5 Friction Applications 341x22

FRICTION (applications of friction)

MAIT

Q. 1: What is belt? How many types of belt are used for power transmission? Solution: The power or rotary motion from one shaft to another at a considerable distance is usually transmitted by means of flat belts, V V-belts or ropes, running over the pulley. But the pulleys contain some friction. Types of Belts: Important types of belts are:

Flat Belt: The flat belt is mostly used in the factories and workshops. It is used where here a moderate amount of power is to be transmitted, from one pulley to another, when the two pulleys are not more than 10m apart. V-Belt: The V-belt belt is mostly used where a great amount of power is to be transmitted, from one pulley to another, when the two pulleys are very near to each other. Circular Belt or Rope: The circular belt orr rope is mostly used where a great amount of power is to be transmitted from one pulley to another, when the two pulleys are more than 5m apart.

Q. 2: Explain how many types of belt drive used for power transmission? Also derive their velocity ratio. Solution: There are three types of belt drive: 1) Open belt drive 2) Cross belt drive 3) Compound belt drive

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FRICTION (applications of friction)

MAIT

(1) Open Belt Drive When the shafts are arranged in parallel and rotating in the same direction, open belt drive is obtained. In the following diagram m, pulley 'A' is called as driver pulley because it is attached with the rotating shaft.

Velocity Ratio (V.R.) for Open Belt Drive Drive:

Consider a simple belt drive (i.e., one driver and one follower) as shown in above fig: Let D1 = Diameter of the driver N1 = Speed of the driver in R.P.M. D2, N2 = Corresponding values for the follower Length of the belt, that es over the driver, in one minute = Π.D1.N1 Similarly, Length of the belt, that hat es over the follower, in one minute = Π.D2.N2

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FRICTION (applications of friction)

MAIT

Since the lengthh of belt, that es over the driver in one minute is equal to the length of belt that es over the follower in one minute, therefore: Π.D1.N1 = Π.D2.N2 Or, velocity ratio = N2/N1 = D1/D2 If thickness of belt 't' is given then t)/(D2 + t) V.R = N2/N1 = (D1 + t) (2) Cross Belt Drive: When the shafts are rotating in opposite direction, cross belt drive is obtained. In the diagram, pulley 'A' is called as driver pulley because it is attached with the rotating shaft. Velocity ratio is same as for open belt V.R. = N2/N1 = D1/D2 If thickness of belt 't' is given then V.R = N2/N1 = (D1 + t)/(D2 + t)

(3) Compound Belt Drive: When a number of pulleys are used to transmit power from one shaft to another then a compound belt drive is obtained.

Velocity Ratio for Compound Belt Drive

N4/N1 = (D1.D3)/(D2.D4)

Q. 3: What is slip of the belt? How slip of belt affect the velocity ratio? Solution:

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FRICTION (applications of friction)

MAIT

When the driver pulley rotates, it carries the belt, due to a firm grip between its surface and the belt. The firm between the pulley and the belt is obtained by friction. This firm grip is known as frictional grip. But sometimes the frictional grip is not sufficient. This may cause some forward motion of the driver pulley without carrying the belt with it. This means that there is a relative motion between the driver pulley and the belt. The difference between the linear speeds of the pulley rim and the belt is a measure of slip. Generally, the slip is expressed as a percentage. In some cases, the belt moves faster in the forward direction, without carrying the driver pulley with it. Hence in case of driven pulley, the forward motion of the belt is more than that of driver pulley. Slip of belt is generally expressed in percentage (%). Let v = Velocity of belt, ing over the driver pulley/min N1 = Speed in R.P.M. of driver N2 = Speed in R.P.M. of follower S1 = Slip between driver and belt in percentage S2 = Slip between follower and belt in percentage The peripheral velocity of the driver pulley

Now due to Slip between the driver pulley and the belt, the velocity of belt ing over the driver pulley will decrease Velocity of belt

Now with this velocity the belt over the driven pulley, Now Velocity of Driven = Velocity of Belt - Velocity of belt X (S2 /100)

This formula is used when total slip in % is given in the problem NOTE: If Slip and thickness both are given then, Velocity ratio is,

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FRICTION (applications of friction)

MAIT

Q. 4: Write down different relations used in belt drive. Solution: Let: D1 = Diameter of the driver N1 = Speed of the driver in R.P.M. D2 = Diameter of the driven or Follower N2 = Speed of the driven or follower in R.P.M. R1 = Radius of the driver R2 = Radius of the driven or Follower t = Belt thickness (if given) X = Distance between the centers of two pu pulleys α = Angle of lap (Generally less than 10º) θ = Angle of (Generally greater than 150º) (always express in radian.) µ = Coefficient of friction s = Total slip in percentage (%) L = Total length of belt

FORMULA FOR Velocity Relation:

OPEN BELT DRIVES V.R = N2/N1

Thickness is considered Slip is considered Slip and thickness both are considered Angle of Angle of lap Length of belt

θ = Π – 2α Sinα = (r1–r2)/X

Q. 5: Prove that the ratio of belt tension is given by the T1/T2 = eµq Solution: Let T1 = Tension in the belt on the tight side T2 = Tension in the belt on the slack side θ = Angle of efficient of friction between the belt and pulley. µ = Co-efficient α = Angle of Lap Consider a driven or follower pulley. Belt remains in with EBF. Let T1 and T2 are the tensions in the tight side and slack side. Angle EBF called as angle of = Π.–2α Consider a driven or follower pulley. Belt remains in with NPM. Let T1 and T2 are the tensions in the tight side and slack side.

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FRICTION (applications of friction)

MAIT

Let T be the tension at point M & (T + δT) be the tension at point N. Let d? be the angle of of the element MN. Consider equilibrium in horizontal Reaction be 'R' and vertical reaction be µR. Since the whole system is in equilibrium, i.e., ∑V = 0; Tsin (90 – δθ/2) + µR - (T + δT)sin(90 – δθ/2) = 0 Tcos (δθ/2) + µR = (T + δT) cos (δθ/2) Tcos (δθ/2) + µR = Tcos(δθ/2) + δTcos(δθ/2) µR = δTcos(δθ/2) Since δθ/2 is very small & cos0° = 1, So cos(δθ/2) = 1 µR = δT ...(i) ∑H = 0; R–Tcos(90 – δθ/2)–(T + δT)cos(90 – δθ/2) = 0 R = Tsin(δθ/2) + (T + δT)sin(δθ/2) Since δθ/2 is very small So sin(δθ/2) = δθ/2 R = T(δθ/2) + T(δθ/2) + δT(δθ/2) R = T.δθ + δT(δθ/2) Since δT(δθ/2) is very small So δT(δθ/2) = 0 R = T.δθ ...(ii) Putting the value of (ii) in equation (i) µ.T.δθ = δT or, δT/T = µ.δθ

Integrating both side: Where θ = Total angle of ln(T1/T2) = µ.θ or, T1/T2 = eµ.θ Ratio of belt tension = T1/T2 = eµθ Belt ratio is also represent as 2.3log(T1/T2) = µ.θ Note that θ is in radian In this formula the main important thing is Angle of (θ) For Open belt drive: Angle of (θ) for larger pulley = Π + 2α Angle of (θ) for smaller pulley = Π – 2α For cross belt drive: Angle of (θ) for larger pulley = Π + 2α Angle of (θ) for smaller pulley = Π + 2α (i.e. for both the pulley, it is same) But for solving the problems, We always take the Angle of (θ) for smaller pulley Hence, Angle of (θ) = Π – 2α – for open belt Angle of (θ) = Π + 2α – for cross belt

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