SCIENTIFIC PROCEEDINGS IX INTERNATIONAL CONGRESS ", TECHNOLОGIES, MATERIALS" 2012 ISSN 1310-3946 MODERN TEHNOLOGIES OF PROJECTING, CONSTRUCTING AND MAKING OF CHAIN DRIVES ARE FROM POLYMERIC COMPOSITES

СОВРЕМЕННЫЕ ТЕХНОЛОГИИ ПРОЕКТИРОВАНИЯ, КОНСТРУИРОВАНИЯ И ИЗГОТОВЛЕНИЯ ЦЕПНЫХ ПРИВОДОВ ИЗ ПОЛИМЕРНЫХ КОМПОЗИТОВ

Prof. Dr. Pilipenko O. Mechanical-Technological Faculty of State Technological University, Chernigiv, Ukraine

Abstract: The presented new conception of synthesis of chain drives is from creation of theoretical bases of new methods of computation and constructing taking into account the real dynamic processes, which accompany work of , use of polymeric composite materials, resource-saving technologies and equipment for their realization to serial introduction and industrial mastering of chain-drives, equipped by polymeric components. KEYWORDS: CHAIN DRIVES, DYNAMIC APPROACH, RESOURCE-SAVING TECHNOLOGIES

contour, considered in [3]. In [7] basic attention was 1. Introduction allocated to research: transversal vibrations of branches chain A chain drive is the combined dynamic system both with the contour taking into account the velocity of their movement; concentrated and from distributed masses, every separate to firmness of motion of drive branch of chain contour at the element of which can carry out the specific types of periodic change of her tension (parametric vibrations); vibrations under the action of definite disturbances. The longitudinal vibrations of branches of chain drive; torsion basic disadvantage of existent methods of calculation of vibrations of the system; sources of internal disturbances of chain drives is neglect of dynamic character of loading, on elements of transmission; amplitudes of vibrations and the first place the question of durability of chains [1]. But, dynamic loading in branches chain contour, caused by the without regard to the high load factors (from 6 and anymore), polygonal effect of , different sizes of steps of chain chains continued to disintegrate. The point is that links and accumulated error of chain length, by the determination of parameters came true or quite without the eccentricities of sprockets; to the dynamic irregularity of account of the dynamic phenomena which accompany work rotation of sprockets; total dynamic loading in the branches of chain drive inevitably, or taking into accounts some from of transmission; ways of choice of basic parameters and them by means of too approximate empiric coefficients. optimal parameters of operations of chain drives. But the Besides all calculations touched the simplest chain drives dynamic system of chain drive was limited to again two which consisted of two sprockets and chain contour. sprockets with the masses over brought to them, that enabled Therefore to this day a problem of calculations and at maintenance of basic lines of more combined systems to constructing of combined multimass chain drives is actual on do her analysis simpler. principles of theory of vibrations and operating durability Basic difference of the indicated research from existing by taking into account the real dynamic processes which take then is that first there was the done attempt (what appeared place during their work. fully successful, as further practical applications showed) to The used until now methods of designing chain drives are get universal dependences for the calculation of values of the intended mainly for the elementary two-mass drives, and dynamic loading at different correlations of rigidities of drive they are founded on out-of-date static-empirical concepts, not and driven branches chain contour which is the functions of using latest achievements of science and engineering, and corresponding tensions of branches, on the different stages of therefore do not meet the requirements of modern wear of chain. Development of unified methodology of building any more. The development of science and quantitative estimation of the total dynamic loading in the engineering has resulted in necessity and possibility of branches of chain drive taking into account the basic factors solving the problem of calculations and designing of the of structural, kinematics, technological and operating chain drives based on theory of oscillations and operational character appeared the main result of research [8]. strength regarding really happening dynamic processes [2, 3, By the next stage an analytical decision was carried out for a 4]. Successful solution of economical, energy and ecological 3-mass transmission, but the attempts of analytical decision problems in many respects is application of new for the greater amount of the masses were not crowned by constructional materials in particular polymeric composites success, taking into account education during the decisions for production of machine parts [5, 6]. of boundless equations which do not yield to practical The complex of technologies, being based on dynamic application. Therefore numeral methods, which allowed to approach, application of polymeric composites, resource- create the specialized application packages for an analysis saving with the use of corresponding equipment, optimal and optimal synthesis of chain drives with practically any computer-aided design is presented, allowing yet on the stage amount of the masses on the basis of new (dynamic) of projecting to get the chain drive of high dynamic quality. conception them the automated projecting on the criteria of vibroactivity and vibrodefence, decline of resource- 2. Analysis of researches and basic publications demanding and energy consumption due to application of polymeric composites at the minimum charges of labor and Dynamics of a steady-state motion of 2-mass (from the point time for their development and making [9,10,11], were used of view of theory of vibrations) chain drive, which consisted in future]. Large attention in this period was spared to of drive and driven sprockets and reduced to them the introduction on the row of enterprises of technology of rotating masses, connected by only drive branch of the chain polymeric composites and molds for pressure-die casting at

