ANALYSIS OF INFLUENCE OF DESIGN CHARACTERISTICS OF INCLINED BUCKET ELEVATOR ON THE POWER OF ITS DRIVE

Dep. «Military Training of Specialists of the State Special Service of Transport», Dnipropetrovsk National University of Railway Transport named after Academician V. Lazaryan, Lazaryan St., 2, Dnipro, Ukraine, 49010, tel. +38 (056) 373 19 09, e-mail wbogomas@i.ua, ORCID 0000-0001-5913-2671 Dep. «Military Training of Specialists of the State Special Service of Transport», Dnipropetrovsk National University of Railway Transport named after Academician V. Lazaryan, Lazaryan St., 2, Dnipro, Ukraine, 49010, tel. +38 (056) 373 19 09, e-mail bmw1961@ukr.net, ORCID 0000-0001-9578-3906 Dep. «Military Training of Specialists of the State Special Service of Transport», Dnipropetrovsk National University of Railway Transport named after Academician V. Lazaryan, Lazaryan St., 2, Dnipro, Ukraine, 49010, tel. +38 (056) 373 19 09, e-mail psven68@i.ua, ORCID 0000-0002-1628-3733 Dep. «Military Training of Specialists of the State Special Service of Transport», Dnipropetrovsk National University of Railway Transport named after Academician V. Lazaryan, Lazaryan St., 2, Dnipro, Ukraine, 49010, tel. +38 (056) 373 19 09, e-mail otkachov@i.ua, ORCID 0000-0002-1857-7567


Introdiction
Increasing the pace of economic development is impossible without technical re-equipment of production.The successful solution of this problem is largely determined by implementation of new technologies with the use of stream-flow transportation machines.They have great performance and length of transportation and can replace batch machines in traditional application fields, such as hauling, handling and warehousing operations.These machines have become very popular in mass and high-volume production with wide use of automatic lines.A special type of stream-flow transportation machines is inclined belt bucket elevators.Generally, elevators are the lifts that are used for vertical and steeply inclined (at an angle 60-82 о ) displacement of bulk and piece cargo without intermediate loading and unloading.Their use when transporting materials increase the efficiency of the production process in many industries: chemical, metallurgical, engineering, etc.
The main publications describing the structure, design features, performance and design parameters of elevators, including the inclined ones are the following works [5][6][7][8][9][11][12][13][14][15].To determine the drive power of inclined elevator it is necessary to conduct a detailed calculation of its elements and perform a selection of basic elements of the drive.The order of these calculations is described in detail in the works [8,9].It should be noted that the use of traditional calculation methodology of the elevator's drive requires a lot of time.To improve the design process of the inclined elevator's drive it is necessary to define a scheme that makes it possible to determine the required drive power value depending on the specific design parameters: the type of load, lifting height, track inclination angle and performance using simpler calculations.The works [2][3][4] of one of the authors include similar scheme for vertical elevators and conveyor belts.The natural generalization and continuation of these works will be the construction of schemes for inclined elevators.This is because the inclined elevators as opposed to the vertical ones include the component of tension force related to the force of belt friction on the support elements.

Purpose
The article is aimed to construct and analyze the parametric dependence of inclined elevator's drive power on its design parameters (type of load, lifting height, angle of inclination, performance) taking into account the standard sizes and parameters of buckets and belts.

