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The conveyor belt calculations of different parameters are very important for designing a conveyor system. This article will discuss some important conveyor belt parameter calculations procedure with a practical example. Ads by Google Weighing Equipment www.mt.com/weighing-equipment Balances, Scales and Weighing systems by METTLER TOLEDO! Compare Conveyor Systems CableVey.com/Conveyor_Report Get A Free Report Comparing Tubular Drag Conveyors To Bucket Elevators Conveyor System Provider www.efacec.com.sg Baggage, Parcels, ULDs, Pallets Integration & Solution Provider
The belt conveyor is used for conveying different materials from one location to another. The different components of a belt conveyor system typically are electric drives, pulleys, idlers, and a long belt. A simple conveyor system may look like below:
The basics of the Calculations of Conveyor Belt Design Parameters y
Tb
Belt tension: The belt of the conveyor always experience a tensile load due to the rotation of the electric drive, weight of the conveyed materials, and due to the idlers. The belt tension at steady state can be calculated as:
= 1.37*f*L*g*[2*mi+ (2*mb + mm)*cos ()] + (H*g*mm) ««.eqn.1.1
Where, Tb is in Newton. f = Coefficient of friction L = Conveyor length in meters. Conveyor length is approximately half of the total belt length. g = Acceleration due to gravity = 9.81 m/sec 2 mi = Load due to the idlers in Kg/m. mb = Load due to belt in Kg/m.
mm = Load due to the conveyed materials in Kg/m. = Inclination angle of the conveyor in Degree. H = vertical height of the conveyor in meters. Load
y
due to idlers (mi): This can be calculated as below:
mi = (mass of a set of idlers) / (idlers spacing) «««««..eqn.1.2 Note:
The article ³Design an Idler for a Conveyor Belt System´ has detailed explanation about how to calculate idlers spacing.
y
Power at drive pulley: The power required at the drive pulley can be calculated from the belt tension value as below:
Pp = (Tb*V)/1000«««««.. eqn.1.3
Where, Pp is in KW. Tb = steady state belt tension in
N.
v = belt speed in m/sec. y
Belt tension while starting the system: Initially during the start of the conveyor system, the tension in the belt will be much higher than the tension in steady state. The belt tension while starting can be calculated as:
Tbs =Tb*Ks««««««.. eqn.1.4
Where, Tbs is in
N.
Tb = the steady state belt tension in
N.
Ks = the start-up factor y
Sizing of the motor: The minimum motor power can be calculated as:
Pm = Pp /Kd««««««eqn.1.5
Where, Pm is in Kw. Pp = the power at drive pulley in Kw Kd = Drive efficiency. y
A=
Acceleration
: The acceleration of the conveyor belt can be calculated as:
(Tbs ± Tb)/ [L*(2*mi + 2*mb+mm)]««««««««eqn.1.6
Where, A is in m/sec2 Tbs = the belt tension while starting in
N.
Tb = the belt tension in steady state in
N.
L = the length of the conveyor in meters. mi = Load due to the idlers in Kg/m. mb = Load due to belt in Kg/m. mm = Load due to the conveyed materials in Kg/m. y
Belt breaking strength: This parameter decides the selection of the conveyor belt. The belt breaking strength can be calculated as:
Bs= (Cr* Pp )/ (Cv*V)««««.. eqn.1.7
Where, Bs is in Newton. Cr = friction factor Cv = Breaking strength loss factor
Pp = Power at drive pulley in
Newton.