139 YEAR XX, VOLUME 2, P.P. 139-146 (2012) SCIENTIFIC PROCEEDINGS IX INTERNATIONAL CONGRESS "MACHINES, TECHNOLОGIES, MATERIALS" 2012 ISSN 1310-3946 first sprockets, and then and chains with the aim of η F F x+  2 ω=ω+ 2 [Axx sin( B)k cos( )k ] д ++τω−τω C improvement of dynamic characteristics of chain m C C Z Z m m transmissions and drives. For a scientifically grounded 1 n calculation and choice of chains from polymeric composites where Z 11 ω==ω=ω z...z nn − frequency of without application of groundless of safety factors afterwards disturbances from polygonal effect; m − the brought mass there was considered dynamics of chain drive in transient c processes [12]. In [13] all of it was summarized with the over of the system; ω = − own frequency of examples of the stress-strained state of links of polymeric C m chains and automated calculation of geometry of 13-mass M M R chain-drive. Unfortunately, the results of research of D FR = vibrations of the system; FD = , − forces, dynamics of such chain drive were not published taking into Rn R1 account some awkwardness and more by then issues of the applied to terminal hinges of the loaded branch of chain; А , day, that they were necessary to be decided. Example of the В − coefficients of decomposition in the row of Fourier of automated calculation of dynamics of simpler 3-mass functions of the longitudinal displacements of terminal transmission (with two by a driving and by tightening hinges of branch of chain [13]; k − number of harmonic. ) is made in [14]. Dynamic force in leading branch of the chain contour [13]

 m  F F   ⋅=τ ατ +τ⋅β ατ −τω+τ⋅β  д ++τω C  3. Methods and results )(F с  i eK sin( i+1eK) cos( N) i sin( Z N)k i+1 cos( Z )k     c  m1 mn   3.1.Theoretical prerequisites   (2) Mathematical model of work of n -mass of chain-drive can be written as follows (fig.1): We will consider more detailed the process of vibrations in the system (after completion of some long interval of time), ( ϕϕηϕ  () () ϕϕηϕϕ  )RRRRRRcRRRI +−+−+−+ 11 122112,112211 11 nn 1 (1) which corresponds to the steady-state of operations of drive ϕϕ −−=−+ ′ − ′ +− n ( 11,1 nn 2,11 xx 21 ,11 1 xxn n 1 MRSScRSScRRRc D ;)()() with the purpose of quantitative comparison of dynamic · · · · · · · · parameters during work with polymeric and metallic chains. −+ ϕϕηϕ  + −ϕϕ −+ ϕϕη  + I ii ( −− 11 − ,1 () −− 11 iiiiiiiiiiii () ++ 11 )RRRRRRcRRR iiiii As a result of transformation we will get dependence which ′ ′ describes resilient displacements at the set motion + +1, ( −ϕϕ ++ 11 ) −= − ,1 xiiiiiiiii i x i−1 +1, xiii i −−− x i+1 RSScRSScRRRc i ;)()( · · · · · · · · x)(x A sin( Z ε+δ−τω=τ ) ,

