Handbook forDisc Springs2Please refer any questions to:Schnorr Corporation4355 Varsity Drive Suite AAnn Arbor, MI 48108Phone734-677-2683Fax734-975-0408eMail: sales@schnorr.comInternet: http://www.schnorr.com Adolf Schnorr GmbH + Co. KG 2003All rights reserved. Reprinting, in full or part, is only possi ble with express per mis si on and ack now led ge ment of the source.Compiled by Dipl.-Ing. (FH) Eberhard Fromm and Ing. (grad.) Wolfgang Kleiner.We reserve the right to make technical changes wi t hout no tice. All information is published to the best of our knowledge and has been checked with great care. However, we can accept no respon si bi li ty for errors or omis si ons. We reserve the right to supp ly fea tures other than those specied.Art.-No. 900 507 / 04.03Production: Hela Werbung, Heilbronn 3Theoretical basisThispartcontainsthetheoreticalbasisfor thecal cu la ti onanddesignofdiscsprings. You only need to consult chapter 12 if you yours elf are specifying a special spring size or wish to analyse an existing spring with re gard to load and stress.Practical use of disc springsThispartanswersquestionsresultingfrom the prac ti cal use of disc springs. It is best to select a disc spring by consulting the tables in chapter 9.12345678910 Firm grip for boltsby SCHNORR-Serrated Safety Washers(Rib washers) and SCHNORR HDS Load WashersBasic Calculation p. 13with ExamplesDesign and Operation Limitsp. 29Possible Combinations p. 35Manufacture p. 41Tolerancesp. 49Application p. 55Materialsp. 65Special Types p. 77Dimensional Tablesp. 81Security Elements for p. 137Bolted ConnectionsSupplement p. 149Introductionp. 54ForewordSCHNORR has now manufactured Disc Springs for over 60 years. This period has been marked by extraordinary technical develop-mentsandDiscSpringshavefoundmanynewandimportant applications due to their special characteristics and advantages.In order to meet customer requirements, SCHNORR has con stant ly raised the quality of its products and researched solutions to cus-tomer problems. Looking back, the development of the SCHNORR Handbook for Disc Springs, which had its origin in the 1930s, is a mirror of SCHNORRs endeavours. The 1942 issue, 60 years ago, already contained characteristic diagrams for 21 standard springs as well as application and installation standards and in struc tions for empirically based spring calculations. Each new issue revised the technical content to conform to the state of the art.SCHNORR would like to acknowledge and thank all of its col- leagues at the Technical Universities of Braunschweig and Darmstadt for their suggestions and developments in the eld of disc springs. Their continued collaboration will ensure that the SCHNORR Hand- book continues to be the source of technical advise on Disc Springs, as it has been for many decades.Dieter Jentsch, Manager Adolf Schnorr GmbH + Co. KG5IntroductionA spring stack can con sist of either single springs orparallel spring sets. Disc springs areavailableeitherwithorwithoutcontact ats.A disc spring is a conical shell which can be loadedalongitsaxiseitherstaticallyor dynamical ly. The loads arenormally applied to the upper inner edge and the lower outer edge.Eitherasinglespringorastackof springs can be used.The Story of the Disc SpringAlthough the disc spring has found a wider application during the last few decades, it is still an old established machine component. The original inventor is not known, but more than130yearsago(on26.12.1861tobe precise) Julien Francois Belleville of Dunkirk wasgrantedFrenchPatentNumber52399 for a spring design which already contained theprincipleofthediscspring.Theim- portance this invention achieved is un known, butthefactthateventodayFranceandthe Anglo Saxon countries still speak of Belle- vil le Springs infers a broad dissemination of thisorsimilarsprings.Todaythistendsto denote a disc spring of inferior quality, which stillreectsthenotalwayssatisfactoryde- sign and function of springs at that time. This isnowonderconsideringthatinthelast century neither the theoretical conditions for calculations nor the necessary materials for manufacture were available.Notuntil1917didFr.Duboisdevelopthe theoryonwhichthecalculationofthedisc springisbasedinhisdissertationThe Strength of the Conical Shell [1] at the ETH in Zurich. However, it still took several de ca des until this was adopted in practice. For a long time disc springs continued to be cal cu la ted if at all in accordance with the theory of theatperforatedplate.Thenin1936two Americans,AlmenandLszl,publisheda sim pli edmethodofcalculation[2]whichal-lowed a quick and practically correct me thod for calcu lating disc springs.Asthesetwodocuments substantiate,SCHNORR wasandissubstancially involvedinthede velop -ment of disc springs.194019956IntroductionFeatures of the Disc SpringComparedwithothertypesofsprings,the discspringhasanumberofadvantageous properties, of which the following should be named:1.Verylargeloadscanbesup por ted with a small in stal la ti on space.2.Dependingonthedimensionalrela-tionships, its spring cha rac te ri stic can be designed to be linear or re gres si ve and with a sui ta ble ar ran ge ment also progressive.3.Due to the nearly unlimited number of possiblecombinationsofindi vi du al disc springs, the characteristic cur ve and the column length can be further varied within additional li mits.4.High service life under dynamic load if the spring is properly di men sio ned.5.Providedthepermissiblestressis notexceeded,noimpermissiblere -laxa ti on occurs.6.Withsuitablearrangement,alarge damping effect may be achieved.7.Stockkeepingisminimised,asthe individualspringsizescanbecom-bined universally.8.Because the springs are of an annular shape,forcetransmissionisabso lutely concentric.Onthebasisoftheseexcellentpro per ties, the disc spring has been adopted in nearly all areasoftechnologyduringthelastseveral decades.In the meantime, the disc spring had been introdu ced into nu merous are as of techno l- ogy.Star tingwithap pli ca ti onsinthecon -struc tionofcuttingandpressworktools, wherethediscspringises peciallyad van -tage ousbecauseofthelargenum berof variations possible with the same spring size, new applications were quickly found in ma chi ne, en gi ne and mo tor vehicle manufac-ture.Tech no lo gi calde velop mentisoftenad- van ced rapidly in time of war. The disc spring wasnoex cep ti onanditsspreadingwas stronglypro mo tedbytheSecondWorldWar. For example, its excellent damping char-acteristicswithmultipleparallellayerswere utilised for the suspension of artillery breech- es.Calculationmethodsandmaterialtech- no lo gy were further developed. After the war the conditions were created for the in tro duc-tion of the disc spring into all areas of tech- no lo gy.AdolfSchnorr,whohadfoundedame- cha ni cal workshop in 1908, already began to ex pe ri ment with the disc spring in the 1920s. He needed high-quality springs for precision tools,withwhichhehadmadehimselfa name, and had come across the disc spring afteralongsearch.Ashewasunableto procure them anywhere, he went about pro- du cingthesespringshimself.Initiallyhe producedonlyforhisownneeds,butthe demandhadalreadyincreasedsogreatlyby theearly1930sthathedecidedtogiveup toolmakingforcustomersanddevotehim-selfentirelytothemanufactureofthe SCHNORRSpring.Fromthattimeon SCHNORRhasmanufactureddiscsprings and continually opened up new appli cations withitsmanydomesticandforeigncus-tomers.7Checklist for disc spring designDue to the relatively simple geometrical shape the complexity of disc springs in pro duc tion andapplicationisveryoftenun der ra ted. There are possibilities for mistakes in out- lining a disc spring solution, which in e vi tab ly cause faulty design or even failures later on. Then it is very difcult to nd better sub sti- tu tes, because most of the times the in stal -la ti on space is xed.With a correct design these problems are easy to avoid. The main difculty is to realize 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 summarized here.Spring forceThe calculation of the force of a disc spring is based on a model by Almen and Lszl. Its accuracy in the usable range of the character line of the spring is very good. Yet there is a slowriseatthebeginningofthemeasured load/deectioncurve,becausediscsprings never are perfectly symmetrical. They so to speakhavetobepressedeven.Alsothe spring force rises in the last part of the load/deectioncurvemorethancalculated,when thespringisloadedinbetweentwoparallel planes, since the leverage changes due to the never ideally even surfaces (see chapter 1.7).Static loadingIn the design of a new disc spring a certain stresslevelshouldnotbesurpassedfor static loading. The maximum allowable limit is given by the reference stress om. Its value shouldnotexceedthevalueofthetensile strengthRmofthematerialtoavoidplastic deformations of the spring, i.e. set ting losses (chapter 2.1).Dynamic loadingMostofthediscspringsonlycanbeara limited dynamic load. The life time depends on the load span as well as on the load level (chapter 2.2). The number of cycles, which is to be expected under a certain load con di ti on, canbeestimatedfromfatiguediagrams (chap ter2.2andchapterdiagrams).Itis alsonecessarytopreloaddiscspringsina dynamic application to at least 15% to 20% of their maximum deflection, to avoid com- pres si on-tension alternating stresses in the beginning of the deection range of the spring (chapter 2.2).StackingDisc springs can be stacked face to face (seriesarrangement),whichmeanstheir deections add up, or they can be stacked in the same sense (parallel arrangement), then theirforcesaddup(chapter3).Thelatter inducesincreasedfrictionandastronger hysteresis effect (chapter 6.5). Thus the for ce inloadingdirectionishigherandinun-loading direction lower than the calculated for ce.Applyingsuitablelubrication(MoS2 con tainig grease) can reduce the hysteresis ef fect. The various possibilities of stacking discspringscanbecombinedinastack. Differenttypesofstackinginonespring 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 at qui te fast, which is not allowed in dy na mic loading. If necessary a deection li mi ta ti on has to be provided.GuideThesurfaceofguideelementsindynamic discspringapplicationsalwayshastobe harderthanthediscspringsthemselves.A minimum of 55 HRC is advisable, otherwise 8thesurfacescanbedamaged.Thisagain causes uneven movement during the de ec -tion of the spring. The characteristics will be changed and even fatigue cracks can occur (chapter6.4).Wrongguideclearancealso canchangethedynamicsofloadingina detrimental way (chapter 6.3).Stack lengthFriction and other inuences make a spring stack move unevenly. It deects more on the side of the loading. This effect usually can be neglectedforanormalspringstack,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 stabilized by dividing it with guidewashers,whichasaruleofthumb should have a thickness of at least one and a half times the guide diameter (chapter 6.1).MaterialThe best material for disc springs is standard springsteel.Itisalwaysusedaslongas there are no particular circumstances, which maynecessitateaspecialmaterial.Ingen-eralspe ci almaterialshavealowertensile strengthandmostofthetimesadifferent Youngs mo du lus compared to the standard spring steels. Therefore springs out of these ma te ri als ge ne ral ly cannot be designed with the same free height, which means that the spring forces are lower (chapter 7).TemperatureThedifferentmaterialshavedifferenttem-per ature ranges (see table chapter 7.4). Too hightemperaturesmayhaveatempering offset, which again results in a loss of force and, in extreme cases, in plastic deformation (set ting losses).CorrosionDisc springs can be protected against cor ro -si on either by suitable coatings or by using corrosion resistant materials. Such ma te ri -als are only available in a limited variety of thicknesses (table chapter 7.4). Also almost all high alloy steels may show stress cor ro- si on cracking at high working stresses.Hydrogen embrittlementDuring the application of certain chemical or electrochemical processes (such as galvanic coating) hydrogen can get into the material and can cause delayed brittle fractures. This cannot be avoided entirely by thermal tre at -ment.Thusprocesses,whichdonotbear this risk, are to be preferred.Introduction9In addition to springs as per the dimensions contained in DIN 2093, we manufacture many morespringsizesinaccordancewithour works standard, for which we also applythe quality regulations of DIN 2093. These also includethespringsoftheZserieswith dimensionsininchesandtheKseries intended for the special purpose of preload-ingballbearings.Thetechnicaldataforall these springs of standard spring steel can be found in the tables in chapter 9.Besides these, we also supply many disc springsinspecialsizesfrom3.0mmto 1000.0 mm in diameter and up to a thickness of 80.0 mm of spring steel and all technically possible special materials. Such springs of -Standards for Disc SpringsFor disc springs the following 2 standards are applicable: DIN2092 Disc Springs, calculationand DIN2093 Disc Springs, dimensions and quality specications.Neweditionsofbothoftheseappearedin January 1992. These standards are go verning ourproductionandarealsobasicforthe pre sentSCHNORRHandbookforDisc Springs. DIN2092coversthestandardcalcula-tionsba sedonapaperbyJ.O.Almenand A. Lszl [2] which has been proven in prac- tice for many years.It has been mo di ed in the last few years to include disc springs with contact ats. DIN 2093 contains 3 dimensional series fordiscspringsdifferentiatedbyouterdi-ameter, thickness and h0/t ratio. It also con- tainscomprehensivequalityrequirements fortype,dimensions,material,permissible stress, permissible set, gui de clearance and thetestingofdiscsprings.Detailsofthese re qui re mentscanbefoundinchapter2 and 4 7. The SCHNORR Production Pro gram meDisk Springs from the SCHNORR Product Range10fer the advantage of being optimally ad ap ted to the respective require ments. Howe ver, in each individual case the practicality of pro -duc tionmustbeexamined,andthenal decision always remains ours. We recommend you contact our Tech ni- cal Consulting Service in the design stage, whenwewillgladlyofferourknowledge, experience and resources in the calculation and design of disc springs. From section Features of the Disc Spring it can also be seen that the cha rac te ri stics of the disc spring are also ex cellently suited for locking screw. We have de veloped our Ori gi -nal SCHNORR Serrated Safety Washers for thispur po se.Thesearedetailedinchapter 10 to gether with Load Washers as per DIN 6796.Introduction11Diagram of a Disc SpringFigure 1Singlespring,cross-sectionandpositionofrefe rence pointsSymbols Unit DesignationDe mm Outside diameter Dimm Inside diameterDw mm Diameter at the root of slots in a disc springD0 mm Diameter of centre of rotationE N/mm2Youngs modulusF N Spring force of a single spring F1, F2, F3N Spring force for deectionss1, s2, s3 FcN Calculated spring force of a single spring when at Fges N Spring force of a spring set or stack FN Force lost in setting K1,K2,K3,K4Constants for calculations (see chapter 1) L0 mm Unloaded length of the spring stack or spring sets L1, L2, L3 mm Length of the loaded spring stack or spring setfor forces F1, F2, F3 Lc mm Calculated length of the spring stack or setwhen springs are at NNumber of cycles to failure RN/mmSpring rate W Nmm Spring worka) without contact ats b) with contact atsSymbols and Units12Symbols Unit Designationh0 mm Cone height of an unloaded single spring (calculated h0 = l0 t) h0 mm Cone height of an unloaded spring with reduced thickness t(and contact ats, cal cu la ted h0 = l0 t) iNo. of single springs or sets in series in a stackl0mm Height of an un loaded sin gle springn No. of parallel springs in a sets mm Deection of a sin gle springs1, s2, s3mm Deections relative to loads F1, F2, F3 sges mm Deection of a spring set or stack tmm Thickness of individual t mm Reduced spring thick ness for springs with contact ats(group 3) wM, wRFriction factors = De/Di Diameter ratio Poisson's ratio (for spring steel = 0.3)N/mm2Calculated stress OM, I, II,N/mm2Calculated stress at pointsIII, IVOM, I, II, III and IV as per gure 1 o N/mm2Calculated maximum stress for springswith dynamic loadsu N/mm2Calculated minimum stress for springswith dynamic loadsh N/mm2Stress range for the working strokeof dynamically loaded springs O N/mm2Maximum stress for fatigue resistanceU N/mm2Minimum stress for fatigue resistanceH = O U N/mm2Permissible stress range for fatigue resistanceIntroduction131 ChapterBasic Calculation14Basic Calculation1.1Calculation for a Single Spring........................................................... 151.2Equations for Calculations................................................................ 15 Characteristics.......................................................................................................... 15 Spring Force............................................................................................................... 16 Stress Calculations..................................................................................................... 17 Spring Rate ................................................................................................................ 17 Spring Work............................................................................................................... 181.3Disc Springs without Contact Flats...................................................... 181.4Disc Springs with Contact Flats and Reduced Thickness............................ 191.5Disc Springs of Special Materials........................................................ 211.6Spring Parameters for Dimensions and Calculation................................... 211.7Characteristics of a Single Spring ........................................................ 221.8Calculation Examples ....................................................................... 24151.21.1Therotationofthecrosssectionistherea- son for the various stresses and the spring effect. ThecalculationsassumethatYoungs mo du lus E remains linear for the material, the spring cross-section is rectangular with sharp corners and the spring remains in one plane during deection. The load is applied at points I and III.There is residual stress in the springafterbeingmanufacturedandheat treated and can be ignored.Equations for CalculationsThese are valid for all disc springs: Characteristics ThecalculationsofAlmenandLszlas- sume that a spring ank rotates arround a cen t re of rotation during deection, placed in the centre of the spring ank at diameter D0.Calculation for a Single SpringAlthough today there are more accurate methods of calculation [10] [12] [13], there is no reason to abandon the simple and conve- nientformulasofDIN2092.Forstandard di men si ons they pro du ce values which cor- re spond well to the mea su red results.Figure 2Position of the centre of rotation and point OM 1Formula1DD DD De ie i0 ln /D De i/K1211112