V = belt speed in m/sec. An
Example of Conveyor Belt Calculations
Input data:
Conveyor capacity (Cc) = 1500 t/h = 416.67 Kg/sec Belt speed (V) = 1.5 m/sec Conveyor height (H) = 20 m Conveyor length (L) = 250 m Mass of a set of idlers (m¶i) = 20 Kg Idler spacing (l¶) = 1.2 m Load due to belt (mb) = 25 Kg/m Inclination angle of the conveyor () = 5 Coefficient of friction (f) = 0.02 Start-up factor (Ks) = 1.5 Drive efficiency (Kd) = 0.9 Friction factor (Cr) = 15 Breaking strength loss factor (Cv) = 0.75 Calculation:
0
y
First, we will use the eqn.1.2 for finding out the load due to idlers:
mi = (20/1.2) = 16.67 Kg/m y
We will use the eqn.1.1 for finding out the belt tension in steady state:
Tb = 1.37*0.02*250*9.81*[16.67+ {2*25+ (416.67/1.5)}*cos (5)] + (20*9.81* (416.67/1.5)) = 77556.88 y
The belt tension while starting the system can be calculated by using the eqn.1.4:
Tbs = 1.5 * 77556.88 = 116335.32 y
N.
N
For calculating the power at drive pulley, we will use the eqn.1.3:
Pp = (77556.88*1.5)/ 1000 = 116.335 Kw y
We will use the eqn.1.5 estimate the size of the motor:
Pm = 116.35/0.9 = 129.261 Kw y
A
We will use the eqn.1.6 to find out the acceleration of the motor:
= (116335.32 - 77556.88)/ [250*{(2*16.67) + (2*25) + (416.67/1.5)}]
= 0.429 m/sec2 y
Lastly, we will use the eqn.1.7 to find out the belt breaking strength:
Bs = (15*116.35) / (0.75*1.5) = 1551.33 N/mm
This Bs value is used to select the conveyor belt from the manufacturer¶s catalogue. Conclusion
The conveyor belt calculations methodology discussed in the article is to be used only for the guidance on calculating the initial conveyor design parameters; the final design must be validated by using the FEA or other similar tools before building the prototype. Reference y y y
Dunlop ± Conveyor belt technique design and calculation Bridgestone Conveyor Belt Design Manual The Belt conveyors are the most commonly used powered conveyors because they are the most versatile and the least expensive. Product is conveyed directly on the belt so both regular and irregular shaped objects, large or small, light and heavy, can be transported successfully. B Systems uses only the highest quality premium belting products, which reduces belt stretch and results in less maintenance for tension adjustments. Belt conveyors can be used to transport product in a straight line or through changes in elevation or direction. In certain applications they can also be used for static accumulation or cartons. Generally, this philosophy calls for belt cleaners that are: As far forward (as close to the conveyor discharge) as possible. Positioned out of the material flow. Designed to minimize risk to belt, splice, and cleaner itself. Designed to stand up to ³worst case´ conditions. Illustration of How belt conveyor works Designed for ease of maintenance, including simple blade replacement and reduced frequency of re-tensioning, Belt conveyors are available with either rollers (roller belt) or a solid surface (slider bed) to support the carrying belt. When the materials fall down on the conveyor, the roller under the belt will drive the belt come forward. In this way, we convey the stuff. The conveyers consist of standard parts, which are advanced and simple in structure, easy to maintain. Our vibrating equipment is adaptable for stationary and mobile crushing plants. They are widely used in mining, metallurgical and coal industry to transfer sandy or lump material, or packaged material. According to different transferring equipment, the transfer system can be one independently or multi-conveyers or combined with other transfer equipments. The belt conveyer can be installed horizontally or aslope to meet the needs of different transfer lines. Belt conveyors are the most commonly used powered conveyors because they are the most versatile and the least expensive. Product is conveyed directly on the belt so both regular and irregular shaped objects, large or small, light and heavy, can be transported successfully. B Systems uses only the highest quality premium belting products, which reduces belt stretch and results in less maintenance for tension adjustments. Belt conveyors can be used to transport product in a straight line or through changes in elevation or direction. In certain applications they can also be used for static accumulation or cartons.