I nn ( −+ ϕϕηϕ  −− 11 + − ,1 () −ϕϕ −− 11 nnnnnnnnnnnn () nn ϕϕη  11 )RRRRRRcRRR n +−+ 2 C ⋅ω A ϕϕ −=−+ ′ −−− ′ − where x = − (3) 1, ( nnn 11 ) − ,1 xnnn n xn−1 1, xnn n 1 MRSScRSScRRRc Rnx ,)()( A 2  η  where i = 2,3,4,...,n - 1; I1,..., Ii,...,In − the reduced moments of 222 +ω−ωδ ω ϕ ϕ ϕ cos( ZC )()  Z  inertia of the rotating masses; 1,..., i,..., n1 − current angles of  m  rotation of the masses (sprockets); c ,..., c , ..., c − rigidity of 1,2 i,i+1 n,1 amplitude of deformation at the set motion; the conforming branches of a chain contour; R1,..., Ri,...,Rn n− radiuses of arrangement of joints of a chain contour on sprockets; δ – corner between the vectors of disturbing forces; Sx1,..., Sxi ,..., Sxn , Sx’1,..., Sx’i ,..., Sx’n − functions of a disturbance of ε – difference of phases between resulting frequency of the terminal joints of branches; η − damping ratio; МD, МR − driving forced vibrations and frequency of own vibrations of the moment and moment of resistance accordingly. system. On fig.2 the results of computations of transients are shown in a chain drive, equipped by metallic and polymeric chains which testify to diminishing of maximal effort in a chain during starting of drive in case of application of parts from a polymeric composite (470 N against 542 N). In addition, after completion of transients (0,15s with on an oscillogram) of vibrations pass to the steady-state behavior, thus for a polymeric chain the size of amplitude of these vibrations less than for metallic. Amplitude-frequency characteristics for this case are brought around to fig. 3, illustrating the calculations on (3). From him evidently, that coincidence of frequency of the forced vibrations with own frequency of vibrations of the system (resonance) for cases 2 and 4 takes place at less frequency by comparison to cases 1 and 3, amplitude of vibrations also almost in 3 times less than. Thus, got results of research transitional and set modes of operations of multimass chain drive taking into account a Fig.1. Structural diagram of a multimass chain transmission moment on the shaft of leading mass, moment of resistance Bringing the revolved masses over to the radiuses of location and damping showed that the size of the dynamic loading of end-capping hinges of branch of chain and substituting decreased both at the use of polymeric sprockets with a rotary motion by forward [13] one, writing down differential metallic chain and, in much more degree, during work of equation in relation to deformation of leading branch of polymeric chain on polymeric sprockets and enable scientifically reasonable replacement of metallic chains chain τ we will get: x )( polymeric.

140 YEAR XX, VOLUME 2, P.P. 139-146 (2012) SCIENTIFIC PROCEEDINGS IX INTERNATIONAL CONGRESS "MACHINES, TECHNOLОGIES, MATERIALS" 2012 ISSN 1310-3946 3.2. Natural frequencies and forms of torsion vibrations The decision of the system of differential equations (1) without right parts gives the natural frequencies of the system, one of which equals a zero (a decision numeral methods on PC of the generalized problem of algebra of own values gives the squares of natural frequencies and own forms of vibrations of chain drive with practically any number of masses) : 1  n n n  2  ∑cn ∑cn ∑cn   1 1 1  1 ;0 pp ϕϕ n−1 ==  + +⋅⋅⋅+  , (4) m1 m2 mn     where cn – rigidities of branches of chain contour; m1,…mn – masses of sprockets and reduced to them. Components of equation (2) are essence partial frequencies of the system.

As early as [7] it was experimentally demonstrated that dimensionless coefficient of damping of D=0,06, i.e. less than 0,1 and that is why behaves to the group of small, that does not conduce to curvature dynamic properties, installation-specific without a friction. There difference in frequencies of natural vibrations without the account of friction and with his account folded just 0,24%. This position was confirmed and in-process [12], a table 1 from which is presented here. In a table 1 numeric data over are brought for frequencies of vibrations depending on the change of parameters of model of the system. Table 1. Natural frequencies of vibrations of a chain drives Metal Polymer Metal Polymer chain on chain on chain on chain on Completed metal metal polymer polymer units sprocket sprocket sprocket sprocket s s s s Frequencie Fig.2. Oscillograms of dynamic forces at starting of the s of system, equipped by a metallic (above) and polymeric (down) undamped 612,4 155,0 548,0 153,8 chain natural vibrations -1 ωс, с Frequencie s of damped 611,3 152,6 546,9 151,4 natural vibrations -1 ωд , с Difference of 0,18 1,5 0,2 1,56 frequencies ∆, %

From these tab.1 and fig.3 evidently, that from four considered variants of combination of metallic and polymeric parts of chain drives between variants "polymeric chain on

1 – Metallic chain on metallic sprockets; metallic sprockets" and "polymeric chain on polymeric 2 – Polymeric chain on metallic sprockets; sprockets" the difference of natural frequencies of vibrations 3 – Metallic chain on polymeric sprockets; presents an unimportant size − 0,6% and that is why the first 4 – Polymeric chain on polymeric sprockets. from variants is not of interest both from the operating point of view and from economic, and most difference between Fig.3. Amplitude-frequency characteristics of drive with natural frequencies taking into account a friction and without metallic and polymeric chains taking into account rigidity of such account folds 1,56% and that is why a friction it is teeth of sprockets possible to ignore.

