Rotoforge 2/13/2023

Today we solved two major problems at once... 

1.) We finally managed to find a liner material that survives during extrusion and is extremely effective at preventing welding between the wire feed stock and the motor shaft walls. This welding was previously responsible for nonrecoverable jamming and welding of multiple motors...

 2.) We finally managed to eliminate "candy caning" as seen in the figure below, completely. That is the shear coupling between the wire feed stock and the rotating die has been eliminated without eliminating the energy transfer between the tip of the wire and the inside surface of the die that facilitates frictional heating and extrusion of the wire onto the build plate. this was previously responsible for breaking the feedstock off inside the shaft and causing jams... In short, lubrication and higher RPM helped with this point.

Figure 1.) showing the candy caning of previous iterations of rotoforge wire feed stock... the twisting force imparted due to the force of friction at lower RPM and higher feedstock pressure causes greater shear coupling between the fluidized metal in the die and the rest of the feedstock, this causes twisting and often breakage which results in a jam.

As it turns out conventional motor oil, particularly heavier grades such as 10W-40 and 15W-40 full synthetic contain pressure and shear sensitive additives for reducing wear and oil film disruption such as ZDDP. These additives in tandem with a robust, heat and abrasion resistant mechanical barrier, such as E-glass fiber, provides for an excellent high speed, high temperature tolerant bearing between the metal wire feedstock and the walls of the rotating shaft. This next section includes some points of theory, and may be a little techy so I will try to provide some explanatory graphics and easily referenceable sources for guidance.

 1.) this paper, and a few others provide information on the requirements to print aluminum in the solid state. Their stated operating parameters were:

• 1000 RPM
• Ram force (extruder pressure) = 10 -21 MPa
  
• layer thickness of 1 millimeter
• track width of 20 millimeters
  
• D_f = Feed rod diameter of 15.9 millimeters, A_f, cross sectional area of  198.56 square millimeters
• A_n =Die orifice (nozzle exit area) 70 square millimeters
• Die orifice length of ~10 mm
  
• the extrusion ratio, or the ratio of nozzle exit area to feed rod cross sectional area is ~2.84
• This indicates a nozzle exit diameters of ~9.4 millimeters
• A surface area to volume ratio at their die orifice of ~2.42
• A characteristic working volume of  >= 582.56 cubic millimeters
  
  In our present iteration of Rotoforge, our accessible printing parameters are thus
•  29,000 RPM
• Ram force (extruder pressure) = 7-15 MPa
  
• layer thickness of ~0.1 millimeters
• track width of ~ 2 millimeters
  
• D_f = feed rod diameter of ~1.6 millimeters, A_f, cross sectional area of 2.01 square millimeters
• A_n = Die orifice(nozzle exit area) of 0.717 square millimeters
• Die orifice length of ~1 mm
  
• for the same extrusion ratio as above, this corresponds to a nozzle exit diameter of 0.95 millimeters
• Our resulting surface area to volume ratio would be ~6.17
• a characteristic working volume 5.727 cubic millimeters

Before we consider anything more complicated, such as the specific behavior of dry or lubricated metal on metal friction at low sliding speeds (1-20 m/s), a few important features stand out from comparison of their parameters to ours. 

• 6.17 : 2.42 ratio of surface area to volume ratio implies a ~ 2.5 X larger loss path for heat conduction away from the volume of worked material in the die orifice, on the build plate and inside the feed stock above the die for Rotoforge... this is a point against us in terms of ease of flowing material due to the greater loss of heat generated by friction between the feedstock and the rotating die, but a point for us in terms of die longevity and system thermal control. this also implies that our system could sustain higher proportional mass flow rates while staying in the thermal envelope of the materials used in the die, and other components.
  
  
• 582.56 : 5.727 cubic millimeters volume ratio implies ~100X smaller heat generation due to volume plastic deformation in Rotoforge versus large scale commercial systems.  This again is a point against us in terms of material being flowable, since the total heat evolved is smaller, the feedstock material will generally remain at a lower temperature for a given amount of input energy from friction between the feedstock and the rotating die. this is largely negated by the fact that the total volume, and thus mass of feedstock to heat is also smaller by the same 100X factor.   This bodes well for thermal management as it reduces the total waste heat that must be dissipated from the system to maintain the same proportional mass flow rate of feedstock through the die.
  
  
• With nothing but a guess at the length of the die orifice in the paper above, I cannot say for sure what our proportionate die orifice length should be, but I can guess that shorter is better to within the limits of the hot strength of the die materials as it reduces friction between die walls and extrudate and reduces total extruder pressure required to obtain a given mass flow rate.
  
  
•  Ram force is in the same ball park... Rotoforge could probably do with a better extruder that is less prone to slippage and provides at least 25 MPa of pressure, or about 25 newtons / square millimeter... or for a 1.6mm diameter feed stock, an extruder capable of ~50-100 netwtons total force on the feedstock metal wire.
   
