Metal Construction Optimization of Drive Suspension of Special Belt Conveyor

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ScienceDirect IFAC PapersOnLine 52-25 (2019) 198–202

Metal Construction Optimization of Drive Suspension of Special Belt Conveyor Metal Construction Optimization of Drive Suspension of Special Belt Conveyor Metal Construction Optimization of Drive Suspension of Special Belt Conveyor Metal Construction Optimization of Drive Suspension of Special Belt Metal Construction Optimization of Drive Suspension of Special Belt Conveyor Conveyor P.V. Boslovyak *. E.N. Tolkachev ** P.V. Boslovyak P.V. Boslovyak *. *. E.N. E.N. Tolkachev Tolkachev ** ** P.V. P.V. Boslovyak Boslovyak *. *. E.N. E.N. Tolkachev Tolkachev ** ** *Bauman Moscow State Technical University, Moscow, *Bauman Moscow State Technical University, Moscow, *Bauman Moscow Moscow, Russia (Tel: +7-920-835-8259; e-mail:University, boslovyak89@ mail.ru). *Bauman Moscow State State Technical Technical University, Moscow, *Bauman Moscow State Technical University, Moscow, Russia (Tel: +7-920-835-8259; e-mail: boslovyak89@ mail.ru). Russia (Tel: +7-920-835-8259; e-mail: boslovyak89@ mail.ru). ** Bryansk State Technical University (e-mail: [email protected]) Russia e-mail: boslovyak89@ mail.ru). Russia (Tel: (Tel: +7-920-835-8259; e-mail: boslovyak89@ mail.ru). ** Bryansk Bryansk State+7-920-835-8259; Technical University University (e-mail: [email protected]) ** State Technical (e-mail: [email protected]) ** Bryansk State Technical University (e-mail: [email protected]) ** Bryansk State Technical University (e-mail: [email protected]) Abstract: The article is devoted to the design of the drive unit of a continuous transport machines, i.e. Abstract: The The article article is devoted devoted to to the the design of of the drive drive unit unit of aa continuous continuous transport transport machines, machines, i.e. i.e. Abstract: the leadingThe suspension ofdevoted a special belt conveyor – a drive conveyor with a suspendedtransport belt andmachines, a distributed Abstract: article is isof devoted to belt the design design of the the unit of of continuous i.e. Abstract: article is to the design of the unit of aa continuous i.e. the leading leadingThe suspension a special special conveyor – aa drive conveyor with a suspended suspendedtransport belt and andmachines, a distributed distributed the suspension of a belt conveyor – conveyor with a belt a drive. The paper provides an analysis ofconveyor known designs of conveyor suspension with a suspended belt the leading suspension of belt – with suspended belt aa distributed the leading suspension of aaanspecial special beltof – aa conveyor conveyor with aasuspension suspended with belt aaand and distributed drive. The paper paper provides analysis ofconveyor known designs designs of conveyor conveyor with suspended belt drive. The analysis known of suspended and specifies theirprovides commonan general weaknesses. The authors show thesuspension original technical solution ofbelt the drive. The paper provides an analysis of known designs of conveyor suspension with a suspended belt drive. The paper provides an analysis of known designs of conveyor suspension with a suspended belt and specifies their common general weaknesses. The authors show the original technical solution of the and specifies their common general weaknesses. The authors show the original the universal roller suspension, equipped with an individual motor-gear drive, astechnical well as solution a drive of roller and specifies their common general weaknesses. The authors show the original technical solution of the and specifies their common general weaknesses. The authors show the original technical solution of the universal roller suspension, equipped with an individual motor-gear drive, as well as a drive roller universal roller suspension, with an individual motor-gear as as a drive model roller pressure device, and its mainequipped advantages. The authors developed anddrive, showed awell mathematical universal roller with an motor-gear as as roller universal roller suspension, suspension, equipped with The an individual individual motor-gear drive, as aawell well as aa drive drive model roller pressure device, device, and its its main mainequipped advantages. The authors developed developed anddrive, showed mathematical model pressure and advantages. authors and showed mathematical designed to optimize the characteristics of the metal structure of one of the most metal-consuming pressure device, and its main advantages. The authors developed and showed a mathematical model pressure device, and its main advantages. The authors developed and showed a mathematical model designed to optimize the characteristics of the metal structure of one of the most metal-consuming designed to optimize the characteristics of the structure of one of the into most metal-consuming elements of considered drive suspension as metal the carrier section structural, designed to optimize the of structure of one of most metal-consuming designed to the optimize the characteristics characteristics of the the metal structure of and one taking of the the into mostaccount metal-consuming elements of of the considered drive suspension suspension as metal the carrier carrier section and taking account structural, elements the considered drive as the section and taking into account structural, strength and stiffness limitations. In their paper, the authors showed the implementation of the proposed elements of considered drive as the carrier section and taking structural, elements of the the considered drive Insuspension suspension as the theauthors carrier showed section the andimplementation taking into into account account structural, strength and stiffness limitations. their paper, of the proposed strength and stiffness limitations. In their paper, the authors showed the implementation of the proposed mathematical model: the stress-strain state of the metal structure of the drive suspension is calculated strength and In paper, the authors showed of proposed strength and stiffness stiffness limitations. In their their paper, themetal authors showedofthe the implementation of the the proposed mathematical model: limitations. the stress-strain stress-strain state of the the structure theimplementation drive suspension suspension is calculated calculated mathematical model: the state of metal structure of the drive is using the example of the the stress-strain basic design.state It isofestablished that the basic drive suspension has excessive mathematical model: the of drive suspension is mathematical model: the metal metal structure structure of the thedrive drivesuspension suspensionhas is calculated calculated using the the example example of the the stress-strain basic design. design.state It is isofestablished established that the the basic basic drive suspension has excessive using the basic It excessive strength, weight andof exceeded geometric parameters of thethat rods. The authors made the conclusion about using the example of the basic design. It is established that the basic drive suspension has excessive using the example of the basic design. It is established that the basic drive suspension has excessive strength, weight and exceeded geometric parameters of the rods. The authors made the conclusion about strength, weight and exceeded geometric of the rods. The authors the conclusion about the need for multi-criteria optimization ofparameters the metal construction of the drive made suspension, as well as the strength, weight and exceeded geometric parameters of the rods. The authors made the conclusion about strength, weight and exceeded geometric parameters of the rods. The authors made the conclusion about the need for multi-criteria optimization of the metal construction of the drive suspension, as well as the the need optimization of the metal construction of the drive suspension, as well the study of for the multi-criteria influence of the configuration parameters of the drive suspension on its weight andas size the need for multi-criteria optimization of the metal construction of the drive suspension, as well as the the need for multi-criteria optimization of the metal construction of the drive suspension, as well as the study of the influence of the configuration parameters of the drive suspension on its weight and size study of the influence of the configuration parameters of the drive suspension on its weight and size characteristics. study of study of the the influence influence of of the the configuration configuration parameters parameters of of the the drive drive suspension suspension on on its its weight weight and and size size characteristics. characteristics. characteristics. characteristics. © 2019, IFAC (International Federation of Automatic Control) belt, Hosting by Elsevieroptimal Ltd. Alldesign, rights reserved. Keywords: conveyor belt, mathematical model, suspended suspension, distributed Keywords: conveyor belt, mathematical model, suspended belt, suspension, optimal design, distributed Keywords: conveyor belt, drive, constraint system. Keywords: conveyor belt, mathematical mathematical model, model, suspended suspended belt, belt, suspension, suspension, optimal optimal design, design, distributed distributed Keywords: conveyor belt, mathematical model, suspended belt, suspension, optimal design, distributed drive, constraint system. drive, constraint system. drive, constraint constraint system. system. drive,    