|('`JJ+ lnK2611

lnlnK33 1

lnFormula 2Formula 3Formula 4Formula 5with Cttltttlttt120 014345838

|('`JJ +|('`JJ +|('`JJ'''KC CC41 1222 2 +|('`JJ+Formula 616Spring ForceYoungs modulus E is virtually in de pen dent oftheheattreatmentconditionandtensile strength of the material.For steel springs with dimensions in ac- cor dan ce with DIN 2093, formula 7 provides values which correspond closely to the meas-ured values. The limitations and extent of this are explained in greater detail in chapter 1.Theforceofadiscspringdoesnotin-creaselinearlywiththedeection,butis always regres sively curved. Its pitch, i.e. the rate,decreaseswithincreasingstroke.The rateofcurvatureisdeterminedexclusively by the ratio h0/t, as can be seen in gure 3. See also chapter 1.Formula 7For disc springs manufactured to group 3 with contact ats and reduced thickness, t and h0 must be used (h0 = l0 t): For disc springs manufactured to group 1 and 2 (chapter 4) K4 = 1: Formula 8aFE tK DKstKhtsthtste

|('`JJ|('`JJ +

]]]41 21241242420 0 Figure 3Spring characteristic cur ve with respect to ho/t and s/hoFormula 8bFEtK DK stKhtsthtst0 0

|('`JJ|('`JJ+

]]]41 21241 e24242'''' ''' 'F =EtK D sthtsthtsto o41 21241 e2|('`JJ|('`JJ +

]]]]]Basic Calculation17Stress CalculationsFormula 9Formula 10Formula 11Formula 12Formula 13Here also applies to spring steel. Positive values aretensilestressandne ga ti vevaluesare compressivestress.Itisim portanttore-Spring Rate ThroughdifferentiationofthespringloadF inaccordancewiththedeections,thefol- lo wing formula is obtained for spring rate R: Thespringratebetweenanytwoadjacent points, F1, s1 and F2, s2 can be approximated by means of the following simple formula: mem ber that this the calculated stress is a nominalvalueandthattheactualstressis conside rably lower, as it is consi derab ly in -u enced by the ever-present in ter nal stress.Formula 14 OMeE tK DKst 41322124 leE tK DKstK KhtstK|('`JJ +

]]]41 222124 4 203 lleE tK DKstK KhtstK|('`JJ

]]]41 222124 4 203 ( ) llleE tK DKstK K KhtstK |('`JJ

]]]4112222124 4 2 303 ( ) lVeE tK DKstK K KhtstK |('`JJ +

]]]4112222124 4 2 303 RdFdsE tK DK Khthtstste |('`JJ +|('`JJ||||||||| +

]]]]413321231242420202 Formula 15RF Fs s

2 12 1141905 49522ENmm

/181.3Foralimitedareaofapplicationitcanbe integratedbetweenthetwodeectionss1 and s2.For disc springs without contact ats K4 = 1 and h0 = l0 t. This applies to all disc springs in pro duction groups 1 and 2 (see chapter 2), i.e. with a thickness of up to 6.0 mm. Because of the rectangular cross-section withroundedcor ners,asisspeciedfor springs in groups 1 and 2, the application of load in practice always takes place via slight- ly shortened lever arms (gure 4). Due to the h/H tolerance for the outer and inner dia me -ters, the lever arms are shortened even fur- ther. This results in an increase in the spring load by the factorin virtually all springs compared to the val-ues calculated with formula 7. Spring WorkTheworkdonebyadiscspringcanbe obtainedbyintegratingformula7forthe load F according to the deection s: Disc Springs without Contact FlatsFormula 16W F dsE tK DKstKhtstSe |('`JJ|('`JJ+

