The Physics of Diaphragm Springs - …

1 1 Table of contentspageDiaphragm Springs - General2 Standard Disc Springs or Belleville Springs5 Properties of HAUSSERMANN Diaphragm Springs7 Increasing Load or Deflection with Springs of Given Dimensions7 Design of Diaphragm spring Supports,and Centering8 Hysteresis9 Set in Diaphragm Springs9 Dynamic Loading of Diaphragm Springs9 Torque Transmission with Diaphragm Springs10 Applications of Special Diaphragm Springs10 Summary of the Properties of HAUSSERMANN Special Diaphragm Springs13 The Physics of Diaphragm Springs 2 Note: All dimensions shown in the following charts are given in millimeters (mm) and Newton (N). 1 mm = in. 1 N = daN = 0,22 IbfExample: A Diaphragm spring having 200 mm outside diameter (De), 160 mminside diameter (Di), and mm thickness,would be labelled: Diaphragm spring 200 x 160 x spring force characteristics No other spring type has load-deflectioncharacteristics as adjustable as the dia-phragm spring .

2 Such a spring may have alinear characteristic, a progressive character-istic obtained by proper superimposition, adepressive characteristic, or even a negativecharacteristic. This unique performancemakes this spring a very flexible element ofmachine design, and unequalled by any 1: Nomenclature of Diaphragm springsDiaphragm Springs - GeneralSymbols and nomenclature De= Outside diametermmDi= Inside diametermmt= Thickness of individual springmmho= free cone height of the unloaded individual springmmlo= Overall height of the individual springmmlo= ho+ tF= spring forceNs= DeflectionmmDeflection slinearDeflection sprogressiveDeflection sdegressive-progressiveDeflection sdegressive-horizontal-progressiveDeflec tion sdegressive-negative-progressiveFig.

3 2: Various spring characteristics (diagrammatic) spring force FSpring force FSpring force FSpring force FSpring force F 3 Dependence of spring Characteristic on the ho/t Ratio The spring characteristic is varied withinwide limits by altering the ratio of freecone height ho to thickness t. In fig. 3,height ho has been varied for a given constant thickness t, and in fig. 4 thick-ness t has been varied for a given constantho. The point of inflection occurs whenthe spring is flattened out, and in figs. 3and 4, it is at the intersection of the bro-ken line with the spring characteristic. Both figures are based on a 200 x 160 x spring . Fig. 5 again demonstrates the effect ofthe ho/t ratio upon the spring characte-ristics.

4 Here, however, the spring force Fhas been referred to the free height ho. For any given Diaphragm spring , the fami-ly of curves will supply the applicable ho/tfrom the shape of the desired characteris-tic curve. Example: A Diaphragm spring is supposedto exert a maximum force of about times the force applied in the flatte-ned out position. Read off: ho/t = 2. Or: At what spring deflection will a Diaphragm spring with ho/t = 2 have itsminimum pressure? Find s = ho. Fig. 4: Outline of characteristic as a function of ho/t,where ho= constantho/t = 2= will give a partly horizontal pressure curve; ho/t > 2= will yield a pronounced maximum and minimumforce, with a negative springrate between the maximumand the > 8= will make the springstagnate in the minimumposition, which means that aforce opposite to the originalone must be present in orderto return the spring to its original 3: Outline of characteristic as a function of ho/t, where t = constant 4 Fig.

5 5: Family of characteristics of the Diaphragm spring , with variable ho/t 5 Characteristics of spring Combinations Parallel stacking of Springs will multiplythe individual spring forces, while seriesstacking will multiply the individual de-flections. In the latter case, the maximumdeflection is reached when the individualsprings become suitably combining a number ofsprings (Fig. 7) stacks having a progressivecharacteristic can be obtained. DIN Standard Disc Springs This series is established by DINS pecification 2093, and is supplementedFig. 6: Characteristics of different spring combinations (diagrammatic, disregarding friction)Fig. 7: spring combinations with progressive characteristics (diagrammatic, disregarding friction) spring force FDeflection sSpring force FDeflection sby products of various manufacturers.

6 Theoutside diameters are from 8 to 250 the A series , the ho/t ratio is , forthe B series , ho/t is about , and forthe C series ho/t is approximately Properties 1. Large spring forces with small deflec-tions, hence "stiff" Designed to be depressed no furtherthan the flattening-out point. Actually,the available deflection should notexceed ho, since the spring rollsoff the support, which means a conti-nuous reduction of leverage and hencea disproportionate increase in springforce (Fig. 8). Since the deflection obtainable from anindividual spring is usually insufficient, aseries arrangement must be considered. The spring force is increased by stackingdiscs in parallel; see Diaphragm Springs -General. 6 Properties of Stacked Disc Springs 1.

7 Great forces correspond to large axialand small radial extension of the ele-ments employed. 2. Considerable damping (due to friction),Fig. 8: Dimensions and spring characteristic of a B 90 DIN 2093 Standard disc springespecially for parallel stacking, bywhich friction increases progressivelywith a larger number of discs. Frictionoccurs mainly between the discs andalong the guide rod in the on the number of discs andtheir arrangement, the spring forces are modified by the effects of frictionwhich gives a hysteresis effect (see fig. 9). Fig. 9: Influence of friction (damping) upon the spring characteristics of two sets of parallel andseries stacked spring combinations.( Springs B 90 DIN series 2093) 7 The use of standard disc Springs islimited by: 1.

8 spring characteristics. All standardsprings have a more or less stiff performance. Horizontal or negativecharacteristics are not available. 2. Deflection. This is relatively small andfor single Springs limited to a maximumof ho. To obtain larger deflections, series stacking is required. This demandsmore space and introduces friction. 3. Damping. The friction in a parallel sta-cked spring prevents accurate maintai-nence of specified load characteristics. 4. Fatigue strength. This will reduce consi-derably for more than six series stackedsprings and for parallel arrangements. HAUSSERMANN Special Diaphragm Springs Compared with standard disc Springs ,HAUSSERMANN special Diaphragm Springs have the following properties: 1.

9 Sizes and proportions may be selected at will; we can supply any desired configuration. 2. Any desired spring characteristic may be obtained. 3. The deflection may be extended sincethe spring may be depressed beyond itsflat condition (see Fig. 10), and by theprovision of fingers. Thus a stacking ofsprings can be avoided in most cases. 4. There is no increase in friction (or indamping) and it is easier to obtain relatively exact adherence to a specified force-deflection curve. 5. Excellent fatigue strength even fordynamical loading far beyond flatdependent on the individual springdesign. Increasing Load or Deflection withSprings of Given Dimensions Increasing the spring Force ThroughParallel Stacking From Fig.

10 6 it will be noted that the spring force can be doubled, tripled, means of parallel stacking. To reduce friction between the Springs , the surfacesmay be lubricated. Also, the Springs maybe separated by spacers, such as wirerings, and thus the friction will not bemuch more significant than in the case of single Springs . Fig. 10: Function of a Diaphragm springwith extended deflection range. Fig. 11: Increasing the spring force byparallel stacking Increasing spring Force and ReducingDeflection by Decreasing the Leverageof the spring Support If the leverage between the loading ringand the supporting ring is reduced, thespring force will increase by Kf = DE DIDEF DIFThe deflection is reduced by Ks = 1 KfFig.