How is energy dissipated in a nail gun? 1

[PaulCaliber23]

Hi all,

I'm having trouble working out how much energy will have to be dissipated in a test rig for a nail gun.

From previous testing, I know that a test slug fired from the gun has a mean energy of 100J.

I now want to design a test rig which can fire the gun repeatedly for 100,000 shots.

I have decided that firing a test slug vertically upwards in to the bottom of a heavy piston in a steel tube will be the most suitable design.

Each time the slug is fired from the gun, it collides with a rubber-bottomed piston in a steel tube, thus transferring its energy to the piston by pushing it up the tube. The piston can then bounce up and down in the tube until its energy is entirely dissipated as heat and sound. The process is then repeated 100,000 times.

The problem I have with designing the rig, is working out how high the piston will travel within the tube. I know I'm making a flawed assumption somewhere so please let me know where my flawed reasoning is!

Here is my working and reasoning:

Assumptions:
- neglect energy dissipation due to air drag
- since the rubber bottom of the piston has a very high spring constant, assume that once the piston and slug collide, the slug and the piston both travel with the same velocity

m_s = mass of the test slug = 0.09 kg
m_p = mass of the piston = 10 kg
E_i = energy of the test slug exiting the gun = 100 J
E_f = combined kinetic energy of the test slug and piston immediately after the collision
v_s = velocity of the test slug before the collision
v_f = velocity of both the slug and the piston immediately after the collision

Working out the velocity of the test slug:

v_s = sqrt(2*E_i / m_s) (from the kinetic energy equation)
= sqrt(2*100 / 0.09)
= 47.1 m/s

Using the conservation of momentum principle, determine the velocity of the slug and piston immediately after the collision:

m_s * v_s = (m_s + m_p) * v_f
v_f = m_s/(m_s + m_p) * v_s
= 0.09/(0.09 + 10) * 47.1
= 0.42 m/s

Combined kinetic energy of the slug and piston immediately after the collision:

E_f = 0.5 * (m_s + m_p) * v_f^2
= 0.5 * 10.09 * 0.42^2
= 0.9 J

Thus the maximum height that the piston will reach:

h = E_f / ((m_s + m_p) * g)
= 0.9 / (10.09 * 9.81)
= 9 mm

I then double checked the maximum height of the piston using the conservation of energy equation and the initial energy of the test slug. I assumed that the kinetic energy of the test slug would be entirely converted to gravitational potential energy of the piston once the piston reached its highest point. Thus energy losses due to sound and drag etc were neglected.

h = E_i / ((m_s + m_p) * g)
= 100 / (10.09 * 9.81)
= 1 metre

Thus the maximum height differs significantly depending on the calculation method I use.

Is my conservation of momentum approach correct?
Is my conservation of energy approach correct?

My intuition tells me that the conservation of momentum approach is correct, however, I'm suspicious since I do not believe that the kinetic energy of the system would be reduced from 100J to 0.9J from the collision (i.e. huge energy losses to sound and heat).

Please help!

Thanks,

Paul

 

[IRstuff]

I'm unclear whether your concept is a plausible approach. Most test setups I've run across are ballistic pendulums, where the projectile is non-elastically collided, such that the projectile is embedded in the pendulum, and conservation of momentum is used, because the projectile and the pendulum become one. However, in your description, it seems to me that the nail will bounce off the rubber. Additionally, I don't see where you take into account friction

TTFN
I can do absolutely anything. I'm an expert!
faq731-376 forum1529

 

[hydtools]

I think waht you are seeing is the difference between inelastic and elastic collision. Inelastic collision is not an energy conserving event. So the conservation of energy approach is not the correct solution.

If the test slug was free to rise without hitting a piston, how high would it rise? That would fit the conservation of energy approach.

Ted

 

[3DDave]

If you know how much energy is carried in the slug, then that's how much will eventually be dissipated.

What is the point of the test and why do you want to capture the energy?

 

[hydtools]

That is what I was going to ask, too. What is the objective of the test? Why do you care what the target does? You know the driving energy of the nail gun.

If the objective is to cycle the nail gun 100,000 times presumably without some failure, then I would choose to shoot the nails downward into a barrel that has a few inches, cm, of sand in the bottom to prevent nail rebound and to collect the nails.

Ted

 

[tbuelna]

The one issue I can see is heat produced in the rubber element on the bottom of the piston. Since you intend to perform 100K test cycles, you need to limit the cycle frequency to maintain the temperature of the rubber element within acceptable limits, and this might take more time than you imagine. For example, 100K test cycles at 5 seconds each would take over 138 hours.

 

[gruntguru]

For the nail and piston to travel together the collision must absorb a lot (most) of the energy. Your conservation of momentum calc is correct (conservation of energy incorrect). Might as well fire the nail into the same rubber mounted rigidly (it won't last long before it is saturated with embedded nails).

100J is not much heat.

hydtools solution looks good.

je suis charlie

 

[Tmoose]

Maybe firing the nail gun at a 45 degree angle into the air for the first 10 nails, and measuring the distance travelled as a measure of firing energy. Then repeating every 10,000 nails or so would help determine, in addition to the nail gun still working, if it was also delivering an acceptable amount of energy.

