Gear Train question with centre distance limit

[Moranovich]

Hello please see my problem below,

1. A gear train is to be designed to transmit power from shaft 1 to shaft 2
with the following condition:
(i) Shaft 1 (driven by an electric motor) rotates at 100 revs min–1.
(ii) Shaft 2 is to rotate at 400 revs min–1 in the opposite direction to shaft
1 against a load of 200 Nm.
(iii) The centre of shaft 1 is 300 mm from shaft 2.
(iv) The minimum number of teeth on any gear is 15, all gears must have
a multiple of 5 teeth and have a module of 2 mm.
(v) The maximum number of gears permissible is 4 gears and the
diameter of the maximum gear must be minimised.
(vi) The centres of the gears should lie on a line which is as close to
straight as possible.
(vii) All shafts have a frictional resistance of 5 Nm.3. Attempt at solution:

I have worked out a gear train with 4 gears (2 idlers) so the 1st and 4th gear turn in opposite directions. This gives me the correct final speed 400rpm but not the correct center distance 300mm.

N = no of teeth
N2/N1 = 15/60 = 0.25 100rpm/0.25 = 400rpm at gear 2
N2/N3 = 15/30 = 0.5 400rpm x 0.5 = 200rpm at gear 3
N3/N4 = 30/15 = 2 200rpm x 2 = 400rpm at gear 4

Also I have considered 2 gears but the statement in the question diameter of the maximum gear must be minimised. makes me think this is not correct, but it gives me the correct center distance!

Center = (PCD + PCD)/2 Pitch Circle Diameter
PCD = N x M N=no of teeth M = module ie 2

PCD1= 240 x 2 = 480
PCD2= 60 x 2 = 120
center = (480+120)/2 = 300mm

Please help I have been at this for so long...

Many thanks.

 

[Moranovich]

Apologies was very tired when posted that yesterday!

Here is the rest of the question.

Carry out the following:
(a) Design a gear train which satisfies the above criteria. Use a sketch to
illustrate your design, label the gears A, B, C, etc. from the driver to
the driven gear, and state the number of teeth on each gear.
(b) Determine the input power required at shaft 1.
(c) Specify the efficiency of the gear train as a percentage.
(d) Determine an equation for the efficiency of the gear train in terms of
the load (torque) on shaft 2 (all other factors remaining constant).

 

[JimmyTheBlue]

Was just looking at this one. A quick bit scrap programming on Python gave me -
Diameter: 0.3 N1: 80 N2: 75 N3: 25 N4: 20 Speed: 400.0
Diameter: 0.3 N1: 80 N2: 80 N3: 20 N4: 20 Speed: 400.0

Mathematically -
-> We know N1 = 4N4 by the gearing ratio alone.
-> We know 300 = N1 + 2N2 + 2N2 + N4
-> Thus 300 = 5N4 + 2N2 + 2N3
-> Take minimum value on N4: 15.
-> Thus 225 = 2N2 + 2N3, which doesn't give an integer solution.
-> Take higher value for N4: 20.
-> Thus 100 = N2 + N3, which has integer solutions of factor 5.
-> N2 and N3 are idle gears, so can be any number within the constraints given.
-> Gives a number of solutions.

Bit trial and error, but it gets there.

 

[Big Jock]

JimmyTheBlue and Moranovich is this correct? Seems all a bit too straight forward...

 

[Mollycoddle]

Was just looking at this one. A quick bit scrap programming on Python gave me -
Diameter: 0.3 N1: 80 N2: 75 N3: 25 N4: 20 Speed: 400.0
Diameter: 0.3 N1: 80 N2: 80 N3: 20 N4: 20 Speed: 400.0

Mathematically -
-> We know N1 = 4N4 by the gearing ratio alone.
-> We know 300 = N1 + 2N2 + 2N2 + N4
-> Thus 300 = 5N4 + 2N2 + 2N3
-> Take minimum value on N4: 15.
-> Thus 225 = 2N2 + 2N3, which doesn't give an integer solution.
-> Take higher value for N4: 20.
-> Thus 100 = N2 + N3, which has integer solutions of factor 5.
-> N2 and N3 are idle gears, so can be any number within the constraints given.
-> Gives a number of solutions.

Bit trial and error, but it gets there.

Hi, I may sound dopey but I've read my coursework material, the question and this reply and still can't understand it fully. Please could you explain the mathematical side for a fool ?
Really struggling with this aspect of the course.
Thanks greatly in advance.

 

[Mech01]

Hi, I may sound dopey but I've read my coursework material, the question and this reply and still can't understand it fully. Please could you explain the mathematical side for a fool ?
Really struggling with this aspect of the course.
Thanks greatly in advance.

Did you get there in the end?