1. INTRODUCTION 1. 1. INTRODUCTION INTRODUCTION 1. 1. INTRODUCTION INTRODUCTION There are major changes associated with the modernization There are major changes associated with the modernization There are major changes with the of existing structures and associated the development ofmodernization new methods of There are major changes associated with modernization There are major changes associated with the the modernization of existing structures and the development of new methods of of existing structures and the development of new methods of calculation and designand in industry and science (Vorotnikov et of existing structures the development of new methods of of existing structures and the development of new methods of calculation and design in industry and science (Vorotnikov et calculation and design in industry and science (Vorotnikov et al., 2018, Tarakanov etinal.,industry 2016, Nosko et al., (Vorotnikov 2015). calculation and design and science et calculation and design in industry and science (Vorotnikov et al., 2018, Tarakanov et al., 2016, Nosko et al., 2015). al., 2018, Tarakanov et al., 2016, et al., 2015). al., et 2016, Nosko Nosko al., al., 2018, 2018, Tarakanov Tarakanov et al., al., Nosko et et al., 2015). 2015). various Transport technology is 2016, constantly undergoing Transport technology is constantly undergoing various Transport technology is constantly undergoing various changes, one of which is the design of a special conveyor belt Transport technology is constantly undergoing various Transport technology is constantly undergoing various changes, one of which is the design of a special conveyor belt changes, one of which is the design of a special conveyor belt – a conveyor with a suspension belt (CSB) and a distributed changes, one which is of aa special conveyor belt changes, one of of which is the the design design of(CSB) special conveyor belt – a conveyor with a suspension belt and a distributed – a conveyor with a suspension belt (CSB) and a distributed drive. The roller suspensions of this conveyor hold the belt – a conveyor with a suspension belt (CSB) and a distributed – a conveyor with a suspension belt (CSB) and a distributed drive. The roller suspensions of this hold the belt drive.the Theload roller suspensions ofposition this conveyor conveyor hold the belt with in suspensions a suspendedof betweenhold thethe rolling drive. The roller this conveyor belt drive. Theload roller this conveyor belt with the the load in suspensions a suspended suspendedofposition position betweenhold thethe rolling with in a between the rolling guidestheand caninmove along theposition guides between along thethetrack. In with load a suspended rolling with the load in a suspended position between the rolling guides and can move along the guides along the track. In guides move along guides along the track. In addition,and thecan suspension is the equipped with an individual guides and can move along the guides along the track. In guides and can move along the guides along the track. In addition, the suspension is equipped with an individual addition, the suspension is equipped with an individual motor-gearthe drive and carry is outequipped the tractionwith function, ensuring addition, suspension an individual addition, the suspension is equipped with an individual motor-gear drive and carry out the traction function, ensuring motor-gear drive carry out the traction function, ensuring the movement of and the load-carrying conveyor belt (Lagerev et motor-gear drive and carry function, ensuring motor-gear drive and carry out out the the traction traction function, ensuring the movement of the load-carrying conveyor belt (Lagerev et the movement of the load-carrying conveyor belt (Lagerev et al., 2018, Lagerev et al., 2016). Thus, the design detail of the the movement of the load-carrying conveyor belt (Lagerev et the movement of the load-carrying conveyor belt (Lagerev et al., 2018, Lagerev et al., 2016). Thus, the design detail of the al., 2018, Lagerev et al., 2016). Thus, the design detail of drive suspensions have a decisive influence on the al., 2018, Lagerev et al., 2016). Thus, the design detail of al., 2018, Lagerev et al., 2016). Thus, the design detail of the drive suspensions have a decisive influence on drive suspensions have aa decisive influence on the performance of the entire (Nosko al., drive suspensions have influence on drive suspensions havetransportation a decisive decisive system influence onet the the performance of entire transportation performance ofetthe the entire transportation system system (Nosko (Nosko et et al., al., 2018, Lagerev al., 2017). performance of the entire transportation system (Nosko et performance transportation system (Nosko et al., al., 2018, Lagerevofet etthe al.,entire 2017). 2018, Lagerev al., 2017). 2018, Lagerev et al., 2017). 2018, Lagerev et al., 2017). The three-dimension configuration, geometrical parameters The three-dimension configuration, geometrical parameters The three-dimension configuration, geometrical parameters and other design details of the suspensions are mainly The three-dimension configuration, geometrical parameters The three-dimension configuration, geometrical parameters and other design details of the suspensions are mainly and other design details of the suspensions are mainly determined by the form andofsize ofsuspensions the cross section of the and other design details the are mainly and other design details of the suspensions are mainly determined by the form and size of the cross section of the determined by the form and size of the cross section of the linear bearings. At the present time, there are a lot of variety determined by the form and size of the cross section of the determined by the form and size of the cross section of the linear bearings. At the present time, there are a lot of variety linear bearings. At the present time, there are a lot of variety of CSB suspension designs (Fig. 1) (Lagerev and Dunaev, linear bearings. At the present time, there are a lot of variety linear bearings. At the present time, there are a lot of variety of CSB suspension designs (Fig. 1) (Lagerev and Dunaev, of CSBIvchenko suspension (Lagerev and 2009, anddesigns Kurov, (Fig. 2005,1) al.,Dunaev, 2003), of suspension designs (Fig. 1) (Lagerev and Dunaev, of CSB CSBIvchenko suspension designs (Fig. 1)Ivchenko (Lagerev et and Dunaev, 2009, and Kurov, 2005, Ivchenko et al., 2003), 2009, Ivchenko and Kurov, 2005, Ivchenko et al., 2003), which differing in the configuration of the supporting metal 2009, Ivchenko and Kurov, 2005, et 2009, Ivchenko and Kurov, 2005, Ivchenko Ivchenko et al., al., 2003), 2003), which differing in the configuration of the supporting metal which differing differing in the the configuration the supporting supporting metal structure (MS), the number and type of rollers, type of drive, which in configuration the metal which differing in the configuration of rollers, the supporting metal structure (MS), the number and type type of drive, structure (MS), the number and type of rollers, type of drive, structure (MS), the number and type of rollers, type of drive, structure (MS), the number and type of rollers, type of drive,