]]]]0251242242 022121 Figure 4Cross-section of a disc spring in group 2ThisconditionstakesthestandardDIN 2093 into consi de ra ti on in that the thickness to le ran ces toward the minus side are clearly larger than toward the plus side. Therefore, we ma nu fac ture all springs with a slightly re-duceddiscthick ness.Thisreductioninthe lever arm length is also an ex pla na ti on for the fact that the permissible deviations for thespringloadsforgroups1and2are consi derab lylargertowardtheplusthan the mi nus side.D DD De ie i ' 'Basic Calculation19Disc Springs with Contact Flats and Reduced Thick ness1.4For disc springs with a thickness of more than 6.0 mm, DIN 2093 species small con- tact surfacesat points I and III in addition to the rounded corners. Figure 5 shows a sche- ma tic cross-section of a spring in group 3 as per DIN 2093. The corresponding springs of our factory standard are also manufactured in the same manner. Thesecontactatsimprovedenitionof the point of load application and, particularly for spring stacks, reduce friction at the guide rod. The result is a considerable reduction in theleverarmlengthandacorresponding increaseinthespringload.Thisisinturn compensated for by a reduction in the spring thick ness from t to t.When calculating disc springs with con- tact ats and reduced thickness, the factor K4 mustbecalculatedusingformula6,andt replaced with t and h0 with h0 = l0 t in the equations 7 to 16.Figure 5Cross-section of a disc spring in group 3Thereducedthicknesstisspeciedin accordance with the following conditions: The overall height l0 remains un al te red. Thewidthofthecontactatsistobe appro ximately1/150oftheoutsidedi-ameter. Thespringloadforareduced-thickness spring must be the same at s = 0.75 h0 as for an unreduced spring.The dimension t is specied for those disc springscontainedinDIN2093.Themean factor t/t is: Series AB Ct/t 0.94 0.94 0.96For other springs the factor for t/t is depend-ent on the dimensional ratio and h0/t from gure 6. The curves were calculated for disc springs with OM = 1600 N/mm2. For springs with different stress sOM, we would ask you to contact our Tech ni cal department.Astheoverallheightisnotreduced, springswithreducedthicknessinevitably have an increased ank angle and a greater coneheighth0thanspringsofthesame nominaldimensionwithoutreducedthick- ness. The re fo re, the characteristic curve is altered and becomes more curved. Figure 7 shows the characteristic curves for springs of the se ries A, B and C as per DIN 2093 with and without contact ats and reduced thick-ness.120Figure 6Factor t/t for disc springs with sOM = 1600 N/mm2Figure 7Calculatedcharacteristicsfordiscspringswithand withoutcontactats.Fcisvalidforspringswithout contact ats (continuos line).Basic Calculation2111.5 Disc Springs of Special MaterialsWhenspecialmaterialsareusedwithdif- ferent E moduli and Poissons ratio , it is recommendedthatthecorrespondingE modulusisused,butthatthevalueof 0.91for12beretained.Thisisjustied withthefactthatformula7forsteelwith E=206000N/mm2and=0.3provides loads 8 9% higher, however this is more or lessba lan cedoutagainbyradiiandcross-sec tion-related short ening of the lever arm.1.6 Spring Parameters for Dimensions and Cal cu la ti onOutside diameter DeDisc thickness tDiscspringsaredeterminedessentiallyby the following three parameters:=ho/t =De/t=Outside diameter DeInnendurchmesser DiCone height l0 tDisc thickness tIf at all possible, the parameters above should be within the following values:=1.75...2.5 h0/t =0.4...1.3 De/t=16...40 Forsmallervalues,smallervaluesofh0/t and De/t also apply and vice-versa. Forsteelspringswithdimensionswithin these limits, for mu la 7 can be used wi t hout restriction. For very thin disc springs(De/t > 50) the formula results in spring forces which are too high. For very narrow disc washers with a ratio of diameters of De/Di < 1.75, the shortening oftheleverarmmustbeconsi de redwhen calculatingtheforce.Thisisbrou ghtabout by the rectangular cross-section and by the rounded edges (chapter 1) and results in the calculationoftoolowaload.Inallsuch cases please consult us.221.7 Characteristics of a Single SpringThe value h0/t determines the amount of cur -va ture of the spring characteristic (gure 3). Forh0/t 1.3 is not suitable for long spring stacks, as individual springs within the stack may move unevenly and be over loaded. As a result, such springs should only be used alone. From the dependence of the characteris- tic curvature from the ratio h0/t, follows that the characteristic curve of disc springs of the samedimensionschangeswhentheyare formedtoadifferentheight.Conversely,at the same height h0, a thinner disc will have a moreregressivecharacteristiccurvethana thicker disc (gure 8). On the other hand, the force of the at- teneddiscspringincreaseslinearly.If,for ex amp le, a spring calculation cannot predict this in a satisfactory manner, then a rst step in the form of a change in the free height may already produce the desired load/deection diagram.Here,how ever,thepermissible stress must be observed, as these increase with increasing cone height h0. Figure 8Characteristic of a sin gle disc with different height h0Basic Calculation23For the normal arrangement of disc springs aprogressiveincreaseinthespringforce occursatdeectionsofs>0.75h0which deviatesfromthecalculatedvalue.Thisre- sul tsfromtheshiftintheloadpointsto smaller lever arms, because the disc springs roll on each other or on the abutments. There- fore, it is recommended that only ap prox. 75 to80%ofthespringdeectionisutilised. Forthisreason,thespringforceisonly indicated at s 0.75 h0 in DIN 2093 (gure 10).Ath0/t>_2,thespringforcereachesa maxi mum and then de crea ses again. In some cases the decreasing segment of the curve is utilised.Undercer tainconditionsthespring must be loaded beyond the at position, for whichcertaindesignconditionsmustbe given (gure 9).Figure 9Spring loaded beyond the at position1Figure 10Calculated and actual characteristic241.8 Calculation ExamplesThe section Diagrams contains the cha rac -te ri stics for all springs in our stan dard range. The life lines also allow the fatigue life to be estimatedforvariouswor kingstrokes.In spite of this we show several examples of the calculationandcheckingofdiscspringsbe-low.Example 1: Checking Fatigue Life of a Disc SpringGiven: Spring 45 x 22.4 x 1.75; l0 = 3.05 mm Preload F1=1580 N Final loadF2=2670 N Frequency f=1000/minTo be determined: Is the stress within the acceptable range what is the estimated fatigue life.Solution: Fromthetablesofsection9.2wecan ob tain the following data: s/h0 s [mm] F [N]s [N/mm] 0.250.3251524 433 0.50.6502701 814 0.750.9803659 1148 1.01.3004475 1421Withthehelpofthesefourpointstheload and stress relative to the deection may be drawn.Figure 11Disc spring 45 x 22.4 x 1.75; l0 = 3.05 mmThe following values may be obtained from the diagram (gure 12):s1 = 0.34 mm, s2 = 0.64 mmu = 450 N/mm o = 804 N/mmFrom the fatigue diagram for group 2 springs gure19,weobtainU=450N/mm2 witha maximum stress of O = 920 N/mm2. The re- fo re the spring is fatigue resistant as o< O.Figure 12Diagram for spring 45 x 22.4 x 1.75 mm,l0 = 3.05 mmBasic Calculation251Example 2: Disc Springs with a high h0/t Ratio Given: Guide diameter 30 mm Installed lengthl1= 4,9 mm PreloadF1= 2000 N min. Working de.s2 s1= 1.05 mm Spring loadF2= 2500 N max.Required: Suitable Disc Spring DimensionsSolution: Spring inside diameterDi =30.5 mm Spring outside diameter De =60 mm (selected because of the favourable De/Di ratio). Because of the very small load range and thesmallinstalledlengthonlyaspring with a high h0/t ratio is suitable. Selected: Disc spring 60 x 30.5 x 1.5 mm; l0 = 3.5 mm h0/t = 1.333; = 1.967Calculation: First the factors are calculated using for-mu la 3. 4 and 5: K1 = 0.688 K2 = 1.212 K3 = 1.365Figure 13Disc spring 60 x 30.5 x 1.5 mmThe stress OM can be checked using formula 9:OM = 1048 N/mmThis value lies well under the limit of 1600 N/mm,thespringwillthereforenotset. Nowthespringloadscanbecalculatedto formula 8a, preferably for the 4 deections s = 0.25h0, s = 0.5 h0, s = 0.75h0 and s = h0. One obtains the following values: s/h0 s [mm] F [N] 0.250.5 1338 0.51.0 2058 0.751.5 2367 1.02.0 2469With these 4 points the spring diagram can be drawn.Figure 14 Diagram for spring60 x 30.5 x 1.5 mm,l0 = 3.5 mm26One can read F1 = 2100 Ns1=1.05 mm and for F2 = 2400 Ns2=1.61 mmDeections2 s1=0.56 mmThedeectionofasinglespringisnotsuf- cient, therefore two in series must be used.This arrangement gives:Unloaded length:L0 = 7.0 mm Preloaded length: L1 = 4.90 mmPreloaded deection: s1 = 2.1 mmPreload: F1 = 2100 NDeection s2 = s1 + 1.05= 3.15 mmFinal load F2 = 2390 NTocheckthefatiguelifewemustusethe stressesats1=1.05ands2=1.575mm. Figure 17 shows that point III is the do mi- nant one, this gives:s1: u = 843 N/mm s2: o = 1147 N/mmBy utilising the fatigue life diagram in gure 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 FlatsGiven: Disc spring 200 x 82 x 12 mm; l0 = 16.6 mm h0= 4.6 mm; = 2.439; h0/t = 0.383Required: The spring characteristic and the stres- ses II and IIIAlthough this spring is to our works stand ard weshowbelowhowthecal cula ti onsare madeandresultscanbecheckedinthe tables section 9.2.From the formula 3 to 5we rst calculate the constants K1 to K3:K1 = 0.755 K2 = 1.315 K3 = 1.541The static design can be checked by the cal cu -la ti onofOM,thereducedthicknessisnot considered and we use the values of t and h0. This gives:OM = 1579 N/mmAs the acceptable value for OM is 1600 N/mm, thespringiscorrect.From gu re6and consi de ring d and h0/t the re duc tion factor t /t can be ob tai ned: t/t = 0.958 Therefore t = 11.5 mm and h0 = 5.1 mm.Constant K4 can be calculated from formula 6:K4 = 1.0537 Figure 15 Disc spring200 x 82 x 12 mmBasic Calculation271Figure 16Spring force and stres ses forspring200x82x 12 mm, t = 11.5l0 = 6.6 mmNow from formula 8b, 11 and 12 the spring force and both stresses can be cal cu la ted:s/h0s [mm] F [N] II [N/mm2] III [N/mm2] 0.251.15669244163890.52.31271918907470.753.45 182737142110721.04.623550320111366With this spring the greater values of stress areontheinnerdiameterwhichshouldbe used.FinallythevalueofthestressOM for the reduced thickness can be checked: OM = OM K4 t/tOM = 1595 N/mm2829Chapter 2imitsDesign andOperation L302.1Allowable Stress for Static or Quasistatic Loads...................................... 31 Static Design.............................................................................................................. 31 Permissible Stress ..................................................................................................... 312.2Permissible Stress for Dynamic Loads................................................... 31 Critical Stress Affecting Dynamic Failure.................................................................... 32 Minimum Preload to Prevent Supercial Cracks ........................................................ 32 Permissible Stress ..................................................................................................... 33 Design and Operation Limits3122.1 Allowable Stress for Static or Quasistatic LoadsStatic DesignStatic or rarely changing loads exist when: a)Disc springs carry only static, non-chang-ing loads b)Discspringsaresubjecttooccasional load changes at greater time intervals and lessthan10,000loadcyclesduringthe planned service life. Disc springs are normally designed with an overall height l0, so that they can be attened under static or rarely changing loads without the overall height l0 reducing by more than the permissible tolerance. The stress OM at point OM dened in formula 9applies here.Permissible Stress Plasticde for ma ti onsoccur,whenthe stressesincertainareasexceedtheyield strength.ReferencestressisOM.Itsvalue should not exceed the tensile strength Rm of the material used. For spring steel as per DIN EN 10132-4 and DIN 17221 the tensile strength is Rm1600 N/mm2. For other materials, the respective applicable yield point values must be used. Disc springs as per DIN 2093 and our factory standards listed in the tables in chapter 9 were de si gned according to an earlier me thod using the stress at point I. Forthisreason,someofthesesprings ex ceedtheper mis si blestressatthepoint OM.Asthesespringshavebeenmanu- factured for years with this overall height l0, we have not changed the height. With these typesofspringsthereisthepossibilityof slight setting in use. Dynamicloadsoccurindiscspringswhen theloadcon ti nuous lychangesbetweena preloaddeections1andadeections2. Under the inuence of a change in stress of h,dynamicallyloadeddiscspringscanbe divided into two groups by service life (see also DIN 50100): a)Disc springs with longer life. These disc springsareintendedtowithstandload cycles of at least 2 106 and more without breaking.Ifaconsiderablylon gerlifeis required, please consult us. It may be that only an endurance test can provide exact in for ma ti on. b)Discspringswithalimitedservicelife. These disc springs are intended to achie ve alimitednumberofloadcyclesinthe rangebetween104N 0.6 to < 1.25 +0.03/0.09Group 2 1.25 to 3.8+0.04/0.12 > 3.8 to 6.0+0.05/0.15Group 3 > 6.0 to 16.0 +0.10/0.105.2TolerancesallowedinDIN2093areasfol- lows:For springs in group 3 the tolerance is ap- plied to the reduced thickness t. We use the thickness to ensure that spring loads are within tolerance and therefore will in some cases deviate from the above gu res.Overall Height Tolerances 5.3 t Tolerance for lo [mm] [mm]Group 1 < 1.25 +0.10/0.05Group 21.25 to 2.0 +0.15/0.08> 2.0 to 3.0 +0.20/0.10> 3.0 to 6.0 +0.30/0.15Group 3> 6.0 to 16.0+0.30/0.30 To ensure the specied spring forces, DIN 2093 allows the overall height tolerance to be slightly exceeded.For single disc springs the following maximum deviations are allowed:5.4t Tolerances for F [mm]at the test length lP = l0 0.75 h0Group 1 < 1.25 +25 % /7.5 %Group 2 1.25 to 3.0+15 % /7.5 %> 3.0 to 6.0+10 % /5 %Group 3> 6.0 to 16.0 +5 % /5 %Load TolerancesSingle Disc SpringsWith a single spring the spring force must be checked at the height l0 s. This should be carried out with the spring pressed between twolubricated,hardened,groundandpol- ishedpla tes.Measurementsarealwaysta -ken in loading direc tion.Tolerances535Forthedeterminationofthevariationbe- tween loading and unloading, a stack of 10 springs in single series is used. The stack is tted with a guide rod as described in section 6.3andabutmentplatesinsertedatboth ends as per section 5.4. Before testing, the stack should be loaded with twice the spring force F(s = 0.75 h0).Duringunloadingthemeasuredspring force at the length L0 7.5 h0 must at least reach the percentage of the loading cha rac -te ri stic shown in the table (gure 28). Series ASeries B Series CGroup 1min. 90% min. 90%min. 85%Group 2min.92.5%min.92.5%min. 87.5%Group 3min. 95% min. 95%min. 90%Figure 28Test points on the loading/unloading characteristic curve54Permissible Setting 5.5Allspringsexperiencealossofloadorre-laxa ti on in the course of time, which is pri -ma ri lydependentontheoccurringstress andthetemperature-timecurve.Fordisc springs the stress distribution in the cross-section also plays a role determined by the dimensionalrelationshipsandh0/t.The relaxationcanthereforeberelatedtostress OM,becauseitbestreectsallotherin u -ences.De pendingonthein stal la ti onsitua-tion, the load loss may occur as creeping or relaxation. Creeping is described as a loss of length lwhich the spring suffers under a constantloadF,andrelaxationasalossin load F if the spring is installed at a constant length l. Approximate values for the per mis-si ble re laxa ti on of disc springs under static loadsareprovidedingure29and30.If workingtemperaturesabove100Coccur, were com mendyoucontactourTechnical department.Figure 29Permissible relaxation for disc springs of Ck steelFigure 30Permissible relaxation for disc springs of chro me and chrome-va na di um-alloy steel as per DIN EN 10132-4 and DIN 17221Tolerances55Chapter 6Application56Application6.1Spring Stacks and their Features......................................................... 576.2Alignment of Spring Stacks ................................................................ 576.3Guide Clearance............................................................................. 586.4Guide Elements and Abutments........................................................... 596.5Friction....................................................................................... 60 Causes of Friction ...................................................................................................... 60 The Magnitude and Factors Inuencing Friction......................................................... 61 Calculation of Friction as per DIN 2092...................................................................... 62 Lubrication................................................................................................................. 64 The Effects of Friction ................................................................................................ 64576Spring Stacks and their FeaturesThe best spring arrangement is the one which uses the least number of individual springs. Inordertoachievethisgoal,theoutside diameter should always be as large as pos si-ble. This automatically keeps the stack length short. With an increasing number of disc springs, thefrictionandtheunevende ec tionof individual discs within the stack increa ses. We recommend L0 < 3 De as the ap pro xi ma te stack length. If it is not possible to avoid a longer stack, then it should be divided into 2 orpossibly3partialstackswithsuitable washers. These wa s hers should be guided as exactly as possible (gure 31). Inordertokeepthefrictionwithinre a -sona ble limits, no more than 2 or 3 springs should be stacked in parallel unless a large friction loss is expressly desired. Par ti cu lar-ly in the case of dynamic loading, consi dera- blewarmingmustbeexpectedwith2or more springs in parallel. Whenever possible, the abutments of a disc spring stack should contact the outside diameter, however this is only possible at both abutments with an even number of individual springs or spring sets.6.1Alignment of Spring Stacks 6.2Within a spring stack the disc springs do not always move evenly (gure 32). This naturally leads to overloading at one end of the stack with consequential re duc-tioninfatiguelife.Thisisalsothereason why,withdynamicloads,therstbreaks occur at an end of the spring stack in most cases.Therefore,were com mendthatthe spring stack be aligned on the guide rod with a vee bar and then maintained in position withalightpreload.Afteralignmentthe springstackshouldnotbecompletelyre-laxed. This procedure has been found most satisfactoryinpracticeforminimizingfric -tion in spring stacks. If it is not possible to align the stack for design reasons, the stack shouldbecom pressedatonceortwice. Thisalsohastheeffectofcentrali singthe springs and reducing friction. The friction is usually somewhat less in a vertically arranged stack than in the horizon- tal installation position. It is the re fo re better to have long stacks arranged vertically rather than horizontally. With a dynamically loaded stack there is a running in period during which the friction is reduced, especially with multiple layering. Thereasonforthisisacertainsmoothing effectatboththecontactedgesandthe touching spring anks.Figure 31Division of a long spring stack58Figure 32Example of the uneven deection within a spring stack6.3 Guide ClearanceDisc springs always need a guide element to prevent lateral movement. The guide can be ontheoutsideDeortheinsideDiofthe springs,butinsideguidanceonaboltor shaft is preferred to the outside guidance in a sleeve, because it offers design and eco no mic advantages.For the clearance between the guide and the spring DIN 2093 recommends the follow-ing values. Di or De Clearance to 16 mm0.2 mm over 16 to 20 mm 0.3 mm over 20 to 26 mm 0.4 mm over 26 to 31.5 mm0.5 mm over 31.5 to 50 mm0.6 mm over 50 to 80 mm 0.8 mm over 80 to 140 mm 1.0 mm over 140 to 250 mm 1.6 mmApplication596On compression the spring cross-section turns about a centre of ro ta ti on S on the diameter D0 (gure 33). If in the unloaded con di ti on the contactpointofthespringontheguideis belowahorizontalthroughpointS,thereis noreductioninthein si dedia me ter.The same holds true for an outside guide where the contact point is above the ho ri zon tal. For springswitharatioofh0/t>1thisisnot always the case and a reduction of the inner diameter must be expected. Howe ver, this re ductionismostlyverysmallandwith stan dard springs is covered by the gui de clea rance laid down in table on page 58. The cal cu la ti onstodeterminethevariationsin thediame terareveryeasytodayandwe re com mend you contact our Tech ni cal de -part mentifyourequireadditionalinfor ma -tion on this sub ject.Figure 33Withtherectangularspringcrosssectionjammingat the guide pin during deection is preventedThesevaluesrepresentthedifferencein the diameters. Under certain conditions this guideclearancecanbereduced,e.g.with high-speed spindles. In order to avoid jamming of the individu -aldiscspringsontheguideboltorinthe guide sleeve, the spring cross-sections must be designed to be rec tan gu lar (gure 33). All fourcornersareslight lyroundedwitha radius of approximately t/8.Guide Elements and Abutments 6.4The guide elements and abutments should be hardened if possible to a minimum of 55HRC andaminimumcasedepthof0.8mm.The surfaceoftheguiderodshouldbesmooth and, if possible, ground. For dynam ic applica-tions we re com mend lubrication with a high pressure grease containing MoS2. For static applications guides may be unharde ned.60FrictionDuetofriction,theactualloadsobtained when loading and unloading the spring stack may deviate from the gures calculated. The se variationsareinmanycasesinconve nient, but at times required for application re a sons. Therefore,itisoftennecessarytocal cu la te the friction and take this into consid eration.Causes of Friction6.5Thetotalfrictionwithdiscspringstacks arisesbecauseof4differentcomponents (gure 34):1.Theinternalfrictionthroughelasticde- for ma ti on of the material. It occurs with each deection of the material and cannot be altered.2.Friction on the end abutments through the radial movement between the spring and the abutment surface. This only oc- curs with the end springs in the stack, as there is no relative movement between the other springs to each other.3.Friction of the springs on the guide due to axialmovementofthespringsduring deection.4.Frictionbetweenspringsinthecaseof parallel stacking.Figure 34Friction in disc springsTherstthreetypesoffrictionoccurwith single springs and single series spring stacks. It is therefore a fact that friction with disc springsisalwaysgreaterthanwithcoil springs.Application616The Magnitude and Factors Inuencing FrictionThe amount of friction depends on very many factors:Geometric factors: Shape of the cross section Radii on the corners Amount of guide clearance Surfaceroughnessofthespringsand guide elementsMaterial factors: Material of the springs and guide ele mentsHardness of the springs and guide ele ments Surface protection of the springs Type of lubricantAssembly factors: Number of parallel stacked springs Length of the spring stackLoad dependant factors: Length of spring stroke Speed of loading (frequency)The value of the different factors on the total frictionvariesconsiderablyfromcaseto caseandwecanonlygivethefollowing indications:The geometric factors have already been mentionedinsec tion6.3.Afrequentlyun- der ra tedinuenceisthesurfacetreatment. Forexample,zincplatedspringshaveless friction than those phosphated. With pa ral lel stacking the greatest friction is between the springs, with an increase in proportion to the number of paral lel springs. This can, how ever, be reduced by means of a suitable grea se (see page 64).It is known from experience that relatively largedeections/h0or(s2 s1)/h0cause more friction than smaller de ec tions. The se fac torsshouldallbeconsideredforhigh fre quen cyspringapplications.Becauseof thelargenumberofin uences,itisnot possibletoderiveanexactcalculationfor friction in disc spring stacks.62However, from many tests with various spring sizes a gure has been derived of 2.5% per parallel spring (+ loading, unloading). This results in the following values:1 single spring 2... 3 %2 in parallel4... 6 %3 in parallel6... 9 %4 in parallel 8...12 %5 in parallel 10...15 %Figure 35 shows the principal load variations for one to 4 springs in parallel. Inuence of friction on spring loadCalculation of Friction as per DIN 2092DIN2092,Issue1/92givesamethodof calculatingthefrictionFRonspringload. Thisomitstheinternalfrictionandthefric- tionontheguiderod(section6.5Nos.1 and3).Thismustbeobtainedthroughan ad di tio nalcalculation.Thevaluesbelowfor sur face and edge friction to DIN 2092 give a relatively wide range.Therefore, it is our opinion that, although this process is theoretically cor rect, in the end it does not provide any better results thantheconsiderationofthefrictionwitha simple,per centileaddition.Forcomplete- ness we have shown this calculation method below.The following formula applies:Formula 26F Fnw n wgesRM R