141 YEAR XX, VOLUME 2, P.P. 139-146 (2012) SCIENTIFIC PROCEEDINGS IX INTERNATIONAL CONGRESS "MACHINES, TECHNOLОGIES, MATERIALS" 2012 ISSN 1310-3946 forced vibrations taking into account damping on the Natural frequencies ω j are fully determined by the diagonal continuous spectrum of a frequencies. Will mark that reverse matrix of the masses (moments of inertia) and symmetric tasks of dynamics of chain drive, i.e. finding of the necessary matrix of rigidities of the dynamic system [9], i.e. masses and rigidities on the spectrum of frequencies of own j)( ω j = 1 1 n 1 CCMMf n )...,,...,,( . The own vectors vibrations in general case have an indefinite decision [9]. For are the functions of both the masses (moments of inertia) and the individualizing of these tasks it is possible to examine the rigidities and natural frequencies : systems, in which every mass has only one the degree of )j( liberty (at determination of the masses on the set spectrum of = 12 n 1 n ,C...,C,M...,,M(fX frequencies), or only those tasks in which the number of (5) ω ))C...,C,M...,,M( varied rigidities coincides with the number of degrees of j 1 n 1 n liberty of the dynamic system (at determination of rigidities = 1 n...,,j . on the set spectrum of frequencies), only. Deciding matrix equation relatively ω ,i.e. exposing the Results of computation of squares of circular frequencies j (what is the roots of the presented matrix equation), circular determinant and replacing in future ω j on pϕi , will get in and cyclic frequencies of own torsion vibrations of chain general case n of natural frequencies. For the semicertain drive, got at application program DINAF [9], it is presented system which the dynamic system of chain drive is, will get in a tab.2. As see, in a tab.2 the first own frequency which must be n − 1 natural frequencies, as one of frequencies will always pϕ 0 equal a zero (the system at a zero natural frequency under the equal to the zero, something differs from him that is action of disturbing forces moves as an only solid). Every explained by the errors of calculations, taking into account natural frequency ω is answered by an own vector complication of the system. j On fig.4 relative amplitudes (forms) of own torsion vibration )j()j()j( )j( = 21 n )X...,,X,X(X the components of which the brought masses over of 8-mass chain drive are shown. are determined within an arbitrary permanent general On frequency pϕ 0 = 0 relation of amplitudes of units own )j()j( )j( multiplier, and their relations 21 X/.../X/X n vibrations will be evened one, i.e.: determine the own form of vibrations, which answers an X X X X X X X 1 2 3 4 5 6 7 ======1 natural frequency ω . j X 2 X 3 X 4 X 5 X 6 X 7 X 8 If to boss so that the sum of absolute values of amplitudes Table 2. Results of own frequency computation equaled unit, then will get the rationed form the rationed Square of Circular Cyclic n )j( )j( circular frequency, frequency, multiplier of which = XN . Then the rationed -1 ∑ i frequency s Hz i=1 0.27 0.52 0.08 ~ )( ~ jj )( ~ j)( form will assume an air 1 / 2 /.../ XXX n , where 180899.69 425.32 67.69 ~ j jj )()()( к = к / NXX is the rationed amplitude of own form, 310577.13 557.29 88.70 i.e. fate which is folded by k -th amplitude from the sum of 761920.19 872.88 138.92 absolute values of all amplitudes of j -th form. Will mark 960862.44 980.24 156.01 that minimization of the rationed amplitude of own form 1354116.00 1163.66 185.20 reduces vibroactivity of the dynamic system of chain drive 3824147.00 1955.54 311.23 on this frequency. Varying some or by all masses and rigidities of the 6086154.00 2467.01 392.64 dynamic system of multimass chain drive in some limits * ** * ** The first form of vibrations (relation of amplitudes of X1/X2) к ≤≤ MMM кк ; ≤≤ CCC ; = 1 K...,,k ; takes place on own frequency p = 69.67 Hz, second = 1 L...,,l , it is possible to lead not only own by ϕ1 frequencies but also own forms (by the relations of (X2/X3) – 88.7 Hz, third (X3/X4) – 138.92 Hz, fourth (X4/X5) – amplitudes). Certainly, at plenty of the masses in the system, 156.01 Hz, fifth (X5/X6) – 185.2 Hz, sixth (X6/X7) – 311.23 debugging all natural frequencies from working frequencies Hz and seventh (X7/(X8) – 392.64 Hz. of rotation is succeeded not always, and then the integral index of dynamic quality of chain drive enters into force − coefficient of dynamics: ⋅ DnF += D max 11 K D 1 8 , (6) ⋅1019,0 P1 where FD max is an absolute root-mean-square of the maximal dynamic loading in the branches of chain contour;

n1 it is frequency of rotation of drive sprocket; D1 it is her diameter; P1 it is power on drive sprocket. Thus, optimization of parameters of the dynamic system of multimass chain drive can be conducted on own forms on resonance frequencies, avoiding the calculations of the Fig.4. Relative amplitudes of own torsion vibrations

