1 technical information

1 Technical Information project and design criteria for belt conveyors 9 ® 1 Technical Information project and design criteria for belt conveyors Summary 10 1 Technical information page 9 1.1 Introduction ................................................................ 11 1.2 Technical symbols ..................................................... 12 1.3 Technical characteristics of belt conveyors ............. 14 1.4 Rulmeca key components for belt conveyors .......... 16 1.5 1.5.1 1.5.2 1.5.3 1.5.4 1.5.5 1.5.6 Project criteria ........................................................... Conveyed material ......................................................... Belt speed ...................................................................... Belt width ....................................................................... Type of troughing set, pitch and transition distance ...... Tangential force, absorbed power, passive resistance, belt weight, tensions and checks .................................... Belt conveyor drives and pulley dimensions ................... 36 44 1.6 1.6.1 1.6.2 Rollers, function and design criteria ......................... Choice of roller diameter in relation to speed .................. Choice in relation to load ................................................ 48 49 50 1.7 1.7.1 1.8 1.8.1 1.8.2 1.8.3 Loading of belt and impact rollers ............................. Calculation of associated forces on impact rollers .......... Other accessories ....................................................... Belt cleaners ................................................................. Belt inversion ................................................................. Belt conveyor covers ..................................................... 53 54 58 58 59 59 1.9 Project examples of a belt conveyor ......................... 60 18 18 23 24 32 1.1 Introduction During the project design stage for the transport of raw materials or finished products, the choice of the method must favour the most cost effective solution for the volume of material moved, the plant and its maintenance, its flexibility for adaptation and its ability to carry a variety of loads and even be overloaded at times. The belt conveyor, increasingly used in the last 10 years, is a method of conveying that satisfies the above selection criteria. Compared with other systems it is in fact the most economic, especially when one considers its adaptability to the most diverse and the most difficult conditions. Today, we are not concerned only with horizontal or inclined conveyors but also with curves, conveyors in descent and with speeds of increasing magnitude. However, the consideration in this section is not meant to be presented as the "bible" on project design for belt conveyors. 11 We wish to provide you with certain criteria to guide you in the choice of the most important components and calculations to help with correct sizing. The technical information contained in the following sections is intended to basically support the designer and be integrated into the technical fulfillment of the project. ® 1 Technical Information project and design criteria for belt conveyors 1.2 Technical symbols a A ag ai ao at au B C Ca ca Ca1 cd Cf ch Co Cp Cpr Cq Cr cr Cr1 Ct Cw d D E e f fa pitch of troughing sets length of roller spindle distance between the pulley flange and support pitch of impact sets pitch of carrying sets pitch of transition sets pitch of return sets length of roller shell distance between roller supports static load on the carrying set load on central roller of the carrying set dynamic load on the carrying set dynamic load on the bearing constant of elasticity of the frame/impact roller flats of roller shaft static load on bearing resulting load of associated forces on motorised drum shaft resulting load of associated forces on idler drum shaft coefficient of fixed resistance static load on the return set load on the roller of return set dynamic load on the return set coefficient of passive resistance given by temperature wrap factor diameter of spindle/shaft diameter of roller/pulley modules of elasticity of steel logarithmic natural base coefficient of internal friction of material and of rotating parts coefficient of friction between the belt and drum given an angle of wrap deflection of belt between two consecutive troughing sets deflection of a symmetrical shaft tangential force to move the belt in the direction of movement factor of impact environmental factor contribution factor contribution factor on the central roller of a troughing set tangential force to move the belt in the return direction service factor total tangential force speed factor distance between support brackets weight of lump of material height change of belt corrected height of fall height of fall of material belt-screen height change between motorised drum and counterweight height of fall of material screen - receiving belt distance from centre of motorised drum to the centre of the counterweight connection load volume belt load (material flow) fr ft Fa Fd Fm Fp Fpr Fr Fs Fu Fv G Gm H Hc Hf Ht Hv IC IM IV 12 m mm mm m m m m mm mm daN daN daN daN Kg/m mm daN daN daN __ daN daN daN __ __ mm mm daN/mm 2,718 __ __ m mm daN __ __ __ __ daN __ daN __ mm Kg m m m m m m m /h t/h 3 2 IVT J K K1 σamm L Lb Lt Mf Mif Mt N n P pd pi pic Ppri Pprs qb qbn qG qRO qRU qs qT RL S T0 T1 T2 T3 Tg Tmax Tumax Tx Ty v V W load volume corrected to 1 m/s in relation to the inclination and irregularity of the feed load volume theoretic to 1 m/s moment of inertia of section of material inclination factor correction factor admissible stress load centres dimensions of material lump transition distance bending moment ideal bending moment torsion moment belt width revolutions per minute absorbed power dynamic falling force impact force of falling material force impact on central roller weight of lower rotating parts weight of upper rotating parts weight of belt per linear metre weight of belt density weight of material per linear metre weight of the upper rotating parts referred to the troughing set pitch weight of the lower rotating parts referred to the troughing set pitch specific weight weight of drum length of motorised drum face section of belt material minimum tension at end of load zone tension on input side tension on output side tension on idler drum tension on belt at the point of counterweight connection tension at point of highest belt stress unitary maximum tension of belt tension of the belt at a considered point tension of the belt at a considered point belt speed maximum rise of edge of belt module of resistance α αt β γ δ λ λ1 λ2 η y angle of wrap of belt on pulley inclination of rotating symmetrical shaft angle of overload angle of screen inclination inclination of conveyor inclination of side roller of troughing set inclination of intermediate side roller inclination of external side roller efficiency angle deflection of bearing IVM The symbol for kilogram (Kg) is intended as a unit of force. 13 m /h m /h mm __ __ 3 3 4 daN/mm m m m daNm daNm daNm mm rpm kW Kg Kg Kg Kg Kg Kg/m Kg/m Kg/m Kg/m Kg/m t/m daN mm m daN daN daN daN daN daN daN/mm daN daN m/s mm mm 2 2 3 2 3 degree rad degree degree degree degree degree degree __ degree ® 1 Technical Information Belt conveyor Loading hopper Unloading hopper Carryng troughing sets Impact troughing sets project and design criteria for belt conveyors Return pulley Return idler sets Drive pulley Fig.1 - Basic drawing of a belt conveyor 1.3 Technical characteristics of belt conveyors The function of a belt conveyor is to continuously transport bulk materials of a mixed or homogeneous sort, a variable distance of some metres to tens of kilometres. One of the principal components of the conveyor is the elastomer belt which has a double function: - to contain the conveyed material - to transmit the force necessary to move the load. The belt conveyor is designed to transport material in a continuous movement on the upper part of the belt. The belt surfaces, upper on the carrying strand and lower on the return strand touch a series of rollers which are mounted from the conveyor structure itself in a group known as a troughing set. At either end of the conveyor the belt wraps around a pulley, one of which is coupled to a drive unit to transmit the motion. The most competitive of other transport systems is certainly that of using lorries, With respect to the latter, the belt conveyor presents the following advantages: - reduction in numbers of personnel - reduction in energy consumption - long periods between maintenance - independence of the system to its surrounds - reduced business costs 14 Based on the load, large belt conveyors are able to show cost add savings of up pass to 40-60% with respect to truck or lorry transport. The electrical and mechanical components of the conveyor such as rollers, drums bearings, motors etc.... are produced according to the highest standards. The quality level reached by major manufacturers guarantees function and long life. The principal components of the conveyor, rollers and belt, need very little maintenance providing the design and the installation has been correctly performed. The elastomer belt needs only occasional or superficial repair and as the rollers are sealed for life they need no lubrication. The high quality and advanced technology of Rulmeca may reduce even further, or substitute, the need for ordinary maintenance. Drum lagging has a life of at least two years. The utilisation of adequate accessories to clean the belt at the feed and discharge points yields corresponding improvements to increase the life of the installation with minor maintenance. All these factors combine to limit operational costs, especially where excavation work occurs, or underpasses below hills, roads or other obstacles. A smooth belt conveyor may travel up slopes up to 18° and there is always the possibility to recover energy on down hill sections. Projects have therefore been realised where conveyor system lengths may be up to 100 Km long with single sections of conveyor of 15 Km. Utilising the characteristics of flexibility, strength and economy of purpose the belt conveyor is the practical solution to conveying bulk and other materials. Continuous developments is this field add to these existing advantages. Fig.2.1- Conveyor with horizontal belt. Fig.2.5- Conveyor belt with incline and horizontal where two belts are needed. Fig.2.2 - Conveyor with horizontal belt with incline section, where the space permits a vertical curve and where the load requires the use of a single belt. Fig.2.3 - Conveyor with incline belt and following horizontal section, when the load requires the use of a single belt and where space permits a vertical curve. Fig.2.4 - Conveyor with horizontal and incline section where space does not allow a vertical curve and the load needs two belts to be employed. 