Due to the relatively simple geometrical shape the complexity of disc springs in production and application is very often underrated. There are possibilities for mistakes in outlining a disc spring solution, which inevitably cause faulty design or even failures later on. Then it is very difficult to find better substitutes, because most of the times the installation space is fixed.
With a correct design these problems are easy to avoid. The main difficulty is to realise these in the design stage to get an optimum disc spring solution.
Since for most of the designers the disc spring is not daily bread and to many the rules for disc spring design are little known, the most important aspects are summarised here.
Spring Force
The calculation of the force of a disc spring is based on a model by Almen and Laszlo. Its accuracy in the usable range of the character line of the spring is very good. Yet there is a slow rise at the beginning of the measured load/reflection curve, because disc springs never are perfectly symmetrical. They so to speak have to be pressed even. Also the spring force rises in the last part of the load/deflection curve more than calculated, when the spring is loaded in between two parallel planes, since the leverage changes due to the never ideally even surfaces.
Static Loading
In the design of a new disc spring a certain stress level should not be surpassed for static loading. The maximum allowable limit is given by the reference stress σom. Its value should not exceed the value of the tensile strength Rm of the material to avoid plastic deformations of the spring, i.e. setting losses.
Dynamic Loading
Most of the disc springs only can bear a limited dynamic load. The life time depends on the load span as well as on the load level. The number of cycles, which is to be expected under a certain load condition, can be estimated from fatigue diagrams. It is also necessary to reload disc springs in a dynamic application to at least 15% to 20% of their maximum deflection, to avoid compression-tension alternating stresses in the beginning of the deflection range of the spring.
Stacking
Disc springs can be stacked “face to face” (series arrangement), which means their deflections add up, or they can be stacked in the same sense (parallel arrangement), then their forces add up. The latter induces increased friction and a stronger hysteresis effect. Thus the force in loading direction is higher and in unloading direction lower than the calculated force. Applying suitable lubrication (MoS2 containing grease) can reduce the hysteresis effect. The various possibilities of stacking disc springs can be combined in a stack. Different types of stacking in one spring stack can be used to generate a progressive character line. It is necessary to pay attention to the weaker parts in a combined stacking though, because these normally are pressed flat quite fast, which is not allowed in dynamic loading. If necessary a deflection limitation has to be provided.
Guide
The surface of guide elements is dynamic disc spring applications always has to be harder than the disc springs themselves. A minimum of 55 HRC is advisable, otherwise the surfaces can be damaged. This again causes uneven movement during the deflection of the spring. The characteristics will be changed and even fatigue cracks can occur. Wrong guide clearance also can change the dynamics of loading in a detrimental way.
Stack Length
Friction and other influences make a spring stack move unevenly. It deflects more on the side of the loading. This effect usually can be neglected for a “normal” spring stack, but not for long stacks. Therefore the length of a spring stack should not exceed three times the value of the outer diameter. If it is longer, the stack can be stabilised by dividing it with guide washers, which as a rule of thumb should have a thickness of at least one and a half times the guide diameter.
Material
The best material for disc springs is standard spring steel. It is always used as long as there are no particular circumstances, which may necessitate a special material. In general special materials have a lower tensile strength and most of the times a different Young’s modulus compared to the standard spring steels. Therefore springs out of these materials generally cannot be designed with the same free height, which means that the spring forces are lower.
Temperature
The different materials have different temperature ranges. Too high temperatures may have a tempering offset, which again results in a loss of force and, in extreme cases, in plastic deformation (setting losses).
Corrosion
Disc springs can be protected against corrosion either by suitable coatings or by using corrosion resistant materials. Such materials are only available in a limited variety of thicknesses. Also almost all high alloy steels may show stress corrosion cracking at high working stresses.
Hydrogen Embrittlement
During the application of certain chemical or electrochemical processes (such as galvanic coating) hydrogen can get in to the material and can cause delayed brittle fractures. This cannot be avoided entirely by thermal treatment. Thus processes, which do not bear this risk, are to be preferred.
The value ho/t determines the amount of curvature of the spring characteristics (figure 3). For ho/t < 0.4, thecharacteristics is almost linear, as the value ho/t increases, the curve becomes more regressive. At ho/t = √2 the curve has a nearly horizontal segment (at s = ho it has a horizontal tangent). This means that springs can be developed with an almost horizontal characteristic, which gives very little load increase with deflection. However, this type of spring with ho/t > 1.3 is not suitable for long spring stacks, as individual springs within the stack may move unevenly and be overloaded. As a result, such springs should only be used alone.
