by dirktheeng » Tue Aug 09, 2011 11:49 pm
All,
I did a few calculations to figure out (or at least try to estimate) the clamping force I need to support the monitor. I made the assumption that the pressure exerted outward on the band clamp would be approximately equal all the way around when the band clamp is tightened. In this way, it acts as if it is a hydrostatic pressure. This should be very close to reality as the band clamp is fairly thin and flexible. Realizing this, I could use hoop-stress analysis that we use in pressure vessel calculations. The end of this analysis is that the radially applied force at the interface between the brake and clamp is 2*pi times the tangentially applied clamping force regardless of the size or width of the wheel/clamp combo (keep in mind the stress/pressures change, but the interfacial force relationship remains constant). With this in mind, the only reason you want to have a larger diameter wheel brake is to obtain a lower tortional load at the interface.
With that in mind, it comes down to static friction coefficients. The higher the friction coefficient, the less force I need to support the tortional load created by the monitor.
I went searching for friction coefficients and found a few useful values:
wood-wood dry = 0.25 (however I don't think this accurately represents the surface of laser cut parts... the heat should bring out lignans in the wood and may increase the friction coefficient... further, this is mostly endgrain exposure as it is cut layer of plywood, not long grain, so I don't know how representative this is).
plexiglass-plexiglass = 0.8
rubber-plastic = 1-4
Neglecting the weight of the arm and considering the position with the absolute highest torque (that being the arm completely horizontal), the monitor is about 41.5" away from the pivot, weighing about 10lbs, this creates 415 in-lbs of torque. if the break is 2" in diameter, this means that 415lbs of force must be supported at the interface tangentially. Dividing this force by the coefficient of friction gives the total normal force needed, which can then be divided by 2*pi to give the clamping force needed to generate the normal force. Note, this is the clamping force needed at the interface, if the force is applied on levers farther away from the interface, it is reduced by the ratio of lever arm lengths.
With a friction coefficient of 0.25 (wood to wood), it will require a clamp force of 264lbs. With a COF of 0.8 (acrylic to acrylic), it will require a clamp force of 82.6lbs. With a COF of 2, it will require 33lbs and with a COF of 4, 16.5 lbs.
This is assuming that there is only one clamp for each joint. I can put 2 on each which will half the force needed on each.
As can be seen, it is highly advantageous to get the highest COF possible. This made me think about rubberizing the interface. I found a spray on, non-skid coating called super grip. It lays down a silicone rubber that is very sticky. They say it doesn't attract dirt or dust and remains high friction. I looked at the MSDS and it contains several solvents which are known to be slightly solvating to acrylic. I was thinking about trying to apply an extremely thin coating of this stuff to acrylic. The idea is to dilute it with a solvent like MEK and brush it onto the acrylic surface. The solvent should loosten the suface exposed polymers so they can hopefully intermingle with some fo the rubber compounds. When the solvent evaporates, hopefully I will be left with a somewhat rubberized surface with higher friction properties. Another way may be to lightly sand the brake and clamp in the axial direction to creat ridges that will increase the effective friction of the interface.
I can easily test this out either by buildign the shoulder and upper arm and making various friction surfaces on clamp/brakes or by testing them on incline planes. The coefficient of static friction should be the tangent of the angle at which a static body begins to slide on an incline surface.