15 The following drawings show typical belt conveyor arrangements. Fig.2.6 - Conveyor with horizontal and incline section where the space does not allow the vertical curve but the load may need the use of a single belt. Fig.2.7 - Conveyor with a single belt comprising a horizontal section, an incline section and a decline section with vertical curves. Fig.2.8 - Conveyor with belt loaded in decline or incline. ® 1 Technical Information project and design criteria for belt conveyors 1.4 Rulmeca key components for belt conveyors Fig. 3 illustrates the basic components of a typical belt conveyor. In practice, according to the variety of uses, it is possible to have many other diverse combinations of load and unload areas, elevations, and other accessories. Drive head May be of traditional design or with motorised drum unit. - Traditional Comprises a drive group consisting of a drive drum of a diameter appropriately sized to the load on the belt, and an idler drum at the opposing end. The power is supplied by a direct coupled motor gearbox or by a direct or parallel shaft drive driving the drive drum through a suitably sized couple. - Motorised Pulleys In this arrangement the motor, gearbox and bearings form a complete designed unit inside and protected by the drum shell which directly powers the belt. This eliminates all the external complication of external drive, couples etc. as described above in the traditional design. Today motorised pulleys are produced in diameters up to 1000 mm with a maximum power of 250 kW and with a drive efficiency which may reach 97%. 16 Drive pulley The shell face of the conventional drive pulley or the motorised drum may be left as normal finish or clad in rubber of a thickness calculated knowing the power to be transmitted. The cladding may be grooved as herringbone design, or horizontal grooves to the direction of travel, or diamond grooves; all designed to increase the coefficient of friction and to facilitate the release of water from the drum surface. The drum diameter is dimensioned according to the class and type of belt and to the designed pressures on its surface. Return pulleys The shell face does not necessarily need to be clad except in certain cases, and the diameter is normally less than that designed for the drive pulley. Deflection or snub pulleys These are used to increase the angle of wrap of the belt and overall for all the necessary changes in belt direction in the areas of counterweight tensioner, mobile unloader etc.. Rollers Support the belt and are guaranteed to rotate freely and easily under load. They are the most important components of the conveyor and represent a considerable value of the whole cost. The correct sizing of the roller is fundamental to the guarantee of the plant efficiency and economy in use. Upper carrying troughing and return sets The carrying rollers are in general positioned in brackets welded to a cross member or frame. The angle of the side roller varies from 20° to 45°. It is also possible to arrive at angles of up to 60° using the “garland” suspension design. The return roller set may be designed incorporating one single width roller or two rollers operating in a “V” formation at angles of 10°. Depending on various types of material being conveyed the upper carrying sets may be designed symmetrically or not, to suit. Tension units The force necessary to maintain the belt contact to the drive pulley is provided by a Load hopper Carryng trough set tension unit which may be a screw type unit, a counterweight or a motorised winch unit. The counterweight provides a constant tensional force to the belt independent of the conditions. Its weight designed according to the minimum limits necessary to guarantee the belt pull and to avoid unnecessary belt stretch. The hopper slide should relate to the way the material falls and its trajectory and is designed according to the speed of the conveyor. Lump size and the specific gravity of the charge and its physical properties such as humidity, corrosiveness etc. are all very relevant to the design. The designed movement of the counterweight tension unit is derived from the elasticity of the belt during its various phases of operation as a conveyor. Cleaning devices The system of cleaning the belt today must be considered with particular attention to reduce the need for frequent maintenance especially when the belt is conveying wet or sticky materials. Efficient cleaning allows the conveyor to obtain maximum productivity. The minimum movement of a tension unit must not be less than 2% of the distance between the centres of the conveyor using textile woven belts, or 0.5% of the conveyor using steel corded belts. Hopper The hopper is designed to allow easy loading and sliding of the material in a way to absorb the shocks of the load and avoids blockage and damage to the belt. It caters for instantaneous charging of load and its eventual accumulation. Upper self-centralising set Cover There are many types and designs of belt cleaners. The most straight forward simple design is that of a straight scraper blade mounted on rubber supports (chapter 5). Conveyor covers Covers over the conveyor are of fundamental importance when it is necessary to protect the conveyed material from the atmosphere and to guarantee efficient plant function (chapter 6). Transition troug set Drive pulley or motorized pulley Impact trough set Cleaner Tangential scraper Snub pulley Fig. 3 Return pulley Snub pulley Plough cleaner Return self-centralising set Return set 17 Tension pulley with counterweight Pressure pulley ® 1 Technical Information project and design criteria for belt conveyors 1.5 - Project criteria The choice of the optimum conveyor system and its project design and rationalisation depends on full knowledge of the construction characteristics and the forces involved that apply themselves to all the system components. The principal factors that influence the sizing of a belt conveyor are: the required load volume, the type of transported material and its characteristics such as grain or lump size, and chemical / physical properties. The route and height profile of the conveyor is also relevant. In the following illustrations you may follow the criteria used for the calculation of the belt speed and width, the type and arrangement of troughing sets, the type of rollers to be used and finally the determination of the drum sizes. The angle of surcharge is the angle measured with respect to the horizontal plane, of the surface of the material being conveyed by a moving belt. Fig. 5. This angle is normally between 5° and 15° (for a few materials up to 20°) and is much less than the angle of repose. Angle of repose Fig.4 Angle of surcharge 1.5.1 - Conveyed material The correct project design of the belt conveyor must begin with an evaluation of the characteristics of the conveyed material and in particular the angle of repose and the angle of surcharge. The angle of repose of a material, also known as the “angle of natural friction” is the angle at which the material, when heaped freely onto a horizontal surface takes up to the horizontal plane. Fig. 4. 18 Fig.5 Tab.1 shows the correlation between the physical characteristics of materials and their relative angles of repose. The conveyed material settles into a configuration as shown in sectional diagram Fig. 6. The area of the section “S” may be calculated geometrically adding the area of a circle A1 to that of the trapezoid A2. S = A1 + A2 S A1 A2 Fig.6 The value of the conveyed volume lVT may be easily calculated using the formula: Tab. 1 - Angles of surcharge, repose and material fluency IVT S = _________ [ m2 ] 3600 where: Fluency very high Profile high medium low on a flat belt Angle of surcharge β 10° 20° 25° 30° ß 20-29° 30-34° 35-39° 40° and more Others Uniform dimensions, Partly rounded Irregular material, General everyday Irregular viscous Here may be round particles, very particles, dry and granular particles material as for fibrous material included materials small size. smooth. of average weight example bitumi- which tends to get with a variety of Very humid or very Average weight as as for example nous coal and worse in handling, characteristics as dry such as dry for example cereal, anthracite coal, the majority of as for example indicated in the sand, silica, cement grain and beans. clay etc. minerals. wood shavings, following Tab.2. 5° IVT = conveyed volume at a conveyor speed of 1 m/s ( seeTab.5a-b-c-d ) Angle of repose 0-19° Characteristics of materials and wet limestone sugar cane by dust etc. product, foundry sand, etc. 19 ® 1 Technical Information project and design criteria for belt conveyors Tab.2 - Physical properties of materials Type Average specific weight Angle Abrasive - Corrosive - t/m3 lbs. / Cu.Ft qs of repose ness ness Alumina 0,80-1,04 50-65 22° C A Aluminium chips 0,11-0,24 7-15 - B A Aluminium oxide 1,12-1,92 70-120 - C A Aluminium sulphate (granular) 0,864 54 32° - - Ammonium nitrate 0,72 45 - B C Ammonium sulphate 0,72-0,93 45-58 32° B C Asbestos ore or rock 1,296 81 - C A Ashes, coal, dry, up to 80 mm 0,56-0,64 35-40 40° B A Ashes, coal, wet, up to 80 mm 0,72-0,80 45-50 50° B P Asphalt, binder for paving 1,28-136 80-85 - A B Asphalt, crushed up to13 mm 0,72 45 - A A Bakelite, fine 0,48-0,64 30-40 - A A Barite 2,88 180 - A A Barium carbonate 1,152 72 - A A Bauxite, mine run 1,28-1,44 80-90 31° C A Bauxite, ground, dried 1,09 68 35° C A Bentonite, up to 100 mesh 0,80-0,96 50-60 - B A Borax, lump 0,96-1,04 60-65 - B A Brick, hard 2 125 - C A Calcium carbide 1,12-1,28 70-80 - B B Carbon black pellets 0,32-0,40 20-25 - A A Carbon black powder 0,06-0,11 4-7 - A A Carborundum, up to 80 mm 1,60 100 - C A Cast iron chips 2,08-3,20 130-200 - B A Cement, rock (see limestone) 1,60-1,76 100-110 - B A Cement, Portland, aerated 0,96-1,20 60-75 39° B A Charcoal 0,29-0,40 18-25 35° A A Chrome ore (cromite) 2-2,24 125-140 - C A Clay, dry, fine 1,60-1,92 100-120 35° C A Clay, dry, lumpy 0,96-1,20 60-75 35° C A Clinker 1,20-1,52 75-95 30-40° C A Coal, anthracite 0,96 60 27° B A Coal, bituminous, 50 mesh 0,80-0,86 50-54 45° A B Coal, bituminous, run of mine 0,72-0,88 45-55 38° A B Coal, lignite 0,64-0,72 40-45 38° A B Coke breeze, 6 mm 0,40-0,5 25-35 30-45° C B Coke, loose 0,37-0,56 23-35 - C B Coke petroleum calcined 0,56-0,72 35-45 - A A Concrete, in place, stone 2,08-2,40 130-150 - C A Concrete, cinder 1,44-1,76 90-110 - C A Copper, ore 1,92-2,40 120-150 - - - Copper sulphate 1,20-1,36 75-85 31° A - Cork 0,19-0,24 12-15 - - - Cryolite 1,76 110 - A A Cryolite, dust 1,20-1,44 75-90 - A A Diacalcium phosphate 0,688 43 - - - Disodium phosphate 0,40-0,50 25-31 - Dolomite, lumpy 1,44-1,60 90-100 - B A 20 Table 2 states physical and chemical properties of materials that you have to take into consideration for the belt conveyor project. Tab.2 - Physical properties of materials Type Earth, wet, containing clay A non abrasive/non corrosive B mildly abrasive/ mildly corrosive C very abrasive/very corrosive Average specific weight qs Angle Abrasive - Corrosive - t/m3 lbs. / Cu.Ft of repose ness ness 1,60-1,76 100-110 45° B A Feldspar, 13 mm screenings 1,12-1,36 70-85 38° C A Feldspar, 40 mm to 80 mm lumps 1,44-1,76 90-110 34° C A Ferrous sulphate 0,80-1,20 50-75 - B - Foundry refuse 1,12-1,60 70-100 - C A Gypsum, 13 mm to 80 mm lumps 1,12-1,28 70-80 30° A A Gypsum, dust 0,96-1,12 60-70 42° A A Graphite, flake 0,64 40 - A A Granite,13 mm screening 1,28-1,44 80-90 - C A Granite, 40 mm to 50 mm lumps 1,36-1,44 85-90 - C A Gravel 1,44-1,60 90-100 40° B A Gres 1,36-1,44 85-90 - A A Guano, dry 1,12 70 - B - Iron ore 1,60-3,20 100-200 35° C A Iron ore, crushed 2,16-2,40 135-150 - C A Kaolin clay, up to 80 mm 1,008 63 35° A A Kaolin talc, 100 mesh 0,67-0,90 42-56 45° A A Lead ores 3,20-4,32 200-270 30° B B Lead oxides 0.96-2,04 60-150 - A - Lime ground, up to 3 mm 0,96 60 43° A A Lime hydrated, up to 3 mm 0,64 40 40° A A A Lime hydrated, pulverized 0,51-0,64 32-40 42° A Limestone, crushed 1,36-1,44 85-90 35° B A Limestone, dust 1,28-1,36 80-85 - B A Magnesite (fines) 1,04-1,20 65-75 35° B A Magnesium chloride 0,528 33 - B - Magnesium sulphates 1,12 70 -- - Manganese ore 2,00-2,24 125-140 39° B A Manganese sulphate 1,12 70 - C A Marble, crushed, up to 13 mm 1,44-1,52 90-95 - B A Nickel ore 2,40 150 - C B Phosphate, acid, fertilizer 0,96 60 26° B B Phosphate, florida 1,488 93 27° B A Phosphate rock, pulverized 0,96 60 40° B A Phosphate, super ground 0,816 51 45° B B Pyrite-iron, 50 to 80 mm lumps 2,16-2,32 135-145 - B B Pyrite, pellets 1,92-2,08 120-130 - B B Polystyrene beads 0,64 40 - - - Potash salts, sylvite, etc. 1,28 80 - A B Potassium cloride, pellets 1,92-2,08 120-130 - B B Potassium nitrate (saltpeter) 1,216 76 - B B Potassium sulphate 0,67-0,77 42-48 - B - 21 ® 1 Technical Information project and design criteria for belt conveyors A non abrasive/non corrosive B mildly abrasive/mildly corrosive C very abrasive/very corrosive Tab.2 - Physical properties of materials Type Average specific weight qs Angle Abrasive - t/m3 lbs. / Cu.Ft of repose ness Corrosive ness Quartz 40 mm to 80 mm lumps 1,36-1,52 85-95 - C A Quartz, dust 1,12-1,28 70-80 - C A Quartz, 13 mm screening 1,28-1,44 80-90 - C A Rubber, pelletized 0,80-0,88 50-55 35° A A Rubber, reclaim 0,40-0,48 25-30 32° A A Salt, common dry, coarse 0,64-0,88 40-55 - B B Salt, common dry, fine 1,12-1,28 70-80 25° B B Sand, damp 1,76-2,08 110-130 45° C A Sand, dry 1,44-1,76 90-110 35° C A Sand, foundry, shakeout 1,44-1,60 90-100 39° C A Slag, blast furnace, crushed 1,28-1,44 80-90 25° C A Slate, 40 mm to 80 mm lumps 1,36-1,52 85-95 - B A Slate, dust 1,12-1,28 70-80 35° B A Soap powder 0,32-0,40 20-25 - A A Soapstone, talc, fine 0,64-0,80 40-50 - A A Soda heavy asmes 0,88-1,04 55-65 32° B C Sodium bicarbonate 0,656 41 42° A A Sodium nitrate 1,12-1,28 70-80 24° A - Steel shavings 1,60-2,40 100-150 - C A Sugar beet, pulp (dry) 0,19-0,24 12-15 - - - Sugar beet, pulp (wet) 0,40-0,72 25-45 - A B Sugar, cane, knifed 0,24-0,29 15-18 50° B A Sugar, powdered 0,80-0,96 50-60 - A B Sugar, raw, cane 0,88-1,04 55-65 30° B B Sugar, wet, beet 0,88-1,04 55-65 30° B B Sulphur, crushed under 13 mm 0,80-0,96 50-60 - A C Sulphur, up to 80 mm 1,28-1,36 80-85 - A C Talc, powdered 0,80-0,96 50-60 - A A Talc, 40 mm to 80 mm lumps 1,36-1,52 85-95 - A A Titanium dioxide 0,40 25 - B A Wheat 0,64-0,67 40-42 25° A A Wood chips 0,16-0,48 10-30 - A A Zinc concentrates 1,20-1,28 75-80 - B A Zinc ore, roasted 1,60 100 38° - - Zinc oxide, heavy 0,48-0,56 30-35 - A A 22 1.5.2 - Belt speed The maximum speed of a belt conveyor in this field has reached limits not thought possible some years ago. Very high speeds have meant a large increase in the volumes conveyed. Compared with the load in total there is a reduction in the weight of conveyed material per linear metre of conveyor and therefore there is a reduction in the costs of the structure in the troughing set frames and in the belt itself. The physical characteristics of the conveyed material is the determining factor in calculating the belt speed. Light material, that of cereal, or mineral dust or fines, allow high speeds to be employed. Screened or sifted material may allow belt speeds of over 8 m/s. With the increase of material lump size, or its abrasiveness, or that of its specific weight, it is necessary to reduce the conveyor belt speed. It may be necessary to reduce conveyor speeds to a range in the order of 1.5/3.5 m/s to handle unbroken and unscreened rock of large lump size. The quantity of material per linear metre loaded on the conveyor is given by the formula: IV qG = [ Kg/m ] 3.6 x v where: qG = weight of material per linear metre IV = belt load t/h Nevertheless larger belt widths, relative to the belt load, are used at high and low speeds where there is less danger of losing material, fewer breakdowns and less blockage in the hoppers. From experimental data we show in Tab. 3 the maximum belt speeds advised considering the physical characteristics and lump size of the conveyed material and the width of the belt in use. Tab. 3 - Maximum speeds advised Lump size max. dimensions Belt min. width max. speed A uniform mixed up to mm up to mm B C D 2.3 2 1.65 mm 50 100 400 75 150 500 2.5 125 200 650 3 2.75 2.38 2 170 300 800 3.5 3.2 2.75 2.35 250 400 1000 4 3.65 3.15 2.65 350 500 1200 400 600 1400 4.5 4 3.5 3 450 650 1600 500 700 1800 550 750 2000 5 4.5 3.5 3 600 800 2200 6 5 4.5 4 A - Light sliding material non abrasive, specific weight from 0.5 ÷ 1,0 t/m3 B - Material non abrasive, medium size, specific weight from 1.0 ÷ 1.5 t/m3 C - Material moderately abrasive and heavy with specific weight from 1.5 ÷ 2 t/m3 D - Abrasive material, heavy and sharp over 2 t/m3 specific weight Considering the factors that limit the maximum conveyor speed we may conclude: When one considers the inclination of the belt leaving the load point: the greater the inclination, the increase in the amount of turbulence as the material rotates on the belt. This phenomena is a limiting factor in calculating the maximum belt speed in that its effect is to prematurely wear out the belt surface. v = belt speed m/s qG is used in determining the tangential force Fu. With the increase of speed v it is possible to calculate the average belt load IV with a narrower belt width (and therefore it follows a simpler conveyor structure) as well as a lower load per linear metre and therefore a reduction results in the design of rollers and troughing sets and in less belt tension. The repeated action of abrasion on the belt material, given by numerous loadings onto a particular section of the belt under the load hopper, is directly proportional to the belt speed and inversely proportional to its length. 23 ® Given, using Tab.3, the optimum belt speed, the determination of the belt width is largely a function of the quantity of conveyed material which is indicated by the project data. Troughing sets at 40°/45° are used in special cases, where because of this onerous position the belts must be able to adapt to such an accentuated trough. In practice the choice and design of a troughing set is that which meets the required loaded volume, using a belt of minimum width and therefore the most economic. In the following section, the conveyor capacity may be expressed as loaded volume IVT [m3/h] per v= 1 m/sec. The inclination of the side rollers of a transom (from 20° to 45°) defines the angle of the troughing set Fig.7. Angle of surcharge Distance from edges 0,05 x N + 25 mm β project and design criteria for belt conveyors 1.5.3 - Belt width Troughing set angle λ 1 Technical Information N Belt width Fig. 7 All things being equal the width of the belt at the greatest angle corresponds to an increase in the loaded volume IVT. The design of the loaded troughing set is decided also as a function of the capacity of the belt acting as a trough. In the past the inclination of the side rollers of a troughing set has been 20°. Today the improvements in the structure and materials in the manufacture of conveyor belts allows the use of troughing sets with side rollers inclined at 30°/35°. 24 It may be observed however that the belt width must be sufficient to accept and contain the loading of material onto the belt whether it is of mixed large lump size or fine material. In the calculation of belt dimensions one must take into account the minimum values of belt width as a function of the belt breaking load and the side roller inclination as shown in Tab.4 . Tab. 4 - Minimum belt width in relation to belt breaking load and roller inclinations. Breaking load Belt width N/mm mm λ= 20/25° λ= 30/35° λ= 45° 250 400 400 — 315 400 400 450 400 400 400 450 500 450 450 500 630 500 500 600 800 500 600 650 1000 600 650 800 1250 600 800 1000 1600 600 800 1000 For belts with higher breaking loads than those indicated in the table, it is advisable to consult the actual belt manufacturer. Loaded volume IM The volumetric load on the belt is given by the formula: Iv IM = qs [ m3/h ] where: Iv = load capacity of the belt [ t/h ] qs = specific weight of the material Also defined as: IM IVT = v [ m3/h ] where the loaded volume is expressed relevant to the speed of 1 m/s. 25 It may be determined from Tab. 5a-b-c-d, that the chosen belt width satisfies the required loaded volume IM as calculated from the project data, in relation to the design of the troughing sets, the roller inclination, the angle of material surcharge and to belt speed. ® project and design criteria for belt conveyors β 1 Technical Information Tab. 5a - Loaded volume with flat roller sets v = 1 m/s Belt Angle of width surcharge mm β 300 400 500 650 800 1000 1200 1400 IVT m3/h λ = 0° Belt Angle of width surcharge mm β IVT m3/h λ = 0° 5° 2.5 5° 101.3 10° 5.1 10° 203.2 20° 10.3 20° 411.3 25° 13.0 25° 519.0 30° 15.8 30° 630.1 1600 5° 5.0 5° 129.2 10° 10.1 10° 259.2 20° 20.5 25° 30° 1800 20° 524.8 25.8 25° 662.1 31.3 30° 803.8 5° 8.4 5° 160.5 10° 16.8 10° 322.0 20° 34.1 25° 2000 20° 652.0 43.0 25° 822.7 30° 52.2 30° 998.7 199.3 5° 15.0 5° 10° 30.1 10° 399.8 20° 60.9 20° 809.6 25° 76.9 25° 1021.5 30° 93.3 30° 1240.0 5° 23.5 5° 242.3 10° 47.2 10° 486.0 2200 20° 95.6 20° 984.1 25° 120.6 25° 1241.7 30° 146.4 30° 1507.4 289.5 2400 5° 37.9 5° 10° 76.0 10° 580.7 20° 153.8 20° 1175.8 25° 194.1 25° 1483.5 30° 235.6 30° 1800.9 340.8 2600 5° 55.6 5° 10° 111.6 10° 683.7 20° 225.9 20° 1384.4 25° 285.0 25° 1746.8 30° 346.0 30° 2120.5 396.4 2800 5° 76.7 5° 10° 153.9 10° 795.2 20° 311.7 20° 1610.1 25° 393.3 25° 2031.5 30° 477.5 30° 2466.2 26 3000 β λ Tab. 5b - Loaded volume with 2 roll troughing sets v = 1 m/s Belt Angle of width surcharge mm β 300 400 500 650 800 1000 5° 16,2 10° 18,5 20° 23,1 25° 25,5 30° 27,9 5° 32,2 10° 36,7 20° 45,9 25° 50,6 30° 55,5 5° 53,7 10° 61,1 20° 76,4 25° 84,2 30° 92,4 5° 96,0 10° 109,4 20° 136,6 25° 150,7 30° 165,2 5° 150,6 10° 171,5 20° 214,2 25° 236,3 30° 259,1 5° 242,4 10° 276,1 20° 344,8 25° 380,4 30° 417,0 speed use: x v m3/h λ = 20° To obtain the effective loaded volume IM at the desired belt IM = IVT IVT [ m3/h ] 27 ® 1 Technical Information project and design criteria for belt conveyors Tab. 5c - Loaded volume with 3 roll troughing sets v = 1 m/s Belt Angle of width surcharge mm β 300 400 500 650 800 1000 1200 1400 IVT m3/h λ = 20° λ = 25° λ = 30° λ = 35° λ = 45° 5° 12.5 14.7 16.7 18.4 21.3 10° 14.9 17 18.9 20.6 23.3 20° 19.8 21.8 23.5 25 27.2 25° 22.4 24.3 25.9 27.3 29.3 30° 25 26.8 28.4 29.7 31.4 43.2 5° 25.3 29.7 33.8 37.4 10° 30.1 34 38 41.7 47 20° 39.9 43.8 47.4 50.4 54.8 25° 44.9 48.7 52 54.9 58.8 30° 50.2 53.8 56.9 59.5 62.9 5° 43.2 50.7 57.7 63.8 73.6 10° 51.1 58.4 65 70.8 79.8 20° 67.4 74 80.1 85.2 92.6 25° 75.8 82.3 87.9 92.7 30° 84.4 90.7 96 100 99.2 106 5° 80.3 94.4 107.2 118.6 136.3 10° 94.4 108 125 131 147.1 20° 123 136 147 156.3 169.3 25° 138 150 160 169 180 30° 153 165 175 182 192.7 5° 125.9 148.1 168.2 186 213.8 10° 148.1 169.5 188.7 205.4 230.8 20° 193.5 213.3 230 245.1 265.6 25° 217 235.9 252.2 265.7 283.6 30° 241.2 259.3 274.6 286.9 302.2 5° 207.5 244.1 277.1 306.1 351 10° 243.2 278.4 309.8 337.1 377.9 20° 316 348.5 376.7 400.4 433 25° 353.7 384.8 411.4 433.1 461.4 30° 392.5 422.2 447 466.9 490.8 5° 304 357.5 405.9 448 514.3 10° 356.3 407.9 454 494 554 20° 463.3 510.9 552.3 587 634.9 25° 518.6 564.2 603.2 635 676.8 30° 575.7 619.2 655.7 684 720 5° 424.9 499.7 547.1 626.3 717.2 10° 497 569 633.3 688.8 771.3 20° 644.4 710.8 768.4 816.5 881.9 25° 720.6 784.1 838.8 882.5 939.1 30° 799.2 859.8 910.4 950.6 998.1 28 β λ Belt Angle of width surcharge mm β 1600 1800 2000 2200 2400 2600 To obtain the effective loaded volume IM at the desired belt 3000 speed use: IM = IVT x v [ m3/h ] m3/h λ = 20° λ = 25° λ = 30° λ = 35° λ = 45° 5° 564.1 663.4 752.8 831.2 951 10° 659.2 