Figure 3 – click to enlarge
From the dependence of the characteristic curvature from the ratio ho/t, follows that the characteristic curve of disc springs of the same dimensions changes when they are formed to a different height. Conversely, at the same height ho, a thinner disc will have a more regressive characteristic curve than a thicker disc (figure 8).
Figure 8 – Click to enlarge
On the other hand, the force of the flattened disc spring increases linearly. If, for example, a spring calculation cannot predict this in a satisfactory manner, then a first step in the form of a change in the free height may already produce the desired load/deflection diagram. Here, however, the permissible stress must be observed, as these increase with increasing cone height ho.
At ho/t > √2, the spring force reaches a maximum and then decreases again. In some cases the decreasing segment of the curve is utilised. Under certain conditions the spring must be loaded beyond the flat position, for which certain design conditions must be given (figure 9).
Figure 9 – Click to enlarge
For the normal arrangement of disc springs a progressive increase in the spring force occurs at deflections of s > 0.75 ho which deviates from the calculated value. This results from the shift in the load points to smaller lever arms, because the disc springs roll on each other or on the abutments. Therefore, it is recommended that only approx. 75 to 80% of the spring deflection is utilised. For this reason, the spring force is only indicated at s ≈ 0.75 ho in DIN (figure 10).
Figure 10 – Click to enlarge
Diagram for spring 45 x 22.4 x 1.75 mm, lo = 3.05 mm
Example 2: Disc spring with a high ho/t ration
Given:
Guide diameter 30mm
Installed length l1 = 4,9mm
Preload F1 = N min.
Working defl. s2 – s1 = 1.05mm
Spring load F2 = N max.
Required:
Suitable disc spring dimensions
Solution:
Spring inside diameter Di = 30.5mm
Spring outside diameter De = 60mm (selected because of the favourable De/Di ratio)
Because of the very small load range and the small installed length only a spring with a high ho/t ratio is suitable.
Selected:
Disc spring 60 x 30.5 x 1.5mm (figure 13); lo = 3.5mm ho/t = 1.333; δ = 1.967
Calculation:
First the factors are calculated using formula 3, 4 and 5:
K1 = 0.688
K2 = 1.212
K3 = 1.365
Figure 13 – click to enlarge
Disc spring 60 x 30.5 x 1.5 mm
The stress σOM can be checked using formula 9: σOM = - N/mm2.
This value lies well under the limit of - N/mm2, the spring will therefore not set. Now the spring loads can be calculated to formula 8a, preferably for the 4 deflections s = 0.25 ho, s = 0.5 ho, s = 0.75 ho and s = ho.
One obtains the following values:
s/ho s[mm] F[N]
0.25 0.5
0.5 1.0
0.75 1.5
1.0 2.0
With these 4 points the spring diagram can be drawn.
Figure 14 – Click to enlarge
Diagram for spring 60 x 30.5 x 1.5 mm, lo = 3.5 mm
One can read F1 = N s1 = 1.05mm
and for F2 = N s2 = 1.61mm
Deflection s2 – s1= 0.56mm
The deflection of a single spring is not sufficient, therefore two in series must be used.
This arrangement gives:
Unloaded length Lo=7.0mm
Preloaded length L1=4.90mm
Preloaded deflection s1=2.1mm
Preload F1=N
Deflection s2=s1+1.05=3.15mm
Final load F2=N
To check the fatigue life we must use the stresses at s1 = 1.05 and s2 = 1.575mm. Figure 17 shows that point lll is the dominant one, this gives:
s1: σu = 843 N/mm2
s2: σu = N/mm2
By utilising the fatigue life diagram in figure 19 we can see that the expected life will be in the order of 1,000,000 cycles.
Example 3: Calculation of a disc spring with contact flats
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Disc spring 200 x 82 x 12mm; lo = 16.6mm
Ho = 4.6mm; δ = 2.439; ho/t = 0.383
Required:
The spring characteristics and the stresses σll and σlll.
Although this spring is to our works standard we show below how the calculations are made and results can be checked in the disc springs dimension tables.
From the formula 3 to 5 we first calculate the constants K1 to K3:
K1 = 0.755
K2 = 1.315
K3 = 1.541
The static design can be checked by the calculation of σOM, the reduced thickness is not considered and we use the values of t and ho. This gives:
σOM = - N/mm2
As the acceptable value for σOM is N/mm2, the spring is correct. From figure 6 and considering d and ho/t the reduction factor t’/t can be obtained:
t’/t = 0.958
Therefore t’ = 11.5mm and ho’ = 5.1mm. Constant K4 can be calculated from formula 6: K4 = 1..
