V-belt drive problems

1. A belt drive incorporates a small pulley of 100 mm diameter and a belt whose length is 1100 mm. For speed ratios of (a) 1.5:1   (b) 2:1   (c) 3.15:1, calculate the theoretical shaft centre distance and angle of wrap on the small pulley.
   [ 353, 310, 193 mm]
    
2. ( a)   Use the belt properties of Table 1 to calculate the basic rating of an A-section V-belt with two 100 mm diameter pulleys rotating at 4200 rpm. Check, using the Code tables.   [ 3.07 kW]
   ( b)   If the pitch length of the above belt is 3080 mm, what then is the rating and what is the corresponding power correction factor for pitch length? Check this last value with the Code.   [ 3.50 kW, 1.14]
   ( c)   If the drive in ( a) is required to last for only 10 kh, by what percentage is the above capacity increased?   [ 24%]
    
3. Plot rating versus belt speed, similar to the above rating curves, for an A-section belt. Use pulley diameters of 75, 132, 250, 500 and 1000 mm. Superimpose upon this, trajectories of constant effectiveness : 20, 40, 60, 80 and 100%. Comment upon the effect of pulley diameter on rating as the diameter increases.
    
4. A V-belt drive employs a single B belt of length 2300 mm, together with 200 and 400 mm diameter pulleys. The smaller pulley rotates at 1440 rpm.
   ( a)   What is the capacity of this drive using the Code method ?   [ 6.04 kW]
   ( b)   What is the life of the drive when transmitting 6.04 kW ?   [ 31 kh]
   ( c)   Repeat ( a), but use ( 5a) with the standard life of 26 kh.   [ 6.19 kW]
   ( d)   Check this last result using the program V-belts.
   ( e)   A multi-strand drive, otherwise identical to the above, is required to transmit 12 kW with a duty factor of 1.3. Use ( 5a) to determine the number of belts required.   [ 2.5]
   ( f)   What life may be expected, if 2, or if 3 belts are used ?   [ 5.0, 82 kh]
    
5. Two 1750 mm long A-section belts are incorporated into the drive whose layout is sketched. The wrap angle on the 150 mm diameter motor pulley (1) is 118^o and the pulley rotates at 2880 rpm. The 400 mm diameter driven pulley (2) absorbs the design power of 10 kW. Pulley (3), of 80 mm diameter, is an idler and absorbs no appreciable power.
   Estimate the life of the belts if . . . . .
   ( a)   the pulleys rotate clockwise, or
   ( b)   they rotate counterclockwise, or
   ( c)   the idler is removed and the centre distance between (1) and (2) increased accordingly.   [ 6, 0.6, 14 kh ]
    
6. A 7.5 kW 1445 rpm squirrel cage motor, started direct-on-line, is required to drive a machine tool at a speed of around 860 to 870 rpm. Duty is expected to be 7 hr/day, 5 days/week, 49 weeks/year with 4 years between belt replacements. The centre distance should lie within the range 280 to 320mm.
   Select a drive for this duty.
    
7. Select a suitable hinge location for the pivoted motor drive of the foregoing worked example in which an ABB MBT 132M motor transmits 7 kW to a launderer through three B2500 belts on 180 and 514 mm diameter pulleys, the motor lying vertically under the launderer pulley.
    
8. A blower absorbs 3.5 kW at its design speed of 650 rpm, and is equipped with a 260 mm diameter, 90 mm wide flat pulley. It is proposed to drive it by a pivoted motor, V-flat arrangement.
   Select a squirrel cage motor and finalise the drive, including pivot location.
    
9. A squirrel cage motor is usually equipped with deep groove ball bearings, but life considerations might require replacement of the drive-end bearing by a larger capacity roller bearing when :
       - the shaft load is heavy due to a small belt pulley for example, or
       - the load overhang ('x' in the diagram) is large.
   An ABB motor t

   life (kh)	40	63
   F0 at x=0 (kN)	7.32	6.29
   FE at x=E (kN)	6.18	5.31

   ype M2BA 280 SMA delivers 75 kW at 1485 rpm via a fully loaded belt drive comprising 5 SPB 3150 belts on 212 and 630 mm diameter pulleys at 889 mm centres. From catalogues   [ABB, Fenner] the pulley width   w = 102 mm, the motor shaft length   E = 140 mm, and shaft radial loads   F corresponding to two different bearing lives at two load positions along the shaft are as tabulated :-
   Will the drive-end ball bearing last for the target life of 25 kh or is a roller bearing needed?
    
10. This concerns part-load belt tensions and components with different load-life equations.
    Select a squirrel cage motor and fixed centre belts to drive an agitator at about 700 rpm for 1 kh per annum. The power demand varies cyclically as shown and a 3-year belt replacement period is acceptable.
    The drive should be compact, but not to the extent that the motor's usual ball bearings have to be replaced by roller bearings.
    For the purposes of this problem, motors' maximum shaft loads tabulated in the Motors chapter refer to loads at the end of the shaft (F_E of the previous problem), to bearing lives of 40 kh, and to a load-life index of n = 2.5.