142 YEAR XX, VOLUME 2, P.P. 139-146 (2012) SCIENTIFIC PROCEEDINGS IX INTERNATIONAL CONGRESS "MACHINES, TECHNOLОGIES, MATERIALS" 2012 ISSN 1310-3946 3.3.Dynamic loading and irregularity Displacements of a terminal hinges of branches chain contour written down as follows [9]: tc µ 10 N = 2,1 zk − k τω x1 2 ∑ )1( 2 2 sin k z ; π ,12,1 n ++ rucc 2,1 )1)(( k =1 − zkk 1 )1( 

10 ii +1, tc µ zk N = − k τω xi 2 ∑ )1( 22 sin k z ; π ( − iiii +1,,1 ++ rucc − ,1 ii )1)( k =1 − zkk i )1(  10 − ,1 nn tc µ zk N = − k τω Fig.6. Inertial loadings from irregularity of rotation of xn 2 ∑ )1( 22 sin k z , π ( − nnn 1,,1 ++ rucc − ,1 nn )1)( k =1 − zkk n )1( brought masses k 2 As see, dynamic loading in branches of chain contour, where t − a step of a chain; µ zk = − frequency caused by the polygonal effect of sprockets, and the inertia ω 2 loading from the irregularity of rotation the brought masses zn − 2 1 over arrive at significant sizes. The maximal values of the pϕn dynamic loading have branches 8-1 (103,47 N) and 7-8 − coefficient, in what k − a number of harmonics; 98,96 N. The most values of the inertia loading are observed ωωω zz  ==== ω z − frequencies of at the masses 8 (194,95 N) and 7 − 148,09 H. z 2211 nn On fig.7 the results of computation of dynamic irregularity of disturbances are from the polygonal effect of sprockets; rotation the brought masses over are shown after relationship 21 ,,, zzz n − number of teeth of sprockets; pϕn − xn z ⋅=∆ %1002 , where Rn − radiuses of location of corresponding own frequencies of torsion vibrations; u − a R n I I I n 1 2 n−1 hinges of chain on the teeth of sprockets. The most -ratio; r − ,1 nn  ==== − a relation the I 2 I 3 I n irregularity of rotation is had 8 and the 7 masses (accordingly corresponding brought moments over of inertia; N is a 3,25% and 2%). The least is a 5 mass (she is most− 11,22 constituent which takes into account mainly the difference of kg). phases between the torsion vibrations of nearby sprockets [9]; τ − time. Will mark that the number of harmonics is limited 10 (as well as at determination of frequencies and forms of own frequencies, tab.2), as, as marked early in [7], all even harmonics equal a zero, and account only first from them results in an error less than 5%., i.e. an account 10 harmonics mean practically exact decision of a task. Dynamic loading in branches of chain contour, conditioned by kinematics disturbance (as these vibrations are the result of motion of points of support of branches on the set laws Fig.7. Dynamical irregularity of brought masses rotation [7], but not under the action of disturbing forces), written down, as [9]: 3.4. Stress-strained state of sprockets and chains t 10 sin(k τω ) t 10 sin − πτω jk )2( τ ±=  − k z −± k z 2,1 ()( xxcF 212,1 ∑ )1( 2 2 ∑ )1( 2 2 ) Thermal and stress-strained state of sprockets have been π = − zkk )1( π = − zkk )1( k 1 1 k 1 2 investigated by method of finite elements under operational ...... (7) loads and on the basis of this the methods of construction of polymeric sprockets with elements of regulation by their

On fig.5, 6 the dynamic loading is presented in branches of stress-strained state are proposed (fig. 8). chain contour, caused by the polygonal effect of sprockets (by kinematics disturbance), and inertia loading from the irregularity of rotation the brought masses.

Fig.8. Stress-strained state and design of a polymeric sprocket Basic constructive parameters of a polymeric sprocket based on analysis of her stress-strained state is possible to t t Fig.5. Dynamic loadings in branches chain contour determine as follows: d ⋅≅ z , d 33,0 ⋅⋅≅ z , ∂ π 1 π

143 YEAR XX, VOLUME 2, P.P. 139-146 (2012) SCIENTIFIC PROCEEDINGS IX INTERNATIONAL CONGRESS "MACHINES, TECHNOLОGIES, MATERIALS" 2012 ISSN 1310-3946 t t t used. Using this preliminary operation, we receive a gain in d 2 8,0 ⋅⋅≅ z , d н 3,0 ⋅⋅≅ z , d H 56,0 ⋅⋅≅ z , time as on productivity on simple operations the electro- π π π erosion technology concedes to milling. The remained t allowance remove on a draught mode with the big energy of d 19,0 ⋅⋅≅ z , 85,0 ⋅≅ Bb , 5,0 ⋅≅ bh , 0 π in an impulse, and in process of allowance reduction pass to ⋅≅ softer modes. min 3 bl . On fig. 12 the example of a cut out form-building teeth of a In a figure 9,10,11 the outcomes of computation of stress - sprocket of a matrix by a wire electrode on the electro- strained state of parts of a chain are shown. erosion with numerical programmed control and a corresponding sprocket is shown.

