Force required to open a swinging gate

[Goz83]

TL;DR Summary

Force required to open swing gate using actuator

Hi Guys. I hope everyone is well today.

A swing gate of 2300mm x 750mm (LxH) with a uniform mass distribution totaling 64kg. Assuming the force is applied 500mm out from the hinge, how do I calculate the force required to open the gate?

If needed, the hinges are hook and eyelet type, galvanised steel with a friction co-efficient of 0.25 and a contact area of approx 1200mm^2.

 

[Baluncore]

Welcome to PF.
The force will depend on how quicky you accelerate and then decelerate the gate.
How long does it take to fully open the gate?

 

[Goz83]

Welcome to PF.
The force will depend on how quicky you accelerate and then decelerate the gate.
How long does it take to fully open the gate?

15 seconds. Would be a little less than 90 degrees from fully closed to fully open.

 

[Nugatory]

Do we slam the gate (15 seconds of angular acceleration through 90 degrees and then it smashes into a stop) or do we control the stopping (7.5 seconds of angular acceleration through 45 degrees followed by 7.5 seconds of angular deceleration through 45 degrees to bring the gate to a stop after 90 degrees)?

 

[Goz83]

Do we slam the gate (15 seconds of angular acceleration through 90 degrees and then it smashes into a stop) or do we control the stopping (7.5 seconds of angular acceleration through 45 degrees followed by 7.5 seconds of angular deceleration through 45 degrees to bring the gate to a stop after 90 degrees)?

Great question. For simplicity, let's say the gate is slammed shut. No velocity control features to account for.

 

[Nugatory]

Ok, then we can calculate the average angular velocity required for the gate to rotate through 90 degrees in 15 seconds. Because the gate isn’t moving at time zero the final angular velocity will be twice that.

Now you have information enough to calculate the required acceleration to reach that angular velocity in 15 seconds. From there, the moment of inertia of the gate (you can look it up if you don’t want to calculate it, assuming a rectangular gate for simplicity) will give you the necessary torque and hence the force. Calculate the moment around the hinges to see whether you can ignore the friction there and still get a reasonable approximation.

 

[Baluncore]

Assuming the force is applied 500mm out from the hinge, how do I calculate the force required to open the gate?

Is the force applied with a straight link from a fixed point, which is the anchored end of a linear actuator, the actuator being the long side of a triangle, with the two other side lengths fixed?

Or is the force a circular torque, always applied perpendicular to the attachment point on the moving gate, 500 mm from the hinge axis?

 

[Goz83]

Is the force applied with a straight link from a fixed point, which is the anchored end of a linear actuator, the actuator being the long side of a triangle, with the two other side lengths fixed?

Or is the force a circular torque, always applied perpendicular to the attachment point on the moving gate, 500 mm from the hinge axis?

OK, so the motor end of the linear actuator will be beside the bottom hinge, perhaps 50mm and in parallel. The extension part of the actuator will be anchored 900mm (I just checked the extension) from the hinge on the gate. When the linear actuator retracts, the gate opens inward. When it extends, the gate closes. I will be using a 300kg (or 3000N) linear actuator for the project, but I must find the minimum required force to open/close the gate from that point. I wasn't considering speed, only Force/Torque required to move the gate.

Taking onboard what Nugatory wrote, I worked out the angular velocity to be 0.1047m/s and the acceleration at 0.2408m/s assuming 90 degrees of rotation. Now I need to find the force required.

 

[Baluncore]

OK, so the motor end of the linear actuator will be beside the bottom hinge, perhaps 50mm and in parallel. The extension part of the actuator will be anchored 900mm (I just checked the extension) from the hinge on the gate.

That is a very slender triangle.
The linear actuator has a minimum length when retracted and a maximum length when extended. The distance is measured between the eyes or pins. Can you link to the actuator data sheet, or specify the retracted and extended lengths.

 

[Goz83]

That is a very slender triangle.
The linear actuator has a minimum length when retracted and a maximum length when extended. The distance is measured between the eyes or pins. Can you link to the actuator data sheet, or specify the retracted and extended lengths.

600mm when closed. 900mm when open approx. https://www.amazon.com/gp/product/B07ZVH7R2W/?tag=pfamazon01-20

The actuator motor section is supposed to be very close to the gate hinges. The entire motor section rotates on its own bracket when opening/closing.