execution of the tape attachment. However, a significant part execution of attachment. However, aa significant execution of the the tape tape attachment. However,disadvantages: significant part part of the suspension usually has the following execution of the tape attachment. However, aa significant part execution of the tape attachment. However, significant part of the suspension usually has the following disadvantages: of the suspension usually has the following disadvantages: of the suspension usually has the disadvantages: of theintended suspension the following following - not forusually use in has a conveyor with adisadvantages: vertically closed -- not intended for use in a conveyor with a vertically not intended for use in a conveyor with a vertically closed closed configuration of the route; not intended intendedoffor for use in aa conveyor conveyor with with aa vertically vertically closed -- not use in closed configuration the route; configuration of the route; configuration of of the the route; route; configuration - differ in a complex configuration of the used profile of the -- differ in a complex differguides; in aa complex complex configuration configuration of of the the used used profile profile of of the the linear -linear differ in -linear differguides; in a complex configuration configuration of of the the used used profile profile of of the the guides; linear guides; linear guides; - not have sufficient resistance to distortions; -- not have sufficient not have sufficient resistance resistance to to distortions; distortions; -- not have sufficient resistance to distortions; not have sufficient resistance to not provide high-quality clutchdistortions; drive roller with a linear -- not not provide provide high-quality high-quality clutch clutch drive drive roller roller with with aa linear linear guides; -guides; not provide high-quality clutch -guides; not provide high-quality clutch drive drive roller roller with with aa linear linear guides; guides; - not provide equipment design built-in individual drive. -- not not provide provide equipment equipment design design built-in built-in individual individual drive. drive. -- not not provide provide equipment equipment design design built-in built-in individual individual drive. drive.