I don't think I'd expect the bumpers inside the nail gun would survive 100,000 "dry" firings very well.

 

[hydtools]

Ah, the piston with the rubber face is the target intended to absorb the energy and perhaps not have the gun anvil bushing absorb all the energy.

It might be that a relatively uniform piece of wood target, perhaps fir, and an engineering intern to fire the gun for 100,000 cycles would work.

Ted

 

[PaulCaliber23]

Wow, thanks for all the excellent responses!

Apologies for the late reply to some of your questions.

The objective of the test is purely to determine if and how the gun may fail before having fired 100,000 nails. I want it to be as realistic as possible in that I would like the test slug to be slowed to a standstill over 90 mm (which is the length of a standard nail).

I've considered firing nails in to wood but this would cost too much (the cost of 100,000 nails) and may require too much human input to replace the wood and complexity in that the gun or wood would have to move between each shot. The sand box is a good idea as I could recover the nails; however, it might be difficult to make the conditions realistic. Also, that's a really good idea having an engineering intern fire the gun - a classic intern project! Although the cost of nails would be too high unfortunately.

I have therefore opted to use a 90mm long pin which screws in to a flexible rubber isolator which then screws in to a 2.5kg 'piston'. Thus when the gun fires, its striking pin hits the 90mm long pin (which fits inside the gun's barrel where the nail would sit) which causes the 90mm pin/isolator/'piston' to travel 90mm vertically up inside a seamless steel pipe. The pin/isolator/'piston' assembly then falls back in to the gun's barrel (since it is guided by a lead-in) and bounces until its energy has been dissipated as heat.

I have allowed for the 'piston's weight to be adjustable to account for the assumptions that I've used in the conservation of momentum equation. I will also check the temperature of the assembly to ensure that it isn't getting too hot.

What do you think of this solution?

 

[IRstuff]

Seems to me that your description is counter-intuitive. If the purpose of the test is to determine failure modes, then the "nail" must encounter the same resistance that it would see if it were hitting wood, since that resistance is what determines wear and tear and recoil on the hammer head and mechanism. Your description of "bouncing" doesn't jibe with that. If you don't want to use wood, then some sort of ballistics gel might be appropriate, but it would need to be sufficient dense to mimic the resistance of actual wood. Your intern might be better used to recover the spend nails for reloading into the gun. Seems to me that sand would be the cheapest alternative.

Bouncing implies time, so it's not clear that this is much of a savings

Re-using the same nail seems dubious; there's bound to be some wear and tear on the nail, which might cause jamming.

TTFN
I can do absolutely anything. I'm an expert!
faq731-376 forum1529

 

[TheTick]

If you can't afford the nails, how can you afford to build the product?

 

[hydtools]

Nails will cost about $2000.00. What will you spend for a device that mimics driving a nail into wood? And be sufficiently like nailing to call it valid so that your boss and sales and marketing will accept the results. Labor will be labor either babysitting the device or actually driving nails.

Buy the nails and wood and get it done.

Ted

 

[hydtools]

Stanley Bostitch

Ted

 

[PaulCaliber23]

Yes I agree that the test should be completed with actual wood.

However, the clients would only like to spend a few thousand on a rig which can complete several tests and may also be used for testing a concrete gun prototype.

Thus I think that the cost of nails makes this approach unfeasible (especially for the concrete gun). I like the sandbox approach where I could reuse the nails; however, I can't see how it would provide a more realistic scenario than that which I've come up with (i.e. the sand wouldn't provide adequate resistance as far as I can see).

For my approach, I agree that the recoil and other characteristics will be different; however, by slowing the pin (which is simulating the nail) over the same distance which a nail is driven in to wood (90mm), it will be as close to reality as I can get it given the constraints of the project.

With this extra information (that I have to do several tests and also on a concrete gun for which the nails cost $0.56 each), do you have any suggestions for a better testing method than what I've chosen?

 

[TheTick]

How did you get suckered into including expendables like nails into the cost of the project? Build the rig, let them buy the nails.

 

[gruntguru]

Sounds feasible. Perhaps add a spring to the mass (resistance on a nail increases with penetration distance into the timber). You also need to include any free-travel (near-zero force) of the plunger and nail before it strikes the "timber".

je suis charlie

 

[IRstuff]

"however, by slowing the pin (which is simulating the nail) over the same distance which a nail is driven in to wood (90mm), it will be as close to reality as I can get it given the constraints of the project."

Barely, at best. The spring constant of the rubber is very different than that of wood. Wood doesn't really spring back. Perhaps something thixotropic?

TTFN
I can do absolutely anything. I'm an expert!
faq731-376 forum1529

 

[hydtools]

Industrial felt is available is a variety of densities and shapes. Perhaps experiment to find a felt target that will capture the pin or dissipate just enough energy that the pin would fall free on the far side of the target.

Ted

 

[zeusfaber]

I'm struggling to picture this properly, but is there any risk of the pin damaging the nailgun as the falling piston knocks it back into place?

A.