Fig.9. Picture of distribution of pressure in zones of a contact Fig.12. Cut out of a matrix and cast sprocket 1 ANSYS 5.5.1 FEB 16 2000 MX 19:34:55 NODAL SOLUTION Thus the big clearance on fig.12 in comparison with diameter SUB =1 TIME=1 of a wire electrode (0.2 mm) speaks liberation of elastic UX (AVG) RSYS=0 deformations. PowerGraphics EFACET=1 Manufacturing of matrixes for sprockets, gear wheels and AVRES=Mat DMX =1.138 similar machine elements it can be carried out on electro- SMN =-.011219 SMX =.956685 erosion machine tools with the numerical program -.011219 .096326 management of types 4531Ф3, 4532Ф3, 4732Ф3, Agiecut, X .20387 MN Y .311415 which make a cutting a wire electrode form-building gear Z .41896 .526505 wreaths of matrixes on parameters preliminary entered into .63405 .741595 the program. .84914 .956685 Other progressive method of reception of matrixes of compression moulds of a complicated configuration is the plasma dusting on model of a working layer in the thickness 1 … 3 mm with the subsequent registration of a basic part by

pouring by other metals («bark-like» method). As a result labor input of manufacturing of equipment reduces in 3 … Fig.10. Stresses in chain links 10 times, and the working surface of a matrix does not demand finishing processing as cleanliness of a surface corresponds to cleanliness of a surface of model. Average time of manufacturing of a working layer makes 5 … 30 minutes, hardness reaches it 72HRC. Base materials for creation of polymeric composites are Fig.11. Stress-strain diagrams on internal and external polyamides PА-6 and PA-6.6 manufactures of Chernigiv contours (a) and in a body of a link (b) joint-stock company "Chemical fibre". As a result of their 3.5. Making of chain drives from polymeric updating by different functional additives their physic- composites mechanical properties cardinally improve. Designs of forms are various, as products for which Because of fibre glass presence in a composite material there manufacture they are intended are various. Any form is a deterioration of matrix group elements. To reduce its represents a combination of known knots and details to knots influence, these elements are chrome plated with thickness of and special purpose details. Performance of cooling system a covering till 18-20 mc and polished for giving of a for each compression mould considerably raises equipment demanded roughness of a surface. cost. Therefore, if there are no obstacles, project the The complicated configuration of a sprocket or gear wheel universal cooling block providing working capacity of dictates the form of elements of matrix group. As a result of replaceable packages, including forming and pushing out casting of an experimental batch of polymeric machine systems. elements modes of molding are fulfilled and there are data The way of manufacturing of matrixes is a determinative at for management in technological parameters of manufacturing of compression molds. The most widespread manufacturing of a polymeric machine element (pressure of way of manufacturing of matrixes− milling with the injection of a material, temperatures of processing of a subsequent polishing cannot provide sufficient accuracy, material on zones, compression mould temperature, application of more progressive technologies therefore is temperature melt, speed of rotation , time of a cycle of necessary. One of them is electro-erosion processing of a machine element manufacturing). Use of such metals. At manufacturing of matrixes by this way technological parameters as the data carriers, adapted for preliminary operations − milling and thermal processing are input possibility in management injection automatic

144 YEAR XX, VOLUME 2, P.P. 139-146 (2012) SCIENTIFIC PROCEEDINGS IX INTERNATIONAL CONGRESS "MACHINES, TECHNOLОGIES, MATERIALS" 2012 ISSN 1310-3946 machine, creates possibilities for computerized manufactures force F , on the basis of which will conduct the of machine elements by molding under pressure out of max1 polymeric composites. calculation of strength factor after breaking force of chain Q (safety factor on starting load): On fig.13 is presented for example one type-size of sprocket Q from polymeric composite. k1 = . 1max −= xxcF 21 )( ; x1 , x2 – longitudinal displacement F1max of terminal joints of branches of a chain contour. Stage 2 is determination of force in leading branch of chain

Fmax 2 at steady-state motion, coming from deformation of

branch of chain xA, on the basis of value of which the strength factor accounts (safety factor on load at steadied Q operation): k2 = , where load in a chain on given R + FF 2 operating conditions.