754.8 839.9 913.4 1022.1 20° 853.5 941.6 1017.9 1081.4 1167.3 25° 954 1038.2 1110 1168.2 1242.4 30° 1057.6 1137.9 1204.9 1257.9 1319.9 5° 723 850.1 964.7 1064.9 1217.6 10° 844.2 966.7 1075.6 1169.5 1307.9 20° 1091.9 1204.7 1302.3 1383.3 1492.5 25° 1220 1327.9 1419.6 1493.9 1587.9 30° 1352.2 1454.9 1540.5 1608 1686.4 5° 897.3 1055.2 1197.3 1321.7 1511.5 10° 1047.9 1200 1335.2 1451.8 1623.8 20° 1355.8 1495.8 1617 1717.6 1853.4 25° 1515 1648.9 1762.7 1855.1 1972.1 30° 1679.2 1806.7 1913 1996.9 2094.5 5° 1130.8 1329.5 1508 1663.5 1898.1 10° 1317.4 1508.7 1678.3 1823.8 2035.7 20° 1698.7 1874.7 2026.2 2151.3 2317 25° 1895.9 2064 2206.2 2320.7 2462.4 30° 2099.3 2259.2 2391.8 2495.4 2612.4 2296.8 5° 1366.2 1606.4 1822.3 2010.9 10° 1599.2 1824.5 2029.8 2206.4 2465 20° 2057.2 2270.1 2453.8 2605.9 2808.8 25° 2297.2 2500.6 2673.1 2812.5 2986.6 30° 2544.7 2738.3 2899.3 3029.5 3170 5° 1650.6 1940.6 2200.6 2426.9 2767 10° 1921.4 2200.4 2447.5 2659.1 2965.9 20° 2474.7 2731.3 2951.9 3133.5 3372.4 25° 2760.9 3005.8 3212.7 3378.9 3582.7 30° 3056 3289 3481.8 3631.9 3799.5 1932.9 2272.7 2577.7 2843.6 3244.9 10° 2252 2579 2868.9 3117.7 3480.3 20° 2904.1 3205 3464.1 3678 3961.4 25° 3241.4 3528.7 3771.9 3967.7 4210.3 30° 3589.2 3862.6 4089.3 4266.6 4469.9 5° 5° 2800 IVT 2256.1 2652.5 3008.1 3317.8 3783.9 10° 2627 3008.4 3346.4 3636 4056.8 20° 3384.9 3735.8 4037.6 4286.4 4614.5 25° 3776.9 4111.9 4395.1 4627.7 4902.9 30° 4181.3 4496.9 4763.8 4969.6 5200.3 29 ® λ2 Tab. 5d - Loaded volume with 5 roll troughing sets v = 1 m/s IVT m3/h λ1 project and design criteria for belt conveyors β 1 Technical Information Belt Angle of Belt Angle of width surcharge width surcharge β mm β mm 800 1000 1200 1400 1600 1800 λ1 30° λ2 60° IVT m3/h λ1 30° λ2 60° 5° 236.4 5° 10° 252.4 10° 1762.6 20° 284.6 20° 1972.7 25° 301.4 25° 2081.3 30° 318.7 30° 2193.1 5° 10° 20° 25° 381.8 5° 2058.2 407.8 10° 2186.2 20° 2447.7 485.8 25° 2582.9 30° 513.4 30° 2722.4 5° 566.8 5° 2525.5 10° 603.3 10° 2678.1 20° 678.1 20° 2989.8 25° 716.7 25° 3151 30° 756.6 30° 3317.3 5° 787.8 5° 3030.5 10° 837.6 10° 3210.5 20° 939.5 20° 3579.4 25° 992.1 25° 3770.2 30° 1046.4 30° 3966.9 459 2000 2200 2400 2600 1659 5° 1038.8 5° 3570.8 10° 1104.6 10° 3782.9 20° 1239.2 20° 4216.3 25° 1308.8 25° 4440.5 30° 1380.6 30° 4671.7 2800 5° 1324.4 5° 4165.6 10° 1408.5 10° 4410.5 20° 1580.4 20° 4910.9 25° 1669.3 25° 5169.6 30° 1761 30° 5436.6 To obtain the effective loaded volume IM at desired belt speed use: IM = IVT x v 30 [ m3/h ] 3000 In the case of inclined belts, the values of loaded volume IVT [m3/h] are corrected according to the following: IVM = IVT X K X K1 [m3/h] Where: IVM is the loaded volume corrected in relation to the inclination and the irregularity of feeding the conveyor in m3/h with v = 1 m/s IVT is the theoretic load in volume for v= 1 m/s K is the factor of inclination Fig.8 - Factor of inclination K Factor of inclination K Corrects loaded volume in relation to the factors of inclination and feed 1,0 0,9 0,8 0,7 K1 is the correction factor given by the feed irregularity The inclination factor K calculated in the design, must take into account the reduction in section for the conveyed material when it is on the incline. Diagram Fig.8 gives the factor K in function of the angle of conveyor inclination, but only for smooth belts that are flat with no profile. δ 0 2 4 6 8° 12° 16 18 Angle of inclination In general it is necessary to take into account the nature of the feed to the conveyor, whether it is constant and regular, by introducing a correction factor K1 its value being: regular feed irregular feed most irregular feed. If one considers that the load may be corrected by the above factors the effective loaded volume at the required speed is given by: IM = IVM x v [m3/h] 31 δ Given the belt width, one may verify the relationship between the belt width and the maximum lump size of material according to the following: belt width ≥ max. lump size - K1 = 1 - K1 = 0.95 - K1 = 0.90 ÷ 0.80 20 ® 1 Technical Information project and design criteria for belt conveyors 1.5.4 - Type of troughing set, pitch and transition distance Type For each troughing set there is a combination of rollers positioned into a suitable fixed support frame Fig. 9; the troughing sets may also be suspended as a “garland” Fig. 10. There are 2 basic types of troughing set base frame: the upper set, which carries the loaded belt on the upper strand, and the lower set, which supports the empty belt on the return strand. •The฀ upper฀ carrying฀ troughing฀ set฀ is฀ generally designed as the following arrangement: - one or two parallel rollers - two, three or more rollers in a trough. The roller frame with fixed supports, with three rollers of equal length, support the belt well with a uniform distribution of forces and load sharing. The inclination of the side roller varies from 20° up to 45° for belts of 400 mm width up to 2200 mm and over. The suspended sets of “garland” design are used incorporating impact rollers to accept the impact under the load hopper, and also in use along the conveyor upper and lower strands where large loads may be carried or on very high performance conveyors. The troughing sets are generally designed and manufactured according to international unified standards. The drawings illustrate the more common arrangements. •฀The฀return฀set฀can฀be฀with: - one or two flat rollers - a trough of two rollers. Fig. 9 - Troughing sets upper strand Return sets - parallel roller plain or impact - roller plain or with rubber rings - 2 rollers plain or impact - 2 rollers plain or with rings - 3 rollers plain or impact 32 The choice of the most appropriate and correct troughing set installation (one needs to calculate the frictional force between the rollers and the belt itself) is the guarantee for the smooth belt start up and movement. The troughing sets on the upper strand of a reversible belt may have the rollers in line with each other and at right angles to the belt as in Fig. 11; in the case of non-reversible belt the side rollers are inclined forward by 2° in the same sense of direction of the belt, as in Fig. 12. Direction of travel Fig. 11 - For reversible belts Fig. 10 - Suspension sets "garland" - 2 rollers plain or with rubber rings for return set Direction of travel Direction of travel Fig. 12 - Only for single directional belts - 3 rollers plain for load carrying Fig.13 - Misalignment of the troughing set may promote belt wandering. - 5 rollers plain for load carrying 33 ® 1 Technical Information project and design criteria for belt conveyors Troughing set pitch to maintain a deflection of the belt within the The trough set pitch ao most commonly used indicated limits. Above all the pitch is also for the upper strand of a belt conveyor is 1 limited by the load capacity of the rollers metre, whilst for the return strand the sets themselves. are pitched normally at 3 metres (au). ao ai Fig.14 au The deflection of the belt between 2 consecutive carrying troughing sets should not be more than 2% of the pitch itself. A greater deflection causes the discharge of the material during the loading and promotes excessive frictional forces during the belt movement due to the manipulation of the material being conveyed. This not only the increases the horse power and work, but also increases forces on the rollers, and overall a premature belt surface wear occurs. Tab.6 advises the maximum pitch for troughing sets in relation to belt width and the specific weight of the conveyed material, At the loading points the pitch is generally one half or less, that of the normal pitch of troughing sets so that any belt deflection is limited to the least possible, and also to reduce the load forces on the rollers. ai Fig.15 The calculation of the minimum pitch for suspension sets is calculated to avoid contact between adjoining “garlands” when the normal oscillation of the sets takes place during belt operation Fig.15. Tab. 6 - Maximum advised pitch of troughing sets Belt width Pitch of sets upper lower specific weight of conveyed material t/m3 < 1.2 1.2 ÷ 2.0 > 2.0 m m m m 1.65 1.50 1.40 3.0 800 1.50 1.35 1.25 3.0 1000 1.35 1.20 1.10 3.0 1200 1.20 1.00 0.80 3.0 1.00 0.80 0.70 3.0 mm 300 400 500 650 1400 1600 1800 2000 2200 34 5 λ 10 4 8 λ= 45 3 6 λ 2 4 0 λ=2 1 2 Fig.16 Lt λ Along this section the belt changes from a trough configuration as determined by the inclination of the rollers of the carrying sets to a flat belt to match the flat pulley and vice versa. The edges of the belt are in this area placed under an extra force which reacts on the side rollers. Generally the transition distance must not be less than the belt width to avoid excess pressures. 650 800 1000 1200 1400 1600 1800 2000 Value of Lt in metres for textile structured belts (EP) Transition distance Lt The distance between the last troughing set adjacent to the head or tail pulley of a conveyor and the pulleys themselves is known as the transition distance Fig.16. Value of Lt in metres for steel cord belts (ST) Fig.19 - Transition distance 2200 Belt width mm In the case where the transition distance Lt is larger than the pitch of the carrying troughing sets it is a good rule to introduce in this transition area troughing sets with inclined side rollers of gradual reduction in angle (known as transition troughing sets). In this way the belt may change gradually from trough to flat avoiding those damaging forces. The graph Fig.19 allows the determination of the transition distance Lt ( in relation to the belt width and to the inclination of the side rollers of the troughing sets), for belts with textile structure EP (polyester) and for steel corded belts (ST). Example: For a belt (EP) 1400 mm width troughing sets at 45°, one may extract from the graph that the transition distance is about 3 metres. It is advisable to position in this section Lt two troughing sets with respectively λ=15° and 30° at a pitch of 1 metre. 45 30 15 Fig.17 Lt at at at ao ao au 35 ao Fig.18 ® 1 Technical Information project and design criteria for belt conveyors 1.5.5 - Tangential force, driving power, passive resistance, belt weight, tensions and checks The forces which act on a running conveyor vary along its length. To dimension and calculate the absorbed power of the conveyor it is necessary to find the existing tensions in the section under the most force and in particular for conveyors with the following characteristics: - incline of more than 5° - length of decline from motion and consists of the sum of the following forces: - force necessary to move the loaded belt: must overcome the belt frictional forces from the carrying troughing sets upper and lower, the pulleys, return and snub etc.; - force necessary to overcome the resistance as applied to the horizontal movement of the material; - force necessary to raise the material to the required height (in the case of a decline, the force generated by the mass changes the resultant power); - variable height profile Fig.20 Tangential force The first step is to calculate the total tangential force FU at the periphery of the drive pulley. The total tangential force must overcome all the resistance that comes - force necessary to overcome the secondary resistances where accessories are present (mobile unloaders, “Trippers”, cleaners, scrapers, rubber skirts, reversing units etc.). The total tangential force Fu at the drive pulley periphery is given by: FU = [ L x Cq x Ct x f ( 2 qb + qG + qRU + qRO ) ± ( qG x H ) ] x 0.981 [daN] For decline belts a negative sign (-) is used in the formula where: L Cq Ct f qb qG qRU qRO H = = = = = = = = = Centres of conveyor (m) Fixed coefficient of resistance (belt accessories), see Tab. 7 Passive coefficient of resistance see Tab. 8 Coefficient of friction internal rotating parts (troughing sets), see Tab. 9 Belt weight per linear metre in Kg/m, see Tab. 10 (sum of cover and core weight ) Weight of conveyed material per linear metre Kg/m Weight of lower rotating parts in Kg/m see Tab. 11 Weight of upper rotating parts in Kg/m see Tab. 11 Height change of belt. 36 When it is necessary to calculate the forces on a variable altitude belt conveyor it may be seen that the total tangential force is made up from forces Fa (tangential force to move the belt, upper strand) and the lesser force Fr (tangential force on return strand) all necessary to move a single uniform section of the belt that comprises the conveyor (Fig.20) thus we have: FU=(Fa1+Fa2+Fa3...)