On the Quantum Theory of Impact Phenomenon for the Conditions of Elastic Deformation of Impacted Body

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1 International Letter of Chemitry, Phyic and Atronomy Online: ISSN: , Vol. 1, pp doi: / 013 SciPre Ltd., Switzerland On the Quantum Theory of Impact Phenomenon for the Condition of Elatic Deformation of Impacted Body Zdziław Pluta, Tadeuz Hryniewicz* Kozalin Univerity of Technology, Raclawicka 15-17, PL Kozalin, Poland * addre: If one ha jut got a hammer every problem eem to remind you the nail. Abraham Malow ABSTRACT The work contain ome of the element of adequate quantum theory of impact phenomenon. Thee element form the prelude to verification of the exitent non-adequate theory of the impact phenomenon. At firt a correct definition of impact ha been formulated. For comparion, the interpretation of the elatic impact according to the exitent knowledge i given. Then, taking advantage of the new correctly formulated the principle of mechanical energy conervation, the energetic tate of impacting body have been decribed. Baing on thi, the formula on dynamic deflection ha been derived. Thi formula i adequate in character and fully correpond with invetigated reality. Keyword: Impact; Quantum (potential); Potential field; Energy; Principle of mechanical energy conervation; Space-time; Dynamic 1. INTRODUCTION In the framework of introduction it i worth underlining the title name of the theory of impact phenomenon thi work ha been devoted to. Thi i a quantum theory and uch a notation wa introduced on purpoe. One would like to tre that it doe not refer only to the theorie decribing microcopic reality. A quantum change in energy take place alo in macrocopic ytem which reflect the preented here theory. Quantum refer imply to the potential, i.e. a meaure of energy, that i a portion of thi magnitude. One hould admit that thee portion refer to the potential behaviour of a body between conecutive energy tate. Thee tate are marked on the neighbouring potential field. The ue of properly formulated principle of mechanical energy conervation on thee field i the key to olve the impact problem that i the dynamic deformation of impacted material. Thi paper i to preent jut an adequate cognition way. SciPre applie the CC-BY 4.0 licene to work we publih:

2 46 Volume 1. SPOTS OF IMPACT PHENOMENON OCCURRENCE Impact occur during operating of a variety of device and intallation. Operating of mot machine, epecially in cae of to-and-fro motion machine, i aociated with impact. Sometime the impact occur in conequence of clearance appearance, where the element are connected, and often the impact loading accompany inevitably with a normal work of machine (mithy/forging machine, pneumatic drill/hammer). The trength calculation of element of that kind of machine are to take into account the impact apect. Stree ariing inide thee element, a well a their deformation, will be many time higher than in cae of their tatic loading only. Selection of a material for uch element i quite an eential problem for material engineer. Therefore at firt thi phenomenon hould be recognized, decribed, and formulated quantitatively. Thi phenomenon, a being coniderably complex, ha not been recognized fully. The analyi of reference of the ubject, preented in the next Chapter, i to reveal what drawback are characteritic for the exitent impact theory. Firt of all there i lack of decription of thi phenomenon, and it appear that there are till no proper cognition method applied. It appear, the claical approach to the conidered problem i not enough now. Impact reult not only from the characteritic of particular machine. It i alo the eence of the machining proce itelf. Platic treatment, epecially free forging, i a good example to illutrate the occurrence of impact a a neceary condition of deired material deformation. The impact phenomenon i ued alo to determine a pecified meaure of material hardne. One of them i Shore method in which the meaure of hardne i bound height of a weight ended with a teel phere or diamond cone, falling down from a determined height on the tudied material. It i known that the Shore clerometer erve for the purpoe. Alo a Poldi hardne teter, a a comparative method, i baed on the impact phenomenon. Impact i a phenomenon the material reitance againt it i invetigated. The reitance of a material to impact i called the impact trength. The Charpy pendulum machine i ued to thi kind of durability/trength reearch. The impact occur alo during material treatment by mean of a high-preure waterabraive jet a well a the abraive jet only. Apart from the other, the problem of mapping of curvilinear trajectory in the machining zone, a well a evaluation of the urface roughne formed with thi method, occur here [1]. According to the reference [1], the equation of thi trajectory correpond with the logarithmic piral. It alo ay that in the reference, e.g. in [, 3] there i an attempt to equalize the trajectory by parabola or by mean of a polynomial of higher degree. Given example of decription of the determined trength invetigation and machining procee where the phenomenon of impact occur indicate that the problem i not o well known. The Author reject the up-to-date claical tool. Thee tool are not ued to olve the problem becaue they rather overhadow a proper olution. Therefore ome new tool are created. Thee new tool allow for different thinking about the impact problem with the reult being it final olution. Included at the beginning the aphorim i referred jut to the content of lat paragraph. Let thi hammer-nail link of the cognition proce (Fig. 1) be ome ort of the warning ign on the way to cognition of the natural reality.