2 ⋅= xcF A . Minimum safety factor on a resonance frequency 2 Q ω ⋅ A k = ⋅= xcF x = c 2min , where 2max Amax ; Amax ⋅ωη . R + FF 2max z Fig.13. Example one type-size of sprocket m

Comparing the obtained safety factors k1 , k2 , k2min with an On fig.14 is presented example type-size of chain from acceptable value, it is possible to draw a conclusion about a polymeric composite stress-strained state of which is shown capability of operation by the designed chain drive on given on fig.9,10,11. operating conditions. In [16, 17,18] and previous paper [19] constructing of integrated parts of chain drive and philosophy of its projecting were written up. Therefore the example of such computation is here led only. Number of sprockets 3 Coordinates of their Frequencies of their centers : rotation: 1 134.000 .000 1 300.000 2 .000 .000 2 180.000 3 682.000 3 321.430 60.670 Array of their location Fig.14. Example one type-size of chain 1 1 1 Profile for ГОСТ 591-75 3.6. Designing of n-mass chain drives Coefficient of exploitation 1.400 Structural and parametric synthesis of multimass chain drive Amount of rows of chain 1 based on building up of optimal structural scheme consisting Coefficient of 1.800 of combination of two-mass modulus, i.e. of the aggregate of Power 1 0.5 partial systems topologically forming practically any great Tenure of employment 2400 number of chain drives with any quantity of masses Type of chain ? (sprockets) arranged by variable manner in Cartesian F1=76.44 coordinate system has been carried out. Set code as a chain 3 The main task of power calculation are determination of Set row of chain 1 strength factor of chain coming from the known loading of F1=67.68 tension. The excellent feature of this calculation is that as a A chain found ПР 25.4 possible coefficient of strength factor is applied the generally The entered brought masses over: 1,725999Е+01 accepted in machine building coefficient of [к]=2,5, as a 2.843999Е+01 2.00000Е+0 chain is selected coming from life. A calculation is Entered materials of sprockets: P P P conducted in two stages. 1 stage − determination of maximal force in a chain during starting for prevention of his break as N XX PD PP a result of by incongruous character of the appointed 1 .12665 55.392 20.141 acceleration of . This force is determined from the 2 .007323 51.945 32.484 decision of the system of equations in accordance with the 3 .004356 15.317 35.251 chosen law of acceleration of engine [15].For this purpose numerical values settle accounts for a substitution in the Mark Length of Tenure of Dynamic Dynamic system: rigidity of chain с, coefficient of damping η , sizes of chain employment loading factor the brought masses mi (coming from the set moments of chain mm links inertia) over and the decision of the system turns out in a time domain which equals duration of transients in the ПР 3251 128 2400 44.75 1.18 system. Determine the most value of the applied dynamic 25.4

145 YEAR XX, VOLUME 2, P.P. 139-146 (2012) SCIENTIFIC PROCEEDINGS IX INTERNATIONAL CONGRESS "MACHINES, TECHNOLОGIES, MATERIALS" 2012 ISSN 1310-3946 Number Coordinates Diameter Amount of Position is 7.Пилипенко О. И. Исследование динамических явлений, of teeth in a возникающих при установившемся режиме работы sprocket Х У contour роликовых цепных передач. Дисс….канд техн.. наук 05.161 – машиноведение и детали машин. Львов. 1 1364 0 121 15 1 политехн. ин-т, 1969 – 232с. 2 0 0 202 25 1 8.О.І. Пилипенко. Визначення сумарних динамічних 3 682 61 113 14 0 навантажень, зумовлених факторами конструктивного, технологічного, кінематичного та експлуатаційного

