You need to supply 2 items.  How fast do you need the roll to come up to speed, and how good are the bearings/type of bearings?

A little 1 HP motor would do it if you have a while and the bearings are REAL good (low friction).

You must calculate the inertia of your system and find in how much time you want the motor to get to the speed you want.  This is basically the same formula as F=MA (Newton's law) but in a rotationnal system.  This is an approximation that does not take friction into account but friction must be negligible compared to inertias.

To find the torque at the motor, it will be proportionnal to the ratio of the diameters of paper's roll and motor whelle

Get the friction coefficient of the rubber and paper and by calculation you'll find back the pressure you need, considering the torque you need.

Note that pressure needed is independant of motor wheel diameter in theory but will vary slighty in practice.

The more you want to accelerate faster, the more pressure you need and a bigger motor you need.

Robin

Mech eng.
Canada

Hi pharoofthermo

Following the early reply you need to calculate the "moment of inertia" of your paper roll and shaft first ie:-

   moment of inertia for solid shaft (I) = m x d^2/(8)
    
   where m = mass of shaft
         d = dia of shaft
    



   moment of inertia for hollow shaft (I) (paper roll)=
    
     m1 x d1^2/(8) - m2 x d2^2/(8)

   where m1 = mass of paper roll as though it was solid
         m2 = mass of paper roll which would be the id of
              the roll (in this case the id of the paper
                        roll would be the shaft)


   next add these 2 results together and that will be the
   total moment of inertia for your system.

   to find the torque required to bring your system upto
   speed use the following formula

        T = I x ((w2 - w1)/t)

    where T = torque req to bring roll & shaft upto speed

           w2,w1 = final and intial angular velocity of
                   shaft and paper roll

           t = time that you want the system upto speed
               (you can choose any value and work the torque
                out from the above formula)

           I = the total moment of inertia

 once you have the torque you can calculate the the
 tangential force on the shaft which needs to be exerted by
 the tyre.

 I am not sure how you calculate pressure in the tyre although rolling friction as stated earlier will come into it.The complication here for myself is that the tyre will deform to some degree and I am not sure what area the pressure will be working over. The only two suggestions for this problem are 1/ use trial and error and pressurise the
                    tyre to various pressures and try it
                    out.

                  2/ perhaps somebody in the automotive
                     line could help out with the last
                     part.

Hope this is of some help

 

Hi again!

Following the previous reply, the friction force is, in theory, indepentent of the surface area.  It is F=uN where the force you can apply tangetial to the roll (F) is dependant to the normal force (N) and a friction coefficient.

This force F os the furce you'll use to calculate torque required at roll and torque required at motor b multiplying by the radius of the roll.

I do not see any coefficient of friction for paper to rubber but wood on metal is around 0.25.  I say around because they can vary with many factor and can doulbe in no time.  Furthermore, the theory says that the phenomenom is independant of the surface of contact but the surface has some effect.

Robin

Hi robindbois

Whilst I see formula regarding friction in the same light as you have shown above which is dry friction, I would point out that the friction force is actually "almost" independant of "apparant area of contact" but the friction force which is determined by the true area of contact, is proportional to the load applied.
Further it is interesting to note that if you reduce the pressure in your car tyres you will get additional grip on the road surface.

regards desertfox

Thanks for the help guys!  I now see a path to the answer.

Pharo of Thermo

Hi,

Can you please attach a sketch of rubber wheel coupled to the motor.As usual,it is easy to calculate external inertia and therby we can calculate motor Power.Do you use inverter drive for this particular motor.If so you can set the accelaration time for this system and you can arrive at the motor Power.If Inverter drive is not there, you may have to assume accelaration time of a normal squirrel cage induction motor as 2-3 sec and calculate the power by using inertia formula.

Let J0 is the sum of inertia reflected at motor shaft

Then Accelaration torque= J0 x 2 pi N/60 t

Where pi= 3.14
N= Rated speed
t= Accelaration Time

You can normally overload the motor by 6 to 7 times for 2- 3 secs. Check whether you get the torque within this limit

Once you perform this calculation , I can help you out to find the pressure required at the wheel.Its better to divide your problem into 2 halves

1> without rubber wheel estimate motor power by using inertia formula

2>Introduce rubber wheel and re iterarte the motor power. I need your schematic sketch to do that

You can contact me at sudev.krishnanair@bwir.com

Good luck

Bye

Sudev Nair