resolution hard body problem

[lucadileta]

hello to all and thank you in advance to all those who will answer me. I find myself solving a problem as described by the photo but I can not get physically sensible results.

a plate of small thickness but not negligible mass has an initial speed v0.
Such slab crosses a vertically aligned pair of rollers, of which, at the lower one, is applied a drive couple given by an electric motor while, the upper one, is free to rotate.
to the upper roller is also applied a force that will generate the friction necessary to press the plate between the two rollers during the passage of the same.
the peripheral speed of the lower roller I call it vf and represents the reference speed to which the plate must be accelerated at the end of its complete journey between the rollers.
the materials of the three cups is the same (steel)

the objective of the exercise is to assess the behaviour of the plate if:

- v initial plate is smaller, equal to or greater than the peripheral one of the lower roller (which constant vf wheel)
- evaluate the resistant torque generated by the inertia of the plate that is accelerated to vf

Could someone explain to me the setting of the problem?

greetings
♪

 

[biz]

If v0>vf and f allows it there is slip.
If v0=vf there is no problem.
If v0<vf and f allows it there is slip.
if there is no slip because f large enough then a moment equal or contrary to the m2 couple is born.

_The resistant torque generated by the inertia of the slab can be evaluated simplified, for example, assuming the mass of the plate concentrated on the periphery of the grinding roller, applying the known formulas.

 

[meccanicamg]

this type of exercise is that of the classic ponchroll with only one motorized roller. something on the forum find.
Besides also other posts on carts with wheels and motorization can be useful to set the kinematics and equations. attention that in all of this you also have the friction volving that is the resistance to rolling.

 

[lucadileta]

News@meccanicamgfirst of all thanks to both for the answers: my qualitative reasoning is as follows:

in case the speed of the plate is less than the peripheral of the engine roller we will have that the latter will accelerate the plate at its peripheral speed. as a strong moment instead we will have the inertia of the plate and inertia to the rotation of the led roller

in case the speed of the plate is equal to that peripheral of the motor roller we will have that the latter will suffer a resistant moment due to the inertia to the rotation of the duct roller that in order not to have crawling with the plate will rotate at an angle speed greater than that of the motor roller

in case the speed of the plate will be magiore of that peripheral of the motor roller, it will be the plate itself to accelerate it as it will have to do the same for the led roller

all depends on the friction that is at stake... and that's where I get confused

 

[biz]

What's wrong with you? but do you have to do punctual or first approximation calculations?

 

[lucadileta]

What's wrong with you? but do you have to do punctual or first approximation calculations?

hi biz, I want to make specific calculations that then I will go to use in different configurations of the same machine and consequently estimate the power absorbed by the engine. Attached I decomposed the 3 bodies and illustrated the forces of the system (it neglects the weight strength for each body).