You are required to design a speed gearbox made up of spur gears with three stages of speed reduction apart from the belt-pulley stage) to impart a total of 20 spindle speeds with 5 speeds in stage 1, 2 speeds each in the second and the third stages of the gearbox. The spindle will be driven from a 7 kW motor with 1420 rpm. The motor speed will be reduced first at the belt-pulley stage before it is transmitted to the three stage-speed gearbox for further reduction. The following additional information are available for the design:

• Lowest speed of the spindle is 63 rpm.
• Efficiency of the belt pulley drive is 98.5%
• Minimum allowable diameter of the driving pulley is 100 mm and the maximum diameter of the driven pulley is 200 mm.
• The minimum and maximum allowable transmission ratios are 1:4 and 2:1 respectively (for spur gears).

For the above design perform the following:

a) Write down the structural formula of the gearbox.

b) Draw the Ray (Structure) diagram for the above structure formula and indicate the distance for 1 log Φ , the range ration in number of divisions, the spindle speeds, shaft numbers etc.

c) Identify the critical stage (group) in the ray diagram, drawn under Q1 (b) and give justifications for your answer.

d) Calculate the required value of the geometrical progression ration for the critical group and select the maximum possible standard value of progression ratio, Φ from the consideration that the speed transmission range ration in any gearbox stage with spur gears is less that equal to 8 (Range ratio £ 8).

e) Calculate for the above value standard value of Φ the boundary conditions in number of log Φ divisions for the belt-pulley and the gearbox stages for the construction of the speed chart.

f) Calculate the value of the highest speed of the spindle (20 ^th Speed) for the given value of Φ and the lowest given value of the spindle speed.

g) Calculate the total number of log Φ divisions from the motor speed to the lowest spindle speed.