+(Fr1+Fr2+Fr3...) Where: Fa = tangential force to move a single section of the belt upper strand Fr = tangential force to move a single section of the belt lower strand Therefore the tangential force Fa and Fr will be given by: Fa = [ L x Cq x Ct x f ( qb + qG + qRO ) ± ( qG + qb) x H ] x 0.981 [daN] Fr = [ L x Cq x Ct x f ( qb + qRU ) ± ( qb x H) ] x 0.981 [daN] Using the indication (+) for belt sections that rise (-) for sections that fall L4 H3 L3 H H1 L2 H2 L1 Fig.20 - Varying altitude profile Driving power Noting the total tangential force at the periphery of the drive pulley, the belt speed and the efficiency "η" of the reduction gear, the minimum necessary driving power is: FU x v P= [kW] 100 x η 37 ® 1 Technical Information project and design criteria for belt conveyors Passive resistance The passive resistance is expressed by a coefficient which is dependant on the length of the belt conveyor, ambient temperature, speed, type of maintenance, cleanliness and fluidity of movement, internal friction of the conveyed material, and to the conveyor inclinations. Tab. 7 - Coefficient of fixed resistance Centres Cq m 10 4.5 20 3.2 30 2.6 40 2.2 50 2.1 60 2.0 80 1.8 100 1.7 150 1.5 200 1.4 250 1.3 300 1.2 400 1.1 500 1.05 1000 1.03 Tab. 8 - Coefficient of passive resistance given by temperature Temperature °C + 20° + 10° 0 - 10° - 20° - 30° Fattore 1 1,01 1,04 1,10 1,16 1,27 Ct Tab. 9 - Coefficient of internal friction f Horizontal belt conveyor of materials and of the rotating parts speed m/s rising and gently falling 1 2 3 4 5 6 0,0160 0,0165 0,0170 0,0180 0,0200 0,0220 Rotating parts and material with standard internal friction Rotating parts and material with high internal friction in from 0,023 to 0,027 difficult working conditions Rotating parts of a conveyor in descent with a brake from 0,012 to 0,016 motor 38 Belt weight per linear metre qb The total belt weight qb may be determined adding the belt core weight, to that of the belt covers upper and lower allowing about 1.15 Kg/m2 for each mm of thickness of the covers themselves. Tab.10 - Belt core weight qbn Breaking force of belt Belt with textile inserts (EP) Belt with metal inserts Steel Cord (ST) N/mm Kg/m 2 Kg/m 2 2.0 - 200 250 2.4 - 315 3.0 - 400 3.4 500 4.6 5.5 630 5.4 6.0 800 6.6 8.5 1000 7.6 9.5 1250 9.3 10.4 1600 - 13.5 2000 - 14.8 2500 - 18.6 3150 - 23.4 The weights are indicative of the belt core with textile or metallic inserts in relation to the class of resistance. In Tab.11 the approximate weights of rotating parts of an upper transom troughing set and a lower flat return set are indicated. The weight of the upper rotating parts qRO and lower qRU is given by: Tab.11 - Weight of rotating parts of the rollers (upper/lower) Belt Roller diameter width 89 Pprs Pprs qRO = ao [Kg/m] where: Pprs = weight of upper rotating parts ao =upper troughing set pitch au [Kg/m] where: Ppri = weight of lower rotating parts au = return set roller pitch Ppri Pprs 133 Ppri Pprs 159 Ppri Pprs 194 Ppri Pprs Ppri Kg 400 — — — 500 5.1 3.7 — 650 9.1 6.5 — 800 10.4 7.8 16.0 11.4 — 1000 11.7 9.1 17.8 13.3 23.5 20.3 15.7 1200 Ppri qRU = mm mm 108 17.5 26.7 20.7 — 1400 29.2 23.2 — 1600 31.8 25.8 — 1800 47.2 38.7 70.5 55.5 2000 50.8 42.2 75.3 60.1 2200 — — — — 39 ® 1 Technical Information project and design criteria for belt conveyors Belt tension It is necessary to consider the different tensions that must be verified in a conveyor with a powered belt system. The sign (=) defines the limiting condition of belt adherence. If the ratio T1/T2 > efa the belt will slide on the drive pulley and the movement cannot be transmitted. From the above formula we may obtain: T1 = Tensions T1 and T2 The total tangential force FU at the pulley circumference corresponds to the differences between tensionsT1 (tight side) and T2 (output side). From these is derived the necessary torque to begin to move the belt and transmit power. Fig.21 T1 A α B FU = T1 - T2 T2 Moving from point A to point B Fig. 21 the belt tension changes exponentially from value T1 to value T2. The relationship between T1 and T2 may be expressed: T1 ≤ e fa where: fa = coefficient of friction between belt and drum, given by the angle of wrap e = natural logarithmic base 2.718 40 + T2 1 T2 = FU fa = FU x Cw e -1 The value Cw, which defines the wrap factor, is a function of the angle of wrap of the belt on the drive pulley (may 420° when there are double pulleys) and the value of the coefficient of friction fa between the belt and pulley. Fu T2 T2 FU Thus the calculation of the minimum belt tension values is able to be made to the limit of adherence of the belt on the pulley so that the position of a tensioner may be positioned downstream of the drive pulley. A belt tensioning device may be used as necessary to increase the adherence of the belt to the drive pulley. This will be used to maintain an adequate tension in all working conditions. On the following pages various types of belt tensioning devices commonly used are described. Tab. 12 gives the value of the wrap factor Cw in relation to the angle of wrap, the system of tensioning and the use of the pulley in a lagged or unlagged condition. Given the values T1 and T2, we may analyse the belt tensions in other areas that are critical to the conveyor. These are: - Tension T3 relative to the slack section of the return pulley; - Tension T0 minimum at tail end, in the material loading area; Tab. 12 - Wrap factor Cw Drive arrangement Angle of wrap tension unit or counterweight screw tension unit pulley pulley unlagged lagged unlagged - Tension Tg of the belt at the point of connection to the tension unit device; lagged - Tension Tmax maximum belt tension. 180° 0.84 0.50 1.20 0.80 T1 fattore di avvolgimento CW T2 T1 T2 T1 200° 0.72 0.42 1.00 0.75 210° 0.66 0.38 0.95 0.70 220° 0.62 0.35 0.90 0.65 240° 0.54 0.30 0.80 0.60 380° 0.23 0.11 - - 420° 0.18 0.08 - - T2 Tension T3 As already defined, T1 = Fu +T2 T0 =T3 T1 and T2 = FU x Cw The tension T3 that is generated at the belt slackside of the tail pulley (Fig.22) is given from the algebraic sum of the tensions T2 and the tangential forces Fr relative to a single return section of the belt. Therefore the tension T3 is given by: T3 T2 T3 = T2 + ( Fr1 + Fr2 + Fr3 ... ) [daN] Fig. 22 41 ® 1 Technical Information project and design criteria for belt conveyors To fr ao ( qb + qG ) T3 Fig.23 Tension T0 The minimum necessary tension T3 at the slack side of the return pulley, besides guaranteeing the belt adhesion to the driving pulley so as to trasmit the movement must also guarantee a deflection not superseding 2% of the length of pitch between consecutive trounghing sets. Furthermore the tensions must avoid material spillage from the belt and excessive passive resistance caused by the dynamics of material as the belt travels over the troughing sets Fig. 23. The minimum tension T0 necessary to maintain a deflection of 2% is given by the following formula: T0 = 6.25 (qb + qG) x a0 x 0,981 [daN] where: qb = total belt weight per linear metre qG = weight of conveyed material per linear metre a0 = pitch of troughing sets on upper strand in m. The formula derives from the application and essential simplification of theory, when considering “catenaries”. To alter as desired the deflection to a value less than 2%, the figures 6.25 may be substituted by: - for 1.5% deflection = 8,4 - for 1.0% deflection = 12,5 42 In order to have a tension able to guarantee the desired deflection, it will be necessary to apply a tensioning device, also effecting the tensions T1 and T2 to leave unchanged the circumferential force FU = T1 - T2. Tension Tg and tensioning devices Tension devices used generally on belt conveyors are screw type or counterweight. The screw type tension unit is positioned at the tail end and is normally applied to conveyors where the centres are not more than 30/40 m. Where conveyors are of larger centres the counterweight tension unit is used or winch style unit where space is at a premium. The tension unit minimum movement required is determined as a function of the type of belt installed, that is: - the stretch of a belt with textile core needs a minimum 2% of the conveyor centres; - the stretch of a belt with metal or steel core needs a minimum of 0.3 + 0.5% of the conveyor centres. Typical tension device Maximum tension (Tmax ) This is the belt tension at the point where the conveyor is under the greatest stress. Fig.24 T3 T1 T3 T2 Normally it is coincidental in value with tension T1. Along the length of a conveyor with variable height change and in particular where conditions are variable and extreme, Tmax may be found in different sections of the belt. In this arrangement the tension is regulated normally with the occasional periodic check of the tensioning screw. Fig.25 T3 T1 T3 T2 Tg In this arrangement the conveyor is tensioned using a counterweight. Tg = 2 ( T3 ) [daN] T1 Fig.26 Working load and belt breaking strain Tmax is used to calculate the unitary maximum tension of the belt Tumax given that: T2 Ht T3 Ic T3 Tmax x 10 Tumax = Tg N [N/mm] where: N = belt width in mm; Also in this arrangement the conveyor is tensioned using a counterweight. Tg = 2T2 + 2 [( IC x Cq x Ct x f ) ( qb + qRU ) ± ( Ht x qb )] 0,981 [daN] Tmax = tension at the highest stress point of the belt in daN. In which: IC = distance from centre of drive pulley to the counterweight attachment point Ht = belt height change from the point where the counterweight applies itself to the point where the belt exits from the slack side of the pulley, measured in metres. Correct dimensioning verification The belt will be adequately dimensioned when the essential tension T0 (for the correct deflection of the belt) is less than the calculated tension T3 the tension T2 has always to be T2 ≥ Fu x Cw and is calculated as T2 = T3 ± Fr (where T3 ≥ T0 ). 43 As a security factor one may consider the maximum working load of the belt with textile core to correspond to 1/10 of the breaking load of the belt (1/8 for a belt with steel core). ® 1 Technical Information project and design criteria for belt conveyors 1.5.6 - Belt conveyor drives and pulley dimensions Type of drives Conveyors requiring power up to 250 kW are traditionally driven at the head pulley with electric motor, gearbox, pulley, guards, transmission accessories etc., or, alternatively by motorised pulley. Fig.27. In the drawings Fig.28 a comparison is made between the space needed for two drive systems. Belt conveyors that need power over 250 kW utilise the conventional drive pulley arrangement but also with two or more motor gearboxes. Fig.27 The motorised pulley is used today more and more as the drive for belt conveyors thanks to its characteristics and compactness. It occupies a minimal space, is easy to install, its motor is protected to IP67, all working parts are inside the pulley and therefore it needs very limited and occasional maintenance (oil change every 10.000 or 50.000 working hours with synthetic oil). 