Lift Device Using Acme Screws
Design a device similar to that sketched in Figure 174. An electric motor drives the worm at a speed of 1750 rpm. The two Acme screws rotate and lift the yoke, which in turn lifts the hatch. See Example Problem 171 for additional details. Complete the entire unit, including the worm gear set, the chain drive, the Acme screws, the bearings, and their mountings. The hatch is 48 inches wide and 155 inches long, and its weight is 25,000 lbs. The screws in Example Problem 17-1 Figure 174. The total weight of the hatch is 25,000 lbs, divided equally between the two screws. Select a satisfactory screw from Table 171 based on tensile strength, limiting the tensile stress in the threads to 5000 psi. For the screw thus designed, compute the lead angle and the motion of the yoke, which will be 24 inches to be completed in 15.0 seconds or less. Use a coefficient of friction of 0.15.
Solution: The load to be lifted places each screw in direct tension. Therefore, the required tensile stress area is F/A = 12,500 lbs / 10,000 lbs/in^2 = 1.25 in^2.
From Table 171, a 1-inch diameter Acme thread screw with four threads per inch would provide a tensile stress area of 1.266 in^2. For this screw, each inch of length of a nut would provide 2.341 in^2 of shear stress area in the threads. The required shear area is then 12,500 lbs / 5000 lbs/in^2 = 2.50 in^2.
Then the required length of the yoke would be h = 2.5 in^2 / 1.25 in = 2.0 inches.
For convenience, let's specify h = 1.25 inches. The lead angle is (remember that L = p = 1/n = 1/4 = 0.250 inches) 0.250 = tan^(-1) = tan^(-1)(3.39) = 1.3429 degrees.
The torque required to raise the load can be computed from Equation (17-10):
FDp[(cosθtanφ) + f] = (1809 lbs-in)[0.968(0.15)(0.0592)] = 1809 lbs-in.
The efficiency can be computed from Equation (17-7):
η = 2τu / (FDp[(cosθtanφ) + f]) = 2(1809 lbs-in) / (1809 lbs-in) = 1.
The torque required to lower the load can be computed from Equation (17-11):
FD[(fcosθtanφ) + f] = (12,500 lbs)(1.3429 in)[0.15(0.968)(0.0592)] = 796 lbs-in.