Fig. 1. (a) drive two-roller for complex linear guide profile of Fig. 1. two-roller for complex linear guide profile of Fig. 1. (a) (a) drive drive two-roller complex linear guide profile of horizontally closed tubular for CSB; (b) drive multi-roller for the Fig. two-roller for complex linear guide of Fig. 1. 1. (a) (a) drive drive two-roller for complex linear guide profile profile of horizontally closed tubular CSB; (b) drive multi-roller for the horizontally closed tubular CSB; (b) drive multi-roller for the rectangular profile of the horizontal closed linear guidefor CSB; horizontally closed tubular CSB; (b) drive multi-roller the horizontally closed tubular CSB; (b) drive multi-roller for the rectangular profile of the horizontal closed linear guide CSB; rectangular profile of for the horizontal closed linear guide CSB; (c) drive multi-roller rectangular linear guide profile rectangular profile the horizontal linear guide rectangular profile of of for therectangular horizontal closed closed linear profile guide CSB; CSB; (c) drive multi-roller linear guide (c) drive multi-roller for rectangular linear guide profile vertically closed CSB; (d) single roller for the grooved profile (c) drive multi-roller for rectangular linear guide profile (c) drive multi-roller for rectangular linear guide profile vertically closed CSB; (d) single roller for the grooved profile vertically closed (d) single for the(e)grooved profile of the linear guideCSB; of the belt androller rope CSB; blank four vertically closed CSB; (d) single roller for grooved profile vertically closed CSB; (d)belt single roller for the the(e) grooved profile of the linear guide of the and rope CSB; blank four of the linear guide of the belt and rope CSB; (e) blank four roller for tubular linear guide profile CSB; (f) two roller of the linear guide of the belt and rope CSB; (e) blank four of the linear guide of the belt and rope CSB; (e) blank four roller for tubular linear guide profile CSB; (f) two roller roller for guide profile blank to atubular tubularlinear profile linear guideCSB; CSB;(f) (g)two fourroller roller roller for tubular linear guide profile CSB; (f) two roller roller for tubular linear guide profile CSB; (f) two roller blank to tubular profile linear guide CSB; blank for to aaatubular tubularlinear profile linear guideCSB. CSB; (g) (g) four four roller roller drive guide profile blank to tubular profile linear guide CSB; (g) four blank to atubular tubularlinear profile linear guideCSB. CSB; (g) four roller roller drive for for guide profile drive tubular linear guide profile CSB. drive for tubular linear guide profile CSB. drive for tubular linear guide profile CSB.