Figure 15 – Click to enlarge
Disc spring 200 x 82 x 12 mm
Figure 16 – click to enlarge
Spring force and stresses for spring 200 x 82 x 12 mm, t’ = 11.5 l0 = 6.6 mm
Now from formula 8b, 11 and 12 the spring force and both stresses can be calculated.
s/ho s[mm] F[N]
σll
[N/mm2]
σlll
[N/mm2]
0.25 1.15 416 389
0.5 2.3 890 747
0.75 3.45
1.0 4.6
With this spring the greater values of stress are on the inner diameter which should be used. Finally the value of the stress σOM for the reduced thickness can be checked:
σOM’ = σOM . K4 . t’/t
σOM’ = - N/mm2
In practice the presence of corrosive media is no common and the forms of attack so numerous that it is not possible to deal with the entire problem in detail here. It can only be established here that ordinary spring steel must offer no corrosion protection of their own. Therefore, disc springs of these types of steel must be protected again:
Phosphating
This is a standard process generally applied to all low alloy steels unless otherwise agreed. A zinc phosphate layer is produced on the surface, which is then impregnated with corrosion-protection oil. The protection achieved in this way is sufficient in the vast majority of all cases. Primarily for inside applications, but also out of doors, if the springs are installed with weather protection, no additional protection is required.
According to DIN , the designation for phosphate treatment is: Surface coating as per DIN Fe/Znph r10 f.
Browning
This process simply produces an oxidised surface, which is then coated with a corrosion-resistant oil. The corrosion resistance is not as good as phosphating, therefore this treatment is mostly used where a phosphate coating or its abrasion is a problem.
DIN defines browning as follows: Surface coating as per DIN Fe/A f.
Metal Surface Treatment
Zinc is by far the most commonly used coating metal. As it lies lower than steel in the electrochemical series at room temperature, it forms a so-called cathodic protection and is attacked first by corrosion. With a chromated surface the onset of corrosion can be significantly delayed. The most effective in yellow chromating, which should always be chosen over clear chromating.
Cadmium also offers very good corrosion protection, but is only rarely used now for environmental protection reasons.
Nickel is resistant to a large number of media and is frequently used as a coating metal. It is placed higher than steel in the electrochemical series, i.e. in the cases of the formation of a local element (e.g. at a damaged point in the nickel coating) nickel acts as a cathode and the base metal is attacked. For this reason the nickel must always be a dense, non-porous coating.
Electroplating
With electroplating virtually any metal can be precipitated as a surface coating. However, when treating high-tensile steels – such as those always used for disc springs and lock washers – the danger of hydrogen embrittlement cannot be excluded with the current state of technology. Post plating bake is also no guarantee that this risk is completely eliminated. Therefore, we only use electroplating if it is specified as mandatory or there is no other alternative.
Designation of a galvanically produced 8µm thick zinc coating with transparent chromating is: Surface coating as per DIN Fe/Zn 8 cB.
Mechanical or Peen Plating
With this process the parts to be treated are moved in a barrel together with peening bodies e.g. glass beads, and a so-called promoter and the coating metal (preferably zinc) is added in powdered form. This powder is deposited on the surface and is compacted by the peening bodies. An even, mat coating results, which can then be cremated like a galvanic coating. The usual layer thickness is 8µm, however thicknesses up to 40µm are possible. It is of particular importance that no hydrogen embrittlement can occur when the process is carried out properly.
Designation of a mechanically applied 8mm thick zinc coating with yellow chromating is: Surface coating mech Zn 8 cC.
Metal Spray
This treatment is primarily for disc springs with diameter above 150mm which cannot be mechanically zinc plated. As a rule, sprayed zinc coatings are relatively thick and have a granular surface which also makes them excellently suited as a base for paints. However, the adhesion in inferior to mechanical zinc coating and it may become delaminated during dynamic loading.
Chemical Nickel Plating
With this treatment, also known as ‘electro-less nickeling’, a nickel-phosphor alloy is precipitated onto the surface with a chemical method. This results in a thick, hard layer with sharp contours and outstanding corrosive and abrasion resistance. The coating is usually applied in layers with a thickness of 15-30µm.
Dacromet Coating
This is an inorganic silver-grey metallic coating of zinc and aluminium flakes in a chromatic compound. The parts are treated in a barrel or on racks and the coating then baked on at over 280oC. Dacromet-treated springs exhibit excellent resistance in a salt spray test. With the usual processing technology there is no possibility of hydrogen embrittlement.
Special requirements such as corrosive or high temperature environments often require the use of materials designed for these applications. These materials, in general, have lower tensile strength than standard materials and should only be, if absolutely necessary. These springs have a lower overall height than comparable sizes made of standard materials resulting in lower spring force. This must be taken into consideration using these materials.