Generally, this philosophy calls for belt cleaners that are: As far forward (as close to the conveyor discharge) as possible. Positioned out of the material flow. Designed to minimize risk to belt, splice, and cleaner itself. Designed to stand up to worst case conditions. Designed for ease of maintenance, including simple blade replacement and reduced frequency of re-tensioning, Belt conveyors are available with either rollers (roller belt) or a solid surface (slider bed) to support the carrying belt. When the materials fall down on the conveyor, the roller under the belt will drive the belt come forward. In this way, we convey the stuff.
y
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The idlers are an important part of a belt conveyor system; they provide stability to the conveyed materials. There are mainly three types of idles used in the industry namely, flat idlers, trough idlers, and garland idlers. In this article we will discuss only the flat type belt conveyor idler design. The Basics of Flat Idler Design
Typically, the following inputs are used for starting up the design process of the flat idler: y y y y
Capacity of the conveyor generally expressed in tons per hour. Bulk density of the conveyed materials generally expressed in tons per cubic meter. Conveyor belt width generally expressed in meters. Belt speed generally expressed in meters.
The output aims from the design process are: y
The spacing of the idlers generally expressed in meters.
y y y
The idler speed generally expressed in meters per second. Load on each idlers. Idler diameter generally expressed in meters.
The following design equations are used across the industry for calculating the different design parameters of the flat idlers: y
Spacing of the idlers
S = (8*T1*H)/ (mb+ml)*g««««..1.1 Where, S is in meters T1= Belt tension near the idlers as shown in the picture (N) H=Belt sag (m) mb = weight of the belt (kg/m) ml =Weight of the conveyed material (kg/m) g =Acceleration due to gravity y
The weight of the conveyed material can be further calculated as
ml= (10*W)/ (36*V)««««1.2 Where, mb is in kg/m. W = Capacity of the conveyor (tons per hour)
V = Belt speed (m/sec) y
Idler speed
N = (60*V)/ (*D)«««««1.3 Where, N is in RPM. V = Belt speed (m/sec) D = Diameter of the idlers Loads on each idlers y
F= (10*W*S*g)/ (36*V)««««1.4
Where, F is in Newtons g = Acceleration due to gravity W = Capacity of the conveyor (tones per hour) S = Spacing between the two idlers. V = Belt speed (m/sec) y
Maximum bending stress on the idlers
b= (8*F*L)/ (3**D3)««««««..1.5 Where, b is in Newtons per square meter F = loads on each idlers (Newton) L = length of the idlers (Meter) D = diameter of the idlers (meter) One
Practical Belt Conveyor Idler Design Example
Now, let¶s see how to use the basic design equations for actual design purpose. We will take the following data as input: Capacity of the conveyor W = 1000 t/h Belt speed V =1.68 m/sec Belt tension near idler T1=50000 N Idler length L =1.2 m Belt sag = 0.015 m
Weight of the belt mb=15 kg/m Idler speed N= 50 rpm Design procedure: y
First, we will calculate the weight of the conveyed material using the eqn.1.2 as:
ml = (10*1000)/(36*1.68) = 165.34 kg/m y
Now, to calculate the spacing between the two idlers we will use the eqn.1.1
S=(8*50000*0.015)/(15+165.34)*9.81 = 3.391 m y
The diameter of the idler can be calculated from the eqn.1.3 as below:
D= (60*1.68)/ (3.14*50) = 0.64 m y
Total load acted on each idler can be obtained from the eqn.1.4 :
F=(10*1000*3.391*9.81)/(36*1.68)=5500 N y
Maximum bending stress applied on each idlers can be obtained from the eqn.1.5 as below:
b= (8*5500*1.2)/ (3*3.14*0.643) = 21385.176 N/m2 If the maximum bending stress calculated from the above equations is higher than the accepted limit of the bending stress then, you have to reconsider the input assumed parameters, for example you may have to set the lower idler speed or you have to think of the lower belt sag value, so that idler spacing got reduced and so the load per idler. Conclusion
There are three types of idlers used in the conveyor industry, out of which only the flat belt conveyor idler design calculations are discussed here theoretically. We have not used the factor of safety in the design calculations here, or in other words the factor of safety is considered as one through out the calculations. The theoretical calculations are ideal for the preliminary design. FEA tools like Ansys or Pro Mechanica should be used for the final virtual validation of the design. References y y
Limberoller Belt Conveyor Idlers Bridgestone Conveyor Belt Design Manual
