OF DEPENDENCE OF BELT CONVEYER DRIVE POWER ON ITS DESIGN PARAMETERS

Purpose. A drive is one of the basic elements of belt conveyers. To determine the drive power it is necessary to conduct calculations by standard methodologies expounded in modern technical literature. Such calculations demand a fair amount of time. The basic design parameters of a belt conveyer include type of load, design efficiency, geometrical dimensions and path configuration, operation conditions. The article aims to build the parametric dependence of belt conveyer drive power on its design parameters, that takes into account standard dimensions and parameters of belts, idlers and pulleys. Methodology. The work examines a belt conveyer with two areas: sloping and horizontal. Using the methodology for pulling calculation by means of belt conveyer encirclement, there are built parametric dependences of pull forces in the characteristic conveyer path points on the type of load, design efficiency, geometrical dimensions and path configuration, operation conditions. Findings. For the belt conveyers of the considered type there are built parametric dependences of drive power on type of load, design efficiency, geometrical dimensions and path configuration, operation conditions, taking into account the belt standard dimensions and corresponding assumptions in relation to idler and pulley types. Originality. This is the first developed parametric dependence of two-area (sloping and horizontal) belt conveyer drive power on type of load, design efficiency, geometrical dimensions and path configuration, operation conditions that takes into account standard dimensions and parameters of belts, idlers and pulleys. Practical value. Use of the built drive power dependences on design parameters for the belt conveyers with sloping and horizontal areas gives an opportunity of relatively rapid determination of drive power approximate value at the design stage. Also it allows quality selection of its basic elements at specific design characteristics and requirements. The offered dependences can be used for determination of general character of drive power dependence on the project efficiency.


Introduction
Transporting machines are important elements of transport and industrial construction sector.Continuous-transport machines are the foundation of the comprehensive mechanization of cargo handling, industrial processes, they increase productivity and efficiency.The most common type of continuous transport is belt conveyors.Belt conveyors are the continuous-type machines, the main ele-ment of which is vertically closed rubber belt that encircles the end pulleys, one of which is usually the drive one, the other -the idler one.Belt conveyors are widely used in the chemical, metallurgical, machine-building industry, for production of building materials, transport and industrial construction, at the coal preparation plants.
The analysis of publications shows that for determining the conveyor drive parameters, particularly its power, it is necessary to conduct calculation for its pulleys, pulling element (belt), pulling calculation and to select the basic drive elements.The procedure of these calculations is described in detail in [7,8].But the use of traditional conveyor drive calculation methods takes some time.Today, the constant development of almost all industries demands more rapid decision-making in the design of continuous-transport machines, which are elements of the production lines.Therefore, to improve the belt conveyor drive design process it is desirable to determine a scheme that allows using the more simple and quick calculations to determine the necessary value of the drive power depending on the design parameters.Such a scheme is proposed for elevators in [2,3].

Purpose
The work aims to build the parametric dependence for drive power of the belt conveyor with sloping and horizontal areas on type of load, design efficiency, geometrical dimensions and path configuration, operation conditions.

