The torque-speed curve of a 3-phase ac motor nema design type d can be approximated with the parabola: t=-410-5n2+0.0059n +100 where t is in nm and n is in rpm. the motor drives the drum of a hoist (see fig. 5-36), via a gear reducer with the reduction ratio i=60: 1. find the steady state ascending speed in m/s of a crate with mass m=1500 kg, knowing that the drum has a radius of 180 mm. consider that:

The speed of the crate is 0.52m/S

Explanation:

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The first step to solve this problem is to find the necessary torque to raise the load, for this we use the following equation

T=mgr

m=mass=1500kg

t=torque

g=gravity=9.81m/s^2

r=radius=180mm=0.18m

T=(1500)(0.18)(9.81)=2648.7Nm

the second step is to find the torque on the motor side using the reduction ratio for this we divide the torque found by 60

The third step is to find the turning speed with the torque speed equation and solving the quadratic equation

T=

The fourth step is to solve the quadratic equation which results in N =1656.6RPM(remember take the positive solution)

the fifth step is to find the speed of rotation at the output of the speed reducer for this we divide by 60

finally to find the speed of the box remember that it is the product of the speed of rotation in Rad / s by the radius in m

V=

The speed of the crate is 0.52m/S