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

This section presents design process information that is common to each of the coil spring types supported by ODOP:Spring.

For specifics, see:

- Advanced Spring Operations
- Spring Materials
- Select Size and Select Catalog
- Spring Design References
- Compression Spring
- Extension Spring
- Torsion Spring

- Spring basics
- The essential challenge of spring design
- Force-Deflection relationships
- Allowable stresses and Factor of Safety
- How to judge a good spring design
- Technique
- Names
- Spring Constraints
- Constraints common to both compression and extension springs
- Factor of Safety
- Materials
- End Types
- Cycle Life
- What To Do If
- References
- Restrictions

This section provides a limited amount of introductory material on spring design in the context of the ODOP:Spring program.

It is not the intent of the ODOP:Spring documentation to teach spring design. The ODOP:Spring program is aimed at experienced spring designers and engineers who have some background in strength of materials and failure theories. The Spring Design References documentation section contains a list of reference works that cover spring design. This section should be read in conjunction with other sections of the ODOP:Spring documentation. In particular, refer to the specific spring type sections for additional details on variable Names and Force-Deflection Diagrams.

The challenge of any engineering design problem is to select values for those parameters that are under the designer's control such that the design produces the desired performance.

Even with something as simple as a coil spring, the design problem can be presented in dozens of different ways. Sometimes the problem is stated in terms that specify A, B and C, requiring X, Y and Z to be calculated. Other times the problem is stated in terms that specify X, Y and Z, requiring A, B and C to be calculated. Therefore, it is not realistic to solve the design equations for a single set of inputs and outputs. It is simply not possible to make all design problems fall neatly into a step by step procedure.

ODOP:Spring approaches this characteristic of design by letting the designer to express what is known about the problem, and what needs to be achieved and then providing an ability for the program to search for an acceptable solution.

In coil spring design, it is parameters like outside diameter, wire diameter, free length, and number of coils that are directly under the designer's control. Other variables like spring rate, stress, cycle life, solid height, initial tension or tendency to buckle are a consequence of the selection of the physical parameters. As with any design situation, there are significant limitations on the range of values that the various parameters and variables can take on.

Typically a designer can express his goals for the performance of a given design in terms of one-sided limitations that ODOP:Spring refers to as constraints. For example, the outside diameter must be less than X, the inside diameter greater than Y, the solid height less than Z.

Sometimes the designer's limitations are two sided. For example, it may be necessary to select appropriate values for directly controlled parameters (wire diameter, outside diameter, number of coils) such that another variable (such as spring rate or length at a given load) is exactly equal to a specified value.

Material properties are another good example of a designer's limitations. If massless, infinitely strong materials were available at negligible cost, spring design would be relatively easy. Because the range of available materials is limited and the spring properties just get better as the material properties improve, ODOP:Spring implements material properties as Calculation Inputs rather than as Independent Variables to be searched over. If material properties were allowed to vary during the search, the program would always select the strongest material that it could find.

In summary, the essential challenge of spring design is to take what is known about the problem and select values for the independent variables that achieve the required performance. If available materials will not deliver this performance, it is necessary to make some compromises. ODOP:Spring provides tools to assist in the process of making those compromises, but the ultimate responsibility for the design rests with the designer.

Each of the spring type specific sections presents a Force-Deflection Diagram. Most of a spring design problem can be stated in terms of those diagrams. New users need to understand the diagram and understand the names that ODOP:Spring uses in order to specify a design problem.

The vertical axis in each diagram is force. The horizontal axis is distance; either deflection or spring length. The force-deflection relationship of a cylindric coil spring of uniform pitch (refer to Restrictions ) is linear. The slope of the line is the spring Rate measured in force per unit deflection.

ODOP:Spring produces information about four points on the force-deflection curve. As described in the What To Do If section (below), specifying both force and deflection for any two points will completely specify the force-deflection line. Any additional specification on Rate or one of the other points will over-specify the problem. Unless the redundant specification is exactly in line with the other values, the conflict will keep ODOP:Spring from finding a feasible solution. Consistent specification of constraints and FIX values is the responsibility of the ODOP:Spring user.