Methodology
The value of belt conveyor drive power depends on many factors.The main parameters affecting its value are: type of load, design efficiency, load lifting height and conveying distance, required load transportation path configuration, conveyor operation conditions.The design diagram of the conveyor under study and its approximate belt tension chart are shown in Figure 1.
Initial data for design calculations of the examined belt conveyor are as follows: − Transported material; − Conveyor efficiency; − Height or angle of the conveyor sloping area, H or β respectively; − Lengths of conveyor sections and radius: 12 For further study we determine that the conveyor has grooved three-roller idlers with 20 o angle on the loaded belt and row straight idlers -on the return belt.
Taking into account the data of the tables 8.1 and 8.2 of [8] we present in Table 1 the basic properties of the load that are needed for further calculations: The belt speed values in Table 1 are counted as the mean in a given range of possible values for the set load.
The belt width required for the set efficiency E is calculated by the formula e 1,1 0, 05 where cs k -cross-section coefficient of the material on belt (Table 1); k β -coefficient for crosssection decrease of the material on belt due to its partial bulking into the side opposite to the travel direction (p.403, [8]); ρ -bulk density of transported material (Table 1), t/m 3 .
The determined belt width value is rounded up to the nearest biggest number of a standard row of belt width: 400; 500; 650; 800; 1 000, 1 200 mm.
For convenience of further research, we will do some algebraic transformation in the expression (1).The result is as follows: For unambiguous determination of the required width to achieve the conveyor design efficiency the ratio E k β must appertain to some range of values.These ranges are shown in Table 2.The value E k β depends on the belt width, type of load and accepted load material density.The limit values of the ranges in Table 2  For further calculation the conveyor pulling element circuit is divided into straight and curved sections (see Fig. 1a).To determine the belt tension we use the method of pulling calculation by circuit.
We adopt the conveyor drive with one driving pulley, the wrap angle of which is 180 γ = °.The pulley surface is lined with rubber.
The efforts in the belt entering the drive pulley are determined by Euler's formula: where µ -friction factor between the belt and the pulley surface; γ -belt wrap angle of drive pulley, radian; e µγ -pulling factor (Table 3).There are two unknown terms 1 S and 8 S in the equation (3).To formulate the second equation it is necessary to encircle the pulling circuit from point 1 to point 8, expressing the tension at all points through the tension at point 1.The specific weight of the material on belt is determined by the formula where 3.6 -coefficient that depends on the belt speed, N•s/kg•m.The specific weight of moving parts of upper and lower idlers is determined by formulas: " " where ' i G , " i G -weight of rotating parts of upper and lower idlers respectively.
The spacing of upper and lower idlers i l on the path is taken according to the table 8.3 [8].The lower row idlers are arranged with the double i l spacing.
Using the data from tables 8.3 -8.5 [8] and the formulas ( 5) -( 6) we calculate the specific weight of moving parts of upper and lower idlers.The following table shows the values of the specific weight of moving parts of upper and lower idlers depending on the belt width and load density.
Using the data in table 1 and the formula (4), we built dependence of the loaded material specific weight on the belt width and the conveyor efficiency.The resulted data are shown in Table 5.
The belt running meter weight is calculated by the formula 0.01 where B and b δ should be substituted in millimetres.
Using the formulas ( 7) -( 8) we obtained the dependence of the belt linear weight value on the number of gaskets and the belt width (Table 6).
The basic principle of the encirclement method is to identify the specific points of the path, where there are changes of belt tension.Herewith the tension in the following ( 1 i + ) point equals the sum of the belt tension in this ( i ) point and the belt transport resistance at the section between these points: Наука та прогрес транспорту.Вісник Дніпропетровського національного університету залізничного транспорту, 2016, № 1 (61) Belt tension at point 2 is calculated by the formula where 12 W -belt transport resistance at the section between the points 1 and 2; ( ) where w -belt transport resistance (Table 7), which depends on the type of bearing, lubrication, sealing, dustiness of atmosphere and other conditions.
For further research it is assumed that 0.03 w = (operation conditions are heavy, lower idlers are straight, upper idlers are grooved).Using the tables 5 and 6, we obtained the expressions for tension force values at point 2, depending on the belt width and load density (Table 8).
Belt tension at point 3 is calculated by the formula 3 2 where k -coefficient for increase in belt tension due to idler pulley rotating resistance (Table 9).
Belt tension at point 4 is calculated by the formula where 34 W -belt transport resistance at the section between the points 3 and 4; ( ) where w -belt transport resistance coefficient (Table 7).If 0.03 w = (operation conditions are heavy, lower idlers are straight), then the dependences for tension force values at point 4 by belt width and load density are shown in Table 11.
Belt tension at point 5 is calculated by the formula 5 4 where k -coefficient for increase in belt tension due to idler pulley rotating resistance (Table 9).In the considered conveyor design the belt wrap angle of pulley is 180 o (Fig. 1), therefore, we assume that 1.05 k = .
Dependencies for tension force values at point 5 by belt width and load density are shown in Table 12.
Belt tension at point 6 is calculated by the formula where 56 W -belt transport resistance at the section between the points 5 and 6; ( ) ( ) where w -belt transport resistance coefficient (Table 7).If 0.03 w = (operation conditions are heavy, upper idlers are grooved), then the dependences for tension force values at point 6 by belt width and load density are shown in Table 13.
Belt tension at point 7 is calculated by Euler's formula: where w -friction factor between the belt and the idler surface; α -belt wrap angle of battery of idlers, radian.Belt wrap angle of battery of idlers: Dependencies for tension force values at point 7 by belt width and load density are shown in Table 14.

Findings
For convenience of further research we depict the dependencies of the table 15 in the following form: ( ) Solving the system of equations for the limiting state, in which there is no pulley slipping, we get: ( ) Now equating the right parts of expressions (22), we get: , , , , , , ( ) Using algebraic manipulations we obtain: ( ) ( ) The pulling effort considering the drive pulley rotation resistance is determined by the formula where 1.08 k′ = -drive pulley rotation resistance coefficient.
Substituting the expressions (23) and (24) into the formula (25) we get: ( ) The belt conveyor drive is more often designed with cylindrical double reduction gear.The kinematic diagram of the drive is shown in Fig. 2.
Rated motor power is calculated by the formula p о 1 000 where o F should be substituted in Newton; v -in meters per second; η -drive efficiency factor.
The drive efficiency factor is determined by the formula: i n = we determine the installed motor power by the formula: Dependencies for the motor power value by belt width and load density are shown in Table 16.

Originality and practical value
We developed parametric dependence of drive power of the belt conveyer with sloping and horizontal areas on type of load, design efficiency, geometrical dimensions and path configuration, operation conditions that takes into account standard dimensions and parameters of belts, idlers and pulleys.
Use of the built dependences gives an opportunity of relatively rapid determination of approximate value of the drive power for the belt conveyers of considered design, as well as it allows qual- ity selection of its basic elements at specific design characteristics and requirements.
The proposed dependences can be used for determination of general impact of the design efficiency and other parameters on the conveyor drive power.

Conclusions
For belt conveyors with sloping and horizontal areas we built parametric dependence of drive power on the design parameters: type of load, design efficiency, geometrical dimensions and path configuration, operation conditions.Such dependences allow calculating the required drive power value, taking into account the type and the physical and mechanical properties of load, the lifting height value, the transport length and design efficiency, using only one formula, chosen depending on design characteristics.

Table 2 Ranges of ratio values E k β corresponding to type of load and belt width Ranges
of ratio values E k β , t/h, with the belt width, mm

Table 5 Dependence of loaded material specific weight m q on belt width and conveyor efficiency
o δ = mm, 2 n δ = mm, while 6 1.6 2 8 1.6 b

Table 8 Belt tension at point 2
2S at load density ρ , N/m

Table 9
Value of coefficient k

Table 12 Belt tension at point 5
5S at load density ρ , N/m