3 International Letter of Chemitry, Phyic and Atronomy Vol Fig. 1. Hammer-nail link of the cognition proce. 3. CRITICAL ANALYSIS OF LITERATURE INFORMATION ABOUT IMPACT Of the impact phenomenon jut an enigmatic information i found. To tudy the category of mechanical phenomena bearing in mechanic the name of impact, the method being the theorem of impule i till applied. The impact i called a [4]: Such a phenomenon, during which in a very hort time (e.g. in time equaling to few thouandth part of a econd) the amount of motion of material ytem obtain an increment/increae not very mall one but of the ame order a the amount of motion of the ytem. It i worth remaining at thi paragraph to analyze critically ome thing. Let ome terminological quetion be the ubject of thi analyi. The claical mechanic ay about the amount of motion of a material ytem by referring thi notion to the momentum of the ytem. What for i that unneceary erroneou terminological tructure? Though motion i a mind magnitude [5] o it i immeaurable unlike in cae of phyical magnitude. Thu one cannot ay about the amount of motion. The category of amount concern the magnitude which poe unit, that i the magnitude of phyical nature. The next terminological quetion of which the eence i analogou and contradict to the rule of monomiality [6] require that only one name mean that notion. It concern the impule for which the ynonym i, according to the exitent knowledge, time-effect. There are notion of theorem of impule or momentum, or ometime of momentum and time-effect. It appear the impule i quite different than time-effect, becaue impule i the derivative of acceleration, wherea the time-effect i the derivative of inertia force. Such a differentiation of magnitude i noted at a proper decription of variable motion or dynamic of a material body. That i not poible in the frame of claical mechanic and thi i why the time-effect i determined apparently/artificially. It i done by mathematical tranformation of a formula on inertia force, thi formula being the econd Newton law. One may add that o called the d Alembert principle wa formed by the ame way Quo vadi, cience? A to the definition of impact, it doe not explain anything. The amount of motion of a ytem obtain uch increment a the amount of a ytem, or impetu of a ytem gain uch increae a the ytem impetu. No clarification! Viciou circle! A critical analyi i required concerning thi fragment of exitent knowledge on the impact phenomenon. Thi critic i to revel reaon of the cientific impoibility a to the quantitative decription of the impact. Further it i aid that the impule theorem doe not