1 1 ( )Where: F=Calculated spring load to formula 7n=Number of springs in parallelwM =Coefcient of surface frictionwR =Coefcient of edge friction=On loading+=On unloadingWithn = 1formula 26 describes relation-ships for a single spring between 2 at pla tes. For the friction coefficients wM and wR, DIN 2092 gives the following values:Figure 35Inuenceoffrictiononspringforceforvariousparallel stackingsApplication636 Series par DIN 2093wMwR Series A 0.005...0.030 0.03...0.05 Series B 0.003...0.020 0.02...0.04 Series C 0.002...0.015 0.01...0.03Whencalculatedwiththesevalues,formula 26providesthefol lo wingnumbers,which are con siderably easier to understand:n = 1 n = 2n = 3 Series A+3.09... +5.26+3.63... +8.70 +4.17... +12.362.91... 4.763.38... 7.41 3.85... 9.91 Series B +2.04... +4.17+2.35... +6.38 +2.67... +8.701.96... 3.852.25... 5.66 2.53... 7.41 Series C+1.01... +3.09+1.21... +4.71 +1.42... +6.380.99... 2.911.19... 4.31 1.38... 5.66These results are presented in gure 36.Figure 36Frictionfordiscsprings as per DIN 2092 Alteration of the calculated spring load through the friction is in %.+ = Increase in load when loading / = Reduction in load when unloading

