Belt Tension Theory Driving or slack side tension (T2) To determine the minimum tension which must be introduced into the belt as it leaves the driving pulley, to ensure that the effective tension or power can be transmitted into the belt passing around the drive pulley, without slip. Prior to going into this analysis, it is necessary to understand the effect that friction and wrap angle have on the driving characteristics of a pulley. These are discussed below :- (a) Friction Factors The fundamental equation for conveyor drive calculations is: T1 / T2 = e θ Figure 1: Typical Drive Pulley Where: T1 and T2 are the tight and slack side tensions respectively. e = 2,718 θ = angle of wrap in radians = coefficient of friction between belt and drive pulley The tensions and angle of wrap are fairly tangible and are determined by the configuration of the machine and the loads on it. , however, is not well understood, difficult to measure and subject to wide variation with different materials and environmental conditions. The following factors will determine the selected coefficient of friction :- (i) Belting Material The shore hardness, type of rubber and the age of the belt will have an effect on the coefficient of friction. (ii) Drive Pulley Construction This can be a bare steel pulley or it can be lagged to increase the coefficient of friction. The lagging can have different shore hardness, which changes the coefficient of friction. It can be grooved, which improves the coefficient of friction in certain wet conditions, but again it must be remembered that the coefficient will reduce in time because of the ageing of rubber and the blocking of the grooves in the rubber lagging, or due to wear on the lagging.
This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
Transcript
Belt Tension Theory
Driving or slack side tension (T2)
To determine the minimum tension which must be introduced into the belt as it leaves the driving pulley, to ensure that the
effective tension or power can be transmitted into the belt passing around the drive pulley, without slip.
Prior to going into this analysis, it is necessary to understand the effect that friction and wrap angle have on the driving
characteristics of a pulley.
These are discussed below :-
(a) Friction Factors
The fundamental equation for conveyor drive calculations is: T1 / T2 = eθ
Figure 1: Typical Drive Pulley
Where:
T1 and T2 are the tight and slack side tensions respectively.e = 2,718θ = angle of wrap in radians
= coefficient of friction between belt and drive pulley
The tensions and angle of wrap are fairly tangible and are determined by the configuration of the machine and the loads on it. , however, is not well understood, difficult to measure and subject to wide variation with different materials and
environmental conditions.
The following factors will determine the selected coefficient of friction :-
(i) Belting Material
The shore hardness, type of rubber and the age of the belt will have an effect on the coefficient of friction.
(ii) Drive Pulley Construction
This can be a bare steel pulley or it can be lagged to increase the coefficient of friction. The lagging can have different shore hardness, which changes the coefficient of friction. It can be grooved, which improves the coefficient of friction in certain wet conditions, but again it must be remembered that the coefficient will reduce in time because of the ageing of
rubber and the blocking of the grooves in the rubber lagging, or due to wear on the lagging.
Click here to go to the pulley section where more information can be found on: Pulley types and Pulley lagging .
(iii) Working Conditions
The conditions under which the installation will operate, i.e. will conditions be dry or wet, and if wet, to what extent? What size and what type of material? Fine powdery material can reduce the coefficient of friction by acting as a lubricant
between the pulley and the belting. If the material to be handled is oily, it will reduce the coefficient of friction drastically
especially under wet conditions.
(iv) Design Conditions
The following design conditions will effect the coefficient of friction :-
Angle of wrap of the belt around the drive pulley. The maximum tension to be transmitted via a drive pulley
The maximum face pressure between the belting and drive pulley. This will not only effect the
coefficient of friction but will also limit the selection of the type of lagging for a pulley.
Figure 2: Force Distribution on Pulley Face
For example, in figure 2 above :-
Face pressure PF can be calculated as follows
Fn = 2T Sin dθ/2
PF = Fn/r d = T/r with dθ = 0
where:
PF = face pressure kPar = pulley radius (mm)Fn = force on pulley, kN/mTave = belt tension, kN/m
θ = angle of wrap, degrees.
Extreme pace pressure would result in peeling and rolling away of the pulley cover / lagging, especially at the drive pulleys
where there would be belt creep.
High tension steel cable belts are usually the only place where face pressures become a factor in lagging, pulley and drive
selection.
Soft rubber lagging is not usually suitable for drives of more than 100 kW per pulley and slide-lagging is usually limited to
drives of 400 kW per pulley, but the lagging thickness will have an obvious effect on this.