4 48 Volume 1 allow to determine the variability of intantaneou force in time. Hence the character of thi function i unknown. Here again the notion of an intantaneou force appear. The intantaneou force i the force referred to one intant of time, o one cannot conider it in time (or collection/et of intant). It i imply a thrut/oppoition force of the deformed material, or contact force. The claical theory of colliion of olid bodie, created by a erie of invetigator, beginning from Galilei, and finihing on Newton, aumed the collided bodie a ideally rigid and the proce of colliion a momentary. That theory enabled only to determine effect of colliion, i.e. change of velocity of the colliding olid, or internal veracitie of the impact phenomenon. Time of it duration, magnitude of the contact force and deformation remained completely non-clarified. The Hertz theory partly olve thi problem. It i baed on the hypothei that relation between the contact force and pot deformation of the bodie at impact i the ame a at their tatic compreion. In fact thi hypothei i equivalent with avoiding of the inertia force. Therefore experimental check/proof of thi theory revealed only a atifactory agreement of calculation and experimental data. However, it i too little! Baed on the literature one could develop the impact phenomenon. Let u finih thee conideration by referring to [7] where further cientific development related to the dicued ubject are preented. However, the analyi of the literature indicate that there i no exact olution, a to the quantitative decription, of the impact problem. For the olution, the principle of mechanical energy conervation (properly undertood, i.e. other than up-to-date claical one), will be ued. Thi newly formed principle ay that if an undone work i added to the done gravitational work, the planned work i obtained. Jut a few word about Hertz theory: thi relation between the force and deformation during impact i really the ame a at the tatic contact of material bodie. That i known but doe not mean the neglecting of inertia force. Thee force, a well a other force being the meaure of interaction of the bodie during impact, are independent from each other. They are to be conidered eparately and cloer explained. 4. DEFINITION OF IMPACT PHENOMENON Impact ha not been properly defined a yet that i evident in the preented critical literature analyi of the ubject. It wa not poible becaue even decription of the ubject phenomenon ha erroneou tructure and doe not explain the eence. Therefore the exitent claical theory of impact i not adequate and doe not refer to the invetigated reality. Impact i a phenomenon of dynamic character (where i the dynamic, the impact occur). The problem i the dynamic ha not got a proper interpretation. The exitent cience, baed on the o called d Alembert principle accepted a a paradigm, doe not decribe the variable motion (thi motion prove of the body dynamic, and not the ma of the body). All thee olution of differential equation, contituted in accordance to the d Alembert principle, do not correpond with the real motion but are rather decription of fictitiou/ apparent motion. Thi principle, a itelf, i fictitiou in nature [8]. A general definition of the impact phenomenon hould be a follow: Impact i the phenomenon of dynamic deformation of material bodie. Thi definition correpond with any rule obligatory at creation of all definition [6]. Of coure, one could formulate the definition in a way the dynamic notion would not be opened but only with a determined explanation, e.g. the dynamic take place in pace-time only, that i between potential field. Therefore the impact definition may be formulated a follow: Impact i the

5 International Letter of Chemitry, Phyic and Atronomy Vol phenomenon of deformation of material bodie in pace-time. The notion of pace-time, potential field, a well a the claification of the former one are preented in reference [9-11]. Now one could develop thi general definition by formulating ome detailed definition what could mean a parallel creation of claification of the impact phenomenon. Therefore, taking into account the claification dicriminant, being the tate of aggregation of a material body, one hould introduce and define the notion of: mechanical, hydraulic, pneumatic impact. Therefore the definition of mechanical impact hould be: Mechanical impact i the dynamic phenomenon of deformation of olid. The next claification criterion i, e.g. the type of deformation of impacted body (treated a the rigid body, or a olid), or elatic, platic, elato-platic deformation. Then going further, more detailed definition hould be given, e.g. the elatic mechanical impact would be defined a: Elatic mechanical impact i a phenomenon of dynamic deformation of a olid, with the deformation being elatic in character. The graphical illutration of thi claification of impact phenomenon i preented in Fig.. However, the mechanical impact i to be conidered, without further development of other type of impact. The Fig. contain ome exemplified branche of claification of the impact phenomenon. Fig.. Claification of the impact phenomenon. 5. INTERPRETATION OF THE ELASTIC IMPACT ACCORDING TO EXISTENT KNOWLEDGE Earlier decribed the claical theorem of impule doe not allow to decribe the coure of impact nor even it terminal parameter. Of impact itelf one judge only baed on a determined relation between the velocitie of bodie before impact and after it (that i about retitution coefficient). To determine dependence between the dynamic and tatic deflection of an elatic element, blown by a determined rigid body, the o called principle of energy conervation i commonly ued. It i uually aumed that a ma of ideally elatic element i negligibly mall in relation to the ma of hitting body. Such a pecific ytem will be analyzed here:

6 50 Volume 1 according to the exitent claical knowledge, and then uing a new revolutionary impact theory, being adequate in it character. Let the body of weight Q (Fig. 3) ret at vertically ituated pring of the rigidity coefficient k (here a pecific mechanical rigidity, or elaticity i conidered, o at the ame time one may aume the elaticity coefficient). The elatic deflection of the element with the tatic deflection h ha occurred. Fig. 3. Energetic tate of a body referred to the impact phenomenon. In the next tep, thi body i lifted to the height h o. That reulted the primarily compreed pring returned to the free initial tate. The ditance between thi weight and a free frontal urface of pring, denoted by ymbol H, form (together with the ytem parameter h o ) the characteritic of the econd ytem tate. In the next tep the hitting body (the third ytem tate) fall down, hit the pring and deflect it. Thi time the deflection, a the dynamic one h d, i repectively bigger than the primary tatic deflection. No force i marked here, no particular potential field i marked nor named, i.e. no ytem characteritic adequate to it real behaviour ha been introduced. The attempt wa made to keep the claic exitent coure of argumentation/reaoning in the form of natural till repected one. The three decribed ituation have been eparated only, by the number (1,, 3), which correpond to the tatic energetic tate of a material body, with firt two tate being temporary and the third, intantaneou one. The temporary tate may lat for a determined erie/equence of moment/intant. The intantaneou tate mean it lat jut one moment. Further on, thee energetic apect will be dicued. The o called principle of energy conervation wa ued. The tage of uch directed creative action reult from the indicative cheme of particular force coure (Fig. 4). According to the claical interpretation of reality they are the following force: gravity force

7 International Letter of Chemitry, Phyic and Atronomy Vol Q and the elaticity force S. Both force have been preented in function of the path/way length h of the material body. Fig. 4. The coure of the o called potential energy and deformation energy. According to the mentioned principle, lo of potential energy of the weight Q, which equal: T Q H (1) i equal the energy of deformation gained by the elatic element. That former energy i equal: h d where the ymbol S d denote the dynamic force of elaticity. Taking into account that: S d h U d () Sd kh d (3) the o called elatic energy of deformation i written by the following formula: kh U d (4).

8 5 Volume 1 Therefore, by comparing formulae (1) and (4), the following form of the conervation principle i obtained: khd QH hd (5) and further on, becaue of: Q kh (6) it aume the following configuration: wherea developed, take thi form: After olution of the equation, due to h d, one obtain: kh khd H hd (7) hd hhd h H 0 (8). h h h h H (9) d auming the poitive olution, a negative () ha no phyical ene. Therefore, finally: h h h h H (10). d By analyzing the lat dependence one may determine h d alo for H = 0. Then h d = h. One may admit, that i a pity no phyical ene of the whole reaoning ha been given by taking care of uch a ene at the end of the path/way. In the lat picture (Fig. 4) there are hatched area which correpond with the o called potential energy of the weight, a well a deformation energy. The apparent in Fig. 4 the interrogative ign mean the exitent grounded knowledge form much room for a doubt. Putting aide the dicuion on ariing terminological ubject one ha to tate that cience ay about the equality of work: gravitational and elatic one, repectively. They are no energie nor their change. One hould ak, where i the inertia force of the body. Hence the analyzed ytem contain three bodie: earth, pring, and the body impacting the pring. Therefore three force hould be conidered: gravity force Q, elaticity force S, and inertia force B (o many force a bodie). The lat one ha been omitted. One hould admit there cannot be equality of work in uch a body motion, that i in the free motion. Even after taking into account the inertia force, there will not be equality in the particular work. The equality occur but in the forced motion. It touche the work done: by determined bodie and over the determined bodie. Therefore the impact phenomenon may be properly decribed only by uing properly undertood the principle of mechanical energy conervation.