64LubricationThelargevariationingure36showsthe inuence of lubrication on the friction. The choiceofthecor rectlub ri cantisthere fo re oftenofde ci si vein u ence.Aswellasre-ducing fric tion, it can prevent gal ling of one spring on another when stac ked in par al lel. Similarly, it can help prevent corrosion. The lubricants which may be used are: Oil is frequently used for springs in ma chi ne construction, especially with central lub ri ca-ti on or an assured continuous oil supply. Grease is more suitable if relubrication is dif cult or cannot be done on a regular basis. Slip paints are based on MoS2 and are an ele gantsolutiontoprovidingpermanent lubrica tion. It also provides a high degree of cor ro si on resistance.The Effects of FrictionFriction mainly affects the deection of the spring, i.e. it modies the spring loads. It must be added when loading the spring and subtractedwhenthespringisunloaded. Between the actual loading and unloading curve there is a hysteresis loop. The effect of the number of parallel springs onthe hys-teresis is shown in gure 35. This frictional workisturnedintoheatandwithhigh fre quen cy dynamic loading this can be con- siderable. In such cases, single stacked disc springs should be prefered and good lubri-ca ti on is essential. With spring energy storage the hys teresis isatotallossandcannotberecovered. Howe ver,withspringsfordamping,this hy ste re sis effect is useful and the frictional work is a measure of the damping.Application65Chapter 7Materials667.1General Requirements............................................................................................. 677.2Standard Materials.................................................................................................. 68 C 60S ....................................................................................................................... 68 C 67S, C 75S............................................................................................................ 68 51 CrV 4................................................................................................................... 687.3Materials for Special Requirements....................................................................... 68 Corrosion Resistant Steels......................................................................................... 68 X 10 CrNi 18-8 ......................................................................................................... 68 X 7 CrNiAl 17 7 ........................................................................................................ 69 X 5 CrNiMo 17 12 2 ................................................................................................. 69 Steels for Higher Temperatures.................................................................................. 69 X 22 CrMoV 12 1...................................................................................................... 69 X 39 CrMo 17-1 ....................................................................................................... 70 Copper Alloys............................................................................................................. 70 CuSn 8 ..................................................................................................................... 70 CuBe 2 ..................................................................................................................... 70 Nickel and Cobalt Alloys............................................................................................. 70 NIMONIC 90............................................................................................................. 71 INCONEL X 750 and INCONEL 718 .......................................................................... 71 DURATHERM 600 .................................................................................................... 717.4Table of Material Properties................................................................................... 72 Materials677General RequirementsTheessentialofaspringisthatithasthe quality to react to loading by elastic de for ma -ti on. There fore, materials with high elasticity are necessary. As in each case a small design is desired, spring materials should have the highesttensilestrengthandahighelastic limit.Inadditiontohighstrainintheelastic region, there must also be sufcient pla sti ci ty. This allows the manufacture of cold for med springswhichwillnotbreakthroughthe grea test unforeseen overloading. Moreover, a high fatigue limit is required which is however not a characteristic value ofthematerialas,forexample,thetensile strength. For a high fatigue strength, a high degreeofpurity,ahomogenousstructure andasmoothcarbon-freesurfacearepre- sup po sed.These requirements are ful l led very well by steel, therefore most springs are made of steel. Apart from this there will be the re qui-re mentinsomecasesforcorrosionresi -stance, heat resistance or anti-magnetic pro -per ties whe re special ma te ri als will be requi-red.An important property of spring material isYoungsMo du lus(E).Fromthismaterial constant is derived a linear re la ti onship be-tween load and deection. The E of steel is practically not affected by heat treatment, butitistem pe ra turedependentandthis mustbetakenintoconsiderationathigher working temperatures (gure 37).7.1Figure 37Temperaturedepen dence ofEandrelatedre duc -tion in load68Materialsfordiscspringsareprincipally supplied in the following forms: Cold rolled strip as per DIN EN 10140Hot rolled strip as per DIN EN 10048 Plate as per DIN EN10029 Forgings as per DIN 7521 and 7526Inthetablesonpages72to75listthe pro per ties of all the materials from which disc springs are manufactured. The follow-ing notes give clarica tion of this.Standard Materials 7.2C60S:Bothtypesarequalitysteels asper DIN EN 10132-4. We use them for our Original Schnorr Serrated Safety Wa s hers and Load Washers as per DIN 6796 where the loading is only static. C 67S and C 75S: These high grade steels asperDINEN10132-4areusedforcold formed springs to group 1. For lightly loaded springs,forexampleourKspringsfor preloading ball bearings, these ma te ri als can be processed in the spring-hard condition.Specialrequirementssuchascorrosiveor high temperature enviroments often require the use of materials designed for these applica-tions. These materials, in general, have low-er tensile strength than standard ma te ri als andshouldonlybespecied,ifabsolutely Materials for Special Requirements 7.3ne ces sa ry. These springs have a lower over- allheightthancomparablesizesmadeof stan dard materials resulting in lower spring force. This must be taken into consideration using these materials.Corrosion Resistant SteelsX10CrNi18-8(1.4310):Thischrome nickel alloyed steel as per DIN EN 10151 is the materialmostusedforcorrosionresistant springs. Becau se of its austenitic structure with ferritic inclusions, it cannot be hardened intheusualway,butbycoldformingitcan obtain the strength required for disc springs. Consi dera blecoldfor mingisne ces sa ryand thestrengthre du ceswithincre asingthick-ness.The re fo re,thematerialisnor mallynot availa ble thic ker than 2.5 mm. In fact, springs can only be supplied to this thick ness. Where- asthema te ri alinthesoftcon di ti onishardly magnetic,thecoldwor kingprocesswillmake itmoreorlessma gne ticagain,makingit unsuitableforcom ple te lynon-magnetic springs.51CrV4(1.8159):Thisisachrome vanadiumrenedalloysteelofthehighest quality. It is available in cold rolled form as per DIN EN 10132-4, hot rolled and forgings as per DIN 17221 for the manufacture of disc springs. It has very good through-hardening ca pa bi li ty and is therefore suitable for mak ing springs up to 50 mm thick. The re laxa ti on is lessthanfornon-alloyedsteel(seesection 5.5), which allows use up to 250C (with a suitable reduction in load).Materials697Steels for Higher TemperaturesWhen considering springs for use at higher working tem pe ra tures it must be remember-edthatbothtensilestrengthandYoungs modulus E are reduced compared with the values at room temperature.X22CrMoV121(1.4923):Thisheat treatable chrome-molybdenum steel has been used very successfully for heat resistant disc springs. Springs of 1.5 to 6 mm thickness aremadefromstriporplate.Forthicker springs, forged rings can be used.Figure 38 shows the mechanical pro per- tiesandYoungsmodulusEwithrespectto temperature.Itshouldbenotedthatwitha chromecontentof12%thissteelisnot corrosion resistant.Figure 38Yield stress and E mo du lus of steel X 22 Cr MoV 12 1 with respect to temperature. X 7 CrNiAl 17 7 (1.4568): This steel as per DIN EN 10151 precipitation hardened produces an austenitic/ferritic struc ture. It will also be pro cessedintheworkhardenedcondition andmaybeharde nedbysub se quentheat treatment. A disadvan tage compared to steel 1.4310isthelowercorrosionresist ance andsen si ti vi tytostresscor ro si on.We there fore only recommend its use for springs over2.5 mmthicknessifnoothermaterial is availa ble. X 5 CrNiMo 17 12 2 (1.4401): The strength of this material is somewhat less than eit her of the two forgoing. Not wi th stan ding that it offers higher corrosion re si stance and low-estmagnetism.Al thoughalsocon tai nedin DIN 17224, it is often difcult to obtain and therefore only sel dom used.70 X 39 CrMo 17-1 (1.4122): Here we have a chro me-mo lyb de num al loyed heat treatable mar ten si tic steel which is also suitable for corrosion resistant springs. Be cau se of the molybdenum it may be used up to 400C. However,atthesetemperaturesboththe ten si le strength and E are re du ced.In order to achieve the required pro per- ties, this steel must be har de ned to higher values which rai ses the question of stress cor ro si on. Unfortuna tely, in the li ght of cur- rent technical know ledge we cannot com-pletelydis countthepossibilityofdelayed brittle fracture.Copper Alloys CuBe 2 (2.1247): Beryllium copper is an out standing spring material. This heat treat-ablealloyhasstrengthvaluescom pa ra ble with steel. How ever, Youngs 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.Copper alloys are absolutely non-magnetic andhaveverygoodelectricconductivity. Moreover,theyarecorrosion-resistant against many media. These characteristics makethemsuitableformanydiscspring applications. CuSn 8 (2.1030): Tin bronze as per DIN EN 1654 is an alloy of copper and tin, which obtains its spring properties from cold work-ing.Thetensilestrengthiscertainlylower than spring steel and the E modulus is only 55%ofthevalueforsteel.Thismustbe consideredinthespringcalculationandal -lowstheiruseinapplicationswhereverylow spring loads are required.Nickel and Cobalt AlloysFrom the large number of nickel-chrome and nickel-chrome-cobalt based alloys some have achievedimportancefordiscsprings.By alloyingwithaluminium,titaniumand/or niobium/tantalum they are precipitation har- den a ble. These ma te ri als are very tough, that is to say they have high strength and a low elasticratio.Therefore,theprobabilityof more set in the spring must be considered. Against this are the outstanding fatigue pro -per ties. With correct spring proportions this is good over the total spring travel. Because ofthematerialcompositiontheyhaveout- stan dingcorrosionresistancetomanyme -dia. All these alloys are very expensive and often hard to work, and as a rule have long deliveries.Theyarethereforeonlyused whe re no other material is suitable due to tech ni cal considerations.Materials717NiCr20Co18Ti(Nimonic90)(2.4632, 2.4969):Thesenickel-chrome-co baltalloy givestheleastproblemsinprocessingandis therefore the most often used. It has very good heat resist ance and can be used up to 700C with suitable dimensioning. NiCr 15 Fe 7 TiAl (Inconel X 750) (2.4669) and NiCr 19 NbMo (Inconel 718) (2.4668): Thesenickel-chromealloysareprac tically cobalt-free, and are therefore used in reactor applications. The hardening process is difcult and expensive. The ap pli ca ti on is limited and onlyusedinspecialcases.NIMONICand INCONELaretradena mesofIncoAlloys International. DURATHERM 600: This is a heat treatable alloy of the cobalt-nickel series with outstand-ing mechanical properties. At a tem pe ra -ture of 0C the material is non-magnetic. It can be used at very high temperatures (600C and over). Theveryhighpriceofthisalloy limitsitsusetoveryspecialap pli ca ti ons. DU RATHERMisatradenameofVa cu um -schmel ze GmbH in Hanau.72Table of Material Properties7.4Short NameAISI Mat.-No. Standard Chemical Analysis in %Steel for Normal ASTMApplicationsC Si Mn Spring Steel C 60S1060 1.1211DIN EN 10132-40.57...0.65 0.15...0.35 0.60...0.90 C 67S1070 1.1231DIN EN 10132-40.65...0.73 0.15...0.35 0.60...0.90 C 75S1078 1.1248DIN EN 10132-40.70...0.80 0.15...0.35 0.60...0.90 51 CrV 46150 1.8159DIN EN 10132-40.47...0.55 max. 0.400.70...1.10 DIN 17221 0.47...0.55 0.15...0.40 0.70...1.10 Corrosion Re si stant SteelX 10 CrNi 18-83011.4310DIN EN 10151 0.05...015max. 2.0max. 2.0X 7 CrNiAl 17-7 6311.4568DIN EN 10151 max. 0.09 max. 0.7max. 1.0X 5 CrNiMo 17-12-2 3161.4401DIN EN 10151 max. 0.07 max. 1.0max. 2.0X 5 CrNi 18-103041.4301DIN EN 10151 max. 0.07 max 1.0 max. 2.0Heat Resistant SteelX 22 CrMoV 12-1 1.4923DIN EN 10269 0.18...0.24 max. 0.50.40...0.90 X 39 CrMo 17-11.4122DIN EN 10088-20.33...0.45 max. 1.0max. 1.5Copper Alloys Sn PBeCuSn 82.1030DIN EN 1654 7.5...8.50.01...0.4 CuBe 22.1247DIN EN 1654 1.8...2.1 Nickel and Cobalt AlloysNiCr CoNiCr 20 Co 18 TiHEV6 2.4632 / 2.4969Balance18.0...21.0 15.0...21.0 (Nimonic 90) 5829C (AMS)NiCr 15 Fe 7 TiAl 6882.4669 70.0 min.14.0...17.0 1.0 max.(Inconel X 750) 5542L (AMS)NiCr 19 NbMo 5596J (AMS) 2.4668 50.0...55.0 17.0...21.0 1.0 max.(Inconel 718)Duratherm 600 Balance1240...41 Nickel and Cobalt Alloys (contd.)S PBNiCr 20 Co 18 TiHEV6 2.4632 / 2.49690.015 max. 0.03 max.0.02 max.(Nimonic 90) 5829C (AMS)NiCr 15 Fe 7 TiAl 6882.4669 0.015 max. 0.020 max.(Inconel X 750) 5542L (AMS)NiCr 19 NbMo 5596J (AMS) 2.4668 0.015 max. 0.015 max.0.006 max.(Inconel 718)Duratherm 600 Materials737P max.S max.Cr V MoNi N0.025 0.025max. 0.40 max. 0.10 max. 0.400.025 0.025max. 0.40 max. 0.10 max. 0.400.025 0.025max. 0.40 max. 0.10 max. 0.400.025 0.0250.90...1.20 0.10...0.25max. 0.10 max. 0.400.030 0.0300.90...1.20 0.10...0.20 0.045 0.01516.0...19.0 max. 0.8 6.0...9.5 0.040 0.01516.0...18.0 6.5...7.8 0.045 0.01516.5...18.5 2.0...2.510.0...13.0 max. 0.110.045 0.01517.0...19.5 8.0...10.5 max. 0.110.025 0.01511.0...12.5 0.25...0.350.80...1.20 0.30...0.800.040 0.0315.5...17.5 0.8...1.3max. 1.0Ni + CoCuBalancemax. 0.3BalanceTi AlC SiMnFeCuZr 2.0...3.0 1.0...2.00.13 max. 1.0 max.1.0 max. 1.5 max. 0.2 max.0.15 max.2.25...2.750.40...1.000.08 max. 0.50 max. 1.0 max. 5.0...9.0 0.5 max. 0.70...1.150.3...0.70.02...0.08 0.35 max. 0.35 max. Balance0.2 max. 1.8...2.2 8.7 Nb + Ta MoW 0.7...1.2 4.8...5.5 2.8...3.3 4 3.974Short NameAISIMat.-No.StandardPhysical and Mechanical Properties ASTMREFDensityE-modulus in kN/mm2 Steel for Normal Kg/dm3 at RT100200300 ApplicationsCCCC Spring SteelC 60S10601.1211DIN EN 10132-47.85206202 C 67S10701.1231DIN EN 10132-47.85206202 C 75S10781.1248DIN EN 10132-47.85206202 51 CrV 461501.8159DIN EN 10132-47.85206202196 DIN 17221Corrosion Re si stant SteelX 10 CrNi 18-83011.4310DIN EN 101517.90190186180 X 7 CrNiAl 17-76311.4568DIN EN 101517.90195190180171 X 5 CrNiMo 17-12-23161.4401DIN EN 101517.95180176171 X 5 CrNi 18-103041.4301DIN EN 101517.90185179171 Heat Resistant SteelX 22 CrMoV 12-11.4923DIN EN 102697.7216209200190 X 39 CrMo 17-11.4122DIN EN 10088-27.7215212205200 Copper AlloysCuSn 82.1030DIN EN 16548.3115110 CuBe 22.1247DIN EN 16548.8135131125 Nickel and Cobalt AlloysNiCr 20 Co 18 TiHEV62.4632 / 2.4969 8.18220216208202 (Nimonic 90)5829C (AMS)NiCr 15 Fe 7 TiAl 2.46698.28214207198190 (Inconel X 750)5542L (AMS)NiCr 19 NbMo 5596J (AMS)2.46688.19199195190185 (Inconel 718) Duratherm 6008.50220215208202 Materials757The values quoted for E-modulus and tensile strength are for reference only.The range of working temperature and thickness only serve as an indication.Theheattreatmentandthehardnessofdiscspringsmadefromheatresistantsteelsis deviating from the standards mentioned above. WorkingTensileThicknessAvai la bi li ty400500600TemperatureStrengthrange CCCN/mm2mm20...+100115017500.2...7.0easy20...+100120018000.1...2.5easy20...+100120018000.1...1.5easy50...+200120018000.3...80easy200...+200115015000.2...2.5easy200...+300115017000.2...4.0less easy200...+200100015000.2...1.6difcult200...+200100015000.2...1.6less easy17916750...+500120014001.5...20easy19050...+400120014000.3...6.0easy50...+1005906900.1...6.0easy260...+200127014500.1...2.5easy193187178200...+700 1100to 6.35dif cult179170158200...+600 1170to 6.35difcult179174167200...+600 1240to 6.35difcult195188200...+550115015500.1...2.0difcult7677Chapter 8Special Types78Special Types8.1Disc Springs for Preloading Bearings..................................................................... 798.2Slotted Disc Springs ................................................................................................. 798.3Disc Springs with Trapezoidal Cross-Section .......................................................... 80 79With every ball bearing there is radial play so itmayfunctioncorrectly.Thisradialplayor clear ancecancauseconsi dera blenoiseat high spe eds. In many cases it is possible to achieve a quiet running bearing assembly by the use of a suitable disc spring to apply an axial load to the bearing. Similarly, the springs can be used to accommodate the build up of tolerances or ther mal movements within the assembly. SCHNORR has, in close co ope ra- ti onwithSKFinSchwein furt,designeda special ran ge of disc springs for this purpose our K springs for ball bearings. In ad di- ti ontothenormalrangeslottedsprings are available up to a diameter of 95 mm. This specialdesigngeneratesverysmallloads andwillaccom modatelargedeections (section 9.5). We will be pleased to send our specialKSpringleaetonre quest.Be-causeofthedifferentdimensionsofthese springs com pa red with nor mal disc springs, the load and di men sio nal to le ran ces of DIN 2093 (chapter 5) do not apply.ForthedimensionsofKDiscSprings plea se see section 9.5.Disc Springs for Preloading Bearingsismostimportantwiththistypeofspring that the permissible stresses in the annular portionarenotexceededand,ifnecessary, theoutsidediametermustbeincreasedto compensate.The inclusion of slots on either the inner or outer diameter creates a lever which works on the unslotted portion of the spring. This has the effect of reducing the spring load and increasingthedeection(gure39).The resultingspringhasasoftercharacteristic withalargedeectionandinpro portionto the outside diameter smaller spring loads. It Slotted Disc SpringsFigure 39Slotted Disc Spring8.28.1880Takingtheselimitationsandafewdesign features into account, this type of spring has many possible applications. The classic ex -amp le is the automo tive clutch spring. No-tablearetheslot tedballbearingpreload springs which give extremely low loads (see section 8.1 and the dimension tables section 9.3).The rst approximation for the calcula- tion of slotted disc springs can be achieved by con sidering the lever arm and the formula in section 1.2.Theloadsgenerateddependtoalarge extent on the shape of the slots or the cor re- spon dingngers.Thedeectionofthen- gersisonlyasmallpercentageofthetotal de ec tion and can be ignored. An exact cal- cu la ti on is given in[7]. If you need to consi der theuseofslottedDiscSpringswere com-mend you contact our Technical department so the design and manufacture may be dis- cus sed.Disc Springs with Tra pe zoi dal Cross-Section 8.3By the use of a trapezoidal cross-section it is possible to equalise the stresses on the spring upper and lower surfaces. The advantageous tensile stresses on the lower surface contrib -utetoabetterfatiguelife.Theequalcom- pres si ve stres ses on the upper surface result in more set. A similar distribution of the ten-silestressesatpointsIIandIIItogivethe optimumfatiguelifecanalsobeachieved witharec tan gu larcross-sectionspringif the ratios and h0/t are correctly chosen [5] [6]. In this regard therefore, the trapezoidal cross-section offers no advantages. Com pa red with a stan dard spring having a similar angle on the top surface, a trapezoidal spring will give lessdeection.Thiscanbeincreasedby includingintermediaterings,butthesewill alsoincreasetheoverallstacklengthand require more space.Themainadvantageofthetrapezoidal cross-sectiondiscspringistheabilityto limit the stroke without additional parts. It is the re fo re possible to design a spring which isre la tive lyfatiguefreeoverthecomplete de ec tion range with relatively little increase in load towards the end of the stroke. With the same installation space and un- der consi deration of the permissible stres -ses, no more favourable spring data (more forceormoredeec tion)canbeachieved with disc springs with a trapezoidal cross-section than with springs with a square cross-section. Thesefewadvantagesandthehig h er ma nu fac tu ringcostsarethereasonswhythe tra pe zoi daldiscspringisofnopractical impor tance today.Figure 40Disc Spring withtrapezoidal cross sectionSpecial Types81Chapter 9Dimensional Tables829.1Explanation of the Tables........................................................................................ 83 Article Reference........................................................................................................ 83 Load and stress specications ................................................................................... 839.2Dimension Tables for SCHNORR Disc Springs .......................................................... 849.3Dimension Tables for Corrosion Resistant SCHNORR Disc Springs........................ 989.4Dimension Tables for Heat Resistant SCHNORR Disc Springs ............................... 1089.5Dimension Tables for SCHNORR K Disc Springs................................................ 1289.6Dimension Tables for SCHNORR Z Disc Springs ................................................ 134Dimensional Tables8399.1 Explanation of the TablesThefollowingtableslistthespringstoDIN 2093aswellasthosetoSchnorrWorks Standards. Those to DIN 2093 are shown in heavy type. The prex A, B and C show the corresponding series.All sizes are normally keptinstockandtheheavytypedoesnot indicate a better delivery. The article number quoted is for normal manu facturefromspringsteelwithphos -pha te nish.theundersideatpointIIorIIIwhicheveris the greater.Static or infrequently loaded springs may becompressedtotheatcondition(see section2.1).Itshouldbenotedthatfrom s = 0.75 h0 the actual characteristic pro gres -si ve lyincreasesfromthatcalculated(see sec tions 1.7 and gure 10).Fordynamicapplicationthecalculationin section 2.2 must be completed. With the help of the drawn graph for stress and the fatigue life dia grams (gures 18 20) the expected dy na mic life may be obtained without cal cu -la ti on.All values are based on a Youngs mo d u lus Eof206000N/mm2with=0.3andare thereforeonlyvalidforDiscSpringsfrom springsteeltoDINEN10132-4andDIN 17221 (e.g. 51 CrV 4 or C 67S). The use of other materials necessitates re cal cu la ti on with the correct value for Youngs modulus E. For lower tensile strength the free height h0 and theoverallheightl0mustbeamended(see chapters 1 and 2).When considering the use of special sizes or springs from special materials we re com-mendyouleavetheworktous.Wewillbe pleased to go through the necessary cal cu la- ti ons quickly, at no cost and advise you of the possibilities of manufacture.Figure 41Cross section with main dimensionsArticle ReferenceReference for a Disc Spring with De = 40 mm. Di = 20.4 mm and t =1.5 mm: Disc Spring 40 x 20.4 x 1.5 or for a spring to DIN 2093: Disc Spring DIN 2093-B 40 or with the article number: Disc Spring 012800Load and stress specicationsThe load and the corresponding stresses are givenforthefourpointss=0.25h0, s = 0.5 h0, s = 0.75 h0 and s = h0. This allows the relevant graphs for load and stress to be accurately drawn.At s = 0.75 h0, DIN 2093 quotes rounded values for the deection s. Spring load F and thecorrespondingstresssarecalculated exactlyfortheroundedvalues.Thequoted stress at s = 0.75 h0 is the tensile stress on 849.2 Dimension Tables for SCHNORR Disc SpringsArticle Ordering Dimensions Weight/ StressNo.1000 pcs. OM DeDit l0 h0 h0/tat s = h0 [mm] [mm][mm][mm] [mm][kg] [N/mm2]

