Need help on gear train problem MDM practice

[Engineer_562]

Hello All,

I am preparing for MDM exam and came across this problem. I have solved it with best of my knowledge and not getting the right answer. Attached is the problem and here is my solution. Can you tell what is wrong with this solution.

eq 1: Wa/Wb= Nb/Na

eq 2: Wd/We=Ne/Nd

solving for Nd using given data in problem. I get 48 teeth, which is not the right answer. 

 

[Saurabh9978]

I get 96 teeth , not sure what is wrong with my calculation 

 

[Engineer_562]

Saurab. Thanks!

Basically, we should be able to write equations for where gear teeth meet, relating velocities to number of teeth. I know that part. I am just not sure how to relate the rod from center of A to rod between B and D.

 

[monty01]

Hey 562, i'm not sure if you're still in need of some help with this one, but here goes anyway:

One of the keys here is that the velocities of B and D are the same (both tangential and rotational).  Because the ring gear is fixed, the velocity of gear B center is r(b)*w(b).  Per the diagram, gear b rotates ccw about its axis, and rotates cw about the sun gear.  Gear D will follow along in the same manner.

Now that we know the tangential velocity of the center of gear D, we can look at the contact point between D & E.  V(contact) = V(d) + V(d/contact) <-- meaning velocity of center of gear d RELATIVE to contact point.  Here is where directions will make a difference, and to clarify, i'm working with the right side view of your graphic above.  V(d) = r(b)w(b) because V(d) = V(b), and V(d/contact) = - r(d)w(d).  The negative is important, because due to its rotation direction, the velocity of d RELATIVE to contact point is opposite that of V(d).

Now, V(contact) is also equal to r(e)w(e).  Thus,

r(e)w(e) =  r(b)w(b) - r(d)w(b)

w(e) & w(b) are both known or can easily be calculated.  The radius ratios can be replaced with number of teeth ratios, then it's just a math exercise to find N(d).

Hope this helps!   

On edit:  When I say tangential velocities of D or B above, I'm referring to the center of the gears.