Kinetics, Dynamics and Energy of Solid on the Example of a Tool Fixed Flexibly: Part 3 Energy

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1 Internatinal etters f Cheistry, Physics and Astrny Online: -9-5 ISSN: 99-84, Vl. 5, pp 6-6 di:.85/ SciPress td., Switerland Kinetics, Dynaics and Energy f Slid n the Exaple f a l Fixed Flexibly: Part Energy Zdisław Pluta, adeus Hryniewic* Ksalin University f echnlgy, aclawicka 5-7, 75-6 Ksalin, Pland *E-ail address: adeus.hryniewic@tu.ksalin.pl ASAC his wrk is a cntinuatin f the prbles f kinetics and dynaics f slid n the exaple f a tl fixed flexibly under cutting. Present wrk is cncerned n the develpent f wrk and energy. A special attentin has been paid t the wrk descriptin by underlying a distinctness and lack f cnnectin with the energy ntin. Plariatin f these tw agnitudes has been revealed. An adequate and extended definitin f energy in general, with echanical energy in particular, is frulated. here are three kinds f echanical energy cnsidered, lcated n the stable static ptential field being ne f the liits f the achining space-tie. hey are the fllwing energies: repel, inertial, and gravitatinal. Prper easures/ptentials have been assigned t these energies, treating the energy as a ental ntin, having n physical eaning in cntrast t the ptential as the physical agnitude. Keywrds: l; Machining space-tie; Ptential field; Wrk; Energy; Ptential; Mechanics. INODUCION he Authrs wrk [] is referred t, cncerning an adequate apprach t cutting by the tl fixed flexibly. Part f the paper was fcused n the kinetics [], whereas in Part the dynaics f the syste was cnsidered extensively []. Stred energy f the tl will be prvided n the basis f energy ntin, the prperly understd echanical energy f a slid/aterial bdy. An iprtant task is t prvide descriptins f the phenena n adequately defined fundaental ntins.. YPES OF WOKS IN HE MACHINING SPACE-IME In the cutting/achining prcess, the actual types f wrk are as fllws: plastic wrk, the wrks related t elastic strain energy, heat generatin, tl-wrk/tl-chip frictin, tl vibratin, etc. siplify the calculatins, fr ur cnsideratin in the achining space-tie, the fllwing types f echanical wrks are taken int accunt: wrkpiece wrk, wrk ver tl, and wrk ver tl fix with Earth (gravitatinal fix). his is an pen access article under the CC-Y 4. license (

2 Internatinal etters f Cheistry, Physics and Astrny Vl. 5 7 he echanical wrks are as fllws: repel, inertia, and gravitatin. he repel wrk, perfred by the wrkpiece, is the su f wrks perfred ver tl and tl fix with the Earth. herefre (.) All these wrks are perfred in vertical directin, in accrdance with the directin f particular frces, that are the fllwing frces: repel, inertia, and gravity. he wrk is a prduct f frce and path length (n the directin f this easure f deterined reasn), if the frce is a cnstant agnitude. his refers t the gravity frce. If a frce is characteristic with a deterined variability, then the crrespnding wrk shuld be expressed by eans f integral. herefre all the wrks are expressed by frulae d d p d g (.) (.) d d d p d g (.4) where the upper liit f integratin crrespnds with the sae with the height f the achining space-tie (see Fig. []). Nw the acceleratin p will be expressed as the functin f path length. d this, the functin expressed by frula (.4 []), then f t, is t be transfred. his is t separate the expnential ter t present it as the functin f crdinate. herefre t e (.5) It will be substituted t the frula (. []), that results in p (.6) Nw, by expressing the inertia frce by the prduct f ass and acceleratin accrding t the frula (.5 []), ne btains p, p e t

3 (.7) and g g (.8) y substituting the frula (.7) in the place f integrand (.), ne btains d d d (.9) After substituting the frula (.8) in the place f integrand (.4), ne btains nw d d g d d g g g g (.) y regarding the values f agnitudes, g,, ( 8. kg; 8 9. g s- ; 7.85 ; s) in the frulae (.9 []), (.7) and (.8), ne btains g N (.) (.) with the value fr, the inertia frce N, and fr 7.85 that frce equals N. he repel frce, calculated acc. t the frula (.8), equals 8 Vlue 5