9 International Letter of Chemitry, Phyic and Atronomy Vol ADEQUATE PRINCIPLE OF MECHANICAL ENERGY CONSERVATION IN USE FOR DESCRIPTION OF THE IMPACT PHENOMENON The mechanical energy, the principle of conervation of thi type of energy, and impact phenomenon are to be conidered. In [1], the ene of inertia notion wa preented. Before the conervation principle i preented here, in reference to the impact phenomenon decription, it i worth preenting the definition of inertia and mechanical energy [1,13]. The inertia of a body i it uceptibility/tendency to take the mot advantageou it tate, that i table one : thi definition of inertia indicate clearly the ene/turn of meaure of thi magnitude. Thi force will be alway directed into the table tate of the body. The mechanical energy i the energy of olid, and thi i the definition of that magnitude with the potential a the meaure. It i one of many type of energie, a fundamental magnitude with the following definition, a: The energy of a body i it ability to perform a work at tranition to the neighbouring potential field. The principle of energy conervation (energy meaure or potential) ay that the um of all energie on all potential field i unchanged and contant [1]. Thu the general notation of that principle poee the following form: n i1 V i idem (11). The grounded, common, claical, o called principle of the mechanical energy conervation ha nothing to do with the properly undertood the mechanical energy. Telling the truth, the exitent knowledge in thi ubject may be eventually treated a the principle of ummation of the gravitation work in the variable motion cycle. Symbol V i of that decription mean the meaure of a non-determined energy, i mean the potential number, and n i the number of all potential. More detailed notation of the preented principle, referred to the particular potential field (0, 1,,, j), ha the following configuration: n 0 V n 0 1 j 1 V... n j i i i1 i1 i1 V i idem (1). Here the ign j denote the number of conecutive potential field, and ymbol n j number of potential referred to thi field. Coming to decription of the impact phenomenon, at firt it i worth determining the energetic tate of the ytem under a forced motion. Thi will allow to know the relation occurring between particular force and the gravity force. Then, after taking to analyi the ytem in a free motion referred to the impact, thi knowledge will be needed. When a ytem i in a table tate (Fig. 5), then the inertia force B o i the bigget one and co-exit with the gravity force Q. The tate of co-exitence i denoted by a ymbol, then Q B o. The tatic equilibrium of the ytem i recorded here by the following equality: Q = S o, where S o mean the initial elaticity force. From that the former record doe not reult that any energetic tate (here, a table tate) take place imultaneouly. Not before, the extended record (Q B o = S o ) reveal that mytery at full length.

10 54 Volume 1 Fig. 5. Coure of particular force under variable forced motion. After thee explanation the principle of energy conervation on initial field, zero potential field, may be recorded a: It more exact form may be preented a follow: V S V V idem (13). Q S Q B h S h Qh B h idem B 0 (14). The particular ymbol mean here: V S elatic potential, V Q gravitation potential, V B inertia potential, B o initial inertia force, or the inertia intenity of potential field, repectively. Thu S o i elatic intenity, and Q gravitation intenity of thi field. It i worth preenting in more detail the characteritic of thi potential field [14-]. Thi i a temporary table tatic potential field (SSPF), o the whole ytem i in temporary table tatic energetic field. The following energie are on thi field: elatic, gravitation, and inertia. To replace the body on a neighbouring, firt potential field, ome external timulu hould be ued. Let it be a biologic body (a palm). In a moment, being on intantaneou table tatic potential field (SSPF), that timulu introduce ytem to the pace-time determined by the length h (dotted area). In thi area, there are four different bodie in action, i.e. the biologic body, earth, ubjected body, and an elatic element. The coure of force, interacting one on another, i different in character that i apparent from the analyzed Fig. 5. On the next, or firt a marked, potential field, temporary and untable tatic potential field (USPF), there i no elatic energy. It ha been replaced here by the biologic energy. The

