Belt Drives Calculation
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Belt drives Updated April 2008 Purpose To develop the knowledge and skills required to carry out the selection of a wedge belt drive system.
Objectives At the end of this section you should be able to: 1. Describe the various types of belt drive 2. Select a suitable wedge belt for a given power transmission 3. Select suitable pulleys and determine the speed of the driven shaft 4. Determine the centre distance between the pulleys and pitch length of the belt
5. Determine the number of belts required 6. Determine the radial (overhung) load caused by a belt drive given the ratio of the belt tensions 7. Finalise the design, including selection oftaper lock bushes (if used)
Belt drives are widely used for transmitting rotational mechanical power from one rotating shaft to another. They are light, inexpensive, quiet and capable of transmitting reasonably large amounts of power. There are several manufacturers/distributors of belt drives in Australia. The data in the manual was taken from theFenner Catalogue. Belt drive pulleys can be plain bushed or taper bushed for use with taper-lock bushes. All the pulleys supplied by Fenner are of taper-lock bush type. The advantage of the taper-lock bush is that no key is required, it is easy to install and does not weaken the shaft (does not cause as much stress concentration) as a keyed bush. There are many types of belt drive but for the purposes of this module you need only to be able to select the wedge belt type. These are a type of vee belt that have largely superseded the older type of vee belt. They have a deeper profile and are capable of transmitting more torque and power than the older type.. The two types are interchangeable on the pulleys, so even if a vee belt was originally in place, it can be replaced by a wedge belt if necessary without changing the pulleys. The power that can be transmitted by a wedge belt drive depends upon a number of factors, namely: The angle of contact The greater this is, the more torque and power can be transmitted. If both pulleys are not of the same diameter, then the smaller pulley is the one that determines the maximum torque and power that can be transmitted. Not only does the smaller pulley have a shorter length of contact, but it also has a smaller angle of contact than the larger pulley, so it will always be the first to slip. In cases where the pulleys are not the same diameter, the angle of contact will depend also upon the centre distance between the shafts. The greater the centre distance, the greater the angle of contact. For this reason, centre distances should not be below the recommended minimum value (sum of the pulley pitch diameters) unless there are special circumstances.
The wedge angle of the belt (and groove). Because you will be selecting a standard belt you are not able to change this angle which is usually 34° or 38° depending upon the size of the belt and the size of the pulleys. The coefficient of friction. You have little control over this because it is determined by the belt material and the pulley material (and finish). In practice it is important to keep oil and grease off the belt and pulleys because this will reduce the friction (and could deteriorate the belt). Why would it not be a good idea to use a rough surface on the pulley to increase the coefficient of friction? The pulley diameters. The larger the diameters, the greater the torque and power. This is simply because for a given belt tension force, the larger the pulley, the larger the torque (torque = force x radius) and hence the greater the power for a given speed. This is why it is not a good idea to choose pulleys that are too small. On the other hand if the pulleys are too large, the belt speed increases, centrifugal tension increases and the drive takes up more space. So a reasonable compromise is needed when choosing pulley pitch diameters. Initial belt tensions. The higher the initial tension in the belts, the greater the torque and power that can be transmitted. At rest, when no power is being transmitted, the belt tensions are equal on both sides of the pulleys. As the pulleys rotate and transmit power, the belt tension rises in one side (tight side) and reduces in the other (slack side). However, the sum still stays the same. When the ratio of the belt tensions reaches a certain limiting value, slipping will occur. Hence the greater the initial tension in the belts, the greater the torque and power that can be transmitted before slipping occurs. However, it is not a good idea to have too much tension because this will place high radial loads on the shaft and bearings and also will reduce the belt life considerably. For this reason, initial belt tensions should be set carefully. In their catalogue, Penner detail the practical method for pre-setting the belt tensions. This method requires a belt tension indicator (which is really just a force gauge) that measures the force at the centre of the belt required to cause a standard deflection (16 inn per m of span). There is a recommended value for this force that should be adhered to when the belt drive is
initially installed. As the belt wears, the initial tension needs to be re-set, so the designer should allow for an adjustment method. Adjustment can be provided by moving one shaft further away from the other or by means of an adjustable jockey pulley. This pulley should be located on the inside of the drive on the slack side as close as possible to the larger pulley and should have a diameter at least equal to the smaller pulley. The size of the belt. The larger the belt section, the greater the tension that can be carried by the belt and the greater the torque and power. In the Data Manual, four sizes of wedge belt are given, namely: SPZ, SPA, SPB, and SPC. These are listed in increasing size, with the SPZ being the smallest and the SPC being the largest. The number of belts. Belt drives with a single belt are the most common but belt drives are often used with 2 to 6 belts in parallel on multi-grooved pulleys. In the larger sizes up to 8 belts may be used. Clearly, the torque and power increase in direct proportion to the number of belts.
