Machine Design - II ME 441 Lecture 6-2: Flexible Mechanical Elements Belts, Ropes and Chains Chapter 17 Dr. Mohammad A. Irfan Oct 12, Zul Hajj 1436

2 Tentative Lecture Schedule:

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Announcement Quiz No. 2 Spur Gear Force Analysis Date: Sunday Oct 18 th Mid Term Exam : Sunday Oct 25 th Chapter 13 and Chapter 14 4

Where do we use belts 5

For Power Transmission: Between pulleys Car: between crankshaft and fan For Carriage: Cement Factories 6

Belts vs. Chains Belts Chains Use When: Speed: Disadvantages: Advantages: High Speed, Low T High T, Low Speed 2500 < V t < 7000 ft./min. V < 1500 ft./min. Must design with standard lengths, wear, creep, corrosive environment, slip, temp., when must have tension need idler Must be lubricated, wear, noise, weight, vibration Quiet, flexible, low cost Strength, length flexibility

Belt Design 8 Input Parameters: HP transmitted Center Distance Working Conditions Loading Conditions Life of Belt Output Parameters: Belt Sizing: Material (leather, polyamide) Length of Belt Width of Belt Thickness of Belt

Selection of Belts 9

Aim of this lecture To learn how to select a belt (Length, thickness,width, material etc.) that will transmit the required HP over the required distance without breaking or slipping 10

Belts Types 1. Flat Belts 2. Round Belts 3. V- Belts 4. Timing Belts 11

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Belt Nomenclature 13 Note: θ is in radians

Cross Belt Geometry 14

Belt Tensions 15 F 1 = Tension on Tight Side F 2 = Tension on Slack Side Where : f = coefficient of static friction (created) between belt and pulley φ = θ d Is the belting equation in simple form For derivation see article 6-8 in Statics Book by Meriam Note: 1. Friction is created when you pull a belt on the neck of a pulley Note: 2. The above equation is valid when the belt is not slipping rather slip is impending

If we assume that there is no slippage in the belt, then the linear velocity of each pulley rim is equal to the belt velocity. Therefore, the rim velocities (linear) of the two pulleys are equal.

Centrifugal Forces on Belt 17 Or in terms of belt geometry Where V = belt velocity = π d n m/s w = γ b t is the weight of the belt (per unit length of the belt) ; b and t belt width and thickness in meters γ is weight density of the belt in N/m 3 Finally the effect of F c on the belting equation is: b t

Providing Initial Tension 18 Initial Tension F is provided in the belts so that the belts are tight and can transmit torque. Without initial tension the belts will not transmit any torque

Transmitted Power (Horse Power) H = (F 1 - F 2 ) V Units: N. m/s = J/s = W 19 F 1 = Tension on Tight Side F 2 = Tension on Slack Side

Belt Design - I Notes: F a = Allowable Tension in belt (provided by manufacturers) (Table 17-2 pp. 869) Severity of Flexing is given by pulley correction factor C p Table 17-4 pp. 870 Correction for velocity C v is given in Figure 17-9 pp N/m N m

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22 Note there is a minimum pulley dia. to have some minimum angle of contact

23 Note for 600 ft/min C v = 1 Note: Max limiting speed 6000 ft/min 30 m/s

Belt Design - I Notes: F a = Allowable Tension in belt (provided by manufacturers) (Table 17-2 pp. 869) Severity of Flexing is given by pulley correction factor C p Table 17-4 pp. 870 Correction for velocity C v is given in Figure 17-9 pp N/m N m

Design HP and Nominal HP Severity of service is given by K s Table Factor of safety is given by n d Hence: H d = H nom K s n d Motor HP So the motor HP is increased by 2 factors to become the Design HP. Design HP is the HP for which you design the belt, not motor HP

26 Electric Motor Car Engine Forging Hammer Till here

Belt Design - II 27 T = H nom K s n d / 2 π n find necessary Torque, since 2 π n T = H d f ‘ ’ = friction created between pulley and belt due to pulling f = coeff. of static friction as per table

Recall: Angles of Friction (GE 201 Statics) Consider block of weight W resting on board with variable inclination angle  No friction No motion Recall: Tan φ s = μ s or φ s = Tan -1 μ s Tabulated value of friction Controlled Angle of slope

Recall: Angles of Friction (GE 201 Statics) Consider block of weight W resting on board with variable inclination angle  No friction No motion Motion impending Motion Recall: Tan φ s = μ s or φ s = Tan -1 μ s

Belt Design - II 30 T = H nom K s n d / 2 π n find necessary Torque, since 2 π n T = H d f ‘ ’ = friction created between pulley and belt due to pulling f = coeff. of static friction as per table

Belt Design Problem CW A polyamide A-3 flat belt 150 mm wide is used to transmit 11 kW under light shock conditions where K s = 1.25 and a FOS 1.1 is appropriate. The shafts are 2.4 m apart. The 150 mm driving pulley rotates at 1750 rpm with loose side on top. The driver pulley is 450 mm in diameter. (a) Estimate the Centrifugal Force and Torque (b) Estimate the allowable F 1, F 2, F i and allowable power H a (c) Test for belt slipping (d) Estimate the FOS 31

HW Flat Belts: Example 17-2 Problems: 17-1, 17-3, 17-5,