Helical Compression Spring Design and Special Considerations
In determining the proper compression spring design the designer usually has a few known details. Load, movement, and space allowed are the factors generally known at the start of the design process.
There is also a pretty good idea as to how the spring is to be installed. What type of bearing surface the spring will be on or the method of holding the spring in place.
Considering all the above, let's now look at the methodology of proper compression spring design.
In a helical compression spring design the deflection is proportional to the load. This is the same as most other springs. This means that the load/deflection curve is basically a straight line as you can see in the sketch.
When you hear the term index in relation to springs it means the ratio of the mean diameter of the spring to the diameter of the wire. The preferred index range is 4 to 12.
If it is less than 4 the spring may be too difficult to make and too highly stressed. If it is more than 12 the spring becomes too flimsy, tangles easily, and the coils may slip over one another as it gets compressed to solid.
The larger the index the greater the deflection in comparison to the solid height.
The wire in a helical compression spring design is stressed in torsion. There are bending stresses also, but they can be ignored
except when the pitch angle is over 10 degrees.
The Wahl factors, which compensate for the stress concentration at the inner diameter of the coiled wire, are used here for ALL stress calculations on helical compression designs and extension spring designs.
is the formula for stress. When computing the 2% stress point or fatigue of a spring, use of the Wahl correction factor, Kw1, will give you the most accurate prediction.
The chart above also shows the factor Kw2 which includes the increment in stress resulting from direct shear but does not include curvature effects. This factor should be used instead of Kw1 when looking for the maximum stress with all set out.
Number of Coils or Turns
Spring rate is inversely proportional to the number of active coils. We suggest that the designer always specify the number of coils as a reference number. This is because, in most instances, the spring manufacturer will have to vary the number of coils to meet the other print requirements.
The number of active coils should not be less than two. Though, I personally have had to manufacture parts with less than two active coils. This is the exception.
The ends of the spring can be closed or open(see diagram at top of this page). If closed ends are specified for the design then that means there must be at least two inactive coils. The closed ends can be ground (to provide more bearing surface) or just closed and squared.
closed and ground closed and square
This is the length of the spring when all the coils are compressed and touching each other. On ground end springs the nominal solid height is the total number of coils times the wire diameter. On springs with closed ends only the solid height is the total number of coils times the wire diameter, plus one extra wire diameter.
If your compression spring design calls for plating or some type of coating, keep in mind this will increase the solid height.
Solid height should be specified as a maximum dimension. It should NOT be the same as the calculated nominal solid height. This is especially true when the wire size is under 0.100 inch and their are many coils.
It is a good practice to just add a half wire diameter to your calculation. With larger wire sizes and fewer coils this allowance can be decreased.
This is the length over all of the spring in the fully unloaded position (free position). If their is no load specified in the compression spring design then you should call out a free length tolerance on the print.
If loads are specified, then the free length should be a reference dimension. This allows the spring manufacturer to vary the free length to meet the load requirements.
Direction of Coiling
A helical compression spring can be specified as either left hand or right hand. If you do not specify on the print which hand , then the spring may be coiled either way.
If springs are nested, they must be coiled in opposite directions. If a spring works over a screw thread, it shoud be coiled opposite to the thread direction.
left hand wound right hand wound
Use of Square or Rectangular Wire
Most compression springs are made of round wire. The use of wire other than round in a compression spring design should be avoided because of added cost and problems with availability. However, when space for the spring application is limited and solid height restraints are extreme, the use of square or rectangular material permits greater energy storage in less space.
Note that square or rectangular wire "keystones" in coiling in accordance with the formula given. This axial dimension increase must be accounted for in the solid height calculations. You could also purchase special-section "keystone" wire that will compensate for the keystone deformation and wind up rectangular in shape after coiling.
The load for compression springs made from rectangular wire can be calculated from the formulas given and the chart below on the Wahl stress correction factor, KE. Dimension b is the longer side of the rectangle and t is the shorter side. Orientation of the wire in the spring has no effect since the wire is stressed in torsion.
The torsional stresses are calculated from the formulas given where K1 is given in the chart below. KE and KF stress concentration factors are given in the two additonal charts.
- D = mean diamter(OD minus wire diameter)
- C = spring index D/d where d = wire diameter
- P = load
- f = deflection
- G = shear modulus, or modulus of rigidity, psi
- N = number of active coils
- S = stress, psi
Stress Correction Factor KF
When building your compression spring design clearance must be allowed to permit free functioning of a compression spring that operates in a hole or over a rod. This clearance needs to be approximately 10% of the spring's diameter. If the deflection range is great, the maximum diameter increase from loading needs to be considered.
If the free length of your compression spring design is more than four times the mean diameter then stability in deflection will become a problem. In these cases the spring needs to be guided, either in a tube or over a rod. This will minimize buckling, but friction against the tube or rod then becomes a problem. This friction will affect load readings. This is especially true in long springs with a small diameter.
The curves in the chart below show the limit of deflection that can be expected without objectionable buckling. This chart assumes the ends of the free spring are practically square with the axis, and the load is axial.
Curve A indicates the buckling will occur with values above and to the right of the line. This is for squared and ground springs with one end on a flat surface and the other end free to tip.
Curve B indicates that buckling may occur for a squared and ground spring, both ends of which are compressed against parallel plates, if the values fall above and to the right of the curve. This is the most common condition.
For cases where extremely long travel is required compared to the spring diameter it is a good idea, if possible, to use a combination of several individual springs end-to-end with guides between the springs to avoid binding and buckling.
Some Compression Spring Design Hints
Stress depends upon the volume of material in the spring within a given load and deflection. If you can increase the volume of material in your spring you will decrease the stress level. You can do this in several ways -
- Increase the number of active coils
- Increase the wire size
- Increase the outside diameter
- Use a rectangular wire or nested springs
Here is a great page that will explain more about stress -
Designing for Choice of Operating Stress
The ratio of total deflection to solid height depends upon the index (mean diameter divided by wire diameter). The larger the index the greater the deflection in comparison to the solid height.
The size of a spring depends on the work required. Graphically, this is the area under the load/deflection curve. Algebraically this is 1/2 x load x deflection. The amount of work and the size of the spring can be decreased by reducing either load or deflection.
The clearance between L2(the second load height) and Ls(solid height) should be about 10% of f2(travel from free length to the second load height). This will avoid the non-linear load region near the solid height.
Now, before you get started, here is a good simple work sheet to put your thoughts on before working up that design, or asking someone else to quote you a spring for your application.
Compression Spring Pre-Design Work Sheet
Now it's time to go our page on "Compression Spring Design Techniques". This will give you some hands on applications of everything discussed above. You'll also see a handy logic diagram for use in future design work.
Before finalizing any design you must read this page on "Design for Manufacture and Assembly". This page is full of handy charts and gives an insight into the manufacturing problems and added cost due to thinking only of application, not manufacture or assembly.
If you want another perspective on compression spring design that takes a more technical view you can go to the "Department of Mechanical and Materials Engineering The University of Western Australia ". These are notes for their mechanical engineer design class.
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