ODOP:Spring can use a table of material properties to determine permissible stress levels for various commonly used spring materials. This process is described in greater detail in the section below titled MATERIALS. The included table of material properties contains values for tensile strength at two wire diameters, (.010 inch and .400 inch) plus conversion factors to produce estimates of allowable stresses for both static and cyclic (endurance) applications. The allowable shear stresses (Stress_Lim_Endur and Stress_Lim_Stat) are calculated from the tabulated values of tensile strength and the conversion factors (%_Tensile_Endur and %_Tensile_Stat) for each new wire diameter.

Because allowable stresses change for each new wire diameter considered, ODOP:Spring works in terms of a "factor of safety". A factor of safety may be described as measuring "how much better the design is than it HAS to be". Specifically, factor of safety is allowable stress divided by actual stress. For example, if a spring is made of wire that has an allowable stress of 100,000 psi, when that spring supports a load that generates 50,000 psi of stress, the factor of safety is 2.00.

The factor of safety concept applies to both static loads and cycle life. The calculation of FS_CycleLife includes the material's endurance limit (Stress_Lim_Endur), static load and fluctuating component of stress in a calculation originally developed by Soderberg. Additional information on this calculation is available in the sources listed in Spring Design References.

Additional discussion on these topics is available in the sections below on Factor Of Safety and Cycle Life.

Selection of materials from the ODOP:Spring materials table is covered below in the Materials section and in the tutorial.

The interpretation of a "good" spring design depends strongly on the intended application. It is possible that some applications will require a spring to operate at stress levels that would make it totally unsuitable for other, only slightly different applications.

The Report tabs present crucial information about the performance of a design in a specialized, compact format.

In general, a finished design should not have significant remaining constraint violations. In particular, L_2 below L_Solid in a compression spring is a sign of problems that need to be resolved.

The force-deflection characteristics of a coil spring are approximately linear in the range of 20 to 80 % of available deflection. Outside this range, effects of end coils and non-uniform coil pitch influence the accuracy of analytical predictions.

For compression springs, the Report tabs will produce an informational message any time that more than 80 % of available deflection (%_Avail_Deflect) is used at the second load point. Note that the default start point ("Startup") supplied with ODOP:Spring has %_Avail_Deflect constrained to be less than 90.0 per cent. Thus in the "as supplied" condition, ODOP:Spring will frequently select designs that produce this informational message.

The factor of safety at point 2 should be greater than 1.0. Some specialized compression spring applications may require a factor of safety less than 1.0 in the solid condition. There is risk that a spring may "set" and not return to its original free length if deflected beyond a factor of safety of 1.0.

If minimum weight is desired, the spring needs to operate at relatively high stresses. Unless the design of a compression spring is constrained by rate or solid height considerations, the factor of safety at point 2, solid and cycle life should all be close to 1.0. If a long cycle life is not necessary, the FS_CycleLife may actually be less than 1.0. A minimum weight design should have the value of %_Avail_Deflect close to the maximum value for allowable for the application.

If low risk of failure or a long cycle life is desired, the spring should operate at relatively low stresses. The spring should have factors of safety, including FS_CycleLife, that are significantly greater than 1.0.

If a compression spring is intended for operation without lateral support it should have a ratio of free length to coil diameter (Slenderness) below approximately 4 to avoid buckling. Lateral support is usually provided by operation in a sleeve or over a post. The constraint Slenderness MAX can be used to restrict the search to designs that will not tend to buckle. Note that the value of Slenderness is not constrained in the default start point ("Startup") and thus the search may produce designs that are prone to buckling. The compression spring REPORT 1 tab will provide an indication as to the possibility of bucking for your specific design and loading condition.

Please review the discussion in the Restrictions section of the documentation to insure that you apply ODOP:Spring appropriately. The design equations in the current release of ODOP:Spring do NOT cover all possible spring applications.

More precise treatments of this subject are available in the sources listed in the Spring Design References section of the documentation.

