# Torque calculation-help needed

1. Sep 2, 2009

### pramura

Hello everyone!

I need a help from your side. I need the calculation for pulling torque needed to rotate a swing gate hinged at two points.Weight of the gate is 130kg, width 5ft(1.524m) and height is also 5ft. Upper hinge is 0.381m from top and lower hinge is 0.381m from bottom.
Do i need to include the total weight of the gate for this torque calculation, because the gate is supported by two hinges.

what is the suitable motor for this application?

2. Sep 2, 2009

### Staff: Mentor

You will need to calculate the Moment of Inertia for the gate about the axis of rotation, and you will need to specify how quickly the gate should be accelerated in the move. Those numbers will lead you to the torque. Are you familiar with those terms? If not, www.wikipedia.org has reasonable introductions...

3. Sep 2, 2009

### pramura

Thanks for your reply berkeman. Yes, for torque calculation we need moment of inertia and angular acceleration.I need to open the gate from 0 to 90 degrees in 15 secs. I calculated moment of inertia but for acceleration if I use constant speed motor to open the gate how can i calculate angular acceleration. I converted degrees into radians and i got 0.1047176 rad/s2. Is that correct.

4. Sep 5, 2009

### nvn

Perhaps assume constant acceleration, alpha1, from 0 to theta1 radians. Then, using kinematics, compute final angular velocity, omega1, at theta1. Using statics, compute the frictional moment M, assuming a high mu value (rusty hinges). Motor torque T to overcome the total moment would be T = M + I*alpha. Perhaps turn off the motor at theta1 radians. Now T in the above equation becomes zero; therefore, solve for alpha2 to obtain the constant deceleration from theta1 to 90 deg. The initial angular velocity from theta1 radians to 90 deg is omega1. Using kinematics, compute the final (latching) angular velocity, omega2, at 90 deg. Using kinematics again, you can now compute the total swing time. Play around with this until you get what you consider to be an acceptable minimum (and maximum) latching angular velocity, and a total swing time of 15 s. You might want a damper or spring to handle the latching impact, to avoid damaging the structure (?). Maybe someone can let us know if the above approach sounds valid or incorrect.

5. Sep 5, 2009

### nvn

pramura: Here is the key to solving the approach described in post 4. If you put all the above information together, it happens that T and t1 have a unique solution, as follows. (The motor is turned on at theta0 = 0 rad, when omega0 = 0 rad/s, which occurs at t0 = 0 s.)

t1 = (M*tt^2 + 2*I*omega2*tt - 2*I*thetat)/(M*tt + I*omega2),
T = (M*tt + I*omega2)/t1,

where T = motor torque (N*m),
t1 = time at which motor is turned off (s),
tt = gate total swing time (s),
thetat = gate total swing angle (rad),
M = frictional moment (N*m),
I = gate mass moment of inertia about hinge axis (kg*m^2),
omega2 = gate final (latching) angular velocity (rad/s).

After you compute T and t1, you can compute any other quantity, such as the following, using kinematics or kinetics.

alpha1 = gate constant angular acceleration while motor is running (rad/s^2),
alpha2 = gate constant angular acceleration while motor is not running (rad/s^2),
theta1 = swing angle at instant motor is turned off (rad),
theta2 = swing angle after motor is turned off (rad) = thetat - theta1,
t2 = gate swing time after motor is turned off (s) = tt - t1,
omega1 = gate angular velocity at theta1 (rad/s).

You can develop your own frictional moment M, but I arbitrarily used M = 2[0.5*Dp*muk*H + 0.5(1.25*Dp)*muk*V], where Dp = hinge pin diameter (m), muk = hinge kinetic coefficient of friction, H = horizontal reaction force applied to each hinge (N) = (m1*g)*0.5*(1.524 m)/(0.762 m), V = vertical reaction force applied to each hinge (N) = 0.5*m1*g, and m1 = gate mass (kg). Parameters omega2 and muk are fundamental input parameters you must specify to define your design.

It is interesting to see what happens to T as you decrease muk. Hint: To compute alpha1 and alpha2, see post 4.