machine design - ii me 441 lecture 6-2: flexible mechanical elements belts, ropes and chains chapter...

Machine Design - IIME 441

Lecture 6-2: Flexible Mechanical ElementsBelts, Ropes and ChainsChapter 17

Dr. Mohammad A. IrfanOct 12, 201528 Zul Hajj 1436

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Tentative Lecture Schedule:

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Announcement

Quiz No. 2Spur Gear Force AnalysisDate: Sunday Oct 18th

Mid Term Exam : Sunday Oct 25th

Chapter 13 and Chapter 14

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Where do we use belts

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Where do we use belts

For Power Transmission:• Between pulleys• Car: between crankshaft and fan

For Carriage:• Cement Factories

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Belts vs. Chains

Belts Chains

Use When:

Speed:

Disadvantages:

Advantages:

High Speed, Low T High T, Low Speed

2500 < Vt < 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

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Input Parameters:

HP transmittedCenter Distance Working ConditionsLoading ConditionsLife of Belt

Output Parameters:

Belt Sizing:Material (leather, polyamide)Length of BeltWidth of BeltThickness of Belt

Selection of Belts

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Aim of this lecture

To learn how to select a belt (Length, thickness,width, material etc.)

that willtransmit the required HP over the

required distance without breaking or slipping

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Belts Types

1. Flat Belts2. Round Belts3. V- Belts4. Timing Belts

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Belt Nomenclature

13Note: θ is in radians

Cross Belt Geometry

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Belt Tensions

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F1 = Tension on Tight Side

F2 = Tension on Slack Side

feF

F

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Where : f = coefficient of static friction (created) between belt and pulleyφ = θd

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

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22rmFc

Or in terms of belt geometry

g

wVFc

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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/m3

Finally the effect of Fc on the belting equation is:

b

t

feF

F

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Providing Initial Tension

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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 = (F1 - F2 ) V Units: N . m/s = J/s = W

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F1 = Tension on Tight Side

F2 = Tension on Slack Side

Belt Design - INotes:Fa = Allowable Tension in belt (provided by manufacturers)

(Table 17-2 pp. 869) Severity of Flexing is given by pulley correction factor Cp

Table 17-4 pp. 870Correction for velocity Cv is given in Figure 17-9 pp. 867

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N/m

N

m

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

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Note for 600 ft/min Cv = 1

Note: Max limiting speed 6000 ft/min30 m/s

Belt Design - INotes:Fa = Allowable Tension in belt (provided by manufacturers)

(Table 17-2 pp. 869) Severity of Flexing is given by pulley correction factor Cp

Table 17-4 pp. 870Correction for velocity Cv is given in Figure 17-9 pp. 867

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N/m

N

m

Design HP and Nominal HP

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1. Severity of service is given by Ks

Table 17-151. Factor of safety is given by nd

Hence:

Hd = Hnom Ks nd

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

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Electric Motor Car Engine

Forging Hammer Till here

Belt Design - II

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T = Hnom Ks n d / 2 π n find necessary Torque, since 2 π n T = Hd

f‘’ = friction created between pulley and belt due to pulling

f = coeff. of static friction as per table

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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 φs = μs

or φs = Tan-1 μs

Tabulated value of friction

Controlled Angle of slope

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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 φs = μs

or φs = Tan-1 μs

Belt Design - II

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T = Hnom Ks n d / 2 π n find necessary Torque, since 2 π n T = Hd

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 Ks = 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 F1 , F2 , Fi and allowable power

Ha

(c)Test for belt slipping(d)Estimate the FOS

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HW

Flat Belts: Example 17-2Problems: 17-1, 17-3, 17-5, 17-10

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