Download Cable Pulling, Truck Mounted, Side Arm (Hydraulic Boom) Stress

Cable Pulling, Truck Mounted, Side Arm (Hydraulic Boom)
Stress Analysis
Known:
1. Maximum slope: 17% ( 0.17 x 45⁰ = 7.65⁰ = ϴ )
2. Maximum speed on max slope: 7 mph
3. Maximum speed on level ground: 15 mph
4. Cable length: 1,100 feet
5. Cable unit weight: 11 Lbs/ft
6. At times the 1,100 ft of cable is looped 4 times, lifted 11.2 ft and pulled along the roadbed
7. Coefficient of static friction µ: unknown maybe rubber or plastic
A. Rubber on Sand:
B. Rubber on Rock:
C. Rubber on Solids: µ = 1-4 (Machinery’s Hdbk)
W = Weight of cable = 1,100 ft x 11 Lbs/ft = 12,100 Lbs
The speed at which the cable is pulled affects the power required to pull it, not the force
required to pull it because:
Force x Distance = Work (Lb-ft)
Work/unit time = Power, e.g. (Lb-ft/min)
Therefore the speed is not a factor to be considered for determining load or force on the Arm.
Also the friction actually decreases above a certain velocity1 and static friction is greater than
dynamic (kinetic) friction.2
So for the worst condition of pulling uphill, the total side force on the arm is found from
summing the forces parallel to the slope:
∑p = 0 = P - F – F1 where
P = Total Parallel Force
F = Frictional Force = µN; N = W(cos 7.65⁰) = 12,100 (0.9911) = 11,992Lbs
F = 11,992µ = 11,992( ? ) =
F1 = Parallel Component of Weight = W(sin 7.65⁰) = 12,100 (0.1311) = 1,611Lbs
Solving for
P = F + F1 = 11,992µ + 1,611 =
Vertical load:
Pv = 4 x 11.2ft x 11Lbs/ft = 493Lbs
Calculate Compressive Force in Arm and Tension in Restraining Cable:
1
Ref: Machinery’s Hdbk 21 Ed, p544; Listing 3. At very low velocities the friction is independent of the velocity of
rubbing. As the velocity increases, the friction decreases.
2
Ref: Machinery’s Hdbk 21 Ed, p544: A greater force is required to start a body from a state of rest than to merely
keep it in motion because the friction of rest is greater than the friction of motion.