Consider the simplified transmision sample problem shown in Figure I below. In this figure, mating gears...

   

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Consider the simplified transmision sample problem shown in Figure I below. In this figure, mating gears were shown to only exert tangential forces on each other. In reality, mating spur gear teeth will exert both tangential forces and radial forces' due to the involute profile shape of the teeth (see Chapter 15, Figure 15.7). Let the diameters of gears B and D be 4.25 in while the diameters of gears A and C be 2.25 in. All other dimensions and the input torque are shown in the Figure. (20 pts) For the purposes of shear and bending moments, model the shaft supporting gears A and D as a single ("effective") shaft. Develop and plot shear and bending moment diagrams for shear and bending in the horizontal (x- z) plane (V,(x)and M,(x) and for bending in the vertical (x – y) plane (V,(x) and M,(x)) for both the "effective" shaft and for the shaft supporting gears B and C. Assume x = 0 corresponds to the bearing locations II and IV. Timput = 4150(lbf. in) Trouse Transmission in low gear a = 1.5 in. b = 4 in. c = 1.5 in. T output) Fis Flls Fils F4 FAB Fwa Toutput FBAZ Fils FCD Fls FpC FIV4 Figure 1: Transmission Example Consider the simplified transmision sample problem shown in Figure I below. In this figure, mating gears were shown to only exert tangential forces on each other. In reality, mating spur gear teeth will exert both tangential forces and radial forces' due to the involute profile shape of the teeth (see Chapter 15, Figure 15.7). Let the diameters of gears B and D be 4.25 in while the diameters of gears A and C be 2.25 in. All other dimensions and the input torque are shown in the Figure. (20 pts) For the purposes of shear and bending moments, model the shaft supporting gears A and D as a single ("effective") shaft. Develop and plot shear and bending moment diagrams for shear and bending in the horizontal (x- z) plane (V,(x)and M,(x) and for bending in the vertical (x – y) plane (V,(x) and M,(x)) for both the "effective" shaft and for the shaft supporting gears B and C. Assume x = 0 corresponds to the bearing locations II and IV. Timput = 4150(lbf. in) Trouse Transmission in low gear a = 1.5 in. b = 4 in. c = 1.5 in. T output) Fis Flls Fils F4 FAB Fwa Toutput FBAZ Fils FCD Fls FpC FIV4 Figure 1: Transmission Example

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