Theoretical Foundation for Mechanical Products Service Life Prediction

Transcription

1 Theoreticl Foundtion for Mechnicl Products Service Life Prediction V V Konovodov 1, A V Vlentov, T V Lfetov 1, M N Bslev 1 Novosibirsk Stte Agrrin University 147 Nikitin St, Novosibirsk, Russi; phone: (383) Yurg Institute of Technology, ffilite of Tomsk Polytechnic University 6 Leningrdsky St, Yurg, Russi; phone: (38451) e-mil: vlentov@mil.ru Abstrct. The rticle presents theoreticl foundtions for prediction of service life of mechnicl products, bsed on the ftigue theory nd ftigue limit. Ultimte mplitude nd ultimte stress digrms re presented. Wohler curve, chrcterizing mteril durbility, is constructed on the results of the tests. Anlyticl studies show tht bout hlf of the griculturl mchinery filures occur for production resons. This rte hs been mintining t the sme level for the pst 15 yers. Opertion life of complex mechnisms is usully determined by durbility of the wekest components nd prts. For exmple, life of high pressure hoses, composed of high-pressure sleeves nd nozzles is determined by durbility of sleeve screening brid if creful embedding of nozzles. The service life of internl combustion engines depends on durbility of vlve springs, specifying the output prmeters of engines, nmely fuel consumption nd cpcity. 1. Timeliness of the reserch Service life of suspensions is determined by durbility of the spring min pltes, life of crbide cutting tools - by durbility of crbide pltes if relible connection to holders, life of working bodies of feed mills nd tillge mchines - by durbility of their working bodies, etc. Thus, to predict service life of mchines, method is to be developed for prediction of durbility of components or prts, which re the wekest components in the whole mchine. Durbility of ny mchine element is chrcterized by the number of lod cycles before filure. The problem of determining the durbility of components or prts, nd hence service life of mchines nd mechnisms is being studied constntly; but it hs not been resolved definitively. For components of griculturl mchinery, exposed to extreme stresses (in res of stress concentrtion, locles of high tempertures nd residul stresses) strength clcultions (strength of mterils) re trditionlly used, which cn be indequte nd sometimes inpproprite. As result, for exmple, cbles, hving tenfold sfety mrgin, collpse under lods which re significntly lower thn the design lods. Content from this work my be used under the terms of the Cretive Commons Attribution 3.0 licence. Any further distribution of this work must mintin ttribution to the uthor(s) nd the title of the work, journl cittion nd DOI. Published under licence by Ltd 1

2 Modern computtionl methods llow determining durbility (sfety fctor of durbility) of components or prts, under certin mgnitude nd nture of stress [1], which does not gurntee their uptime. Therefore, development of methods of forecsting of sfety nd durbility under multiple-cycle ftigue is n urgent tsk. New techniques of engineering clcultions bring bout fundmentlly new opportunities for lifetime ssessment of griculturl mchinery t the design stge nd during their opertion. Methods of reserch, uthenticity nd vlidity of the results: Stresses, vrible in time, occur in structurl elements under lod, vrible in mgnitude or direction. For exmple, the cr xle is bent under the weight lod of the cr. In the upper prt of ech xis cross section norml tensile stresses occur. During the motion the wheel nd the xis, rigidly connected to the wheel, rotte, nd ech point of the xis lterntely moves from the top (extended) of the hlf-section, to the bottom (compressed), nd vice vers. Vrible stresses rise in shfts of mchines, in brided sleeves of high-pressure hoses, in vlve springs of internl combustion engines, in spring pltes, in suspensions, in working bodies, etc. Time-scle stress vritions cn be represented by grph; time t or the number of cycles of certin frequency N is plotted on the bsciss xis, vlue of norml σ stress or tngentil τ stress - on the ordinte xis. It is usully ssumed, tht time-scle stress vritions re chrcterized by sine curve (see Figure 1). cycle Figure 1. Time-scle stress vritions In fct, s shown by numerous experiments [], the type of the curve is irrelevnt; mteril strength t vrible stresses depends minly on stress vlues: σ nd σmin. Popultion of ll successive vlues of stress vritions for one period of chnge is clled the stress cycle. The lrgest (lgebriclly) stress of the cycle is clled imum nd is denoted σ (or τ for tngentil stresses). We principlly consider norml stresses. For tngentil stresses similr conclusions, formuls nd clcultion procedures re pplicble. Algebric hlf-sum of imum nd minimum stress of the cycle is clled the verge stress.

3 min (1) Algebric hlf-difference of imum nd minimum stresses is clled the cycle mplitude. а min () Averge stress of the cycle cn be either positive or negtive. The mplitude of the cycle is lwys positive. If stresses σ nd σmin re equl in mgnitude nd opposite in sign, then the cycle is clled reversed. In the reversed cycle σv = 0, nd σ=σ= σmin If stress σ nd σmin re not equl in bsolute vlues, the cycle is clled irregulr. Irregulr cycle cn be lternting (where σ is positive nd σmin is negtive) or constnt (when both σ nd σmin hve the sme sign). In prticulr cses, when σmin or σ is equl to 0, the cycle is clled fluctuted. Rtio of σmin stress to σ stress is clled rtio R of cycle irregulrity. R min (3) Stress cycles with the sme vlues of irregulrity rtio re clled like. For reversed cycle R = -1, for fluctuted cycle R = 0, if stresses hve positive vlues. Results of the reserch To determine durbility, specil testing of mteril mechnicl properties (ftigue) is crried out. For these tests, series of identicl smples (t lest 10) re produced. Pure bending tests with reversed cycle of stress vritions re the most common. They re crried out in the following order. Figure. Wohler curve for R = -1 3