A typical spring design process should start by entering what is known about the problem. As described in more detail in the Introduction section of the documentation, any time after starting ODOP:Spring and reaching the main page, a complete spring design is already defined. Use the numeric entry fields plus FIX checkboxes to alter that existing design to reflect what is known about the problem at hand.

Entries on the View menu can be used to examine the current state of the design.
Look at the main page multi-colored Feasibility Indicator
and bold red or orange values to understand which constraints are violated.
Use the **Action : Search** menu item
to have ODOP:Spring select values for the free Independent Variables that reduce
(and hopefully eliminate) constraint violations thus achieving a feasible design.

Typically, the process of designing a completely new spring should start
with (at least) Wire_Dia and Coils_T in free status.
Once a feasible design is established,
the **Action : Select Size** menu item can be used to select
the nearest standard wire size from the appropriate standard sizes table.
After the selection, an additional search should be executed to
adjust values of the remaining Independent Variables to compensate for
the change in Wire_Dia.

Additional information on operating techniques is presented in the documentation sections Introduction, Getting Started and Select Size and Select Catalog. The demo and tutorial sessions supplied with ODOP:Spring provide detailed commentary on how to solve a variety of problems. The tutorial section named guidedDesign is specifically constructed to support appropriate solution techniques.

ODOP:Spring contains many kinds of names. Menu item names are discussed individually in menus. Names for Independent Variables, Dependent Variables, Calculation Inputs and Constraints are discussed in this section and in the specific sections covering compression, extension and torsion springs.

In general, the names are constructed for consistency and to have common prefixes. Names frequently have multiple words, or abbreviations hooked together with the underscore (_) character. For example, the free length is named L_Free to be consistent with other length names (L_Solid, L_1, and L_2).

The names for Independent Variables, Dependent Variables, Calculation Inputs and Properties are defined in the initialState.js file. Name changes in this file carry forward to all future designs based on it.

The force deflection diagrams contained in the specific spring type sections may assist understanding of this discussion of spring names. Additional information is contained in the Spring basics section above.

ODOP:Spring produces information about four points on a spring's force - deflection curve. The information includes length, deflection, force, outside diameter, inside diameter, stress and static factor of safety. This information is listed in a compact format by the Reports. The equations assume that the spring will operate between two load points, named 1 and 2, somewhere in the spring's elastic region. It is entirely possible for point 1 to correspond with the spring's free state, or for a compression spring, point 2 can correspond to the spring's solid condition. In fact, because the force-deflection equations don't know anything about the spring's solid condition, point 2 can be set to represent an impossible situation requiring the spring to be compressed beyond solid. In this situation, the constraint on %_Avail_Deflect will be violated. The search feature will attempt to resolve the conflict.

For specifics on names associated with each spring type, see:

While most of ODOP:Spring constraints are obvious, a few need a bit of additional explanation. The following section covers constraints that are established in the default start point ("Startup").

Checkboxes and numeric entry fields may be used to establish additional constraints on any variable, dependent or independent. Unchecking a checkbox will eliminate any constraints, including the default constraints, established by the default start point ("Startup"). Further information is available in the Spring basics section above and in the NAMES sections of each of the specific spring types and in Terminology.

L_Stroke MIN is a lower constraint on L_Stroke, the length difference between point 1 and point 2. Refer to the force-deflection diagram in the documentation section for each specific spring type for an illustration of L_Stroke.

ID_Free MIN is established by the default start point ("Startup") because it discourages the search from investigating designs with a zero or negative inside diameter, and there by encountering numerical difficulties.

FS_2 MIN and FS_2 MAX work together to keep the design in a reasonable range of working stress. FS_2 MIN works to keep the design from being overstressed. FS_2 MAX works to keep the design from being understressed and overweight.

FS_CycleLife is the factor of safety produced by the Soderberg cycle life calculation. If a design has FS_CycleLife greater than 1.0, then the combination of average stress and the fluctuating component of stress for that design is reasonably small compared to the endurance limit. In this situation, an application cycling between point 1 and point 2 may expect a life that exceeds the value selected for Life_Category. Remember that the endurance limit will vary as a function of the material selected, the surface treatment (shot peening), and the selected cycle life.

