maximum power with torque

[vit46]

Hello, I'm trying to solve an exercise of mechanics applied to machines.

the exercise gives me:
the driving couple equal to: -awm + 500
and maximum power of 20kw

asks me to find the value of knowing the maximum power.

I tried to solve this way:

maximum power =motor couple (maximum) * angle speed(wm) maximum

tracking the drive couple on a known chart that we have maximum torque of 500 nm but angle speed nothing. by doing this reasoning I go to eliminate the letter to which I instead want to calculate.

Can anyone help me?

Thank you.

 

[ramjet]

couple motrice = -a wm??? ?
What language are you talking about? ?

 

[vit46]

couple motrice = -a wm??? ?
What language are you talking about? ?

a is the parameter to find, wm is the angle speed.

this is the complete track:

Consider a transmission consisting of:

a motor with characteristic c(ωm) = −aωm + 500 and inertia im = 1kg m2

a transmission characterized by yield η=0.9 and transmission ratio i=4 a user with characteristic of the resistant torque r(ωu) = 60ωu +3000 and inertia iu=10kg m2 .

a) calculations b knowing that the maximum power of the motor is 20kw and the equation of dynamic balance of the system is written

b) the speed of the regime in the real and ideal case, the stability of the systems obtained and the result obtained is explained

c) it is evaluated if the system can be started without need of friction and the acceleration to the point is evaluated

d) qualitatively draws the characteristic of the strong torque (reduced to the motor) and drive on a single graph indicating the stationary conditions and other significant points of the curves, both in the real case and in the ideal case.


It has been resolved completely, but there is an error on the calculation of a

 

[meccanicamg]

If you place the steps we can see the stump.
If it's the classic mtu with inertia and what else, you'll have all the terms.
start making the balance and see.

 

[MekIng]

Hi.
This point of the problem in my opinion is similar to an analysis exercise 1 however I try to answer,

you could try to write the equation of power as
(wm)

Whereas c(wm)= -awm+500 as the text of the problem and putting to system the two
p(wm)=(-awm+500)wm=-awm2+500wm

at this point the expression of the power just obtained
d/dwm(p(wm)=-2awm+500

is equal to zero to find wm to which the maximum power corresponds
d/dwn(pmax)=0=-2awm(pmax)+500
wm(pmax)=250/a

inserts the value just found in the expression of the power and sets it equal to 20000w obtaining the value of a (3,125)

 

[vit46]

Hi.
This point of the problem in my opinion is similar to an analysis exercise 1 however I try to answer,

you could try to write the equation of power as
(wm)

Whereas c(wm)= -awm+500 as the text of the problem and putting to system the two
p(wm)=(-awm+500)wm=-awm2+500wm

at this point the expression of the power just obtained
d/dwm(p(wm)=-2awm+500

is equal to zero to find wm to which the maximum power corresponds
d/dwn(pmax)=0=-2awm(pmax)+500
wm(pmax)=250/a

inserts the value just found in the expression of the power and sets it equal to 20000w obtaining the value of a (3,125)

Hi.

thank you all for the answers.

meking will propose this solution to the prof, as soon as I receive reply I will let you know if it is correct.

anyway thanks for your availability.