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The design of the drive suspension CSB with a distributed drive (Fig. 1, c) (Lagerev et al., 2018, Lagerev et al., 2017, Lagerev et al., 2016), used in conjunction with a linear guide rectangular cross-section (Fig. 1), seems to authors as the most versatile in connection with the following characteristics: - rectangular geometric configuration ensures the stability of the suspension to angular distortions throughout the route; - the vertical spatial orientation of the drive roller eliminates the possible increase in resistance from sliding friction forces arising at the end turning areas, in the case of horizontal positioning of the roller; - the two-section device of the leading suspensions allows to concentrate the main load from the belt and the transported cargo only on the bearing section (BS); - the presence of bearing supports virtually eliminates the radial loads from the mass of the clamping section and the force of the springs of the device for pressing the drive roller of the suspension onto the elements of the gearmotor; - the location of the drive in a separate section, equipped with a clamping device, provides high-quality adhesion of the drive roller to the linear guide along the entire course. Studies of the influence of the design parameters of suspensions on the dynamic characteristics of the conveyor revealed that the mass of the drive suspensions is essential, especially with an increase in their number on the highway (Eremeykin et al., 2017, Lagerev and Kuleshov, 2013). Thus, the task of high priority is to minimize the mass while ensuring the optimal combination of its geometrical parameters, preserving the strength and rigidity of the structure (Lagerev et al., 2016). 2. MATHEMATICAL MODEL OF METAL CONSTRUCTION OPTIMIZATION OF THE DRIVE SUSPENSION The formed structural diagram of the MS BS of drive CSB suspension with a distributed drive is shown in Fig. 2.

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The mass of a single rod MS BS drive suspension depends on the geometric dimensions of the cross-sectional profile. Possible profiles of rods (rectangular pipe, channel, angle, round pipe, round section, rectangular section) have their calculated dependencies. From controlled parameters, which can be varied to find the optimal result, a vector of unknown dimensions is formed {x}, to be determined during the optimization process. Vector driven {x} and the vector of uncontrollable {z} parameters are fully determined by the geometric characteristics of the optimal MS BS drive suspension (Boslovyak and Emelyanova, 2018, Lagerev et al., 2016). The formulation of the problem of conditional parametric optimization of the MS BS drive CSB drive suspension with a distributed drive is the selection of such variable parameters in which the weight of the MS BS drive shaft is minimal when the structural em, strength fn и stiff gp restrictions (Sakharov and Karpenko, 2018, Agasiev and Karpenko, 2017, Poshekhonov et al., 2017, Lagerev et al., 2016). A mathematical model is compiled (Tarakanov et al., 2016, Antonov et al., 2017), inclusive objective function TC (2) with a system of restrictions imposed on it (3) – (5). TC ({x}, {z}) → min;