As described in the documentation section on Cycle Life below, ODOP:Spring is capable of directly calculating Cycle_Life only for materials contained in the materials table. The FS_CycleLife variable is the only way of gaging cycle life for user defined material properties (Prop_Calc_Method = 2 and 3).

FS_CycleLife MIN is a lower constraint level associated with FS_CycleLife. A value less than 1.0 will permit designs that risk failure in high cycle applications.

For additional information about Prop_Calc_Method, see: Spring Materials and Material Properties and Advanced Spring Operations.

```
allowable stress
Factor of Safety = ------------------
actual stress
```

Factor of Safety may be interpreted as: "How much better this design is than it HAS to be."

In other words, the Factor of Safety is a measure of how much stronger a system is than it needs to be for an intended load.

**Example:**

A design with a factor of safety of 2.0 has stresses that are half of the
allowable stresses and thus "it is twice as good as it HAS to be".

ODOP:Spring works in terms of a "factor of safety" because allowable stresses change for each new wire diameter considered. If specific stress limits are imposed on a design, it is not possible to automatically adjust to higher allowable stresses whenever smaller wire diameters are considered by the Search process. Because many spring design professionals are accustomed to designing to specific stress limits, ODOP:Spring also permits a Design to Stress approach.

The factor of safety concept applies to both static loads and cycle life. The calculation of FS_CycleLife includes the material's endurance limit (Stress_Lim_Endur), plus static and fluctuating components of stress in a calculation originally developed by Soderberg. Stress_Lim_Endur is normally determined by the materials table and the user's selection of cycle life and surface treatment (shot peening) with Life_Category. Additional information on the cycle life calculation is available in the documentation sections for the specific spring types and also in the resources listed in Spring Design References.

Refer to additional discussion in the sections titled Spring basics (above), Names (above and specific spring type sections) and Cycle Life (below). Selection of materials (and corresponding material properties) from the ODOP:Spring materials table is covered in the Materials section (next, below) and in the Tutorial.

See also: https://en.wikipedia.org/wiki/Factor_of_safety

Refer to: Materials

The current version of the ODOP:Spring program implements six spring end types for compression springs and five different end types for extension springs. In addition, the user can define specialized end conditions. These end types are represented by the Calculation Input End_Type which has the following possible values:

Compression | Extension | |||
---|---|---|---|---|

1 | OPEN | 1 | FULL_LOOP | |

2 | OPEN&GROUND | 2 | 75%_LOOP | |

3 | CLOSED | 3 | FULL_HOOK | |

4 | CLOSED&GROUND | 4 | 75%_HOOK | |

5 | TAPERED_C&G | 5 | CLOSE_WOUND_COIL | |

6 | PIG-TAIL | |||

7 | USER_SPECIFIED | 6 | USER_SPECIFIED |

For a compression spring, the end type directly impacts calculation of Inactive_Coils. L_Solid, pitch and other variables are affected indirectly. For an extension spring, the end type directly impacts calculation of Hook_Deflect_All, End_ID, Extended_End_ID, L_End and L_Extended_End. Other variables are impacted indirectly.

More detail on how to handle end types is provided in the documentation sections on the specific spring types:

Additional information on spring end types is available in the resources listed in Spring Design References.

This section presents a discussion of cycle life considerations and describes the Soderberg calculation and the ODOP:Spring interpretation of FS_CycleLife. A discussion of hook stresses in extension springs appears in the Extension Spring section.

ODOP:Spring provides two different approaches to the cycle life issue. For materials contained in the materials table (Prop_Calc_Method=1), ODOP:Spring will calculate cycle life directly. This calculation is based on the "modified Goodman method". Note that the value produced by this calculation applies only to body coils and is only approximate. It is useful in comparing the relative effect of different loading conditions, or relative performance of different designs, but you should expect results in practice to vary widely from the cycle life value predicted.