Design and selection of belt drive systems In your applied mechanics (or dynamics) you should have learnt how to calculate the maximum torque and power that can be transmitted by a vee or wedge belt drive, given the coefficient of friction, angle of contact, groove angle and slack-side tension under load. For the purpose of mechanical design you will now learn to use the manufacturers catalogue in order to design and select a belt drive system. Note The calculation of torque and power based on mechanics principles will usually overstate the amount of torque and power: This is because this calculation does not consider the stresses in the belt and the allowable stress that depends upon the belt material and method of construction.
Study guide http://www.fennerdrives.com/assets/Opm_V_belts.pdf http://www.fptgroup.com/downloads/friction_wedgebeltdrive s.pdf
Reference: Mechanical Design Data Manual Chapter 3 (Click to read pdf below. Do not print these notes on CADLAB printers!)
Belt drives notes and example; Belt_notes.pdf
Belt drives data pages; Belt_data.pdf
1. Types of Belt Drives: Read the Preamble on page 50 of the Data Manual. Recognise the various types of belt drives available. 2. Minimum Diameter: Look at Table 1 on page 56. This gives you the minimum pulley diameter for a given power and faster-shaft speed. 3. Service Factors. Look at Table 3 on page 56. This gives you a service factor which takes into account shock loading and the hours per day of operation. You will encounter a similar factor in the selection of many other mechanical power transmission components. Note that in most cases, the drive is a speed-reducing one. If the drive is speed-increasing one, then an additional service factor should be applied (as shown in this table). 4. Power/Speed Graph: Look at the graph on page 57. This shows you where each size of belt can be used according to the power and speed. You may like to use coloured pencil or highlighter pen to shade the various lines to make this graph easier to use. 5. Correction Factors: Given on page 58 and the power ratings given on pages 59 to 64. 6. Pulley Dimensions: Given on pages 65 to 72. These are all for use with taperlock bushes. Taper-lock bush details are given on page 73. 7. Read the selection method given in pages 50 to 52. It is not necessary that you work through this in detail at this stage because it won't mean much to you until you try and work through a problem on belt selection. 8.
Study the Worked Example on page 54 in conjunction with the selection method.
Work through Exercises 1 and 2 in this section.
Types of belt drives. Belt drives can be broadly categorised into two groups, positive(no-slip, toothed belts) and non-positive(slip, friction belts). Traditionally belts have been of the nonpositive (friction) type which include flat belts and vee belts. In recent times toothed belts have become popular for use in electro-mechanical systems such as video machines, turntables and higher power applications such as servo drives and camshaft drives. These are not treated here. Flat belt and Vee belt drives. The following discussion on belt drives is limited to flat belts and vee belts where power is transmitted by friction. These belt drives are subject to creep and even slip, depending on the load being applied, and hence the drive ratio cannot be considered positive. Flat belts with long centre distances were common in many industries in the past. A central prime mover (eg. a steam engine) would generate power and belts would be used to transmit power to various machines. These types of arrangement can still be found in some textile industries. Today short centre drives are still in common use but more often vee belt drives are used. Flat belts were commonly made from leather but today are usually made from rubber (cotton fabric or cord impregnated and bound together by vulcanised rubber). Leather belts are made from leather from the butt of the hide. Their ultimate tensile stress varies from 20 to 35 N/mm2. Flat rubber belting is usually used as it is cheaper, has a higher coefficient of friction, is more resistant to moisture and is stronger than leather belting. Initial tensions in rubber belts vary from about 2.5 to 4N per ply per mm width. Tensioning the belt results in elongation so belts are made approximately 1 per cent shorter than the theoretical tape line measurement. Belts can be purchased in endless form or made endless in the field by means of a vulcanised splice. Rubber belts will stretch about 2 per cent over their nominal life so it is desirable to provide centre distance adjustment. Maximum power ratings are dependent on belt strength, angle of contact, small pulley diameter, beltspeed in m/sec and service conditions. Pulleys are generally made from cast iron or fabricated from steel. Flat belt pulleys
