a machine must be driven at 100 r/s from a belt pulley of 600 mm diameter revolving at 72 r/s . the maximum tensile force on the belt must not exceed 3000n .assume that the ratio of the tensile force is 2,5:1. A Diameter of the driven pulley. B the power in kW that can be transmitted
To find the diameter of the driven pulley (A) and the power in kW that can be transmitted (B), we need to use the concept of speed ratio and power transmission in belt drives.
Speed Ratio (SR) is defined as the ratio of the rotational speed of the driver pulley to the rotational speed of the driven pulley. It is given by the formula:
SR = N₁/N₂
Where N₁ is the rotational speed of the driver pulley and N₂ is the rotational speed of the driven pulley.
From the given information, we know that the driver pulley has a diameter of 600 mm and is revolving at 72 r/s. We also know that the driven machine must be driven at 100 r/s.
First, let's calculate the speed ratio:
SR = 72 r/s / 100 r/s
SR = 0.72
Now, the belt tension ratio is given as 2.5:1, meaning the tension on the tight side of the belt is 2.5 times the tension on the slack side of the belt.
Let's assume the tension on the slack side of the belt is T. Then, the tension on the tight side of the belt will be 2.5T.
The maximum tensile force on the belt is given as 3000 N. So we have:
2.5T - T = 3000 N
1.5T = 3000 N
T = 2000 N
Now, let's calculate the belt tensions on both sides:
Tension on the slack side = T = 2000 N
Tension on the tight side = 2.5T = 2.5 * 2000 N = 5000 N
Next, we can use the belt power transmission formula to find the power in kW that can be transmitted:
P = (T₁ - T₂) * v / 1000
Where P is the power in kW, T₁ is the tension on the driver pulley side, T₂ is the tension on the driven pulley side, and v is the velocity of the belt in m/s.
To find the velocity of the belt, we need to calculate the circumference of the driver pulley:
Circumference = π * Diameter
Circumference = π * 600 mm
Circumference = 1884.96 mm = 1.88496 m
Now let's calculate the power transmission:
P = (5000 N - 2000 N) * 1.88496 m/s / 1000
P = 5.9448 kW
Therefore, the diameter of the driven pulley (A) is unknown and the power in kW that can be transmitted (B) is 5.9448 kW.