It is required to design a two-stage spur gear reduction unit with $20^{\circ}$ full depth involute teeth. The input shaft is connected to $10 \mathrm{kW}, 1440 \mathrm{rpm}$ motor through a flexible coupling. The speed of the output shaft shall be approximately 180 $\mathrm{rpm}$. The starting torque of a motor is 150$\%$ of rated torque. The gears are made of plain carbon steel with an ultimate tensile strength of 700 $\mathrm{N} / \mathrm{mm}^{2}$ and heat treated to a surface hardness of 340 $\mathrm{BHN}$. Design the gear and specify the dimensions.

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