factor.

The stress in the spring coil is calculated for simple torsion and its calculated value is a theoretical value. In fact, the stress in the coil is higher because the curving of the coil causes an additional bending stress. Therefore, the stress is corrected using a corrective coefficient (see row [1.19]) for the purpose of a strength check.

### 6.6 Ultimate fatigue strength in torsion.

Maximum permissible stress of the spring material for infinite life and zero-to-maximum stress fluctuation.

Determination of the maximum fatigue strength of the spring is based on the ultimate fatigue strength of the chosen material and the given course of loading of the spring using a Goodman's fatigue diagram.

## Spring check calculation. [7]

The first of the supplementary calculations can be found in this paragraph. This calculation includes three functions.

1. Calculation of parameters of a spring of known dimensions.
After entering the known parameters of the working cycle in the section [7.2] and dimensions of the spring in rows [7.7, 7.9, 7.17, 7.20], other parameters of the spring are calculated and the strength check is performed automatically. The data on the calculated spring can be transferred using the button in row [7.27] to the chapter of results [4], where some other parameters of the spring are calculated and a strength check of a spring exposed to fatigue loading is possibly performed . All check boxes in rows [7.9, 7.17, 7.20] must be disabled for this function of the calculation.
2. Modification and fine tuning of parameters of the spring designed by the design calculation.
Similarly as the other two supplementary calculations, it is possible to use this calculation for fine tuning of parameters of the spring (e.g. rounding of dimensions of the spring), designed using the design calculation in chapter [3]. The data on the designed spring can be transferred to the calculation using the button in row [7.1]. In the course of modification, you are informed on any possible exceeding of the recommended values of some of the parameters of the spring by a change in color of this parameter to red. The modified data can be now transferred back to the chapter of results [4] using the button in row [7.27]. It is advisable to visually check in the chapter of results whether the modified spring meets all needed checks. All check boxes in rows [7.9, 7.17, 7.20] must be disabled in the course of calculation.
3. Manual design of the spring.
This calculation enables experienced users to carry out a design of a spring for the given parameters of the working cycle. When designing the spring, it is recommended to proceed as follows: diameter of the spring, diameter of the wire, number of coils, length of the spring [7.7,7.9, 7.17, 7.20]. After entering one parameter, the recommended values of the following parameters are calculated automatically. When designing a spring, it is better to enable check boxes of these parameters. The application then automatically determines the given parameters following a change to the higher positioned parameter. For facilitation of the design, the input boxes of the spring diameter and number of coils are completed by roll-up strips, which quicken entering and changes to values of these parameters. In the course of the design, you are informed on any possible exceeding of the recommended values of some of the parameters of the spring by a change in color of this parameter to red. The data on the designed spring can be transferred using the button in row [7.27] to the chapter of results [4], where some other parameters of the spring are calculated and a strength check of a spring exposed to fatigue loading is possibly performed.

## Calculation of working forces of the spring. [8]

The calculation located in this paragraph includes two functions.

1. Calculation of working forces with a spring of known dimensions.
After entering parameters of the working cycle in section [8.2] and dimensions of the spring in rows [8.7, 8.8, 8.11, 8.12], the working forces needed to squeeze the spring to the desired length and the strength check are performed automatically. The data on the designed spring can be transferred using the button in row [8.22] to the chapter of results [4], where some other parameters of the spring are calculated and a strength check of a spring exposed to fatigue loading is possibly performed.
2. Modification and fine tuning of parameters of a spring designed using the design calculation.
Similarly as the other two supplementary calculations, it is possible to use this calculation for fine tuning of parameters of a spring (e.g. rounding of dimensions of the spring) designed using the design calculation in chapter [3]. The data on the designed spring can be transferred to the calculation using the button in row [8.1]. In the course of modification, you are informed on any possible exceeding of the recommended values of some of the parameters of the spring by a change in color of this parameter to red. The data on the designed spring can be transferred to the chapter of results [4] using the button in row [8.22].

## Calculation of working lengths of the spring. [9]

The calculation located in this paragraph includes two functions.