11 International Letter of Chemitry, Phyic and Atronomy Vol principle of um energy conervation (their meaure, or potential) on thi field ha the following form: V F V V idem (15) Q B where V F denote the biologic potential. A detailed record of that energetic equilibrium ha the following tructure: F Q B h Fh Qh B h idem (16) where F 1 denote a biologic force (intenity of the biologic firt potential field), B 1 i the inertia force on thi field, or it inertia intenity. The gravitation intenity worth to admit ha not undergone to a change. By connecting the formulae (14), (16), one obtain the equation in the form: S0 Q B0 h F1 Q B1 h (17) and after taking into account, S o = Q B o, a contraction of the equation by h and ome other operation the following record i obtained: F B Q (18). 1 1 Taking into account further equilibria of the ytem on the firt field (force equilibrium), recorded thi way: F Q (19) 1 B 1 lead to the ytem of equation (18), (19), of which the olution due to F 1 and B 1 give the reult: 3 1 F1 Q B1 Q (0). Tranmiion of the body to another, a higher poitioned potential field, a een in Fig. 5, will not reult in a change of equilibrium of all force. Therefore the ame relation will be taking place there a well. Let u conider now a free motion of the body with an impact phenomenon that happened at ome time. The body will be firt carried up at height H againt a free urface of pring where S = 0 (Fig. 6). Releaed from the palm pre/queeze, the body will be at firt moment on an intantaneou untable tatic potential field (USPF), and further it will be paing through the conecutive (0, 1,, ) alo intantaneou potential field.

12 56 Volume 1 Fig. 6. Coure of force in a free motion, correponding with impact phenomenon. The principle of energy conervation on three conecutive potential field will be analyzed. Such a limitation reult from the goal preented here: derivation of an adequate formula on dynamic deflection. In connection with thi, the coure of force for a pace-time being ituated between thee field, have been marked in Fig. 6 (olid line). In addition, the coure of force for only one of the conecutive pace-time have been introduced (dahed line). At firt thi principle for zero initial (0) and econd () potential field ha been formulated. Then the attention will be concentrated on the firt (1) field where for H > 0 thi kind of energy doe not occur. The principle of conervation of all intantaneou mechanical energy on the mentioned firt two potential field ha the following form: and after more detailed approach: V 0 0 Q V V V V (1) B Q 0 B0 h0 S h Qh B h B S Q h () where h o denote length of the firt/initial, and h of third pace-time.

13 International Letter of Chemitry, Phyic and Atronomy Vol Due to the equality of neighbouring pace-time: econd and third (h 1 = h ) one could treat the ame record a the law of threhold moment lever, a it wa done earlier in [13]. In thi cae only the firt um of moment correpond with potential, and the right ide, recorded a: S h 1 + Qh 1 +B h 1 would mean the um of threhold moment. Knowing that B o = B 1 =B = Q:, that wa pointed out earlier (ee formula (0)), taking into account alo: h0 H h (3) h h 1 h d h (4) Q kh (5) S k h h kh (6) d 1 after doing ome mathematical operation, ha been obtained finally: 1 1 hd hhd 3h h H 0 (7). Now thi equation hould be olved and a poitive reult taken in view of getting the dependence earched between dynamic and tatic deflection of the elatic element. And thi i: h 1 h H hd 1h h (8). 4 4 Thi i a final mathematic form of the principle of mechanical energy conervation. It may be treated a it pecific concluion coming out of the ubject principle, recorded in a general form (1). If in the frame of olution analyi, H = 0, i ubtituted, one obtain h d = 1.5h, and not h d = h a it i in the exitent theory. One hould tre, that the firt reult ha been confirmed by the experiment, and thi i of great importance. Alo the dependence (8) ha been confirmed by an experiment. That polarization of reult, coming out of the improper claical exitent decription of reality, hould draw an attention of cientit epecially in view of further development of cience. It i worth determining thi energy (internal potential U * ) on the econd field, marked with ymbol 1. Then one may formulate the principle of energy behaviour for the firt two potential field. It i preented a: Qh0 B0 h0 Qh1 B1 h1 S1 h1 U (9). Having in mind that B o = 0.5Q, B 1 = S 1 = Q, h o = H + h, h = h d h, Q =kh, one obtain a a reult: 3 kh H h kh h h U 3 d (30) what after olving, due to U *, give:

14 58 Volume 1 U 9 kh 3kh h d 1 H (31). For H = 0, or the ituation determined by dependence h d = 1.5h, the internal energy potential of thi energy U * = CONCLUSION Preented above the adequate decription of a portion of energetic reality indicate on urgent need to verify the exitent non-adequate theory of impact phenomenon. The range of problem connected with thi phenomenon i quite large. That proper dependence between dynamic and tatic deflection ha been jut derived. It i concerned only with the firt cycle of impact but there are more cycle. Further energetic tate of the conidered ytem have not been decribed yet. Alo the coure of all force in particular pace-time have to be decribed. Temporal coure of thee magnitude alo have not been determined. It i neceary to preent temporary characteritic coure in time of uch magnitude which are the kinetic characteritic of thi ma-elatic ytem. One could indicate ome other magnitude that hould be determined in the frame of the in-depth analyi of impact phenomenon. All thee have o big cognition pace that one cannot place them in one article, or even a cycle of thi type of paper. A eparate book i needed with the propoed title a e.g. Quantum theory of impact phenomenon. It i not the end, becaue alo decription of other phenomena alo hould be verified, and there are lot of them. Summing up, one hould tate that the claical mechanic require a general verification which could allow to formulate adequate in fact decription of the reality. They are generally perpective tak but they are worth noticing at preent, thi way throwing light on further path for the cognition of natural reality. Reference [1] E. Wantuch, R. Kot, Problem of accuracy and curvilinear mapping in high-preure abraive-water-jet treatment. Proceeding of XXVI Scientific School of Abraive Treatment, Łódź, September 003, pp [] A. Momber, R. Kovacevic, ASME Manufacturing Science and Engineering 68(1) (1994) [3] A. Momber, R. Kovacevic, Principle of Abraive Water Jet Machining. Sprinper Verlag Berlin Heilderberg New York, [4] J. Buchholz, J. Leyko, General mechanic. Dynamic (in Polih). PWN, Warzawa-Łódź [5] Zdziław Pluta, Normalizacja 9 (1994) [6] M. Mazur, Technical terminology (in Polih), WNT, Warzawa [7] S. D. Ponomariev (ed.), Contemporary method of trength calculation in the machine building. Dynamic loading (in Polih), PWN, Warzawa 1957.

15 International Letter of Chemitry, Phyic and Atronomy Vol [8] Zdziław Pluta, LAB 6 (004) [9] Zdziław Pluta, NIT (Nauka, Innowacje, Technika) 5-6 (004) [10] Zdziław Pluta, Tadeuz Hryniewicz, Journal of Quantum Information Science 1 (011) [11] Zdziław Pluta, Tadeuz Hryniewicz, Journal of Quantum Information Science 1 (011) [1] Zdziław Pluta, LAB (Laboratoria, Aparatura, Badania) (004) [13] Zdziław Pluta, LAB 1 (005) [14] Zdziław Pluta, Tadeuz Hryniewicz, Int. J. Adv. Manuf. Technol. 4 (009) [15] Zdziław Pluta, Tadeuz Hryniewicz, Int. J. Adv. Manuf. Technol. 43 (009) [16] Zdziław Pluta, Tadeuz Hryniewicz, Int. J. Adv. Manuf. Technol. 51 (010) 35-43, DOI: / [17] Zdziław Pluta, Tadeuz Hryniewicz, Int. J. Adv. Manuf. Technol. 6(5) (01) [18] Zdziław Pluta, Tadeuz Hryniewicz, Tribology Tran. 55() (01) [19] Zdziław Pluta, Tadeuz Hryniewicz, International Letter of Chemitry, Phyic and Atronomy (013) [0] Zdziław Pluta, Tadeuz Hryniewicz, International Letter of Chemitry, Phyic and Atronomy 3 (013) [1] Pluta Z., Hryniewicz T., International Letter of Chemitry, Phyic and Atronomy 4 (013) [] Pluta Z., Hryniewicz T., International Letter of Chemitry, Phyic and Atronomy 6 (013)