• Without reference to non-extant exact theory, but with some papers for your perusal if you care for more details..  in general, the force of friction decreases with speed in soft metal - hard metal contacts. In effect, high shear rates and elevated temperatures due to friction, in the absence of welding, produce a situation like a metallic fluid bearing. This very imprecisely means that for our system specifically, between aluminum and stainless steel, the force of friction should decrease linearly with RPM, thus reducing the net shear strain on the wire feed stock away from the die-feed stock interface.
•  Simultaneously, the energy released due to this sliding fluidized metal friction between metallic surfaces, scales as the surface velocity squared. given that our die orifice is ~2.7 mm in circumference, and is rotating at ~29,000 RPM, our effective surface speed at the orifice edge is 78,300 millimeters / minute, or approximately ~1.305 meters/second. The surface speed of the large commercial system at the die orifice is ~28,200 millimeters/minute, or approximately, ~0.433 meters/second. this means, comparatively, that our "frictional energy" is about 9X larger, per unit feed stock surface area,(due to 3X the surface velocity and the velocity square in the energy term) at the interface between our wire and die, than their rod and die assuming the same applied extruder pressure and assuming the same coefficient of friction (this is almost certainly false, but within an order of magnitude).   This means we should be in the ball park, in spite of the larger thermal loss paths and smaller volume, all other things equal, to print aluminum 6061-T6 with our current Rotoforge setup.
  
• If we move to a more powerful and faster spinning off the shelf motor or belted offset spindle drive, at 60,000 RPM, we could obtain surface speeds at the orifice of ~2.8 meters / second, or about ~36X the surface friction energy of the large commercial system.  TLDR; more speed is better when it does not adversely effect longevity. cost or safety.  More input energy at the feed stock - die interface results in a lower feedstock viscosity, and a larger mass flow rate through the orifice for a constant extruder pressure.  
  
  So you might be wondering as I have, what is the holdup!?
  The answer seems relatively simple : Material confinement! 

In short, because the end of the wire is under pressure, at elevated temperature and shear rates, and is thus behaving as a fluid, it flows to fill the space available to it! 

Figure 2). You can see the expansion of the 1.6 mm diameter Al6061 feedstock to 2.2mm diameter foot, where it contacts the interior of the rotating die. 2.2mm is the internal diameter of the hollow motor shaft to which the die is tightly attached. The feed stock has expanded to fill the diameter of the hollow shaft, because it is unconstrained radially and so, once fluidized under pressure, flows through the path of least resistance(outward toward the walls with the centripetal force) until it fills its container.

This expansion of the end of the wire results in an increase in diameter to ~2.2-2.4 millimeters. This results in an increase of surface area to nearly ~4 square millimeters, thus cutting the pressure applied by our extruder at least in half.  Hence why the material can begin to flow, and then stop flowing once the pressure is reduced due to the larger area of contact.

Figure 3.) Initially the feedstock is a simple cylinder with a diameter of 1.6 mm and a surface area at the tip of ~2.01 mm squared. There are two flow paths available given the finite extruder pressure... once the feedstock is heated by friction and begins to flow, the extruder pressure and centripetal force cause it to flow into the open flow paths.

Given our limited pushing power, 14-30 netwons at most, dividing that force over twice the area easily brings us from ~7-15 megapascals of pressure to ~2-7 megapascals. Which is below the threshold flow stress for Aluminum 6061 at it's solidus of 595 celcius, and below the extrusion pressure used in the above paper, by a factor of at worst, 10X, and at best 1.5X ... we may have 9X the input energy per surface area of feed stock, but if that energy is spread over 2X as much area, and we lose 2.5 X as much energy to thermal dissipation, we would already be behind in terms of the viscosity of our feedstock(in response to the decreased energy density) at the die opening, despite this increased surface friction energy working for us.

Figure 4.) Once the feedstock has begun to flow into the die orifice and has filled the initially open flow paths, the extruder pressure decreases, as the force the extruder can apply is constant, but the bearing area of the end o the wire has increased in proportion to the square of its change in radius. now 2.2 mm in diameter, its effective surface area is ~4 square mm. This cuts the extruder pressure at least by half. Additionally, contact with the walls further increases this bearing area over which the extruder force is spread, thus further decreasing the pressure. To make this worse, the extrudate has its own bearing area to contribute, and a relatively large surface area on which friction in the die orifice can act. This increases the reaction forces substantially. Thus extrusion stops.

 Our next order of business will be producing a new die shape, that constrains the feed stock and prevents this expansion at the interface as much as possible, in order to force extrusion through the die opening preferentially without substantially increasing the area of contact. Additionally, an extruder upgrade is certainly in the cards.  A new offset spindle design capable of at least a sustained ~60,000 RPM  is probably a near term improvement as well. 

 

Figure 5.) The new Rotoforge tool design which will hopefully confine the fluidized metal to the interior of the die, and maintain a constant bearing area, so that the extrusion pressure can remain constant at constant extruder force, and the feedstock material can be continuously extruded.  Ideally the tip catch will hold a tight fit to the end of the wire, without introducing too much additional fricton, and when the wire expands and fluidizes at the tip, it will be captured in the catch and the material will have nowhere to go but through the orifice.

 Thanks for taking the time to read this far if you have! Looking forward to posting some real results in the next month!

Back to the lab!