Diameter of pulleys must be selected to minimise the face pressure for rubber to 1 000 kPa.
Minimum Pulley Diameters: Fabric Belting or Steel Cord Belting
b) Drive Factors
Most references publish tables of drive factors for various values of and this tends to obscure the fact that is faily arbitrarily
chosen.
The drive factor, 'Cw' is defined as
Cw = 1 / eθ - 1
and
T2 = Cw Belt Power (kw) / Belt Speed (m/s)
T1 T2 = Te
and
T2 = CwTe
The use of drive factors is to be discouraged. Designers are urged to select carefully for each application.
Values of published by various authorities are shown in Table 1 below:
Table 1: Typical Friction Factors for Drive Pulleys
CONDITION CEMA STEVENSADAMSON
BRIDGESTONE LINATEX REMA TIP TOP
Bare Pulley 0.25 0.35 0.1 - 0.3 -- --
Lagged 0.35 0.35 -- -- --
Dry Lagged 0.35 0.35 0.35 0.6 0.4 - 0.45
Wet Lagged 0.35 0.35 0.2 - 0.3 0.8 0.35
Wet and Dirty Lagged 0.35 0.35 0.2 0.4 0.25 - 0.3
These values are the limiting conditions (when the belt is on the point of slipping). The actual coefficients of friction
developed between surfaces are, in practically all cases where slipping does not occur, in excess of those shown above.
Therefore, the convention of using these values, whilst convenient, does not reflect what exactly occurs at the drive.
With a working drive, the higher tensioned part of the belt is stretched more than the lower tensioned section, thus the belt
entering the positive drive will be travelling faster when it leaves it. (In a regenerative drive the opposite is true).
The elastic recovery of the belt occurs over only a part of the total angle of contact and it is at this point, (where creep
takes place), that all the driving is done, while making full use of the coefficient of friction.
It is only over this 'active part' of the wrap angle (See fig. 4 below) that the classical tension formula can be applied, because this is where the limiting condition occurs. This is an approximate solution as it varies with both creep and angle of
wrap.
A typical graph of '' against creep rate is shown below in Figure 3.
Figure 3: Graph of '' against Creep Rate
Figure 4 shows the drive conditions where the 'passive' arc is between 'A' and 'B' and all the drive is transmitted between
'B' and 'C' which is called the 'active arc', with '' being dependant on creep rate.
Figure 4: Diagram indicating 'active' and 'passive' arc on a drive pulley.
By maintaining a constant T2 and increasing T1 the active arc will increase, until it uses the whole of the wrap angle. A further increase in T1 will cause slipping and a reduction in the power transmitted. To realise the importance of the
variations in '' consider the following:
Comparing =0,2 and 0,4 for θ=3,66 radians then;
T1/T2 = 0,27 and T1 / T2 = 4,32 respectively
i.e. for the same T1, T2 will have to be more than doubled to drive without slipping at = 0,2.
c) Rubber Specification
Except for Linatex, which is a special material, most references mention no particular rubber specification. Also, very little
attempt is made to allow for conditions such as dust which must affect drive performance.
According to figures quoted by Bridgestone we should use = 0,2 for wet and dirty application instead of the conventional 0,35. This value applies only in the limiting case and the Bridgestone factors are very conservative. This has been verified by Stevens Adamson, who claim that the actual coefficient is likely to be in the range of 0,5 to 0,6 but 0,35 is used for safety and to allow for high starting torques. No distinction is made for chevron lagging as the grooves are for drainage
only.
It is interesting that very little attention is paid to the actual rubber material with which the pulleys are lagged. The coefficient will vary with the hardness and type of rubber on the pulley and on the belt as well as with external, or
environmental conditions.
The standard rubber lagging used has a hardness of 55 shore and this is supposed to be a good compromise between grip and long life. However some companies insist on a much harder material in the range of 65 to 70 for long life. Rema Tip
Top use 65 to 70 for heavy duty drives but go down to 50 for lighter duties.
Softer, more cohesive rubbers are used, but there is a greater tendency for the rubber to shear internally and eventually
pull off. Coefficients claimed for soft rubbers are shown in Table 2 below.