44 Fig.28 Pulley diameters The dimensioning of the diameter of a head pulley is in strict relationship to the characteristics of the type of belt used. In Tab. 13 the minimum diameters recommended in relation to the type of belt used are indicated, avoiding damaging de-layering of the belt layers or laceration of the reinforcing fabric. Tab. 13 - Minimum pulley diameters recommended Belt breaking load Belt with textile core EP DIN 22102 N/mm Belt with steel core ST DIN 22131 Ø motorised return pulley pulley direction change Ø motorised return pulley pulley direction change mm drum mm pulley 200 200 160 125 - - - 250 250 200 160 - - - 315 315 250 200 - - - 400 400 315 250 - - - 500 500 400 315 - - - 630 630 500 400 - - - 800 800 630 500 630 500 315 1000 1000 800 630 630 500 315 1250 1250 1000 800 800 630 400 1600 1400 1250 1000 1000 800 500 2000 - - - 1000 800 500 2500 - - - 1250 1000 630 3150 - - - 1250 1000 630 Minimum diameters recommended for pulleys in mm up to 100% of the maximum working load as recommended RMBT ISO bis/3654. This table must not be applied to belt conveyors that convey material with a temperature over +110°C or for conveyors installed where the ambient temperature is less than -40°C. 45 ® 1 Technical Information project and design criteria for belt conveyors Sizing of the drive pulley The shaft of the drive pulley is subject to alternating flexing and torsion, causing fatigue failure. To calculate correct shaft diameter it is necessary to determine the bending moment Mf and the torsion moment Mt. The bending moment of the shaft is generated as a result of the sum of the vector of tensions T1 and T2 and the weight of the pulley itself qT Fig.29. Mif =  Mf + 0,75 2 x Mt2 [daNm] T1 Mif x 1000 W = ___________ σamm [mm3] T2 qT Fig.29 T1 π T2 W= Cp 32 qT x d3 [mm3] from the combination of simultaneous equations we may discover the diameter of the shaft as follows: The dimensioning of the shaft diameter requires the determination of various values. 3 d= W 32  _______ π x [mm] These are: the resultant of tensions Cp, the bending moment Mf, torsional moment Mt, the ideal bending moment Mif and the module of resistance W. Tab.14 - Suggested value of Proceeding in order we have: Steel type Cp =  (T 1 + T2)2 + qt2 [daN] Cp Mf = x 2 ag [daNm] σ daN/mm2 38 NCD 12,2 C 40 Tempered 7,82 C 40 Normalised 5,8 Fe 37 Normalised 4,4 P Mt = x n 954,9 [daNm] where: P = absorbed power in kW n = r.p.m. of the drive pulley 46 Fig.30 ag Sizing of the tail or return pulley shaft and change direction pulley In this case only shaft flexure must be considered, torsional loads are not a factor in fatigue failure. The bending moment Mf must be determined as generated by the resultant of the sum of the vectors of belt tensions where the belt is before or after the pulley and the weight of the pulley itself. In this case, treating the pulley as an idler one may consider Tx=Ty. In Fig.31 and 32 various arrangements for an idler return pulley are indicated. The bending moment is given by: Cpr Mf = x 2 ag [daNm] the module of resistance is found from: Fig.31 - Tail or return pulley Limits of deflection and angle for drive and idler pulleys After having sized the shafts of different pulleys, one is required to verify that the deflection and angle of the shaft does not exceed certain values. In particular the deflection ft and the angle αt must respect the relationship: C Mf x 1000 W= σamm Tx ft max ≤ [mm3] 1 αt ≤ 2000 500 Fig.33 ft given the module of resistance: π Ty W= qT Tx Ty x 32 d3 [mm3] αt ag the diameter of the shaft is given by: Cpr ag b C qT 32  W_______ π 3 d= x (Cpr 2)ag C ft = ________ [ 3(b+2ag)2- 4ag2 ] ≤ ____ 24xExJ 2000 [mm] Fig.32 -Change direction pulley Tx Tx Ty Ty Tx Ty qT where: ag = expressed in mm E = module of elasticity of steel qT qT Tx (20600 [daN/mm2 ]) Ty Cpr = Tx qT Cpr Tx Cpr 1 (Cpr 2 ) αt = ________ ag (C - ag) ≤ ______ 2xExJ 500 Ty + Ty - qT J = sectional moment of inertia of the shaft (0,0491 D [mm ]) Cpr = load on shaft [daN ] ft = shaft deflection [mm] αt = shaft angle at the pillow blocks [rad] 4 qT 47 4 ® 1 Technical Information project and design criteria for belt conveyors 1.6 - Rollers, function and design criteria In a conveyor, the elastomer belt represents the most perishable and costly item. The rollers that support the belt along its length are no less important, and therefore they should be designed, chosen and manufactured to optimise their working life and that of the belt itself. The resistance to start up and rotation of rollers has a great influence on the belt and in consequence to the necessary power to move the belt and keep it moving. In the following sections we should examine other factors such as the: •฀balance and start up resistance; •฀tolerances; •฀type of roller shell; characteristics of the tube and thickness - the fitting of the end caps; •฀frictional resistance and impact resistance; The body of the roller and that of its end caps, the bearing position and its accompanying system of protection, are the principal elements which impact the life and torque characteristics of the roller. Refer to chapter 2 where the construction criteria of rollers for belt conveyors are presented along with the factors which must be taken into account for a correct project design. Fig.34 •฀type of bearing -protection system; -fit to the spindle and end caps; -lubrication; -alignment; •฀spindle: characteristics and manufacturing tolerances. 48 1.6.1 - Choice of roller diameter in relation to speed We have already stated that one of the important factors in the design of a conveyor is the speed of the belt movement in relation to the load conditions required. Tab. 15 - Maximum speed and numbers of roller revolutions Belt speed m/s n 50 1.5 573 63 2.0 606 76 2.5 628 89 3.0 644 where: D = roller diameter [mm] v = belt speed [m/s] 102 3.5 655 108 4.0 707 133 5.0 718 Tab.15 gives the existing relationship between maximum belt speed, roller diameter and the relative r.p.m. 159 6.0 720 194 7.0 689 From the belt speed and roller diameter we are able to determine the revolutions per minute of the roller using the formula: v x Roller diameter mm 1000 x 60 n= D x [r.p.m.] π In choosing the roller it is interesting to note that even if a roller of larger diameter exhibits a higher inertia on start up, it actually yields, other conditions being equal, many advantages such as: less revolutions per minute, less wear of bearings and housing, less rolling friction and reduced wear between the roller and the belt. r.p.m. The correct choice of diameter must take into consideration the belt width. Tab.16 shows the diameter of rollers in relation to belt width. Tab.16 - Roller diameter advised Belt For speed width ≤ 2 m/s 2 ÷ 4 m/s ≥ 4 m/s mm Ø roller mm Ø roller mm Ø roller mm 500 89 89 650 89 89 108 800 89 108 89 108 1000 108 133 108 133 1200 108 133 108 133 1400 133 159 133 159 1600 133 159 133 159 159 194 159 194 1800 159 159 2000 159 194 2200 and more 194 194 194 133 159 194 133 133 159 133 159 133 159 133 159 159 194 194 194 One may have indicated more diameters where the choice will be made in relation to the material lump size and the severity of working conditions. 49 ® 1 Technical Information project and design criteria for belt conveyors 1.6.2 - Choice in relation to load The type and dimensions of rollers used in belt conveyors depends mainly on the width of the belt itself, the pitch of the troughing sets, and above all, the maximum load on the rollers most under pressure, not withstanding other correction factors. The calculation of load forces is normally made by the project designer of the plant. Nevertheless, as a check or in the case of simple conveyors, we present the following concepts for determining the facts. The first value to define is the load on the troughing sets. Following this, depending on the type of troughing set (carrying, return or impact), the number of rollers in a transom or frame, the angles of the side roller, the material lump size and other relevant factors as listed below. One is able to calculate the roller load with the maximum force for each type of troughing set. Furthermore there are some correction factors keeping count of the plant working hours per day (service factor), of the environmental conditions and of the speed for the different diameters of the rollers. The load value obtained in this way may be compared with the load capacity of the rollers indicated in this catalogue valid for a project life of 30,000 hours. For a theoretically different life, the load capacity may be multiplied by a coefficient reported on Tab.22 corresponding to life required. Principal relevant factors: Iv v ao au qb Fp = = = = = = Fd Fs Fm Fv = = = = belt load t/h belt speed m/s pitch of the troughing sets upper strand m pitch of the return roller set m weight of belt per linear metre Kg/m participation factor of roller under greatest stress see Tab.17 (depends on the angle of the roller in the transom) impact factor see Tab.20 (depends on the material lump size) service factor see Tab.18 environment factor see Tab.19 speed factor see Tab. 21 Tab. 17 - Participation factor Fp - loaded rate on the most loaded roller 0° 20° 20° 30° 35° 45° 1.00 0.50 0.60 0.65 0.67 0.72 30°-45° 60° ~ 0.52 - 0.60 0.47 Shorter central 5 rollers roller garland 50 Tab. 20 - Impact factor Fd Tab. 18 - Service factor Life Fs Less than 6 hours per day 0.8 From 6 to 9 hours per day 1.0 From 10 to 16 hours per day 1.1 Over 16 hours per day 1.2 Material lump size Belt speed m/s 2 2.5 3 3.5 4 5 6 0 ÷ 100 mm 1 1 1 1 1 1 1 100 ÷ 150 mm 1.02 1.03 1.05 1.07 1.09 1.13 1.18 150 ÷ 300 mm 1.04 1.06 1.09 1.12 1.16 1.24 1.33 1.06 1.09 1.12 1.16 1.21 1.35 1.50 1.20 1.32 1.50 1.70 1.90 2.30 2.8 0 in layers of fine material Tab. 19 - Environment factor Conditions Fm Clean and regular maintenance 0.9 Abrasive or corrosive material present 1.0 Very abrasive or corrosive material present 1.1 150 ÷ 300 mm without layers of fine material 300 ÷ 450 mm Tab. 21 - Speed factor Fv Belt speed Roller diameter m/s 60 76 89-90 102 108-110 133-140 159 0.5 0.81 0.80 0.80 0.80 0.80 0.80 0.80 1.0 0.92 0.87 0.85 0.83 0.82 0.80 0.80 1.5 0.99 0.99 0.92 0.89 0.88 0.85 0.82 2.0 1.05 1.00 0.96 0.95 0.94 0.90 0.86 mm 2.5 1.01 0.98 0.97 0.93 0.91 3.0 1.05 1.03 1.01 0.96 0.92 3.5 1.04 1.00 0.96 4.0 1.07 1.03 0.99 4.5 1.14 1.05 1.02 5.0 1.17 1.08 1.00 Tab. 22 - Coefficient of theoretical life of bearing Theoretic project life of bearing 10'000 20'000 30'000 40'000 50'000 100'000 Coefficient with base 30'000 hours 1.440 1.145 1.000 0.909 0.843 0.670 Coefficient with base 10'000 hours 1 0.79 0.69 0.63 --- --- 51 ® 1 Technical Information project and design criteria for belt conveyors Load calculation Having defined the roller diameter in relation to the speed and the number of revolutions one may then proceed to calculate the static load on the carrying troughing set using the following formula: IV Ca = ao x ( qb + 3.6 x v ) 0,981 [daN] The static load on the return roller set, not having any material load present, is given by the following formula: Cr = au x qb x 0,981 [daN] The dynamic load on the return roller set will be: Cr1 = Cr x Fs x Fm x Fv [daN] Multiplying then by a working factor we have the dynamic load on the transom: Ca1 = Ca x Fd x Fs x Fm [daN] Multiplying