Advanced Spring Design: Special Cases and Resolutions
This page discusses advanced spring design techniques for many cases that we do not discuss on our other design pages. What we will talk about here is how applications, environments, and other factors can effect the performance of the spring. These factors must be looked at to create a spring that will meet the performance expectations needed.
Advanced Spring Design: Dynamic Loading-Impact
To begin our look let’s take a spring that is to provide an accelerating force or to absorb shock and decelerate a load. The following formulas are applicable to helical extension and compression springs.
For a load with impact (or final) velocity “v”
k = spring rate, lb./in.
g = gravitational constant (386.4 in. per sec.2
f = deflection, in.
P = load. lb.
v = velocity, in/sec.
Ws = spring weight, lb.
vm = maximum velocity
va = actual velocity
These formulas assume that the spring is weightless. Take note when the ratio of the weight of the load to the spring weight drops to 4. Then the energy involved in accelerating the spring mass becomes appreciable and must be taken into account. Assume that all the moving mass of the spring is concentrated at the moving end of the spring. Then the above formulas can be corrected by using the term, (P + Ws
/3), instead of P, where Ws
is the spring weight in pounds.
If the advanced spring design calls for increasing acceleration, larger springs are needed to deliver the needed energy. When the load/spring weight ratio drops below 1, the spring is heavier than the load. The limiting factor is not the energy stored, but the rate at which it can propagate. The velocity of wave propagation is related to the speed of sound in the spring material. This is a factor of the density and modulus and not a factor of spring dimensions. Also, this velocity is stress limited. The ultimate attainable velocity is determined:
S = stress, psi
G = shear modulus, or modulus of rigidity, psi
= density, lb. per in.3
This reduces to vm = S/131 in./sec. for steel.
The significance of this formula is that a natural “velocity barrier” exists for all spring materials – for steel at about 1,380 in./sec. It is not related to spring size or dimension. A very heavy spring would accelerate a large rock or a small pebble to the same ultimate velocity. This is because the mass of the spring, not the mass of the load, limits the velocity.
In our discussion on advanced spring design this factor is important where the ratio of load/spring weight is below 1. The graph here facilitates design in this region. The maximum attainable velocity, based on the design stress, is given as a ratio to the maximum velocity of an unloaded spring for different load/spring ratios.
Advanced Spring Design: Stranded Wire Springs
Long springs with many coils subjected to high rates of load applications, as in automatic weapons, encounter shock-wave motion or displacement of spring coils. The spring can be literally torn apart. Stranded wire springs are often the solution to such problems. This is because of the frictional resistance set up by the selective movement between strands.
The helix of the spring must be opposite in direction to the helix of the strands. This will allow the strands to bind together when the spring is compressed. This type compression spring may be wound with 2, 3, or more strands. If 4 or more strands are wound then a center wire core is used for stability. The ends on all these type springs should be soldered, brazed, or welded to prevent unraveling.
The stranded wire spring can be considered as single wire springs arranged in parallel. The spring rate derived on this basis is given by
k = Kn(Gd4/8D3N)lb./in.
K = correction factor
n = number of strands
d = wire diameter
D = mean diameter (OD – d)
For a 3 strand spring, K = 1.05.
An approximate formula for torsional stress in each wire of the strand is given:
S = (8PD/
The maximum allowable stress should not exceed a range of 55 to 60% of tensile strength of the material after set is taken out.
Assume ds is the wire diameter of a stranded wire spring. Assume d is the wire diameter in a single wire spring of the same mean diameter D and spring rate k as the stranded wire spring. The maximum stress in a single wire of the stranded wire spring will be smaller than the stress in a single wire spring. Therefore, if the number of strands
=2, then ds>0.79d
=3, then ds>0.69d
=4, then ds>0.63d
Advanced Spring Design: Dynamic Loading-Resonance
Resonance or surge of cyclically loaded springs occurs when the operating frequency is near the natural period of vibration of the spring or one of its multiples. This resonance can increase individual coil deflection and stress to levels considerably above the calculated stress at maximum deflection. It can also cause spring “bounce” and resultant loads much lower than calculated at minimum deflection. To avoid this resonance, the fundamental frequency of the spring should be at least 13 times the operating frequency.
The following formulas for natural frequency of vibration apply to helical springs:
1) Compression spring (both ends fixed)
n = 13,900d/ND2 cps for steel
2) Extension spring (one end fixed)
n = 6950d/ND2 cps for steel
3) Torsion spring (fixed at both ends)
n = 16,080(d/D2N) cps for steel
4) Torsion spring (one end free)
n = 8040(d/D2N) cps for steel
n = vibrations per second of spring vibrating between its own ends.
Advanced Spring Design: Dynamic loading-Vibration Damping and Isolation
A spring must utilize some energy absorbing method to stop the vibration if it can not be designed completely free of resonant frequency effects, or if it is to serve as a vibration damping device. Keep this in mind in your advanced spring design. The methods normally used are friction devices in which the spring rubs against another element like an internal dampener coil, an arbor or housing, or another portion of the spring.
If the exciting force is at a single frequency, the spring can usually be designed to a variable frequency by using variable pitch in the coils. This will give it a band of resonant frequencies rather than a single sharp peak.