4 Internatinal etters f Cheistry, Physics and Astrny Vl. 5 9 g (.) with the value fr the repel frce ( ) 7.85 that frce equals ( ) N. Having at dispsal the values f agnitudes, g,, N, whereas fr, ne ay calculate nw, accrding t the frulae (.), (.9), and (.), particular wrks, such as: gravity inertia, and repel. herefre, g J (.4) J (.5) g J (.6) he wrk unit is jule (J), that results fr peratin n the units kg kg N J SI (.7) s s kg s kg s N J SI and the equality f units f particular wrks SI SI SI (.8) (.9) In Fig., the geetric iage f inertia wrk and dependence f inertia frce n the displaceent f tl, are presented. Fig. presents this kind f iage f the gravity wrk and dependence gravity frce n the displaceent f tl. In Fig., there is the geetric iage f the repel wrk and the dependence f repel frce n the displaceent f tl. Particular wrks are presented by the dashed areas under the plts f crrespnding t the the dependences f frces n the higher described the independent variable.

5 Vlue 5 Fig.. Geetric iage f inertia wrk and the dependence f inertia frce displaceent f tl. n the Fig.. Geetric iage f gravity wrk and the dependence f gravity frce n the displaceent f tl.

6 Internatinal etters f Cheistry, Physics and Astrny Vl. 5 Fig.. Geetric iage f repel wrk and the dependence f repel frce f tl. n the displaceent. ENEGY OF HE SOID/OO FIXED FEXIY All agnitudes cnsidered earlier [-], bth kinetic and dynaic nes, described the tl behaviur in the achining ne. he tl was ving in vertical directin between the neighburing ptential fields: stable static ptential field SSPF and instantaneus unstable static ptential field ASPF. On these fields the cutting tl pssessed deterined energetic states. On the btt field, that is SSPF, it was under the stable energetic state, whereas n the upper field ASPF there was the instantaneus unstable energetic state nted [4-9]. hat is a generally clarified atter f stred energy f the slid/tl fixed flexibly. It is clearly evident that the energy cannt characterie a tl placed in the space-tie. herefre the wrk, as ne f any dynaic agnitudes, is nt an energy nr its easure. hus the identificatin f energy with wrk is grundless and errneus. It is tie nw t clarify the atter. Hwever, first the existent knwledge n echanical energy, which is the energy f a slid, is t be given. It is wrth nting that it is