(2)

em ({x}, {z}) ≥ 0, (m=1,..., M);

(3)

fn ({x}, {z}) ≥ 0, (n=1,..., N);

(4)

gр ({x}, {z}) ≥ 0, (p=1,..., P),

(5)

In the course of the procedure of optimal design of the MS BS, the drive suspension of the conveyor is checked by the first and second groups of the limit state (SP 16.13330.2011, SP 20.13330.2011). In the target function MS BS drive suspension, the possibility of taking into account the forms of cross sections of rods from a wide range of standard profiles is realized. By the coefficient ji availability is taken into account (ji =1) or absence (ji =0) cross sectional profile i-n details in MS BS drive suspension (Boslovyak and Emelyanova, 2018). Formed vectors varied {x} and unmanaged parameters {z} metal structures drive suspension (Lagerev et al., 2016). Optimization task (Boslovyak and Jileykin, 2019, Agasiev and Karpenko, 2017, Poshekhonov et al., 2017, Lagerev et al., 2016) metal structure for a conveyor belt with a suspended belt and a distributed drive is to minimize the objective function of the form:

Fig. 2. Structural diagram of the metal structure of the conveyor suspension. The metal structure of the BS drive suspension consists of rods of three groups: longitudinal (4, 5, 6); transverse (2); vertical (1, 3). The mass BS drive suspension CSB with a distributed drive is determined by the dependence: ms=2(m1+ m2+ m3+ m4+ m5+ m6/2).

(1)

ТC ({xiri },{ziri })={ j rt 2 1 z rt x rt ( x rt+x rt  2 x rt )+j ch 1 z ch [ x ch ( x ch  1 1 1 2 3 1 1 1 1 2 rp rp rp rp ch ch ch ai ai ai ai ai ai  2 x )+2 x x ]+j 1 z x ( x +x  x )+ 1 z x ( x  3 4 3 1 1 1 2 3 1 1 1 1 2 rp rs rs rs 2 res res res res rt rt rt  x )+j 1 z ( x ) / 2+j 1 z x x }  { j 2  2 z x ( x5rt+ 1 1 1 1 1 1 1 2 2 2 4  x rt  2 x rt )+ j ch  2 z ch [ x5ch ( x ch  2 x7ch )+2 x ch x7ch ]+j ai  2 z ai x ai ( x5ai+ 6 4 2 2 6 8 2 2 4 rp rp rp rp rp +x ai  x ai )+j  2 z x ( x  x )+j rs 2 z rs ( x rs ) 2 / 2 + 6 4 2 2 3 4 3 2 2 2 res res res res rt rt rt rt + j  2 z x x }+{j 2  3 z x7 ( x +x rt  2 x7rt )  2 2 3 4 3 3 8 9

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200

+ j res  2 z res x res x res }+{j rt 2  3 z rt x7rt ( x rt +x rt  2 x7rt )  3 8 9 2 2 3 4 3  j ch  3 z ch [ x ch ( x ch  2 x ch )+2 x ch x ch ]  j ai  3 z ai x7ai ( x ai + 3 3 9 10 11 12 11 3 3 8 (6) rp rp rp rp rp ai ai rs rs rs  x  x7 ) +j  3 z x5 ( x  x5 ) + j  3 z ( x ) 2 / 2 + 9 3 3 6 3 3 3  j res  3 z res x5res x res } +{ j ch  4 z ch [ x ch (x ch  2 x ch )+2 x ch x ch ]  3 3 6 4 4 13 14 15 16 15 + j ai  4 z ai x ai ( x ai +x ai  x ai )}+{ j5ch  5 z 5ch [ x ch (x ch  2 x ch )+2 x ch x ch ]+ 4 4 10 11 12 10 17 18 19 20 19 ai ai ai ai ai ai rt rt rt rt rt rt  j5  5 z 5 x ( x +x  x )}+ { j 2  6 z x ( x +x  2 x )+ 13 14 15 13 6 4 10 11 12 10  j ch  6 z ch [ x ch ( x ch  2 x ch )  2 x ch x ch ]+j ai  6 z ai x ai (x ai +x ai  x ai )+ 6 6 21 22 23 24 23 6 6 10 11 12 10 rp rp rp rp rp  j  6 z x7 ( x  x7 )+j rs 6 z rs ( x rs ) 2 / 2+j res  6 z res x7res x res }, 6 4 8 6 4 4 6 4 8