are generally crowned for self centring. Vee belts Vee belts are manufactured of rubber, fabric and cord. They provide a quiet, compact and resilient form of power transmission with minimum shock transmission between drive shaft and driven shaft/s. The tapered cross sectional shape of a vee belt causes it to wedge firmly into a sheave groove so that the driving action takes place through the sides of the groove rather than the bottom. Vee belts operate most efficiently at speeds of about 20-25 m/sec. Design of vee belt drives is done using the selection procedure shown below (or on pages 51 and 52 of the Belt_notes.pdf)
SELECTION PROCEDURE FOR VEE BELT DRIVES This selection procedure complies with BS3790. 1. Select service factor. . (a) The type of driven machine will determine the duty. (b) Determine the type of driving machinery and operational hours per day. (c) Select service factor. 2. Calculate the Design power rating. Design power rating = Motor power Service factor 3. Select the belt section. (a) Mark the RPM of the faster shaft on the horizontal axis. (b) Trace upwards along the vertical axis to the design power. (c) At the point were they meet, note the recommended belt section or sections if there is an overlap. Notes: choose 'B' section belts in preference to 'A' section belts. In the overlap between 'B' and 'C' sections, 'C' section belts are likely to be more
desirable as fewer belts will be required. 4. Calculate the speed ratio (R). (Maximum ratio of about 6:1 in a single ratio)
5. Select pulley diameters. (a) Determine recommended minimum motor pulley diameter from the table. (b) Choose a combination of pulley diameters that gives required speed ratio, keeping in mind (a). (c) Record catalogue details of pulleys and bushes. 6. Calculate the belt length based on centre distance (C). If the centre distance is not fixed then use:
To determine belt length use:
Choose a suitable belt and record belt actual belt length and identification number. 7. Calculate the accurate centre distance (CA) based on the belt selected.
8. Determine the basic power per belt for 'A', 'B' and 'C' section belts respectively. Each page has the basic power per belt table on the left hand side and a table on the right hand side for calculating additional power which depends on the belt speed ratio.
(a) Record basic (rated) power per belt from left hand table. (b) Record approximate belt speed from left hand table (c) Record additional power per belt from right hand table. Power/belt = Basic power/belt + Additional power/belt 9. Determine the Arc of contact correction factor. Refer Table 5 (a) Calculate (D-d)/C (b) Record correction factor (c) Record arc of contact () 10. Determine the belt length correction factor. Refer Table 6 . 11. Calculate the number of belts required. Number of
Design power rating (step 4) =
(Power/belt(step 8)arc factor(step 9)length factor
12. Summarise results. Gather the data that is required for a bill of materials/materials list. (a) Pulley catalogue numbers and required dimensions. (b) Taper lock bush catalogue numbers and required dimensions. (c) check bore sizes against shaft sizes.
13. General arrangement drawing. The centre distance CA has a negative tolerance to allow for initial installation of belts over pulleys. CA has a positive tolerence to allow for take up as the belts are tensioned and for adjustment after wear. At the centre of the span tensioning is satisfactory if the belt can be depressed 16mm/meter of centre distance. For installation and take up allowances see DESIGN DATA MANUAL.
WORKED EXAMPLE Problem 1: Design a vee belt drive to transmit power from an A.C. squirrel cage, delta start, motor rotating at 1440 rev/min and rated at 11kW to a fan rotating at 720 rev/min. Centres are to be near to, but not more than, 750mm apart and the driven pulley is not to exceed 355mm outside diameter. The drive is to run a minimum of 18 hours per day. Data: Motor: A.C. squirrel cage, delta start; 11kW ; 1440RPM Fan: 720RPM Centre distance 750mm Driven pulley 355mm O.D. operating hours 18 hours per day
Solution: 1. Service factor (S.F.). Medium duty, 18 hr/day S.F = 1.3 2. Design power rating (D.P.R.).
3. Select vee belt section. Can use either 'A' or 'B' section choose 'B' section. 4. Calculate the speed ratio (R).
5. Select pulley diameters (d)&(D). see - Recommended minimum standard pulley diameters for electric motors. Motor RPM=1440;Power=15kW Minimum Diameter Motor pulley=118mm Maximum O.D. driven pulley=355mm Try D=315mm: d=D/R=315/2=157.5mm
Available combinations (D=315mm) for d=150mm : R=2.1:1 for d=160mm : R=1.97:1 closest R=1.97, d=160mm, D=315mm 6. Calculate belt length (L). Find L based on the centre distance (C) and the pulley pitch diameters d and D.
Choose next smallest belt to this dimension to give centre distance