For more information, see: Goodman relation

For materials not contained in the materials table (Prop_Calc_Method=2 or 3), ODOP:Spring does not have enough information available to directly calculate cycle life and so the Cycle_Life variable is set to zero. In this case, the FS_CycleLife variable described here can be used to get some indication of a design's life in a specific cyclic application.

Use the Calculation Input Life_Category to select one of eight possible combinations of "cycle life conditions" and surface treatments (shot peening) expected in the application of the spring being designed. The selection is used to determine a value for %_Tensile_Endur from the materials table which then is applied to the interpolated value of tensile strength for that material and wire diameter to produce a value for the material's endurance limit (Stress_Lim_Endur).

As illustrated in the tutorial section TUTOR4, the default start point ("Startup") supplied with ODOP:Spring does not provide default constraints for Cycle_Life or FS_CycleLife. Simply designating a Life_Category is not enough to have ODOP:Spring search for designs with a long cycle life. To have ODOP:Spring search for designs with a long cycle life, alter constraint values such as:

```
CHANGE Cycle_Life MIN nnnnnn
CHANGE FS_CycleLife MIN 1.0
```

FS_CycleLife is the factor of safety produced in a calculation originally developed by Soderberg. The calculation of FS_CycleLife includes the material's endurance limit (Stress_Lim_Endur), plus static and fluctuating components of stress.

If a design has FS_CycleLife greater than 1.0, then the combination of average stress and the fluctuating component of stress for that design is reasonably small compared to the endurance limit. A life that exceeds the value selected in Life_Category may be expected in an application cycling between point 1 and point 2.

Remember that the endurance limit will vary as a function of the material selected, the surface treatment (shot peening), and the selected cycle life category.

Additional information on the cycle life calculation is available in tutorial session TUTOR4, in the documentation on the specific spring types and also in the resources listed in Spring Design References.

This section is intended to anticipate some of the more common user problems and suggest solutions.

Check for an over specified problem. Considering that coil springs of uniform pitch and cylindric shape have a linear relationship between force and deflection, specifying both force and deflection at any two points will determine the spring constant. An additional "fix" on Rate or an active L_Stroke MIN constraint will then cause the problem to be over specified and it may be impossible to find any set of independent variables that will not violate the constraints. There are numerous ways to over specify the problem. Have you found one ?

If it is violated, are you really concerned about buckling ? The feasible region will be substantially greater if you are willing to accept a spring that would buckle without additional support.

If either is violated, are you really concerned about fatigue life ? The feasible region will be somewhat larger if you are willing to accept a spring that does not have a great cycle life.

The FS_2 MAX constraint is intended to prevent the search from stopping at an overly conservative design. However in some cases, particularly where force and deflection are specified at two points, it is not possible to find a feasible solution without increasing the value of FS_2 MAX. If you find that your design violates FS_2 MAX in addition to other constraints, and you are willing to accept a more conservative design, increase the value of FS_2 MAX or disable the constraint entirely.

Confirm that you have executed a Search after establishing the FIX.
Use of the Search menu item is always necessary to find the appropriate
values of the independent variables so that the dependent variables take
on their FIXed values.
You may wish to review material contained in the documentation sections
Introduction, and
Terminology.
In the case that one or more constraints are also violated,
Search will find a compromise between violations of the constraints and
failure to achieve the desired value for FIXed state variables.
The nature of this compromise is influenced the values of the internal
variables **(File : Preferences)** FIX_WT, CON_WT, and ZERO_WT.

If you can repeat the problem, please report it. Follow the procedures provided at Contact Us.

ODOP:Spring is constantly undergoing improvement. In spite of years of field experience with the underlying solution techniques and a considerable amount of testing and verification, there is always a possibility of error. Please review the Restrictions section of documentation. Review the material properties. Check the inconsistency with another design method (hand calculator, spreadsheet calculation, etc.). If the problem remains unresolved, please report it. Follow the procedures provided at Contact Us.

Refer to: Spring Design References

Refer to: Restrictions