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