I have attached the first iteration drawing. The gate on the right will be the one with the actuator and the bracket will be attached to the thick post on the far right. Ignore the fold in that gate. It is bifold and teh second section of that gate will be mounted on self close hinges, but it is all part of the same gate. The larger gate to the left will be a sliding gate.

The second image is a newer iteration and gives a better idea of what I am doing.

 

[Baluncore]

The actuator motor section is supposed to be very close to the gate hinges.

I don't believe that is optimum, or even possible.
Unfortunately there is no plan showing the actuator mounting layout.
I will look into the mounting geometry needed for { 600 mm to 900 mm } and 90 deg.

 

[Goz83]

I don't believe that is optimum, or even possible.
Unfortunately there is no plan showing the actuator mounting layout.
I will look into the mounting geometry needed for { 600 mm to 900 mm } and 90 deg.

The following short video would be pretty standard.

I could distance the actuator about 100mm from the hinge if need be. This would widen the base of the triangle.

 

[Baluncore]

I could distance the actuator about 100mm from the hinge if need be. This would widen the base of the triangle.

The actuator has a length of 600 to 900 mm.
Allow ±10 mm at each end for wear, flexing, and errors in construction.
Use as much actuator movement as is available; 610 to 890 = 280 mm.
If you need less movement, use a shorter actuator.

There will be a pin on the gate, some distance from the hinge.
The gate will swing through 90°, and move that pin through 280 mm.
The distance of that gate pin from the hinge axis will be; 280 mm / √2 = 198.0 mm.

If the right angle triangle is symmetrical, the actuator will exert the same force, and have the same speed at both ends of the movement. The actuator will then lie on a line 45° beyond the open gate.

Now place the gate pin on an offset from the gate. That rotates the diagram and brings the fixed end of the actuator closer to the wall, (NOT to the hinge). I believe the offset and pin position will be about 198 mm / √2 = 280 / 2 = 140 mm. The offset will depend on the position of the fixed end of the actuator, close against the wall. But the gate pin will remain 198 mm from the hinge pin.

 

[sophiecentaur]

I did some thinking about a similar problem when trying to design a (cheap) return mechanism for a heavy wooden gate and was frustrated about the problem of using a 'linear actuator'. It that danged Cosine function that works against you, for a compact mechanism.

Have you thought of using a rotary actuator system? (I never followed the idea up, to be honest - the job wasn't important enough). That would give you uniform torque at all angles. One beefy gear, mounted on the axis of the gate hinge could be driven by a pinion / worm / gearbox / motor and the whole thing could be quite compact. For a gate, the driven gear could be cut, so as to have only a quadrant (or whatever angle).

It would be a high torque system which would need to be considered, of course but the basic hinge could be replaced by a heavy duty plane bearing. That would be easy enough to make; A 20mm pin would hold a gate up, with someone swinging on it, even.

It would almost certainly involve some hunting for suitable second hand parts and some skills with welding and cutting. Perhaps a belt (or drum) drive system would be cheaper and easier to adapt.

 

[Goz83]

I did some thinking about a similar problem when trying to design a (cheap) return mechanism for a heavy wooden gate and was frustrated about the problem of using a 'linear actuator'. It that danged Cosine function that works against you, for a compact mechanism.

Have you thought of using a rotary actuator system? (I never followed the idea up, to be honest - the job wasn't important enough). That would give you uniform torque at all angles. One beefy gear, mounted on the axis of the gate hinge could be driven by a pinion / worm / gearbox / motor and the whole thing could be quite compact. For a gate, the driven gear could be cut, so as to have only a quadrant (or whatever angle).

It would be a high torque system which would need to be considered, of course but the basic hinge could be replaced by a heavy duty plane bearing. That would be easy enough to make; A 20mm pin would hold a gate up, with someone swinging on it, even.

It would almost certainly involve some hunting for suitable second hand parts and some skills with welding and cutting. Perhaps a belt (or drum) drive system would be cheaper and easier to adapt.

The amazon link is the system I have purchased already. I am confident it is powerful enough, but I need to show calculations which is not my strong point in mechanics what it comes to force and torque and moment of inertia. Makes my head hurt.