In vibration isolation system the essential characteristic is that the natural frequency of the spring-mass system be as far as possible from the disturbing frequency. The filtering of disturbing forces may be calculated as-
% of force transmitted = (1/(nD/n)2 - 1*) x 100
*If nD/n is less than 1, change denominator to 1-(nD/n)2
nD is the frequency of the disturbing force
n is the natural frequency of the spring mass system
Note that the frequency n in this formula is the frequency of the spring mass system and not the natural frequency of the spring. Actually, the most commonly used formula neglects the spring weight and is only deflection dependent.
The general equation is
Advanced Spring Design: Springs in Combination
Because of space limitation some advanced spring designs use springs in combination. Combinations may be more efficient than a single spring. Spring combinations may also have a load/deflection curve or dynamic characteristics not possible in a single spring.
When two or more springs are used in parallel, the total load is equal to the sum of the loads of the individual springs. The total deflection is the same as the deflection of the individual springs. The total gradient is the sum of the individual gradients.
When two or more springs are assembled in series, the deflection is the sum of the deflections of the individual springs. The load remains the same as the load on the individual springs. The total gradient is the reciprocal of the sum of the reciprocals of the individual springs.
Nested compression springs are a special variety of springs in parallel. This style is useful when a heavy load must be carried in a restricted space, and a single spring design would be overstressed. Note that nested springs are not applicable if the available space is so restricted that a single spring design would have an index of 5 or less.
The following criteria apply to nested springs:
- The springs should be wound alternately left and right hand to prevent intermeshing.
- Clearance between springs must be at least twice the diameter tolerance.
- Load distribution between inner and outer springs varies with the index and the clearance between springs. The first trial should be a load distribution of 1/3 to the inner spring and 2/3 to the outer spring.
- Solid height and free height of each spring should be nearly the same.
- The above steps will result in all springs with the same approximate index.
Advanced Spring Design of High Precision Springs-Rate Linearity
Some springs have a rate that is constant over the entire usable range of deflection. For example, a helical extension spring has an essentially constant rate after the initial tension has been exceeded and before the yield point is reached. A torsion spring exhibits a constant rate within the elastic range. The decrease of diameter as the spring winds down on an arbor is compensated for by the increased number of coils. In both examples, minor deviations from a straight line rate may be caused by loop or end deflection, or arbor friction.
Some additonal concepts to consider in your advanced spring design are the following-
The load/deflection curve of a helical compression spring deviates from a straight line chiefly because of changes in the number of active coils as the spring deflects. If one or both ends are slightly open, the gradient will be lower as the spring starts to deflect. As the deflection continues, the gradient increases. This becomes very pronounced as the length approaches the solid height. In critical applications this effect can be eliminated by an insert which fixes the termination of the active coils, or the end coils can be soldered or brazed together.
Some springs are designed with a non-constant rate – like conical springs and volute springs. Because their rate continues to increase with deflection, they are useful in shock absorbing applications.
A feature desirable in counter-balance springs and springs used in seals is to have a rate close to zero. Belleville spring washers of special configurations, constant force springs, and buckling columns also have a rate close to zero.
You can achieve a snap through action if you choose a part with a decreasing or negative rate for your advanced spring design. Belleville springs can be designed with a decreasing rate over a given deflection range. Buckling flat springs that will snap through are also an application of negative rate.
A motor spring torque output decreases with each turn. The rate of change depends upon the advance spring design and manufacturing technique. A constant force spring motor can have a torque output that is nearly constant over the useful range of the spring.
Note that if the rate must be constant with temperature changes you must use constant modulus alloys like Ni Span C 902. Their span of constant spring rate is normally from approximately -50oF to +150oF. They also show improved control over a larger temperature span.
Advanced Spring Design: Adjustability of Rate
These sketches show several different methods that have been used to adjust the rate of helical springs by altering the number of active coils.
Control of Load at a Given Position
Accurate load control at a given position depends upon:
- The spring dimensions and properties
- Stability in service
Initially a manufacturing technique must be used that will achieve very close tolerance values. Also, you must create a design so that it will neither take a set nor gain load in service.
The designer should consult the spring maker in his advanced spring design since safe stress levels depend upon-
- The spring material
- The service environment
For example, age hardening spring materials like beryllium copper, 17-7 PH, and Ni Span C 902 are often used in instrument applications.
Advanced Spring Design: Hysteresis
Hysteresis occurs when there are frictional losses in the spring support system and the measuring system. It is shown by the deviation between the loading and unloading curves of a spring. The spring material itself appears to account for almost no energy loss due to internal friction. Spring systems such as stacked belleville washers and torsion springs with high initial tension show marked hysteresis. Properly designed extension, compression, or open wound torsion springs show little or no hysteresis.
HERE ARE SOME ADDITONAL DESIGN PAGES THAT MAY BE OF INTEREST TO YOU-
The Basics of Compression Spring Design
Additonal Compression Spring Design Techniques
The Basics of Torsion Spring Design
Additional Torsion Spring Design Techniques
The Basics of Extension Spring Design
You may also refer to our design pages on Volute Springs, Flat Springs, Torsion Bars, Spiral and Power Springs, Constant Force Springs, Garter Springs, Garage Door Springs, Box Springs, and Leaf Springs.
We also have an extensive section devoted to Spring Washers and Belleville Springs.
HERE ARE ADDITONAL REFERENCE PAGES FULL OF VALUABLE INFO
Operating Stress In Spring Designs
Design For Manufacture and Assembly
Effect of Temperature of Environment
Hot Wound Springs Design Characteristics
Design Considerations for Economy
Stay tuned for updated information related to advanced spring design of compression springs, extension springs, torsion springs, and flat springs. Our team and visitors to spring-makers-resource.net will be contributing.
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