then by the participation factor one may obtain the load on the roller carrying the most force (central roller in the case of a troughing set transom where all the rollers are of equal length): ca = Ca1 x 52 Fp [daN] And the load on the rollers of the return roller set, single or double, will be: cr= Cr1 x Fp [daN] Given the values of “ca” and “cr” one may look in the catalogue for rollers (first by diameter) that have a sufficient load capacity. Fig.35 1.7 - Loading of belt and impact rollers The feed system of material falling or dropping onto a belt conveyor must be constructed to minimise or eliminate impact damage to the belt material and surface. This is of particular importance when the material falls from a considerable height and consists of large lumps with sharp edges. The rollers supporting or carrying the belt in the loading zone are normally installed as impact design (with rubber rings), mounted onto troughing set frames set close to each other. In this way the belt is supported in a flexible manner. It is a widely held view that the use of suspension sets of the “garland” design Fig.37-38, thanks to their intrinsic flexible characteristics absorb with great efficiency the impact of materials falling onto the belt and, what is more, the “garland” is able to adapt to conform to the shape of the charge (or load). Fig.36 Fig.37 Fig.38 53 ® The project designer of the conveyor system must take into account that: - the impact of material onto the belt must take place in the conveyor direction and at a speed that approximates to the speed of the belt; NO Please refer to chapter 3 of this catalogue for greater detail regarding the programme of the design of impact rollers with rubber rings of high shock absorbing qualities and for the programme of suspension sets as “garland” design. 1.7.1 - Calculation of associated forces on impact rollers The definition of the correct load fall height Hc may be given by the folowing formula: Hc = Hf + Hv x sen2 γ where: Hf = - the loading hopper is positioned so that material falling from it is deposited as near as possible to the centre of the belt; Hv = γ = Fig.39 fall height from the upper face of the loading belt to the contact point of material contained in the hopper; height from the contact point of material contained in the hopper to the belt face of the lower belt; hopper inclination angle. In the choice of impact rollers we propose to follow two significant design aspects: - constant loading with uniform fine material; - loading with material consisting of large lumps. - the height that the material falls must be reduced to the minimum possible, compatible with the requirements of the plant design. Fig.40 Hf project and design criteria for belt conveyors Particular attention must be paid at the project stage to the feed system and to the design of impact troughing sets. γ Hv 1 Technical Information 54 Constant loading with uniform fine material Impact rollers must be designed not only to carry the load of material arriving on the belt (as in a normal carrying troughing set) but also the impact load from falling material. For loose, homogenous fine material the impact force pi, given the corrected fall height, is calculated according to the following formula: pi where: IV ≅ IV x √Hc ––––– 8 [Kg] = flow of material in t/hr (the belt load capacity) The force acting on the central roller pic, clearly the roller with the most stress, is obtained on consideration of the previously mentioned participation factor Fp. Various factors depend principally on the angle λ wich is the side roller angle: √Hc pic ≅ Fp x pi = Fp x IV x ––––– 8 [Kg] One assumes as a rule: Fp = 0.65 per λ = 30° Fp = 0.67 per λ = 35° Fp = 0.72 per λ = 45° Example: Let us calculate the central roller load in a transom, given that the loading of the material onto the belt is: Iv = 1800 t/h, Hc = 1.5m and λ = 30°: Refer to the paragraph “roller choice” for design characteristics of the most suitable roller. Loading with material consisting of large lumps The force of dynamic load pd on the central roller may be calculated using Gm which is the weight of large blocks of single lumps of material and takes into account the elasticity Cf of the transom and rollers. pd ≅ Gm + where: Gm Hc Cf √( 2 x Gm x Hc x Cf ) [Kg] = weight of large lumps of material [Kg] = corrected fall height [m] = elasticity constant of the transom/ impact rollers. The impact force is considered as distributed over the 2 bearings of the central load carrying roller. The approximate weight of the lump may be extracted from the graph in Fig.41: one may note that as well as taking the length into account the weight depends on the form of the lump itself. On the central roller we have: pic = Fp x pi = 0.65 x 275 = 179 Kg The graph of Fig.42 records the constant of elasticity for the most commonly used systems of support and shock absorbing (fixed troughing sets with steel rollers, fixed troughing sets with rollers with rubber rings, troughing sets with “garland” suspension design) and the impact forces resultant on the roller for varying drop energies of the falling load Gm x Hc. Adding to this load value as considered on a horizontal belt we may obtain the total load on the troughing set central roller. The graph shows above all the static load on the roller bearings derived from Gm x Hc but with a safety factor 2 and 1.5. √1.5 pi = 1800 x ––––– = 275 Kg 8 55 The coefficient of elasticity depends on various factors such as the type of rubber used in the rings, length and weight of the rolers, number and articulation of the suspension set as a "garland", and type and elasticity of the flexible parts used by the stock absorbing supports. The calculation of the dynamic load force pd must fore cast an accurate valuation of these factors. Example: A load of 100 Kg falls from a height Hc of 0.8 m onto a suspension “garland” style set, with rollers made from normal steel (coeff, Cf hypothetically 20,000 Kg/m = 200 Kg / cm). Calculation of the drop energy: Gm x Hc = 100 x 0.8 = 80 Kgm Calculating from the table the dynamic force of fall: pd = 1800 Kg. Assuming a safety factor of 2 we must have bearings that may withstand a static load of 1800 Kg (2 bearings) that is rollers from series PSV/7-FHD (bearings 6308; Co = 2400 Kg). ® 1 Technical Information Fig.41 - Weight of lump of material 1400 900 800 1000 900 800 600 500 600 700 500 600 400 400 300 500 700 300 400 300 200 200 400 300 100 90 80 200 200 100 90 100 90 80 70 70 50 60 80 100 90 80 Wieght "Gm" of a lump of material (Kg) project and design criteria for belt conveyors 70 60 70 60 60 40 50 40 30 50 30 40 20 50 30 20 40 30 20 20 10 9 8 10 9 8 7 6 10 9 8 7 6 10 9 8 7 6 5 4 5 3 7 4 6 5 3 2 4 5 3 2 4 Lb 1 3 2 1 2 3 2 1.2 0.8 0 200 400 600 800 Specific weight Dimensions of lump "Lb" (mm) 56 1000 Fig.42 - Constant of elasticity Cf coefficient security = 2 = 1.5 --3800 --5000 5000- - 4800 4600 4400 4200 --4000 40003800 Bearing static load Co (Kg) 3600 3200 kg /cm =1 00 kg 50 00 Cf =2 Cf Cf 00 =1 2400 =1 0k 2600 kg g/c m /cm 2800 /cm 3000- 2200 ler 1400 1200 S 1000- ol lr tee oc k ve gs i rin th f sh ith wi ith r w nd e w l l la nd Ro Gar rla a G 1600 ab s ro l 1800 or b le rs 2000- er s Cf Dynamic falling force Pd (Kg) 3400 600 Cf = Costant of elasticity 200 0 0 2 3 4 5 6 7 8 10 15 20 30 40 60 80 100 150 Drop energy = Gm x Hc (Kg.m) 57 --3000 - --2000 - --1000 800 400 - 200 300 400 600 800 1000 - 800 - 600 - 400 - 200 - - --3000 - --2000 - --1000 - 800 - 600 - 400 - 200 - ® 1 Technical Information project and design criteria for belt conveyors 1.8 - Other accessories Amongst all of other conveyor components, the belt cleaning system and covers are regarded in certain situations of fundamental importance and must be considered at an early stage in the project design of the conveyor itself. There are a variety of devices used for belt cleaning. The majority of these may be divided into two groups: static and dynamic. 1.8.1 - Belt cleaners Savings in utilising efficient systems of belt cleaning may be amply demonstrated, in particular resulting from a reduction in belt maintenance time and increased production, proportional to the quantity of material recovered in the process and a large increase in the life of moving parts. Fig.44 The static systems that are utilised the most are the most diverse as they may be applied along all positions on the dirty side of the belt. They are acting directly on the belt using a segmented blade. Fig.44 3 1 2 4 5 Fig.43 - Ideal positions for the installation of cleaning devices 1 on drive pulley 2 at about 200mm after the tangential point where belt leaves pulley 58 3 on internal side of belt on the return section and before the snub pulleys or directional change pulley 4 on internal side of belt before the return pulley The dynamic systems where motors are used are of less variety and more costly in terms of capital cost, installation and commissioning. Dirty side Clean side Fig.47 1.8.2 - Belt inversion Fig.45 They consist of pulleys or motorised pulleys on which are assembled or fixed special brushes, that are then in direct contact with the belt. Fig.45 Other cleaners are those of plough or deviator design that are applied to the inside strand of the belt return section. On return sections of the belt on very long conveyors, the belt is turned over 180° to reduce the phenomena of adhesion of material residue on the rollers and on the cross member of the troughing sets. The return strand of the belt may be turned over 180° after the drive drum and subsequently turned to its original position before the return drum. Turning the belt over is generally effected by means of a series of rollers orientated as required. The minimum length to turn over a belt is generally about 14/22 times its width. The rollers on the return set, thanks to this device, are no longer in contact with the carrying upper strand of the belt which is encrusted with material residue. 1.8.3 - Belt conveyor covers Fig.46 They are used to remove material deposited before the drive and return pulleys or certain other points where the material may become trapped between the pulley and belt, affecting the orderly tracking of the belt. Fig.46. After having defined the components of primary importance the project designer considers secondary accessories, such as covers. The necessity to protect the belt conveyor is dictated by the climate, the characteristics of the conveyed material (dry, light, “volatile”) and the type of plant. 