Problem:

The driving shaft shown in Figure (2) is used to transmit the power from the motor (which is connected to pulley A via a flat belt) to the gear at B (which is meshed with the driving spur gear of the sheet metal bender). Pulley A receives power from a motor through a belt with the belt tensions shown. The power is transmitted through the shaft and delivered to the gear B. The forces acting on gear B could be resolved into two components (T and T2). Assume T2 is 15 % of T, the bending moment is completely reversed and the torque is constant. The shaft is machined from Cold Drawn Steel AISI 1020 with E=207 GPa. Using factor of safety of 2.5, determine: (a) The minimum allowable diameter of the shaft based on a static yield analysis using the distortion energy theory. Assume sharp fillet radius at the shoulder. (b) The minimum allowable diameter of the shaft based on a Modified Goodman fatigue-failure criterion. Assume sharp fillet radius at the shoulder. (c) The dimensions of the square key used to transmit the torque between the shaft and the gears if the key is made from AISI 1006 HR steel with 2.5 factor of safety. (d) If the gear is clamped on the shaft using medium drive fit, assume gear is made up from the same shaft material, what is the value of the induced tangential and radial stress on the shaft and gear and what is the minimum transmitted torque? 300 450 45 N 400 300 N 150 250 dia. 300 dia. T2 B T Dimensions in millimeters. Figure (2) The driving shaft shown in Figure (2) is used to transmit the power from the motor (which is connected to pulley A via a flat belt) to the gear at B (which is meshed with the driving spur gear of the sheet metal bender). Pulley A receives power from a motor through a belt with the belt tensions shown. The power is transmitted through the shaft and delivered to the gear B. The forces acting on gear B could be resolved into two components (T and T2). Assume T2 is 15 % of T, the bending moment is completely reversed and the torque is constant. The shaft is machined from Cold Drawn Steel AISI 1020 with E=207 GPa. Using factor of safety of 2.5, determine: (a) The minimum allowable diameter of the shaft based on a static yield analysis using the distortion energy theory. Assume sharp fillet radius at the shoulder. (b) The minimum allowable diameter of the shaft based on a Modified Goodman fatigue-failure criterion. Assume sharp fillet radius at the shoulder. (c) The dimensions of the square key used to transmit the torque between the shaft and the gears if the key is made from AISI 1006 HR steel with 2.5 factor of safety. (d) If the gear is clamped on the shaft using medium drive fit, assume gear is made up from the same shaft material, what is the value of the induced tangential and radial stress on the shaft and gear and what is the minimum transmitted torque? 300 450 45 N 400 300 N 150 250 dia. 300 dia. T2 B T Dimensions in millimeters. Figure (2)