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

 

[dhengr]

PaulCaliber23:
I’ll bet the nail gun manuf’er. and the nail manuf’er. don’t think nails are too expensive when the poor carpenter trying to make a living has to buy their proprietary nails which work only in their gun. I don’t think you’ll be testing the gun accurately and truthfully unless you fire regular collated nails into wood. If you want to design something mechanical design a system which indexes the 2x wooden members under the gun btwn. each firing. Or index the gun on a gun holding system, up and down the wooden members, at regular intervals, btwn. firings. Driving real nails into wooden members (varying btwn. oak, pine, SYP and DF) causes the real world forces and reactions on the gun, to test it: and will also reveal nail jams, bending, breakage, etc. which are problems which the rest of us hope are resolved before we pay a premium for your nail gun.

 

[chicopee]

The potential energy stored in the cylinder is the max energy of which a portion of that energy will need to be dissipated, so this PE is a starting point.

 

[hydtools]

Maybe a little more realistic accounting for the cost of the rig would be to exclude nails and wood. Those are consumables and a cost running the test.

I doubt the nail gun will successfully complete the first test run without failure. So the consumables will have to be in such quantity to eventually complete the last 100,000 cycles without failure.

Ted

 

[Nescius]

Is the goal to test the driving mechanism only? This is just a gut feeling, but I'd expect wear/failure to manifest first as poor feeding of the nails themselves, not as an inability to drive a nail...or a nail analogue piston.

Some other musings:

I'd bet most nail guns spend their lives breathing very wet compressed air. Bone dry shop air won't reflect the real world. This assumes a pneumatic gun, of course.

I'd bet most nail gun mechanisms are infiltrated by some significant amount of abrasive grit. They live in the back of a work truck, on a construction site. A clean shop environment won't reflect this either.

I'm not sure about reusing nails; all the nail gun "ammo" I've ever seen is joined by wire or paper or something. I don't think you can feed a nail gun loose nails.

If the client only wants to spend "a few thousand", the case is even stronger for heading to Home Depot for some wood and nails, not building a machine. A machine would surely look fancy and scientific, but the real world wood/nails marathon could be just as scientifically rigorous. Truly superb data could be gathered, say photos and measurements taken during a full tear down every 10K nails, or whatever. If I were the nail gun product engineer, I'd be salivating over data like this.

However, if the goal is to construct a test stand to COMPARE different nail gun designs...lubricants...maintenance schedules...whatever, THEN I could see the value of building such a machine. Even then, "a few thousand" is wishful thinking.