характеру. Вісник Львівського політехнічного ін.-ту Conclusion №69. Деякі питання динаміки та технології машин. Вид- The use of the worked out models and systems of account of во Льв. ун-ту. Львів, 1973. – С.261-266. mechanical and thermal properties of polymeric composites 9.Пилипенко О.И. Научные основы и синтез цепных for parts of chain-drives allows it is enough exactly to define передач. Дисс … докт. техн. наук 05.02.02 - the general picture of deformation of polymeric parts, set машинознавство, ХГПУ, Харьков, 1996, 467с. character of distribution of stresses and temperatures in the 10.Пилипенко О.И. Моделирование динамической body of part and area of their concentration depending on the системы и проектирование многомассовых цепных applied materials, operating conditions, type sizes and передач из полимерных композитов. Междунар. сб. науч. variants of structural implementation. Passing to the тр. Прогрессивные технологии и системы polymeric parts sharply diminishes the amount of metal- машиностроения. Вып. 6, Т. 2, Донецк, Машиностроение cutting equipment and, thus, energy and raw material, that 1998, С. 294-297. consumed. 11.O.I.Pilipenko. Polymeric Composite Materials in The expounded design technique of chain drives allows to conduct the valuable computation of chain drive (but not only of chain Multimass Chain Drives of Machines. Proceedings of transmission) with chains from a metal, polymeric material or Second International Congress «Mechanical Engineering composites. The distinguishing features of the offered method Technologies’99». September 16-18.1999. Sofia, Bulgaria. – following: Vol.5. P.24-26. - projecting is built in one cycle that allows to step back 12.Пилипенко О.И., Максименко В.А., Козар И.Ф. from many iteration sequences of determination of Динамика переходных процессов цепного привода, parameters of chain drive; оснащенного металлическими и полимерными цепями. - a dynamic constituent which does the got result Материалы междунар. н.-т. конф. «Современные maximally close to the real operation is entered in a проблемы машиноведения» (научные чтения, calculation; посвящённые 105-летию со дня рождения - the offered sequence can be realized in any package of programming which will give possibility to the авиаконструктора П.О. Сухого). Т.1. Гомель, Беларусь, unprepared user quickly to get end-point; 05-07.07.2000. – С.134-137. - the brought methodology over universal, id est at 13.Oleg Pilipenko. Synthesis of Chain Drives Based on insignificant changes her it is possible to take advantage Dynamic Methods, New Materials and Technologies. of for designing of metallic chain drives, which will allow Machine Design. Monograph. Novi Sad, Serbia, 2007. – to facilitate conservative work of their calculation. P.307-314. 14.Пилипенко О.І. Порівняльна динаміка ланцюгової Complex of automatized optimal synthesis of multimass передачі, оснащеної металевою і полімерною натяжними chain drives POSCD built on block principle of module зірочками. Вісник ЧДТУ №40, серія Технічні науки. designing in the form of packets of applied programmes of Чернігів, 2009. – С.56-62. geometric, force, kinematic, dynamic and optimizational 15.Пилипенко О.І., Максименко В.А. Аналіз пуску computations allows the designer working in dialogue with ланцюгового привода при застосуванні двигунів різного PC to build chain contour containing from 2 to 24 masses типу. //Вісник ЧДТУ №13, Чернігів, 2001 – С.35-39. (sprockets) and satisfying the requirements of optimal 16. Oleg Pilipenko. Shape and Mechanical Design of the design: minimum of cost, material capacity, occupied Chain Drives of a Polymeric Composites. Proceedings of the volume, weight and maximum of dynamic quality. 5-th International Symposium about Design in Mechanical Engineering KOD-2008, Serbia, Novi Sad, 15-16.04.08. – References P.135-140. 1. А.А.Готовцев, И.П., Котенок. Проектирование цепных 17.Пилипенко О.І. Конструювання приводних ланцюгів і передач. М.: Машиностроение, 1982, 336с. зірочок з полімерних композитів та технологічної 2. Решетов Д.Н., Левина З.М. Расчеты передач гибкой оснастки для їх виготовлення. Вісник ЧДТУ №37, связью. Вестник машиностроения №12, 1952. серія Технічні науки.Чернігів, 2009.─ С.32-43. 3. Rachner H-G. Stahlgelenkketten und Kettentriebe. Berlin, 18. Oleg I. Pilipenko. Integrated Parts of a Chain Drives of 1962, 221 s. Polymeric Composites. The Journal of the Advanced 4. Комаров М.С. Динамика механизмов и машин. М., Materials and Operations Society. Issue 2, Vol. 1, 2010. Машиностроение, 1969, 296 с. Sofia, Bulgaria − P.22-26. 5. Пилипенко О.И., Преображенский И.Н. Силовые 19.Pilipenko O. Complex approach to providing of chain детали передач зацеплением из полимерных композитов. drives quality. International virtual journal for science, Проблемы машиностроения и автоматизации. technics and innovations for the industry MTM. Published by Международный журнал №3 (33), М., 1990, С.58-62. Scientific-technical Union of Mechanical Engineering.Year 6.Pilipenko O.I. Reinforced Plastics in Designing V, Issue 2/2011. P.21-26. andApplications of the Driving Parts of Machines. Proceedings of XVI-th International Conference “Reinforced Plastics-91”. Karlovy Vary, Czehoslovakia, 1991,p.111- 122.

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