7 Vlue 5 ipssible rather t present all aspects f the prble in this paper. Here se literature references, cncerning energetic aspects f the reality, will be delivered. At the beginning, let us start with the definitin f energy, as the ntin f this agnitude is fundaental and priary fr further cnsideratins. Of curse, there is a definitin f energy in the literature but it is detached fr the reality, r n clearly précised cnnectin is nticed. Se even say there is n definitin f the ntin. he questin is then, why this ntin is used if it is essenceless? Is it really cntentless? And, aybe it is t difficult? he authr f the wrk [] attepts t explain it; he des it with a surprising sincerity - ( ) It sees that is uch easier t understand what is the entrpy than that what is energy. It is difficult t prvide a strict definitin f energy. One ay vaguely accunt that it is ability f a bdy t perfr wrk, r se prperty f bent/crked space-tie, r even the crk itself. ut t be sincere, nne f the definitins is sufficiently cnvincing. Instead, understanding f the entrpy des nt present any difficulties ( ). he scientific actins, aiing at frulatin f the adequate definitin f energy, have halted in the pint, where the energy is identified with wrk. It is wrth prviding at least se exaples f elabratins which cnfir this thesis. It is stated in the wrk [] that the echanical energy in the state I against state II is called the wrk prvided by a syste under transitin fr state I t state II. iterature [] treats the energy as a scalar physical agnitude, expressed in the units f wrk, deterining the ability f a bdy r bdies syste t perfr a wrk under transitin fr ne state t the ther. Definitin f energy, given in wrk [], explains that the energy is the agnitude being the easure f ability f a aterial syste t perfr the echanical wrk. iterature [] prvides infratin that the ntin f energy, as a scientific ter, n the grund f science was intrduced fr the first tie in 87, when has Yung (77-89), prfessr f natural philsphy at the yal Institutin f Great ritain, defined it as a prduct f ass (r weight) f a bdy and its velcity under the secnd pwer. In 8 as prvides that literature that frula was crrected by substituting the unit factr by the factr equal.5. As it appears, that crrectin was intrduced nly fr the purpse t equalie the kinetic energy with wrk. hus until tday the energy is identified with wrk nne the less there is a big difference between these agnitudes. Naturally, there were attepts undertaken t change that state-f-art. Se exeplary elabratins [4-7] prve f that. In thse wrks, the existent state f knwledge n the energy issue has been evaluated critically, indicating that the energy is the ental ntinal agnitude. Hence, it cannt be easured. Furtherre then it results that it des nt have a physical nature r character. he wrd ability has a priary eaning in the definitin f energy, s it ust be put n the first place, in accrdance with the rule f syste [8]. In these circustances ne cannt verlk the definitin f ter: «ptential efficiency, pssibility f ding sething, suitability fr sething». hat definitin has been excerpted fr the vcabulary []. Accrding t that vcabulary, the wrd ptential eans: «sticking t sething, able t ccur, appear in deterined cnditins, by a prper actin; presuable, assuable, pssible t ccur/appear». In the cntext f these explanatins, ne cannt identify the energy with wrk. It is a ental agnitude and this is why a deterined easure shuld be assigned t it. Nt earlier than this easure will be the physical agnitude. he ptential is this easure.

8 Internatinal etters f Cheistry, Physics and Astrny Vl. 5 Nw the adequate extended definitin f energy ay be given because nt all factrs f the reality have been taken int accunt. It is abut the echanical energy, as such refers t the described here reality. he echanical energy, r the energy f slid, is nt nly the ability t perfr the echanical wrk. hat energy is cnnected with the need ver perfring wrk n a deterined bdy. Such a kind f energy ay als indicate n the need t perfr wrk ver the bdy ties with ther bdy. hus the echanical energy is the ability t perfr wrk by a bdy, the need t perfr wrk ver bdy r the bdy ties with ther bdy. here are tw kinds f echanical energy: active, eaning the ability t perfr wrk by a bdy; and passive, infring f the need t perfr wrk ver r the bdy ties with ther bdy. Nw that general definitin f echanical energy shuld be referred t the cnsidered technlgical reality. he active energy is cncerned with the achined wrkpiece which perfrs wrk ver the tl. he passive energy refers t the tl and its gravitatinal ties with Earth. his is abut the fllwing energies: repel, inertia, and gravitatinal. It is tie nw t deterine easures f these particular energies, i.e. ptentials. here will be cnsidered the ptentials f energy n the stable static ptential field SSPF (Fig. 4). All these energies are the static echanical energies, as they refer t the static field. Ptential is defined as the prduct f intensity f a ptential field by the distance between the neighburing ptential fields (here it cncerns the height f space-tie, i.e. ). Intensity f the ptential field is reflected siply by a deterined frce. Fig. 4. Machining space-tie (dtted area) and the syste f initial frces n the stable static ptential field. One ay differentiate here the repel ptential V (.)

9 4 Vlue 5 inertia ptential and the gravity ptential V (.) V (.) where the sybls and dente the initial repel frce (in pint ) and the initial frce f inertia at the sae pint, respectively. he repel ptential is naturally equal t the su f ptentials f: inertia, and gravity. herefre V V V (.) hat eans at the sae tie that the active ptential is the su f passive ptentials. One ay develp nw the frulae n deterined ptentials. It results fr the frula (.5 []) that v (.4) egarding then (.4) in the frula (.), ne btains V v v v (.5) Cparing (.5) with (.9), which are the frulae n the inertia wrk and inertia ptential V, ne states that V (.6) as V (.7) and (.8) Dividing V by, ne btains the fllwing dependence:

10 Internatinal etters f Cheistry, Physics and Astrny Vl V (.9) herefre the inertia ptential is directly prprtinal t the inertia wrk, and the cefficient f prprtinality has the value higher than ne. It results fr the frulae (.) and (.) that the gravity ptential V is equal t the ttal gravity wrk f tl, that is the wrk n the path crrespnding with the distance between the neighburing ptential fields: r V g (.) hus, after substituting the frulae (.5) and (.) t (.), ne btains V g (.) v V g (.) hat is the fr being the law f cnservatin f ptentials, i.e. the easure f energy. hat eans the repel ptential is equal the su f inertia ptential and the gravity ptential. 4. CONCUSION In the fraewrk f extended analysis, the ntin f energy has been explained, with a special attentin t the echanical energy. It was prved that the energy is nt a physical agnitude, but it is rather a ental agnitude, t which a deterined easure shuld be assigned. A deterined ptential, with the nae resulting fr the kind f frce n the ptential field, fulfils the easure rle f echanical energy. One ay state the fact f filling up a gap f existing cgnitive nature in the cntext f stred energy f the tl fixed flexibly. It was filled up with the ntin f energy, a fundaental ntin in the deterined reality in view f understanding it prperly. hat is a pity, even the latest literature [9-], devted t the echanics f slids, have nt taken int cnsideratin that classical ethd f investigatin, acc. t which each prble shuld be begun fr the s called status questinis, i.e. the explanatin f ntins and their definitins. eferences [] Zdisław Pluta, adeus Hryniewic, Internatinal Jurnal f Advanced Manufacturing echnlgy 6(5) () 59-54; DOI:.7/s [] Zdisław Pluta, adeus Hryniewic, Internatinal etters f Cheistry, Physics and Astrny () () 5-47.

11 6 Vlue 5 [] Zdisław Pluta, adeus Hryniewic, Internatinal etters f Cheistry, Physics and Astrny () () -8. [4] Zdisław Pluta, adeus Hryniewic, Internatinal etters f Cheistry, Physics and Astrny 4 () 8-6. [5] Zdisław Pluta, adeus Hryniewic, Internatinal etters f Cheistry, Physics and Astrny 5 () [6] Zdisław Pluta, adeus Hryniewic, Internatinal etters f Cheistry, Physics and Astrny () [7] Zdisław Pluta, adeus Hryniewic, Internatinal etters f Cheistry, Physics and Astrny 7() () 85-. [8] Zdisław Pluta, adeus Hryniewic, Jurnal f uantu Infratin Science (JIS) () () 7-4, DOI:.46/jqis..8. [9] Zdisław Pluta, adeus Hryniewic, Jurnal f uantu Infratin Science (JIS) () () 49-6 DOI:.46/jqis... [] P. Atkins, Galile s finger (in Plish), Editrial Huse EIS. Pnań, 6, st editin. [] M. Sycak, (ed.), Plish vcabulary, Vl., A - K, Warsawa, 978. []. Petrlin-Skwrńska, (ed.), Ppular Encyclpaedia PWN (in Plish), Vl., Świat Książki, Warsawa, 987. [] M. Jeżewski, Physics (in Plish), PWN, Warsawa, 966, 9th editin. [4] adeus Hryniewic, Zdisław Pluta, Understanding the eaching Prcess r the st Essence f Energy, Prc. f the 8 th Wrld Cnference n Cntinuing Engineering Educatin, hee A: Knwledge, Skills and Cpetency, May -6,, rnt, Ontari, Canada,, pp. 5-. [5] Zdisław Pluta, Fru Akadeickie (999) 56-58, 6th year, (eturn t the surces). [6] Zdisław Pluta, A (abratria, Aparatura, adania) 4 (5) 4-46, th year. [7] Zdisław Pluta, Energetyka 7 (5) 496-5, 65th year. [8] M. Maur, echnical terinlgy (in Plish), WN, Warsawa, 96. [9] J.. aylr, Classical echanics (in Plish), PWN, Warsawa, 6, st editin. [].D. andau, J. M. ifsyc, Mechanics (in Plish). PWN, Warsawa, 6, 4th editin (transl. fr ussian). ( eceived 6 May ; accepted June )