Corrosion Resistant Steels
X 10 CrNi 18-8 (1.): This chrome nickel alloyed steel as per DIN EN is the material most used for corrosion resistant springs. Because of its austenitic structure with ferritic inclusions, it cannot be hardened in the usual way, but by cold forming it can obtain the strength required for disc springs. Considerable cold forming in necessary and the strength reduces with increasing thickness. Therefore, the material is normally not available thicker than 2.5mm. In fact, springs can only be supplied to this thickness. Whereas the material in the soft condition is hardly magnetic, the cold working process will make it more or less magnetic again, making it unsuitable for completely non-magnetic springs.
X 7 CrNiAI 17 7 (1.): This steel as per DIN EN precipitation hardened produces an austenitic/ferritic structure. It will also be processed in the work hardened condition and may be hardened by subsequent heat treatment. A disadvantage compared to steel 1. is the lower corrosion resistance and sensitivity to stress corrosion. We therefore only recommend its use for springs over 2.5mm thickness if no other material is available.
X 5 CrNiMo 17 12 1 (1.): The strength of this material is somewhat less than either of the two forgoing. Not withstanding that it offers higher corrosion resistance and lowest magnetism. Although also contained in DIN , it is often difficult to obtain and therefore only seldom used.
Steels for Higher Temperatures
When considering springs for use at higher working temperatures it must be remembered that both tensile strength and Young’s modulus ‘E’ are reduced compared with the values at room temperature.
X 22 CrMoV 12 1 (1.): This heat treatable chrome-molybdenum steel has been used very successfully for heat resistant disc springs. Springs of 1.5 to 6mm thickness are made from strip or plate. For thicker springs, forged rings can be used.
Figure 38 shows the mechanical properties and Young’s modulus ‘E’ with respect to temperature. It should be noted that with a chrome content of 12% this steel is not corrosion resistant.
Figure 38 – click to enlarge
X 39 CrMo 17 1 (1.): Here we have a chrome-molybdenum alloyed heat treatable martensitic steel which is also suitable for corrosion resistant springs. Because of the molybdenum is may be used up to 400oC. However, at these temperatures both the tensile strength and ‘E’ are reduced.
In order to achieve the required properties, this steel must be hardened to higher values which raises the question of stress corrosion. Unfortunately, in the light of current technical knowledge we cannot completely discount the possibility of delayed brittle fracture.
Copper Alloys
Copper alloys are absolutely non-magnetic and have very good electric conductivity. Moreover, they are corrosion-resistant against many media. These characteristics make them suitable for many disc spring applications.
CuSn 8 (2.): Tin bronze as per DIN EN is an alloy of copper and tin, which obtains is spring properties from cold working. The tensile strength is certainly lower than spring steel and the ‘E’ modulus is only 55% of the value for steel. This must be considered in the spring calculation and allows their use in applications where very low spring loads are required.
CuBe 2 (2.): Beryllium copper is an outstanding spring material. This heat treatable alloy has strength values comparable with steel. However, Young’s modulus ‘E’ is only 60% of that for steel. It has very good corrosion resistance and may be used at very low temperatures nearing absolute zero.
Nickel and Cobalt Alloys
From the large number of nickel-chrome and nickel-chrome-cobalt based alloys some have achieved importance for disc springs. By alloying the aluminium, titanium and/or niobium/tantalum they are precipitation hardenable. These materials are very tough, that is to say they have high strength and a low elastic ration. Therefore, the probability of more set in the spring must be considered. Against this are the outstanding fatigue properties. With correct spring proportions this is good over the total spring travel. Because of the material composition they have outstanding corrosion resistant to many media. All these alloys are very expensive and often hard to work, and as a rule have long deliveries. They are therefore only used where no other material is suitable due to technical considerations.
NiCr 20 Co 18 Ti (Nimonic 90) (2., 2.): These nickel-chrome-cobalt alloy gives the least problems in processing and is therefore the most often used. It has very good heat resistance and can be used up to 700oC with suitable dimensioning.
NiCr 15 Fe 7 TiAi (Inconel X 750) (2.) and NiCr 19 NbMo (Inconel 718) (2.): These nickel-chrome alloys are practically cobalt-free, and are therefore used in reactor applications. The hardening process is difficult and expensive. The application is limited and only used in special cases. NIMONIC and INCONEL are trade names of Inco Alloys International.
DURATHERM 600: This is a heat treatable alloy of the cobalt-nickel series with outstanding mechanical properties. At a temperature of 0oC the material in non-magnetic. It can be used at very high temperatures (600oC and over). The very high price of this alloy limits its use to very special applications. DURATHERM is a trade name of Vacuumschmelze GmbH in Hanau.
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