Effect of change in rpm on gear design

EFFECT OF CHANGE IN RPM ON GEAR DESIGN:

Scenario A:

In the accompanying diagram … input from the motor (Gear A) is stepped down 100 times from 1000 RPM to 10 RPM at Gear B. After being transmitted through Gears C and D at just 10 RPM … this 10 RPM Output from Gear D is stepped up 100 times using the step-up arrangement of Gears E and F. Gear F is now rotating at the original 1000 RPM and transmitting power to the Crusher which consumes a hypothetical 10,000 HP.

Scenario B:

How would the “STRENGTH DESIGN” of Gears C and D compare with their “STRENGTH DESIGN” in Scenario A … if we omitted the step-down and step-up Gearing arrangements. In the absence of these Step-down and Step-up arrangements … the motor shaft goes directly into Gear C and causes rotation of both Gears C and D at the much higher 1000 RPM … in turn causing Gear D to output directly into the Crusher at 1000 RPM. In both scenarios the Crusher still consumes the same amount of Power (10,000 HP). In both (ideal) Scenarios the motor is likewise outputting 10,000 HP.

1) Which … (if any) … of these two arrangements would require that Gears C and D be made bigger and stronger?

2) Assuming gears C and D would have to be strengthened in the Step-down / Step-up arrangement as per Scenario A … would there be a direct relationship between the Stepping Ratio and the Strengthening of Gears C and D? In other words would Gears C and D have to be 100 times stronger if the Step-down and Step-up ratios were 100:1 and 1:100 respectively?

3) If answer to question 2 is “yes” … does 100 times stronger necessarily mean 100 times bigger, thicker, etc.? … or is this relationship NOT linear? In other words ... would it be possible that something like a 10% increase in gear thickness will result in a 100 fold strengthening?

Hundred fold thanks in advance!!!

Tony

H:W