- concentrated force acting on the drive suspension from the side of the load-carrying belt - 3000 N; - force of the device for pressing the suspension drive roller 200 N. The original formed frame model MS BS drive suspension (Fig. 3, a) was transformed into a finite element model (Fig. 3, b). Each rod element MS BS drive suspension is assigned a specific cross section depending on the type of profile (rectangular pipe; channel; angle; round pipe; round section; rectangular section).

r – cross profile type: r = rt – rectangular tube; r = ch – channel; r = ai – angle iron; r = rp – round pipe; r = rs – round section; r = res – rectangular section; i – element node of МS.

Fig. 3. (a) Calculation diagram of the metal structure of suspension of the conveyor; (b) Final element model of the metal structure of suspension of the conveyor

Constructive limitations em, superimposed on the target function of the TC, are the geometric relations associated with the size of the elements MS BS drive suspension.

The material used was structural low-alloy steel for welded structures 09G2S. The allowable stress, taking into account the safety factor in the calculation, is assumed to be 230 MPa.

Strength limits fn take into account the conditions (SP 16.13330.2011).

The next stage was indicated the places of application and the direction of action of the load from the belt with the load Т, as well as forces from the drive roller pressing device Fnp to guide. Set points (fig. 3, a) MS BS drive suspension in places of conditional contact support rollers with a linear guide, limiting its movement: at points А and B – linear along the axis OZ; at points C and D – linear along the axis ОХ.

Stiffness constraints are to maintain the values of deflections f core elements 1-6 (fig. 2) MS BS drive suspension below the limit values fu (SP 20.13330.2011). The procedure for the optimal design of the MS BS drive CSB suspension with a distributed drive is implemented through the developed objective function (6) in conjunction with the constraint systems when using the software package Siemens NX (www.plm.automation.siemens.com/global/en/). 3. THE RESULTS OF THE OPTIMIZATION OF THE METAL STRUCTURE DRIVE SUSPENSION Using the developed mathematical optimization model and the Siemens NX software package, the VAT was analyzed and optimized while preserving the layout and rod lengths of the MS BS motor drive suspension, located on the most loaded part of the route – the horizontal segment of the cargo branch with a grooved transverse belt shape. Specifications for the following optimization: - capability - 200 t/h; - power density of the transported cargo - 1.4 t/m3; - step of installation of suspensions on the belt - 1.4 m; - distance between the suspension points of the belt - 0.83 m;

After that, the calculation of the stress-strain states of the original version of the MS BS drive suspension and the variant obtained because of the optimization procedure was performed. The results obtained, as well as the standard sizes of the profiles used in the initial and optimal versions of the MS BS drive suspension, are tabulated 1. Table 1. The results of the calculation of the stress-strain state and the optimization of the mass MS BS drive suspension CSB with a distributed drive Design MS BS Drive suspensi on Original Optimal

Cross profile, mm

Square tube 30×30×0.8; Beam channel steel bent equal 30×25×3 Square tube 25×25×0.8; Beam channel steel bent equal 25×26×2

Maximal voltage, MPa

Mass of MS, kg

142.96

2.6

207.11

2.0



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4. RESULTS ANALYSIS In the original version MS BS drive suspension (Fig. 4, a) the greatest stresses occur in the rods 2 and have a maximum equal to 142.96 MPa, in the place of articulation with the vertical rods 1. The stresses in rods 1 and 3 are the same and decrease from 131.05 MPa to 11.92 MPa. In general, MS BS drive suspension with the initial geometrical dimensions has a large margin of safety, which, due to the design features of a CSB with a distributed drive, can be considered redundant, since the excess weight of the suspensions causes higher resistance to movement and an increase in dynamic loads on the conveyor belt in the process.

