Effect of change in RPM on gear design
EFFECT OF CHANGE IN RPM ON GEAR DESIGN:
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.
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!!!
Why all this circus? If the crusher rpm matches that of the motor, why not drive the crusher directly avoiding totally all gears?
Thanks for your response. Unfortunately ... the matter is a little more complicated than is represented in the question.
We require you to assume that Gears C and D are essential ... because in our final application there will be work getting done WITHIN this "gearbox" ... by a totally different ... but highly complicated arrangement of stuff ... which I've REMOVED for the sake of simplicity ... and simply REPLACED with gears C and D. Once I know how gears C and D are affected ... then I will know how the real components will be affected and thus gain an idea as to how much stronger we will need to make these internal components.
Please assume that gears C and D are ESSENTIAL. Once we know the effect of HUGE step-down ... and then HUGE step-up on "HARD WORKING" Gears C and D ... we will know the effect on our "ACTUAL" components ... and thus be enabled to make decisions about whether or not to proceed with certain sections of the "internals" that we we will be using in this arrangement as represented by C and D.
The reason the crusher was included was simply to show there is a REAL load being transmitted throughout the entire arrangement ... and thus REAL LOADS on gears C and D.
The total amount of work done has to be less than the output at the prime mover shaft. If some 'work' is being done inside the gear box by C and D to that extent the power delivered to the final load will be reduced.
A single stage reduction and increase of 1:100 at very high power does not seem practical as the torque ratio is also 100 plus friction and other transmission losses.
Based on the info provided, it seems a no brainer that direct A-C-D-F transmission will make C and D similar to A and F.
Maybe some Mech CE may come up with a better analysis.