Question
Consider the compound gear train shown in Figure 2. The input shaft (shaft 1) rotates in a clockwise direction at 100 rpm. The pitch diameters of gears A through E are 10 cm, 30 cm, 6 cm, 7 cm and 20 cm. What are the speed and direction of rotation of the output shaft (shaft 4)? If the input power is 100 kW and the efficiency of the gear train is 100%, then what is the output torque from shaft 4? Can this gear train be rearranged as a reverted gear train1 in which the axes of all gears lie in the same plane? If yes, then sketch the layout of this reverted gear train? What is the benefit of a reverted design in this case?
Explanation / Answer
2a. Speed and direction of shaft4 Direction Counter-clockwise. The gears reverse the directionon each shaft Shaft 1 clockwise 2 counterclockwise 3 clockwise 4 counterclockwise . Speed. Shaft 2 = 10cm/30cm Shaft 1 = 1/3 Shaft 1 Shaft 3 = 6cm/7cm Shaft 2 = 6/7 Shaft 2 Shaft 4 = 7cm/20cm Shaft 3 = 7/20 Shaft 3 . Shaft 4 = 1/3*6/7*7/20 Shaft 1 = 1/10 Shaft 1 = 10 rpm . 2b. Torque Shaft 4 = P/ P = 100kw = 10 rmp *2rads-min/60sec-rev = 95.5 N-m . 2c. Reverted Gear Train Yes they can -- you'll have to make a sketch, but they line upperfectly. The center to center distance between Shafts 1 and 2 is (30 + 10)/2 = 20 cm If you line shaft 3 up in the direction of shaft 1, you canplace shaft 4 directly over shaft 1. The center to centerdistances is: 6cm/2 + 7cm + 20cm/2 = 20cm. . You'll have to look up in your book for the reasons, but Iimagine that you would have less off-center torque on the gearboxcasing. You'd also have advantages in a vehicle because youcould make the center of rotation for both be along the center lineof the car. Yes they can -- you'll have to make a sketch, but they line upperfectly. The center to center distance between Shafts 1 and 2 is (30 + 10)/2 = 20 cm If you line shaft 3 up in the direction of shaft 1, you canplace shaft 4 directly over shaft 1. The center to centerdistances is: 6cm/2 + 7cm + 20cm/2 = 20cm. . You'll have to look up in your book for the reasons, but Iimagine that you would have less off-center torque on the gearboxcasing. You'd also have advantages in a vehicle because youcould make the center of rotation for both be along the center lineof the car.