0001006 3.2 0.3 0.450.150.500.044 16230002008 3.2 0.2 0.40.201.000.064 7100003008 3.2 0.3 0.550.250.830.093 13320004008 3.2 0.4 0.60.200.500.126 1421000550 C8 4.2 0.20.450.251.250.055 1003000600 B8 4.2 0.30.550.250.830.080 1505000700 A8 4.2 0.40.60.200.500.107 160500080010 3.2 0.3 0.650.351.170.157 114700090010 3.2 0.4 0.70.300.750.211 131100100010 3.2 0.5 0.750.250.500.266 136500110010 4.2 0.4 0.70.300.750.193 138400120010 4.2 0.5 0.750.250.500.243 1441001300 C10 5.2 0.250.550.301.200.109 957001400 B10 5.2 0.40.70.300.750.170 1531001500 A10 5.2 0.50.750.250.500.214 159500160012 4.2 0.4 0.80.401.000.297 122800170012 4.2 0.5 0.850.350.700.374 134300180012 4.2 0.6 1 0.400.670.450 184100190012 5.2 0.5 0.90.400.800.345 161900200012 5.2 0.6 0.950.350.580.415 170000210012 6.2 0.5 0.850.350.700.310 154400220012 6.2 0.6 0.950.350.580.373 185300230012.55.2 0.5 0.850.350.700.382 1288002050 C12.56.2 0.350.80.451.290.251 1250002500 B12.56.2 0.50.850.350.700.346 1388002700 A12.56.2 0.71 0.300.430.488 1666002750 C14 7.2 0.350.80.451.290.308 1018002800 B14 7.2 0.50.90.400.800.425 1293002900 A14 7.2 0.81.10.300.380.676 155100300015 5.2 0.4 0.950.551.380.468 107900310015 5.2 0.5 1 0.501.000.588 122600320015 5.2 0.6 1.050.450.750.708 132400330015 5.2 0.7 1.10.400.570.828 137300350015 6.2 0.5 1 0.501.000.553 127500360015 6.2 0.6 1.050.450.750.665 1377Dimensional Tables85 6 15 mmDeection s, Load F and Stress at s = 0.25 h0 s = 0.50 h0 s 0.75 h0 s = 1.00 h0

