Acceleration after gearbox

aand74

Member
A
Join Date
Dec 2005
Location
Deinze
Posts
131
From an existing configuration I know the default set acceleration of the motor in rev/sec².
Attached to the motor is a gearbox with ratio 1/10 (gearbox output is 10 times slower then motor).
To know the default acceleration after the gearbox, do I have to devide the motor acceleration by 10 or by 100 (square)?
 
divide by 10:


TL;DR


Unit Analysis (multiply by 1)



Code: 
1 GearboxOutRev(olutions) = 10 MotorRev(olutions)





 1  GearboxOutRev
--  -------------   = 1 (unity)
10    MotorRev




Acceleration:


    MotorRev
 A  --------
        2
       s
 


 = A x 1
because multiplying by unity does not change the quantity.






And since [1/10 GearboxOutRev/MotorRev] is also unity, we can substitute tha, in blue below, t for unity:

Code: 
      MotorRev    [COLOR=Blue][B]  1 GearboxOutRev[/B][/COLOR]
=  A  --------  x  [B][COLOR=blue]-- -------------[/COLOR][/B]
          2        [B][COLOR=blue]10   MotorRev[/COLOR][/B]
         s




    1        MotorRev  GearboxOutRev
=  --  x  A  --------  -------------
   10            2        MotorRev
                s




    1        GearboxOutRev
=  --  x  A  -------------
   10             2
                 s
Calculus


Code: 
                      1
 GearboxOutRev   =   --  x  MotorRev
                     10      


dGearboxOutRev    d(1/10 MotorRev)      1     dMotorRev
--------------  = ----------------  =  --  x  ---------  [Note 1]
    dt                  dt             10        dt






 2                                                    2
d GearboxOutRev      d(1/10 dMotorRev/dt)      1     d MotorRev
---------------   =  --------------------  =  --  x  ----------  [Note 1]
      2                     dt                10           2
    dt                                                   dt
Note 1:


There should be a



Code: 
+ MotorRev d(1/10)
on the end of that, per the product rule:

images




but since 1/10 is a constant, d(1/19) = 0, so that term has been dropped.
 
I like L D[AR2,P#0.0]'s answer.


BUT

drbitboy, that is good info if the gear ratio changes.
We have a command called the Advance Gear Move where the gear ratio changes using a cubic spline. This way feed forwards can be generated for the slave axis. Without feed forwards the slave always lags.

Basically we map the master's position, velocity, and acceleration to the slave's position, velocity and acceleration using the cubic spline and the chain rule.


Yep, I have a Mathcad worksheet for that too.
 
Peter Nachtwey said:
I like L D[AR2,P#0.0]'s answer.


BUT

drbitboy, that is good info if the gear ratio changes.
We have a command called the Advance Gear Move where the gear ratio changes using a cubic spline. This way feed forwards can be generated for the slave axis. Without feed forwards the slave always lags.

Basically we map the master's position, velocity, and acceleration to the slave's position, velocity and acceleration using the cubic spline and the chain rule.


Yep, I have a Mathcad worksheet for that too.
Click to expand...


But we are PLC programmers.
L D should have writed 10dec, so everyone will understand it 10 instead of binary which is 2 on dec. 🔨
 

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