Methodology
In general, for design of stream-flow transportation machines one should have the following basic data: -diagram of machine track with indicated places of loading and unloading; -appointment, conditions and operation mode of machine and the place of its installation; -the required performance; -characteristics of transported cargoes.Thus, the initial data for design calculation of the elevator are such values as the transported material (its density and physical and mechanical properties) lift height of cargo, inclination angle of elevator to the horizon, required performance.
To construct general dependence of drive power on the performance there will be used the required coefficients at the values that make it possible to calculate the corresponding values of the required drive power for specific types of cargoes.
By analogy with [3] let us consider the value α that takes into account the properties of transported cargo for further studies: 3,6v α = ρψ. ( Linear content of the elevator's bucket: where α -is a value that takes into account characteristics of the cargo and is calculated using dependence (1), t m/l h; ψ -is a coefficient of bucket fill (according to the physical and mechanical properties of cargo); t -is a spacing of the buckets, m; ρ -is a cargo density, t/m 3 ; v -is a speed of the belt movement, m/s.According to the value of linear content of elevator's bucket calculated from the formula (2) the type and spacing of buckets in accordance with the table 1 recommended by the wok [9] are selected.Selection of buckets type depends on the properties of the material, which is being transported.Deep buckets are used for free-flowing, dusty and small pieced cargoes; the shallow ones -for non-freeflowing cargoes.
To take account physical and mechanical properties of the cargo, which is being transported in further calculations let us construct the correspondence tables of elevator parameters specified in the Table 1 to the performance value expressed by the formula (2) in the parts of coefficient α .The obtained data will be tabulated in the Tables 2, 3 for elevators with deep and shallow buckets respectively.
Based on the design value of elevator productivity and the type of material, which is being transported according to the Tables 2 and 3, the bucket parameters, their spacing on the belt and the required width of the belt are selected.Characteristics of deep and shallow buckets are shown in the Tab. 4.   For clearness of further research let us take the conveyor belt according to State Standard 20-85 of the type BKNL-150 as traction body of elevator.The actual number of spacer plates of the belt can be 3-6.
The belt thickness is determined by the formula where 1100 b ρ = kg/m 3 -belt density.Involving the formulas (3)-( 4) in the calculation let us present the table of correspondence of width and linear weight of the belt with a different number of insert plies to design values of elevator productivity for deep and shallow buckets.Linear weight of the belt with buckets is determined by the formula: where b m -bucket weight, kg (Tab.8).Linear burden on the loaded strand is determined using the formula: The estimated weight of deep and shallow buckets is given in the Table 8 [9].
Involving the formulas ( 6)- (7) in the calculation and taking into account data from the Table 8 let us determine the dependency of linear load on the loaded strand of elevator on the productivity values for deep and shallow buckets.The obtained results of calculations for belts with different number of insert plies is presented in the Tables 9, 10.Traction calculation of inclined bucket elevator is performed by the method of encirclement, the basic principle of which is to identify specific points of the track where the belt tension is changed.At this tension in the next ( 1 i + ) point is equal to the sum of belt tension in this ( i ) point and the belt movement resistance in the area between these points: In case of drive drum rotation (Fig. 1) in clockwise order the minimum tension will be at the point 2 -2 S .This tension in the belt during normal scooping satisfies the following condition: The belt tension force at the point 3 consists of tension force 2 S , drum resistance and resistance to scooping of cargo

S kS W
where 1, 08 k = -coefficient of tension increase in the belt with buckets when bending around the drum.

Fig. 1. Scheme of inclined bucket elevator
Resistance to material scooping is determined using the formula: where s k -is a coefficient of scooping (Nm/kg), which is determined by specific work expended for scooping of 1 kg of material.At the speed of buck- Thus, substituting formulas ( 8) and ( 11) to (10), we have: Choosing the value 25 s k = N m/kg (which meets all cargoes) we have: We assume that the belt with buckets at the track sections 3-4 and 1-2 (Fig. 1) is supported by direct roller supports.
The specific weight of moving parts of roller supports for loaded (section 3-4) and unloaded (section 1-2) strands is determined by the formulas: where ' r G -weight of rotating parts of the upper and lower rolers.
For further calculations the tables of estimated values of the distances between rollers of loaded strand (Tab.11) and the characteristics and sizes of roller supports shown in the Table 12 will be used.
Ordinary roller supports of the strand 1-2 are set with the spacing " r l , twice as high as ' r l .The dependence of the weight of ordinary roller supports on the belt width is presented in the Table 12.
To facilitate further studies, it is assumed that the cargo has a density in the range of 1 … 2 t/m 3 .Using the formulas ( 14)-( 15) let us present the values of specific weight of moving parts of roller supports for loaded and unloaded strands depending on the belt width and width of the bucket.Calculated values of the specific weight will be presented in the Table 13.For clearness of further calculations at the buckets with width less than 320 mm, let us take the value of specific weight of moving parts of roller supports for loaded and unloaded strands branches 40 oo q = N/m, 20 on q = N/m, respectively.We also accept that working conditions of the elevator will be difficult; therefore, the resistance coefficient of the belt movement along the rollers in future will be equal to 0.03.
Traction forces at the points 1 and 4 are determined using the formulas: where H -lift height of cargo, m; β -inclination angle of elevator, degree; 0,03 c = -resistance coefficient of the belt movement along the rollers.
The dependence of traction forces values at the point 4 calculated by the formula (16) on the value of design productivity, bucket type and amount of insert plies are summarized in the Tables 14-15.
The dependence of the values of tension force at the point 1 calculated by the formula (17) on the value of design productivity, bucket type and amount of insert plies of the belt are summarized in the Tables 16-17.
Tractive effort accounting rotational resistance of the drive drum is determined using the formula: where 1,08 k′ = -is a resistance coefficient of drive drum rotation.
After algebraic transformations in the formula (18) we have: The values of tractive effort taking into account the drum rotation resistance depending on the values of design performance, bucket type (deep and shallow) and the number of insert plies of the belt are summarized in the Tables 18-19.
Tractive effort at the belt with Tractive effort at the belt with Tractive effort at the belt with Estimated kinematic scheme of the elevator's drive is shown in the Fig. 2. Engine power is determined by the formula: о 1 000 Calculated power of the engine is determined by the formula: u n = then using the formulas ( 21) and ( 22) we obtain the following: Dependence of the calculated engine power on the values of design performance, bucket type, number of insert plies of the belt, speed of the belt movement and lifting height of cargo calculated using the formula (23) taking into account data from the Tables 18-19 are summarized in the Tables 20-21:

Findings
Let us analyze the influence of design parameters of inclined bucket elevator for transportation of fine coal on the power of required drive.Taking into account the physical and mechanical properties of fine coal according to the recommendations presented in the work [9] it was selected the belt elevator with spaced deep buckets and centrifugal discharge.The speed of belt movement is 1, 6 v = m/s; fill factor of the bucket 1, 6  v = ; t/m 3 -density of fine coal; lift height of the cargo 10 H = m; inclination angle of elevator to the horizontal 75 β = .Under these conditions the coefficient are: At this the dependence of calculated power of electric engine of the elevator's bucket on the design performance is given in the Table 22.
Taking into account standard values of power of three-phase asynchronous squirrel cage motors of 4A series with synchronous frequency of rotation 1000 rev/min for the drive of inclined elevator for transportation of fine coal it was compiled the table of correspondence of design performance and the required engine power.
Analyzing results of calculations presented in the Table 23 it can be concluded that the dependence of elevator drive power on its design performance (at fixed lift height, type of cargo, the angle of inclination to horizontal) in general is a piecewise constant monotonically increasing function.At this the productivity values given in the last column of the Table 23 should be considered as such, in which the power value varies and is equal to the appropriate value given in the second column of the Table 23.But to the value of 4.61 t/h the power is 0.75 kW due to the minimum of such power in the engines of such class.According to calculations it was plotted the dependence of inclined elevator drive for fine coal transportation on the value of design productivity (Fig. 3).
To determine the graphic dependence of elevator drive power on its inclination angle we take the initial data: transported material -fine coal; productivity Pr 20 = t/h lift height 10 H = m; speed of the belt movement 1,6 v = m/sec.Taking into account the fact that 4,61 t m/l h t α = ⋅ and Pr 20 = t/h for calculation of drive power the dependency in the 5th line and first column will be used (Tab.20).
Substituting the initial data for calculation into resulting dependence we obtain: 76,3 ctg 1751, 2 Graphic dependence of value of elevator drive power when transporting fine coal with design productivity Pr 20 = t/h on the angle of its inclination within 3... 2 β = π π is presented in the Fig. 4.

Originality and practical value
It was plotted the analytical dependence of elevator drive power on its design parameters (type and characteristics of the cargo, lifting height, inclination angle, productivity), which takes into account the standard sizes and types of buckets and belts.
Using this dependence makes it possible rapid determination of the approximate value of drive power of inclined elevators with deep and shallow buckets and performing high-quality selection of its key elements at the specific design characteristics.
Based on the proposed dependences it was plotted graphic dependence of power influence of required inclined elevator's drive on design productivity at the fixed lift height, inclination angle, and the type of cargo.It was also presented the graphic dependence of drive power on the inclination angle of elevator at the other fixed design parameters.

Conclusions
For inclined belt bucket elevators it was plotted analytical dependence of the drive power value on its design parameters.This makes it possible to obtain the required drive power value taking into account the type and physical and mechanical properties of the cargo, the value of lift height, inclination angle, design productivity and working conditions, involving only one calculation formula.As an example of involving the obtained results it was considered the process of plotting the dependence of drive power on the design productivity of elevator for fine coal transportation.For such elevator it was plotted the parametric and graphic dependence of drive power on design productivity and inclination angle of elevator taking into account the standard parameters of buckets and properties of electric engines.It was established that the function of varying the value of elevator power on the design productivity (at fixed lifting height, type of cargo¸ inclination angle) is piecewise and monotonically increasing, and the dependence of elevator power value on its inclination angle (at fixed design productivity, lift height, load type, the speed of belt movement) is non-linear and monotonically decreasing.