Design the gears that would be suitable for a commercial spur gear-train consisting of an input pinion, an idler gear, and an output gear. The pinion is required to mesh with the idler gear which in turn must mesh with the output gear. The required gear ratio for the gearset is 3.5 to 1. The speed of the input shaft is a constant 3000 rpm and the horsepower acting on the input shaft is 25 hp. The required service life of the gearset is 5 years of one-shift operation. Also, the operating temperature of the three gears in the gear-train is 200°F. The gearset design must achieve fatigue factors of safety for both bending and pitting resistance of at least 2 but no greater than 6 Recall that the design of spur gears is an iterative procedure. This is explained in the final two paragraphs (before the problems) on page 772. Also, note that Chapter 18 presents a case study of a power transmission system. The chapter provides a detailed outline which should help to clarify a logical design sequence for this gearset problem The following are some suggested specifications and assumptions that may prove helpful for the initial iteration of the gearset design problem: (i) The diametral pitch is P-6 teeth/inch and the pressure angle is φ-20 (ii) The number of teeth on the pinion gear is 14 and the number of teeth on the idler gear is 17 (iii) The teeth are standard AGMA full depth profiles, ground, uncrowned, and the loads are uniform (iv) The loads are applied at the highest point of single tooth contact (HPSTC) and a minimum quality number of Qv -6 is desired (v) The pinion, the idler, and the gear are Grade 1 -nitralloy steel with a Poisson's ratio v=0.28, a modulus of elasticity E-30x10° psi, and a Brinell hardness number HB-300 Hand calculations must be presented in the report for the initial design iteration. However, a spreadsheet must then be used for further iterations. Include free body diagrams of the pinion, the idler and the gear which clearly show the transmitted loads on the meshing gear teeth