Table 2: Typical Values of for Soft Rubbers
Shore Hardness Dry Wet Wet and Dirty
Rema Tip Top 50 - 55 0.4 - 0.35 0.35 0.25 - 0.3
Linatex 60 0.6 0.8 0.4
The thicker Linatex lagging actually has a fabric layer in the rubber to prevent internal tearing from taking place. The
conclusions which can be drawn from the above are:-
i. Published tables must be used with great care. Careful consideration must be given to the materials involved and the conditions under which the machinery will operate. It is not good enough merely to
look up the 'drive factor' in your favourite catalogue i.e and then press on regardless. ii. Figures published by CEMA, Bridgestone, etc., are conservative and there is scope for intelligent use of
higher factors to reduce belt tensions.
iii. Materials such as Linatex are available which have a much higher value than the usually accepted
values.
iv. If too low a value is chosen for the conditions or the conditions are misinterpreted, drive/belt slippage
may result and serious problems will occur.
Finally, table 3 lists the coefficient of friction which could be used for future designs. This table can be expanded to include
Ceramics.
Table 3: Coefficient of friction - Drive Pulleys
Plant Description Conveyor Construction
Type of Take - Up's
Automatic Manual
Lagged Un-Lagged Lagged Un-Lagged
Wet Plant Covered ConveyorUncovered Conveyor
0.250.20
0.100.10
0.200.20
0.100.10
Semi-Wet Plant Covered ConveyorUncovered Conveyor
0.300.25
0.200.15
0.250.22
0.180.13
Dry Plant Covered ConveyorUncovered Conveyor
0.350.30
0.220.18
0.250.25
0.200.15
With an understanding of the factors effecting the slack side tension T2 it is now possible to continue.
Having calculated the driving or slack side tension from the above analysis.
The resulting tight side (maximum tension) (T1) in the belt at the drive pulley would be :-
T1 = TE + T2 (N).
Sag Tension (Ts)
In many instances the slack side tension as calculated above will be sufficient to ensure that adequate tension is retained at all points around the conveyor. However, in some cases, it is found that if the calculated T2 is used the belt tension at
the tail end of the conveyor is not sufficient to support the loaded belt without undue sag between the idlers.
Under normal circumstances the sag between the idlers is restricted to 2 % of the idler spacing. The tension required (Ts) is
dependent upon the mass of the loaded belt and the idler spacing and is given by the formula :
Ts = 3 x %sag / 100 x IS(carry) x (Wb + Wm) x 9,81 with units of (N)
Therefore it is necessary to carry out a check calculation, taking the tension required to limit sag to 2 % and comparing it to the tension to prevent belt slippage at the drive pulley. If the sag tension is found to be too low to support the load then the T2 tension and thus the tension distribution throughout the conveyor must be increased by the difference between the two
tensions.
Maximum Belt Tension (T1)
To calculate the maximum belt tension, which does not in all cases takes place at the head pulley, the following formulae
must be used :
TI = T2 + TE (N) or,
should Ts be greater than T2 then Ts must be used in place of T2
T1 = (T2 - Ts) + T2 + TE (N)
Belt Tensions/Strength: Fabric Belting or Steel Cord Belting
Unit Tension Conversion
To conclude, the total belt tension as calculated above is usually expressed as a unit tension for reference against various
information tables. This is done by dividing the total calculated tension by the belt width.
Therefore Unit Tension = Belt tension (N) / Belt width (mm) giving units of N/mm width.
Belt covers and carcassCharacteristic Possible problem Solution
Top cover wears quickly High acceleration or side loading of material in loading area
Check conveyor speed. Direct stream of falling material in conveying direction with a
deflector plate
Dirty or sticking idlers Use return idlers with rubber cushion discs, lubricate or replace
sticking idlers
High sag between idlers causes relative movement of material
Increase pretension, reduce idler spacing
Cover to thin Specify thicker top cover
Rubber grade not adequate Choose grade of cover rubber according to material
Severe local wear, longitudinal grooves or damages of top cover
High pressure of seal skirts or chutes on belt surface
Adjust seal skirts perpendicular to belt, modify chute
Seal skirts consist of hard or wear resistant material
Use soft rubber with normal or low wear resistance (do not use
old belts)
Steel sides of chute to close to belt
Adjust distance to belt, increase distance in direction of belt travel
Excessive space between belt and seal skirts
Adjust seals to minimum clearance
Belt sags under impact, allowing material to be trapped under
skirts
Decrease idler spacing, install impact idlers or impact bars
High material volume causes Increase speed, reduce capacity,