4 In the first smple specil device produces stress cycles chrcterized by the vlues σ=σι nd σmin. Stress vlue σι is set ner to ultimte tensile strength σв of the mteril so s to obtin ftigue filure of the smple fter reltively smll number of cycles NΙ. The test result is plotted (in the dopted scle) s point Ι, the bsciss is equl to the number of cycles NΙ, tht cused the smple filure, nd the ordinte shows the stress vlue σι (Figure ). Then, the next smple is bended to filure, if stresses σ =σιι<σι nd σmin= σιι. The test result is plotted s point ΙІ. In the test series, points III, IV, V nd etc. re obtined. Joining the points, we plot so-clled ftigue curve or the Wohler curve (A.Wöhler first studied the phenomenon of ftigue in ), corresponding to reversed cycles (R = -1) (see Figure ). By this method, ftigue curves, corresponding to cycles with other vlues of R, cn be obtined. Limiting stress digrm (LSD) shows the reltionship between the limit cycle prmeters σvσ. LSD is used for functionl connections tht re used in durbility nlysis under vrying stresses. For single point of the digrm, series of identicl smples (t lest 10) should be tested, nd the Wohler curve should be constructed; the ltter shows the vlue of ftigue limit for the cycle with given R. For exmple, tests were conducted t irregulr stress cycle. As result, vlue of ftigue limit σ-ι is found. The coordintes of this limit cycle re: σ =σ=σ-1, σv=0 (see Eq. (1) - (3)). Tht is, the point is on the ordinte (point A) (Figure 3). Figure 3. Digrm of limit mplitudes long σ В For ny irregulr cycle, ccording to the durbility limit R, determined by tests, it is esy to find nd. According to the formul (3), chrcteristic of stress cycle, determined by rtio /, but. Consequently,, where is э (1 ) 4

5 or 1 nd (1 ) (4), (5) In prticulr, for fluctuted cycle (R=0, 1 ) t durbility limit equl to σ 0 cp 0 This cycle corresponds to point C in the digrm shown in Fig. 3. Figure 4. Digrm of limit stresses long σ В This digrm shows ech cycle with two points. For exmple, limit reverse cycle is shown with ( В ) points A nd A1: point B corresponds to limit constnt stress, limit fluctuted 0 0; cycle is shown with points C nd F. To determine ftigue limit for the cycle with rtio R we drw hlf-line t ngle β to the x-xis from zero [7]. Tngent of the ngle is determined by the formul: 5

6 tg min 1 R (6) K-ordinte of crossing between the hlf-line nd limit stress line gives vlue σr= σ. To determine res of cycles sfe from ftigue nd flow, on the hlf-line 0B (points of the hlf-line correspond to time-constnt stresses: σ=σ, σ=0) we plot point tht corresponds to the cycle with σ=σ= σт nd drw from this point two stright lines s shown in Fig..5. Are of sfety life cycle is limited by the segment АА1, xes re limited by the curves AS, A1S1 nd the broken curve STS1. According to numerous studies [3,4,5,6,7], LSD from Fig. 4 cn be simplified s it is represented in Fig. 5,6. Figure 5. Simplified digrm of the limit stresses long σ Т Figure 6. Rel digrm of limit stresses 6

7 Conclusions The proposed method is universl. For exmple, bsed on testing of certin helicl spring, mde of certin steel, LSD cn be plotted for ny helicl springs mde from this steel. In tests it is importnt to find point of the Wohler curve inflection tht chrcterizes springs durbility equl to Nб; tht is, to find point Д (see Fig. 6) experimentlly, but not by stndrd specifictions. References [1] Drkov A.V. Strength of Mterils /A.V. Drkov, G.S. Spiro. - M.: Higher School, p. [] Lsukov, A.A., Mokhovikov, A.A. Influence of tool modified lyer on stress - Strin stte of cutting wedge, Proceedings th Interntionl Forum on Strtegic Technology, IFOST 01 [3] Chernukhin R.V. Relibility of steering gers of truck vehicles// Applied Mechnics nd Mterils Vol p [4] Putilov U.S., Nekrsov Yu.I., Lsukov A.A. Loding of Mnufcturing System Elements t Unstedy Cutting nd the Models of their Arrngement Devitions, Applied Mechnics nd Mterils, Vol. 68 (014), pp [5] Retyunsky O.Y. Method of mking performs for composite reversible cutting pltes // Applied Mechnics nd Mterils Vol p [6] Vlentov A.V., Retyunsky O.Yu. Use of tungsten crbide cutting tools in processing of mining mchinery prts, recovered by surfcing / Mining informtionl nd nlyticl bulletin (scientific nd technicl journl). 01. S3. Pp [7] Vlentov A.V. Retyunsky O.Yu., Konovodov V.V. Incresed durbility nd performnce of cutting tools t processing of weld surfces // Mechnics XXI C