s F s F s F sFc

[mm][N] [N/mm2] [mm][N] [N/mm2] [mm][N] [N/mm2] [mm] [N][N/mm2] 0.038 453430.075 84 7500.110117 1187 0.150153 1753 0.050 122330.100 20 4330.15026 600 0.20030 733 0.063 464010.125 79 7500.190105 1057 0.250126 1290 0.050 693650.100 130 7920.150186 1281 0.200238 1832 0.063 214090.125 33 7530.19039 1044 0.25042 1251 0.063 525010.125 89 9380.190119 1325 0.250142 1621 0.050 783430.100 147 7490.150210 1218 0.200269 1750 0.088 513780.175 82 6970.26098 951 0.350108 1158 0.075 752850.150 133 6630.230182 1168 0.300220 1698 0.063 1044100.125 195 8840.190282 1447 0.250357 2028 0.075 794050.150 140 7600.230192 1084 0.300232 1322 0.063 1103590.125 206 7780.190297 1280 0.250377 1803 0.075 303800.150 48 7020.23058 980 0.30063 1169 0.075 884850.150 155 9120.230213 1303 0.300257 1591 0.063 1223430.125 228 7490.190329 1238 0.250418 1749 0.100 853850.200 141 7140.300178 988 0.400206 1205 0.088 1162930.175 208 6710.260282 1122 0.350352 1687 0.100 2244210.200 405 9540.300557 1600 0.400694 2358 0.100 1504930.200 263 9230.300350 1291 0.400424 1596 0.088 1963720.175 361 8280.260502 1350 0.350641 1990 0.088 1344750.175 239 8940.260324 1249 0.350404 1569 0.088 2145310.175 394 10070.260547 1417 0.350699 1795 0.088 1112450.175 200 5680.260270 955 0.350337 1444 0.113 845060.225 130 9320.340152 1284 0.450160 1542 0.088 1204200.175 215 7910.260291 1105 0.350363 1388 0.075 2394030.150 457 8640.230673 1419 0.300855 1957 0.113 684180.225 106 7700.340123 1061 0.450131 1274 0.100 1204190.200 210 7870.300279 1101 0.400338 1363 0.075 2843900.150 547 8260.230813 1341 0.3001040 1836 0.138 1014010.275 154 7350.410175 998 0.550181 1202 0.125 1333830.250 221 7110.380280 992 0.500321 1199 0.113 1712690.225 302 6300.340409 1093 0.450499 1625 0.100 2143580.200 395 7890.300555 1291 0.400704 1865 0.125 1384240.250 229 7870.380291 1100 0.500334 1331 0.113 1784000.225 314 7520.340426 1060 0.450519 130786Article Ordering Dimensions Weight/ StressNo.1000 pcs. OM DeDit l0 h0 h0/tat s = h0 [mm] [mm][mm][mm] [mm][kg] [N/mm2]

003700156.20.7 1.10.400.570.778 1428003800158.20.7 1.10.400.570.654 1646003900158.20.8 1.20.400.500.740 1881004100 C168.20.40.90.501.250.444 988004300 B168.20.61.050.450.750.672 1333004400168.20.7 1.150.450.640.786 1555004500168.20.8 1.20.400.500.888 1580004600 A168.20.91.250.350.391.002 1555004700186.20.4 1 0.601.500.677 816004800186.20.5 1.10.601.200.850 1021004900186.20.6 1.20.601.001.024 1225005000186.20.7 1.250.550.791.197 1310005100186.20.8 1.30.500.631.353 1361005200188.20.5 1.10.601.200.762 1101005300188.20.7 1.250.550.791.073 1412005400188.20.8 1.30.500.631.213 1468005500188.211.40.400.401.524 1468005550 C189.20.451.050.601.330.651 1052005600 B189.20.71.20.500.710.999 1363005700 A189.211.40.400.401.418 1558005800208.20.6 1.30.701.171.191 1202005900208.20.7 1.350.650.931.393 1302006000208.20.8 1.40.600.751.574 1373006100208.20.9 1.450.550.611.776 1416006200208.211.550.550.551.978 1574006300 C2010.20.51.150.651.300.876 1024006400 B2010.20.81.350.550.691.394 13860065002010.20.9 1.450.550.611.573 15600066002010.211.550.550.551.752 1733006700 A2010.21.11.550.450.411.913 15600068002010.21.25 1.750.500.402.181 19690069002010.21.5 1.80.300.202.610 1418007000 C22.5 11.20.61.40.801.331.361 1178007100 B22.5 11.20.81.450.650.811.799 1276007200 A22.5 11.21.251.750.500.402.814 1534 15 22.5 mmDimensional Tables879Deection s, Load F and Stress at s = 0.25 h0 s = 0.50 h0 s 0.75 h0 s = 1.00 h0

s F s F s F sFc

[mm][N] [N/mm2] [mm][N] [N/mm2] [mm][N] [N/mm2] [mm] [N][N/mm2] 0.100 2223280.200 411 7270.300578 1195 0.400733 1734 0.100 2564790.200 474 9090.300666 1291 0.400844 1624 0.100 3675230.200 689 9970.300982 1423 0.4001261 1800 0.125 843990.250 131 7350.380155 1018 0.500165 1220 0.113 1724200.225 304 7900.340412 1115 0.450503 1377 0.113 2544610.225 461 8710.340641 1238 0.450798 1539 0.100 3083430.200 579 7490.300825 1218 0.4001059 1749 0.088 3633860.175 697 8200.2601004 1287 0.3501319 1831 0.150 853190.300 126 5830.450139 791 0.600137 944 0.150 1303500.300 206 6460.450245 885 0.600267 1070 0.150 1913820.300 317 7080.450400 980 0.600462 1195 0.138 2362530.275 414 6000.410550 1034 0.550672 1580 0.125 2863330.250 523 7450.380733 1256 0.500912 1803 0.150 1404170.300 222 7690.450265 1056 0.600288 1279 0.138 2554340.275 446 8150.410594 1135 0.550725 1412 0.125 3092920.250 564 6600.380791 1124 0.500984 1624 0.100 4253880.200 814 8240.3001181 1309 0.4001537 1842 0.150 1214400.300 186 8090.450214 1106 0.600223 1333 0.125 2334210.250 417 7920.380572 1126 0.500699 1387 0.100 4513820.200 865 8140.3001254 1295 0.4001631 1826 0.175 2144320.350 342 7970.530413 1103 0.700453 1327 0.163 2624160.325 442 7750.490570 1080 0.650668 1320 0.150 3153980.300 557 7480.450751 1048 0.600921 1300 0.138 3743110.275 685 6960.410949 1147 0.5501201 1690 0.138 4943740.275 917 8230.4101288 1336 0.5501648 1944 0.163 1414220.325 219 7760.490254 1067 0.650268 1283 0.138 3044210.275 547 7930.410745 1112 0.550929 1394 0.138 4124520.275 754 8560.4101045 1206 0.5501323 1520 0.138 5444840.275 1010 9200.4101418 1300 0.5501815 1646 0.113 5483790.225 1050 8090.3401531 1301 0.4501976 1821 0.125 8904840.250 1708 10300.3802507 1665 0.5003222 2310 0.075 8574270.150 1695 8770.2302576 1381 0.3003340 1843 0.200 2404880.400 370 8970.600425 1227 0.800444 1478 0.163 3064120.325 533 7710.490710 1083 0.650855 1335 0.125 6933830.250 1330 8150.3801952 1316 0.5002509 182588 23 31.5 mmArticle Ordering Dimensions Weight/ StressNo.1000 pcs. OM DeDit l0 h0 h0/tat s = h0 [mm] [mm][mm][mm] [mm][kg] [N/mm2]