1. Calculation of parameters of a spring of known dimensions for a given loading.
After entering the loading of the spring in section [9.2] and dimensions of the spring in rows [9.6, 9.7, 9.10, 9.11] other parameters of the spring and a strength check are calculated automatically. The data on the designed spring can be transferred using the button in row [9.22] to the chapter of results [4], where some other parameters of the spring are calculated and a strength check of a spring exposed to a fatigue loading is possibly performed.
2. Modification and fine tuning of a spring designed using the design calculation.
Similarly as the other two supplementary calculations, it is possible to use this calculation for fine tuning of parameters of a spring (e.g. rounding of dimensions of the spring) designed using the design calculation in chapter [3]. The data on the designed spring can be transferred to the calculation using the button in row [9.1]. In the course of modification, you are informed on any possible exceeding of the recommended values of some of the parameters of the spring by a change in color of this parameter to red. The data on the designed spring can be transferred to the chapter of results [4] using the button in row [9.22].

Information on options of 2D and 3D graphic outputs and information on cooperation with 2D and 3D CAD systems can be found in the document "Graphic output, CAD systems".

## Setting calculations, change the language.

Information on setting of calculation parameters and setting of the language can be found in the document "Setting calculations, change the language".

### Supplements - This calculation:

#### 3.0 Spring limit dimensions.

When designing a spring, it is not possible to proceed without certain dimensional limitations. Some dimensions or ratios of individual dimensions of the spring are limited by recommended values determined by the respective standards (see e.g. DIN 2095, DIN 2096) and various producers as well. This creates a file of marginal conditions which must be taken into account in the design of the spring.

Therefore, different recommended limit dimensions of the spring may be used which can be modified in this paragraph according to the user's requirements. Minimum values of individual parameters can be entered in the first column, maximum values in the second column. In case of setting more free marginal conditions (by decreasing the minimum or increasing the maximum values), the application selects a suitable solution from a wider range of suitable solutions. This increases the chance of finding a solution of a better quality. On the other hand, this creates the risk that the chosen supplier will not be able to produce the designed spring.

If there are no special requirements for limit dimensions of the spring, the predefined setting can be used. Pressing the button in row [3.8] sets in input fields the implicit values corresponding to the file of marginal conditions for commonly delivered springs.

#### 3.1 Spring index.

This gives the ratio D/d between the mean diameter of the spring and the diameter of the used wire. According to DIN:

4 to 20 - cold formed springs (DIN 2095)

3 to 12 - hot formed springs (DIN 2096)

#### 3.2 Maximum outer diameter of springs.

Cold formed springs - according to DIN 2095, maximum 240 mm. There are commonly delivered springs with even greater diameters.

Hot formed springs - according to DIN 2096, maximum 460 mm.

#### 3.3 Ratio between free spring length and spring diameter.

It is not prescribed by the standard. Usually 1 to 10 with commonly produced springs. Increasing the ratio causes an increasing tendency to side deflection of the spring.

#### 3.4 Maximum free length of the spring.

Cold formed springs - according to DIN 2095, maximum 630 mm.

Hot formed springs - according to DIN 2096, maximum 800 mm.

Springs of even greater lengths are commonly delivered.

#### 3.5, 3.6 Limit dimensions of the pitch of the free spring.

Not prescribed by the standard, usual with commonly produced springs

0.3*D < t < 0.6*D - for wire diameters up to 10mm

1.5*d < t < 0.55*D - for thicker wires

Too small pitch of the spring usually prevents perfect shot peening of the spring.

#### 3.7 Minimum number of active coils.

A minimum of two active coils are prescribed for cold formed springs according to DIN 2095.

A minimum of three active coils are prescribed for hot formed springs according to DIN 2096.

## Workbook modifications (calculation).

General information on how to modify and extend calculation workbooks is mentioned in the document "Workbook (calculation) modifications".

### Supplements - This calculation:

With calculation of springs, it is not possible to intervene in the design calculation of the spring using modifications and changes in the workbook. With regards to the complexity of the task of designing a spring, this calculation is implemented as an internal function of the workbook.

^