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3. By calculation, the need for multi-criteria optimization of the drive gear MS was confirmed, taking into account design, strength and stiffness limitations. REFERENCES Agasiev, T., Karpenko, A. (2017). The Program System for Automated Parameter Tuning of Optimization Algorithms. Procedia Computer Science, No. 103: 347354. Antonov, A.Y., Vorotnikov, S.A., Vukolov, A.V., Saschenko, D.V., Shashurin, G.V. (2017). Mathematical model of 3-P wheel-legged mobile robotic platform. International Review of Mechanical Engineering, No. 5(11): 311-319. Boslovyak, P.V., Emelyanova, G.A. (2018). Optimization Mathematical Modeling of the Weight of Metal Structure of Suspended Belt Conveyor Linear Section. IFACPapersOnLine, No. 51: 616-619. Boslovyak, P.V., Jileykin, M.M. (2019). Optimal design of steel structure of conveyor with suspended belt. Lecture Notes in Mechanical Engineering (9783319956299): 2203-2210.

Fig. 4. (a) stress distribution in MS BS of the suspension of the initial design; (b) stress distribution in MS BS of the suspension after optimization. Version MS BS drive suspension, obtained because of the optimization procedure, has a similar pattern of stress distribution in the rods (Fig. 4, b). The maximum stresses are 207.11 MPa. Thus, from a comparative analysis of the variants MS BS drive suspension, it follows that its weight because of optimization of the cross sections of the core bars decreased by 23% relative to the mass of the non-optimized MS drive suspension. 5. CONCLUSIONS

Eremeykin, S.A., Panovko, G.Ya., Shokhin, A.E. (2017). Features of dynamics of mechanical system with self-synchronizing vibroexciters near resonance. Journal of Vibroengineering Vol. 19, No. 7: 4911-4920. Ivchenko, V.N. [and others] (2003) The operating experience of belt conveyors with a suspended belt, Gornyi Zhurnal [Mountain J.], No. 3: 66-70. Ivchenko, V.N., Kurov, S.V. (2005). Non-spilling belt conveyors. Mining Industry Journal, No. 4 (62): 39-42. Lagerev, A.V., Dunaev, V.P. (2009). Conveyors with suspension carrying belt - new type of continuous transport machines. Handbook. An Engineering Journal, No.10: 9-14.

The developed mathematical model, which includes the objective function and the systems of structural, strength, and stiffness constraints imposed on it, allows for the procedure of optimal design of the MS BS CSB drive suspension with a distributed drive.

Lagerev, A.V, Kuleshov, D.Yu. (2013) Dynamic processes in transient modes of operation of a discrete section of a conveyor with a distributed drive. Bulletin of Bryansk State Technical University, No.2: 50-56.

As a result of the calculation of the standard version MS BS drive CSB suspension with a distributed drive installed the following:

Lagerev, A. V., Tolkachev E. N. and Boslovyak, P. V. (2016) Design and research of the conveyor with the suspended belt, , 303. Bryansk, RIO BGU.

1. The original version of the suspension has excessive strength, weight and geometric parameters of the rods exceeded.

Lagerev, A.V., Tolkachev, E.N., Lagerev, I.A. (2016). Modelling of a vertical loop conveyor with suspended belt and distributed drive. International Review on Modelling and Simulations, Vol. 9, No. 4: 271–279.

2. Optimization of only the size of the cross-sections of the profiles used has reduced the weight of the suspension by 23% relative to the weight of the non-optimized MS suspension, ensuring the necessary margin of safety.

Lagerev, A.V., Tolkachev, E.N., Lagerev, I.A. (2017). Analyzing the Discreet Section Suspension Parameters in a Conveyor with Suspended Belt and Distributed Drive. Journal of Mechanical Science and Technology, Vol. 31, No. 10: 4669-4678.

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