007400238.20.7 1.50.801.141.939 1173007500238.20.8 1.550.750.942.192 1257007600238.20.9 1.60.700.782.472 1320007700238.211.70.700.702.753 14660078002310.20.9 1.650.750.832.270 15000079002310.211.70.700.702.527 15560080002310.21.25 1.90.650.523.172 18060081002312.211.60.600.602.255 14670082002312.21.25 1.850.600.482.807 18340083502312.21.5 2 0.500.333.359 18340086002510.211.750.750.753.105 1371008700 C2512.20.71.60.901.291.994 1238008800 B2512.20.91.60.700.782.543 12380089002512.211.80.800.802.832 15730090002512.21.25 1.950.700.563.526 1720009100 A2512.21.52.050.550.374.219 16220092002810.20.8 1.750.951.193.233 10780093002810.211.90.900.904.062 12770094002810.21.25 2.050.800.645.057 14190095002810.21.5 2.20.700.476.051 14900096002812.211.950.950.953.789 14150097002812.21.25 2.10.850.684.717 15830098002812.21.5 2.250.750.505.645 1676009900 C2814.20.81.81.001.252.760 1282010000 B2814.211.80.800.803.468 12820101002814.21.25 2.10.850.684.317 1702010200 A2814.21.52.150.650.435.166 156201030031.5 12.212.11.101.105.035 125001040031.5 12.21.25 2.20.950.766.268 134901050031.5 12.21.5 2.350.850.577.501 1448010650 C31.5 16.30.81.851.051.313.442 1077010700 B31.5 16.31.252.150.900.725.384 144201080031.5 16.31.5 2.40.900.606.443 1730010900 A31.5 16.31.752.450.700.407.546 157001100031.5 16.322.750.750.388.605 1923Dimensional Tables899Deection s, Load F and Stress at s = 0.25 h0 s = 0.50 h0 s 0.75 h0 s = 1.00 h0

s F s F s F sFc

[mm][N] [N/mm2] [mm][N] [N/mm2] [mm][N] [N/mm2] [mm] [N][N/mm2] 0.200 2793970.400 448 7330.600544 1007 0.800602 1221 0.188 3323840.375 560 7140.560717 988 0.750842 1214 0.175 3912510.350 687 5950.530925 1046 0.7001119 1563 0.175 5073150.350 909 7230.5301249 1241 0.7001536 1820 0.188 4634690.375 802 8770.5601055 1221 0.7501273 1512 0.175 5384510.350 964 8490.5301325 1204 0.7001629 1487 0.163 8704220.325 1627 9230.4902320 1511 0.6502955 2159 0.150 4754290.300 872 8130.4501217 1152 0.6001536 1446 0.150 8633990.300 1630 8680.4502331 1404 0.6003000 2010 0.125 11594730.250 2250 9940.3803338 1586 0.5004320 2178 0.188 4923970.375 870 7450.5601168 1041 0.7501436 1295 0.225 3314990.450 515 9190.680601 1265 0.900635 1519 0.175 3673890.350 644 7300.530868 1031 0.7001050 1268 0.200 5855000.400 1021 9380.6001359 1312 0.8001647 1624 0.175 8483570.350 1573 7920.5302232 1320 0.7002814 1895 0.138 10404250.275 2007 8980.4102910 1410 0.5503821 1988 0.238 3483750.475 553 6920.710661 947 0.950723 1149 0.225 5123850.450 872 7180.6801135 1004 0.9001337 1226 0.200 7373270.400 1339 7350.6001853 1225 0.8002322 1797 0.175 10034240.350 1899 9110.5302745 1478 0.7003511 2074 0.238 5904670.475 992 8700.7101266 1204 0.9501482 1480 0.213 8444510.425 1519 8490.6402089 1200 0.8502590 1491 0.188 11494060.375 2159 8830.5603065 1423 0.7503949 2049 0.250 4355150.500 681 9500.750801 1304 1.000859 1577 0.200 4764140.400 832 7760.6001107 1086 0.8001342 1344 0.213 9075130.425 1634 9680.6402246 1369 0.8502785 1703 0.163 10333710.325 1970 7950.4902854 1281 0.6503680 1806 0.275 5874260.550 951 7880.8301170 1091 1.1001309 1320 0.238 7613850.475 1343 7230.7101800 1009 0.9502207 1254 0.213 10333510.425 1912 7740.6402697 1276 0.8503413 1838 0.263 3844480.525 594 8250.790687 1132 1.050722 1363 0.225 7914490.450 1409 8440.6801923 1194 0.9002359 1478 0.225 12605010.450 2314 9500.6803249 1354 0.9004077 1689 0.175 13913820.350 2669 8140.5303905 1310 0.7005036 1826 0.188 21994810.375 4239 10200.5606148 1607 0.7508054 226790 34 50 mmArticle Ordering Dimensions Weight/ StressNo.1000 pcs. OM DeDit l0 h0 h0/tat s = h0 [mm] [mm][mm][mm] [mm][kg] [N/mm2]

0111003412.312.251.251.256.006 12010112003412.31.25 2.351.100.887.477 13220113003412.31.5 2.51.000.678.948 14420114003414.31.25 2.41.150.927.074 14350115003414.31.5 2.551.050.708.465 15720116003416.31.5 2.551.050.707.911 16580117003416.322.850.850.4310.57 1790011850 C35.5 18.30.92.051.151.284.952 1042011900 B35.5 18.31.252.251.000.806.865 1258012000 A35.5 18.322.80.800.4010.97 16110121004014.31.25 2.651.401.1210.40 12130122004014.31.5 2.751.250.8312.45 12990123004014.323.051.050.5316.63 14550124004016.31.5 2.81.300.8711.89 13920125004016.323.11.100.5515.89 15710126004018.323.151.150.5815.04 1712012700 C4020.412.31.301.307.067 1024012800 B4020.41.52.651.150.7710.53 13590129004020.423.11.100.5514.06 1733013000 A4020.42.253.150.900.4015.72 15950131004020.42.5 3.450.950.3817.52 1871013250 C4522.41.252.851.601.2811.34 1227013300 B4522.41.753.051.300.7415.89 1396013400 A4522.42.53.51.000.4022.77 15340135005018.41.25 2.851.601.2816.138920136005018.41.5 3.31.801.2019.31 12040137005018.423.51.500.7525.79 13380138005018.42.5 4.11.600.6432.14 17840139005018.434.41.400.4738.35 18730140005020.423.51.500.7524.85 13710141005020.42.5 3.851.350.5430.97 15430142005022.423.61.600.8023.82 15110143005022.42.5 3.91.400.5629.68 1653014400 C5025.41.252.851.601.2813.82 10060145005025.41.5 3.11.601.0716.54 1207Dimensional Tables919Deection s, Load F and Stress at s = 0.25 h0 s = 0.50 h0 s 0.75 h0 s = 1.00 h0

s F s F s F sFc

[mm][N] [N/mm2] [mm][N] [N/mm2] [mm][N] [N/mm2] [mm] [N][N/mm2] 0.313 6374290.625 998 7890.9401175 1083 1.2501258 1304 0.275 8153940.550 1395 7340.8301825 1026 1.1002162 1255 0.250 10973210.500 1982 7300.7502725 1225 1.0003397 1807 0.288 9134610.575 1546 8580.8601990 1190 1.1502347 1464 0.263 12244470.525 2192 8410.7902997 1186 1.0503704 1472 0.263 12914950.525 2313 9330.7903163 1316 1.0503908 1635 0.213 20974450.425 4003 9520.6405803 1527 0.8507498 2150 0.288 4584270.575 712 7860.860831 1076 1.150884 1302 0.250 7314090.500 1277 7660.7501699 1073 1.0002059 1329 0.200 18643930.400 3576 8370.6005187 1332 0.8006747 1878 0.350 9044060.700 1459 7501.0501780 1033 1.4001984 1253 0.313 11143760.625 1929 7020.9402550 981 1.2503061 1207 0.263 18003930.525 3363 8550.7904781 1392 1.0506096 1988 0.325 12244300.650 2102 8020.9802758 1122 1.3003281 1376 0.275 19723750.550 3663 8250.8305195 1359 1.1006580 1948 0.288 21823650.575 4030 8100.8605642 1333 1.1507171 1946 0.325 5654220.650 876 7760.9801018 1067 1.3001072 1283 0.288 11094310.575 1953 8100.8602616 1134 1.1503201 1410 0.275 21754840.550 4041 9200.8305730 1314 1.1007258 1646 0.225 23363920.450 4481 8350.6806544 1339 0.9008456 1871 0.238 33514700.475 6453 9970.7109359 1573 0.95012243 2219 0.400 10414970.800 1620 9141.2001891 1253 1.6002007 1514 0.325 15244330.650 2701 8140.9803659 1148 1.3004475 1421 0.250 27733830.500 5320 8150.7507716 1296 1.00010037 1825 0.400 7573250.800 1178 5971.2001375 817 1.6001459 984 0.450 13794230.900 2184 7791.3502606 1069 1.8002837 1293 0.375 19182590.750 3392 6091.1304586 1054 1.5005603 1577 0.400 37034070.800 6733 9171.2009315 1529 1.60011673 2244 0.350 50435300.700 9546 11381.05013688 1824 1.40017650 2590 0.375 19663970.750 3478 7451.1304702 1048 1.5005745 1295 0.338 30083730.675 5601 8171.0107902 1330 1.35010098 1922 0.400 22474660.800 3924 8721.2005222 1220 1.6006329 1509 0.350 32613640.700 6044 8061.0508510 1324 1.40010817 1920 0.400 8544100.800 1328 7551.2001550 1035 1.6001646 1251 0.400 12424470.800 2028 8281.2002512 1145 1.6002844 139792 50 80 mmArticle Ordering Dimensions Weight/ StressNo.1000 pcs. OM DeDit l0 h0 h0/tat s = h0 [mm] [mm][mm][mm] [mm][kg] [N/mm2]

014600 B 5025.4 23.41.40 0.70 22.09 1408014700 5025.4 2.5 3.91.40 0.56 27.52 1760014800 A 5025.4 34.11.10 0.37 32.85 1659014950 C 5628.5 1.5 3.451.95 1.30 20.85 1174015000 B 5628.5 23.61.60 0.80 27.81 1284015100 A 5628.5 34.31.30 0.43 41.57 1565015200 6020.5 24.12.10 1.05 38.16 1284015300 6020.5 2.5 4.31.80 0.72 47.69 1376015400 6020.5 34.71.70 0.57 57.04 1560015500 6025.5 2.5 4.41.90 0.76 44.20 1527015600 6025.5 34.651.65 0.55 52.86 1592015700 6030.5 2.5 4.31.80 0.72 39.94 1572015800 6030.5 34.71.70 0.57 47.77 1782015900 6030.5 3.5 5 1.50 0.43 55.10 1834016050 C 63311.8 4.152.35 1.31 32.53 1315016100 B 63312.5 4.251.75 0.70 44.85 1360016200 633134.81.80 0.60 53.86 1679016300 A 63313.5 4.91.40 0.40 62.13 1524016400 7025.5 24.52.50 1.25 50.78 1135016500 7030.5 2.5 4.92.40 0.96 59.53 1430016600 7030.5 35.12.10 0.70 71.19 1502016700 7035.5 35.12.10 0.70 65.21 1615016800 7035.5 45.81.80 0.45 86.13 1845016900 7040.5 45.61.60 0.40 77.04 1813017000 7040.5 56.21.20 0.24 95.15 1700017100 C 713624.62.60 1.30 44.66 1295017200 B 71362.5 4.52.00 0.80 56.11 1246017300 A 713645.61.60 0.40 88.63 1594017400 80312.5 5.32.80 1.12 82.01 1233017500 803135.52.50 0.83 98.01 1321017600 803146.12.10 0.53 130.0 1480017700 803635.72.70 0.90 91.92 1497017800 803646.22.20 0.55 121.9 1626017850 C 80412.25 5.22.95 1.31 63.54 1311017900 B 804135.32.30 0.77 84.92 1363Dimensional Tables939Deection s, Load F and Stress at s = 0.25 h0 s = 0.50 h0 s 0.75 h0 s = 1.00 h0

s F s F s F sFc

[mm][N] [N/mm2] [mm][N] [N/mm2] [mm][N] [N/mm2] [mm] [N][N/mm2] 0.350 194