# Ideas for drilling a hole (kind of)

Hi all,

I’m trying to solve, more or less, the following problem with FreeFEM. I don’t need an exact solution, but an approximation of the Temperature distribution and the maximum Temperature reached in a concrete material point.

Imagine a cylindrical rod, lets say an steel rod, of radius R and length L=L1+L2.

We drill a hole with a drill bit of diameter D at the middle of the rod, up to a depth of L1.

Both the rod and the drill bit have known heat transfer coefficients, which are not equal.

In a very simplified case, the drill bit advances at a fixed and known speed of V mm/s, and we assume that the heat is produced mostly at the tip of the drill bit.

To make things simpler, the tip Temperature of the drill bit while is drilling at the given speed through the rod material is approximated by a function of time, that goes from ambient temperature at t=0, up to a steady working temperature after some seconds. Its a given function of the problem.

I want the temperature distribution reached when the drill bit stops at the depth L1. I’m mostly interested in the maximum temperature reached in a given point of the rod, perhaps some seconds later the drilling ends.

My plan is start with the tip of the drill bit in the X=0 position, hold it for 1 ms (so to speak) and get a solution, use the solution as the B.C.advancing the drill bit the length of 1 ms x V (the drill advance rate), and so on… until I arrive to the final position at depth L1.

Any ideas welcome.
Lluis

Yes and no,

The problem is to know the head flux between the drill bit and the steel Rod, other wise all other parameter in this problem are know, and you can solve with freeFEM.

yeah, it looks like it is just an energy input at the interface being a function of
material removal rate ( which is probably temperature dependent ) , applied
force and coefficient of friction ( porbably depenedent on a lot of things.
This is likely a steep function of applied force, local temperature, and
interface structure ( lubrication which tends to smoke, or is that just me ? lol ).

Do you want to include details at the interface at nm scale or just
bulk approximate energy input?

A couple of ways to deform mesh and include the material ( concrete or rod)
at each point in a phase variable i guess.

I don’t really want it to be a complex model, because I only need an initial estimate. Lets say that I’m mostly interested in knowing if given a rod-like geometry of the drilled material, the temperature at the bottom of the rod will reach at least 100ºC (for example). If it is more, better I don’t mind, if it’s less, what I’m trying to accomplish is not viable.

Of course, using a simple model, in which the tip of the drill is the only heat flux source (as Mr. Hecht suggested, is better to think in terms of heat flux).

For example, if we know more or less the torque applied to the drill bit, the r.p.m and the advance speed, we can have an estimate of the heat flux at the tip (lets say, a 75% of that amount of power applied).

The model can be more or less accurate, but what I don’t get technically is how to establish the Boundary Conditions, because the “geometry” is changing with time.

Thanks Mr Hecht.

I will guess some heat flux estimate at the tip of the drill bit. For me the problem now is how to establish B.C. with a changing “geometry” of the moving tip.

If its not a tribology problem and you have some known IV input that you can allocate
to the tip, probably as some function of linear velocity, and some efficincy factor
to account for other “losses” then presumably that part is easy. In essence you
have a two phase system of metal and concrete. I have used a DoF for phase
at each vertex and that approach may be suitable for you. FF supports “regions”
that are illustrated in many examples.

I posted the attached earlier. You can see something called “middle” added to a mesh
along with a problem imposing a boundary condition on this “curve.” You can
see the examples for how to extend this to a more complicated set of lines
or curves. You could make a new mesh at each time step for example or