59 Dirty side Clean side ® 1 Technical Information project and design criteria for belt conveyors 1.9 - Project examples of a belt conveyor To clarify our presentation of critical tensions in various sections of the belt conveyor here is a project example. The relative data concerning the conveyed material and its physical/chemical characteristics are as follows: Material: - clinker of cement (Tab. 2 pag.20) - specific weight: 1.2 t/m3 - lump size 80 to 150 mm - abrasiveness: very abrasive - angle of friction natural or at rest: ~ 30° Required load: IV = 1000 t/h corresponding to the volumetric load IM = 833 m3/h Plant characteristics: - centres 150 m - change of height H = + 15 m (rising) - inclination = 6°~ - working conditions: standard - utilisation: 12 hours per day From the data supplied we are able to calculate: speed, belt width, design and type of conveyor troughing sets. Furthermore we may define: the belt tensions in various critical areas and from these the absorbed power and the belt type. 60 Speed and belt width From Tab. 3 (pag.23) we are able to define that the said material may be grouped into B and given that the lump size is 80/150 mm the maximum advised speed results as 2,3 m/s. From Tab. 5 (pag.26-30) we may evaluate which type and design of carrying troughing sets are needed, given the speed just found, that satisfies the volumetric load IM required as 833 m3/h. To obtain the result one must calculate the volumetric load IVT ( for the speed v = 1m/s ) given the inclination of the conveyor δ = 6°. IM IVT = v x K x K1 [m3/h] in which: IM = volumetric load v = belt speed K = crrection coefficient to suit the inclination 6°: 0,98 (diagram Fig 8 pag.31). K1 = correction coefficient to suit the feed irregularity: 0,90 (pag.31) Substituting we have: 833 IVT = 2,3 x 0,98 x 0,90 = 410 m3/h Given the angle of repose of the material in question is about 30° from Tab. 1 pag.19 we may deduce that the angle of surcharge would be established in the order of 20°. Having chosen a carrying troughing set with a transom side roller angle of λ = 30°, the belt width that meets the load requirement IVT of 410 m3/h at 1 m/s is 1000 mm. In our example, given that the belt width is 1000 mm with specific weight of material of 1.2 t/m3 the tables indicate that: - for the return rollers the static load will be: - for the carrying troughing sets the advised pitch is that of 1.2 m; Cr= 3 x 9,9 x 0,981 = 29,2 Cr = au x qb x 0,981 [daN] the dynamic load will be: - for the return sets the advised pitch is that of 3.0 m. Roller choice In Tab. 16 pag.49 with a belt of 1000 mm and a speed of 2.3 m/s we may choose rollers with diameter 108 mm. Cr1 = Cr x Fs x Fm x Fv [daN] Cr1= 29,2 x 1,1 x 1 x 0,97 = 31,2 where: Fv = 0,97 speed factor (it has been considered that relative to 2,5 m/s see Tab. 21, pag.51) We may now proceed to determine the load falling on the roller in the carrying strand and those of the return strand. Assuming we may use a belt with a resistance class equal to 315 N/mm, with cover thickness 4+2, and with a value qb of 9,9 kg/m, we have: - for carrying rollers the static load will be: IV Ca = ao x ( qb + )x 0,981 [daN] 3,6 x v 1000 Ca =1,2( 9,9+ Troughing set pitch The pitch may be chosen as a function of the deflection of the belt between two consecutive troughing sets. We need to verify that the deflection does not supersede 2% of the pitch. A greater deflection may give rise to material mass deformation during the belt movement, and consequently elevated friction. x = Cr1 x Fp [daN] cr= 31,2 x 1 = 31,2 where from Tab. 17 the participation factor with return plain roller set Fp = 1 ) 0,981 = 153,8 Fd x Fs x Fm [daN] Ca1 = 153,8 x 1,03 x 1,1 x 1 = 174,2 where: Fd = 1,03 Fs = 1,1 Fm = 1 from table 20 pag.51 from table 18 pag.51 We are able therefore to choose a belt 1000 mm, the rollers for carring and return idlers both of loaded and return belt (see Chapter 2): from table 19 pag.51 the load on the central roller of a carrying troughing set is given by: ca = Ca1 Then we would be able to determine a major factor: that is major power absorption, giving rise to unusual stresses whether on the rollers or in the belt over and above the premature wear in the cover of the belt. cr the dynamic load will be: Ca1 = Ca Tab. 6 pag.34 shows how to determine the maximum pitch of troughing sets, as a function of the belt width and the specific weight of the conveyed material. 3,6 x 2,3 choosing the return troughing set with plain roller the load on the return roller will be: x Fp [daN] ca = 174,2 x 0,65 = 113,2 where from Tab. 17 pag.50 the participation factor of a troughing set 30° Fp = 0,65 61 - rollers for carrying idlers type PSV1, ø 108 mm, with bearings 6204 of length C = 388 mm with load capacity 148 Kg that satisfies the required loading of 113,2 Kg; - return roller type PSV1, ø 108 mm, with bearings 6204, length C = 1158 mm with load capacity 101 Kg that satisfies the required loading of 31,2 Kg. ® 1 Technical Information project and design criteria for belt conveyors Tangential force and absorbed power We may now determine the total tangential force Fu at the drum periphery extracting the values qRO, qRU and qG. given: D = 108 roller diameter f = 0,017 friction coefficient inside material and of the rotating parts (Tab. 9 pag.38) Cq = 1,5 fixed coefficient of resistance (Tab. 7 pag.38) qb = 9,9 Kg/m (utilising a belt resistance class 315 N/mm with a cover thickness 4+2 Tab. 10 pag.39) Ct = 1 coefficient of passive resistance given by the temperature (for qRO - qRU see Tab.11 pag.39) qRO = weight of rotating parts upper troughing set = pitch of upper sets qRU qG = weight of rotating parts lower troughing set pitch of upper sets = IV 1000 = 3,6 x v 3,6 x 2,3 = 17,8 = 14,8 Kg/m 1,2 13,3 = 3,0 4,4 Kg/m = 120,8 Kg/m The total tangential force Fu is given by the algebraic sum of the tangential forces Fa and Fr relative to upper and lower sections of belt for which: Fu = Fa + Fr Fa Fa = = [daN] [ L x Cq x f x Ct ( qb + qG + qRO ) + H x ( qG + qb ) ] x 0,981 [daN] [150x1,5x 0,017x 1 (9,9+120,8+14,8)+15 x (120,8+9,9)]x 0,981 = 2469 Fr = [ L x Cq x f x Ct ( qb + qRU ) - ( H x qb ) ] x 0,981 [daN] Fr = [150 x 1,5 x 0,025 x 1 (9,9 + 4,4) - (15 x 9,9)] x 0,981 Fu = Fa + Fr = - 92 = 2469 + ( - 92) = 2377 We consider an efficiency of the reduction gear and of possible transmissions as η = 0,86 will be: Fu P = x v 100 x η 62 2377 x 2,3 [ kW] = 100 x 0,86 ≅ 64 kW Tensions T1 - T2 - T3 - T0 -Tg Let us propose to design a conveyor driven by a single driving pulley, rubber covered and positioned at the head, given that the snub pulleys are positioned to give a wrap angle of 200°; a tension device with counterweight positioned at the tail. From Tab. 12 pag. 41 one may determine the wrap factor Cw = 0,42. The tension downstream from the drive pulley is given by: T2 = Fu x Cw One may now determine the tension “Tg” in the belt at the tension unit connection point. The plant project data has foreseen a counterweight tension unit positioned at the conveyor tail end. The counterweight load Tg necessary to maintain the system in equilibrium is given by: Tg = 2 x T3 [daN] Tg = 2 x 961 = 1922 [daN] T2 = 2377 x 0,42 = 998 The maximum tension upstream of the drive pulley will be: T1 = Fu + T2 [daN] T1 = 2377 + 998 = 3375 While the tension downstream of the return pulley is: Belt choice Given the maximum working tension of the conveyor: T1 = 3375 daN. The unitary working tension of the belt for mm of width is given by: T max x 10 Tu max = [N/mm] N T3 = T2 + Fr [daN] 3430 x 10 T3 = 998 - 92 = 906 To derive the maximum deflection between two consecutive carrying troughing sets equal to 2% we must apply the following formula: T0 = 6,25 ( qb + qG ) x a0 x 0,981 [daN] T0 = 6.25 x (120,8 + 9,9) x1,2 x 0,981 = 961 The tension T3 is lower than the T0 therefore we have to provide a counterweight dimensioned to obtain the tension T0. We have therefore to assume T3=T0 and we have to recalculate consequently the tensions T2 and T1 that result: T2 = 1053 [daN] T1 = 3430 [daN] 63 Tu max = 1000 = 34,3 N/mm The breaking load of the belt will correspond with the working load multiplied by a security factor “8” for belts with steel inserts and “10” for belts with textile inserts. In our case we may proceed to choose a belt with resistance equal to 400 N/mm. Because this belt resistance is higher than the one selected in the starting data of this calculation (315 N/mm), the belt weight is higher and we have to recalculate the T1 and T2 accordingly. The resulted tensions are anyway lower than T1 and T2 above, therefore the following calculations will be made using T2 = 1053 daN T1 = 3430 daN ® 1 Technical Information project and design criteria for belt conveyors Diameter of drive pulley shaft Let us utilise a motor gearbox to drive the conveyor in question. Drive pulley data: D = 400 mm diameter (as Tab.13) qT = 220 daN weight of pulley n = 110 r.p.m. ag = 0,180 m distance between the supports and pulley flange Let us determine the resultant Cp of the tensions and the pulley weight (for simplicity let us suppose T and qT perpendicular between them). ( T + T Cp = + qT 2 [daN] 2 )2 1 = ( 3430 +1053 ) 2 + 220 2 = 4488 daN The bending moment will be: Cp Mf = ag x 2 [daNm] 4488 ––––––– 2 = x 0,180 = 404 daNm The torsional moment will be: P Mt = x 954,9 [daNm] n 64 = ––––––– 110 x 954,9 = 555,6 daNm One may now determine the ideal bending moment: Mif =  Mf 2 + 0,75 x Mt2 [daNm] = 404 + 0,75 2 x 555,6 2 = 629 daNm Consequently we derive the value of the module of resistance W given that σamm 7,82 daN/mm2 for heat treated steel C40 Mif x1000 W= σamm [mm3] 629 x 1000 = ––––––––––– 7,82 = 80435 mm3 from which we may find the diameter of the drive pulley motor shaft:  3 d= W X 32 π  3 mm = 80435 X 32 ≅ 93 mm 3,14 The drum shaft diameter on the bearing seats, will be made according the above formula, or the nearer larger diameter available on the bearing. The shaft diameter inside the hub and/or inside the drum (normally the raw shaft diameter) is determined with the formulas described in the paragraph "Limits of deflection and angle for motor and idler pulleys" at pag.47 and in this case the raw shaft diameter results 110 mm. 64 Diameter of return pulley shaft Non-drive pulley data: D = 315 mm diameter (as Tab.13) qR = 170 daN pulley weight ag = 0,180 m distance between the support and pulley flange Let us determine the resultant Cpr of the tensions and the pulley weight (for simplicity let us suppose T3 and qT is perpendicular between them). ( 2T3 Cpr = )2 + qT 2 [daN] = [daNm] = ( 2 x 961 ) 2 + 170 2 = 1930 daN The bending moment will be: Cpr Mf = ––––––– x ag 2 1930 ––––––– x 0,180 2 = 174 daNm Consequently we derive the value of the module of resistance W given that σamm 7,82 daN/mm2 for heat treated steel C40 Mif x1000 W = –––––––––– σamm 174 x 1000 = ––––––––––– 7,82 [mm3] = 22250 mm3 from which we may find the diameter of idler return pulley shaft:  3 d= W X 32 –––––––––– π The drum shaft diameter on the bearing seats will be made according the above formula or the nearer larger diameter available on the bearing. The shaft diameter inside the hub and/or inside the drum (normally the raw shaft diameter) is determined with the formulas described in the paragraph "Limits of deflection and angle for motor and idler pulleys" at page 47 and in this case the raw shaft diameter results 90 mm. 65  3 mm = 22250 X 32 ––––––––––– ≅ 61 mm 3,14 ® 1 Technical Information project and design criteria for belt conveyors Conclusions Using successive steps we have obtained from the data of the relative characteristics of the belt conveyor components the following summary: - the speed of the conveyed material is v = 2,3 m/s - carrying troughing sets with side rollers at λ = 30° - return sets with plain roller - belt width 1000 mm with breaking load 400 N/mm - carrying troughing set pitch 1,2 m - lower return sets pitch 3 m - load roller in carrying troughing set series PSV1, Ø 108 mm, C = 388 mm - return rollers series PSV1, Ø 108 mm, C = 1158 mm - power needed to move the belt conveyor 64 kW - belt deflection between two adjacent troughing sets < 2% 66 - drive pulley D = 400 mm, Ø shaft 100 mm (at the bearing seats and Ø 110 of the raw shaft in the middle) - return pulley D = 315 mm, Ø shaft 65 mm (at the bearing seats and Ø 90 of the raw shaft in the middle) One may consider the use of a traditional drive arrangement (drive pulley + gearbox + transmission gearing) or a motorised pulley. In the later case, a pulley motor may be chosen using the relevant catalogue. The type TM801 of 75 kW with a shaft of 120 mm diameter meets the specification.