grinding media selection
In order to do a good job selecting media for your mill, you must consider the type of mill being used, and what is and is not important to consider. For this reason, this subject will be broken into two sections: Vertical Mills and Horizontal Mills. The following information applies to both types.
First, we must agree that all components of the mill influence the way it runs. If it is important to select the type of media then it also must be important to formulate the product correctly for the mill, feed it at the correct rate, and apply the correct amount of energy. In other words, be it resolved that the formulation is part of the mill. Moreover, we should agree that the fourth law of thermodynamics is alive, well and working in your mill. That is: That all available (generated kinetic) energy input will be sinked in one form or another, and the way it is sinked will influence the way the mill will operate. In any given milling operation, a portion of the main and pump motor’s horsepower will be sinked as shear force and heat, a portion will be spent in the drive devices (belts, pulleys, etc.) and the rest will be put to work in the process of deagglometation. The proportion of the energy going to the work of deagglometation is depressingly low, in keeping with a device that works by transferring energy first through drive belts, then through bearings, then viscously coupling it to the material under process with disk, then finally tot he agglomerates via the formulation. Like Napoleon in Russia, supply line get longer and harder to maintain. Every stage of the process is “lossy”, especially the hydraulic coupling to the particles in the premix. Transfer efficiency even in the most efficient horizontal mills is generally in the area of 3% to 5%.
The object in selecting media to optimize the mill is to increase this transfer efficiency. In order to get a feel for his, however, you have to know what goes on inside the different types of mills.
The first most important thing to remember is that your formulation is part of the mill. What is your formulation like? How does it act under shear? More precisely, is your formulation thixotropic, Newtonian or dilatent? A thixotropic material will decrease apparent viscosity under shear. A Newtonian material’s viscosity is unaffected by shear. Dilatent materials increase apparent viscosity under shear. Of all of these types of materials, the best kind to run in any mill is one which is slightly dilatent, because all other things being equal, it can sink more energy due to its higher apparent viscosity. Far more common is the thixotropic premix, however.
With this type of premix, media selection is important in decreasing mill wear, since when energy is applied, viscosity drops and more energy is sinked to the mill itself. Newtonian materials, almost by definition, are homogenous and seldom need processing in a media mill. Formulating to imitate Newtonian materials is often advisable in a media mill with insufficient cooling capabilities.
Media Selection for Horizontal Mills – The Basics Most media for horizontal mills is more or less spherical, has certain surface characteristics, and has a specific density depending, of course, on the material from which it is manufactured. Materials include lead-free glass (usually soda-lime due to tits tensile strength), Zirconium Silicate, Zirconium Oxide, hardened and non-hardened steel shot, chrome and stainless steel balls and advanced ceramic materials like Yttriadoped cubic zirconia. Prices range from $4.00 to $200.00 per pound. Common sense would say that the most expensive would be a whole lot better media than the cheap-o stuff. Not necessarily so! It depends on your mill and the product that you are running.
First, let’s look at the material that is being processed. The first critical decision that you must make comes after determining the total solids level of you formulation. For most paint folks, this includes pigment and filler solids and resin solids. Determine the percent solids. If the number in this step is below 25 percent, the best bet is to reformulate to a higher solids level. Assuming that the material is between 25 and 100 percent solids, then make a sample and test the viscosity on a Brookfield to get some idea of what its static viscosity is. Materials above 25,000 to 30,000 cps viscosity (unless they are highly thixotropic) will probably be impossible to process in a standard-configuration horizontal mill with agitator disks and normal internal volume. A good operator can use some tricks to get it to run, but it is not something he would want to do every day. In regard to running very heavy thixotropic materials, not all mills are created equal. To do this type of formulation successfully, the best possible easier to separate the media separator (which imparts considerable shear, making it easier to separate the media without causing mill wear,) and an agitated discharge housing, (to keep the material from setting up after leaving the high shear zone, causing mill pressure problems.) So, now we have a formulation which is over 25% solids and below 30,000 cps. What media do we use?
Types of Media
Well, it still depends…on the properties of the media. Among these are shape (or sphericity), surface effects and density. Sphericity is the degree of perfect roundness that the media displays. Certain types of media tend to be rounder than others. In a horizontal mill, this makes a difference. Most doped ceramics, for instance, are pressed in rotary molds and sintered into spheres in an electric furnace. This media is nearly perfectly spherical. Zirconium Silicate and Oxide can vary quite a bit in sphericity, and often tend toward a teardrop shape, which is far from optimal in a horizontal mill. Even closely graded media will display this tendency. On the other hand, some Silicate and Oxide are very spherical, because they are made in the same way as a doped ceramic. This media tends to be a bit more expensive, but is considerably more effective in a horizontal mill. Steel shot is generally made by spraying molten steel down a tall cooling tower, then collecting the shot at the bottom and classifying it according to size. After this, the media is normally “beaten” in a hammermill – type device to bread apart “dumbbells” (two teardrop shaped beads joined at their pointy ends) and generally wear off gross surface irregularities. If this media is used without the beating step, the product under process will pick up all of the media fines, as the media will tend to wear round in the mill. These fines contaminate the product and tend to clog screen-type separator devices, so it is best to eliminate them prior to loading the media in the mill. Glass can be manufactured to a high degree of roundness, but its density is fairly low. Density does not matter as much as roundness in a horizontal mill; since the force of gravity is not considered an important limiting factor to horizontal mill operation. Defects in glass beads are more likely to negatively influence the life of the media than in other types. Bubbles of air inclusions of foreign material or internal fracturing (“shiners”) can cause media fracturing. Surface fracturing causes the media to look “milky”, or frosted, and media thus effected will wear at an accelerated rate.
Horizontal Mill Physics
One might ask the significance of the insistence on roundness for media used in horizontal mills. To fully understand this, we must examine the horizontal mill’s internal physical environment and hydraulic flow characteristics. As we all know, the general physical layout of a horizontal mill includes a horizontal tubular grinding chamber, in which an agitator shaft with agitator disks is centrally located. The agitator disks set up two tori of laminar flow, one on either side of the disk, and the premix material is fed through these tori. The media is homogeneously distributed in these energy tori, not touching or running into each other. The energy is transferred hydraulically from the disk to the fluid in the mill, causing infinitely small layers of laminar flow, in which the media acts solely as a surface to build shear against. Each gap between media amounts to the analog of a rotor/stator homogenizer. The space between the media is changed by varying media loading levels, the number of gaps is changed by varying the media size. As the product is pumped through this fluidized bed of media, the material is deagglomerated in proportion to the shear force generated in the gaps. There is, for all practical purposes, no physical attrition in a horizontal media mill. The media tends not to collide in the high energy areas of the mill, just in the low energy areas around the shaft. If media does happen to collide, the chances are against the media colliding with a pigment particle between them. Of course, the probability increases as the solids level approaches 100 percent…but even then, this happens in the low energy are of the mill, so the energy levels are not significant.
As long as perfectly spherical media is used in the mill, all of the spaces or gaps between the media are the same size. As soon as the media is not spherical, the force of the fluid is not exerted equally on the media’s x, y, and z axes. This, in turn, causes out-of-spherical media to “tumble” in the mill. When this happens, the space between the media is not the same, there are some large gaps and some small gaps. The liquid vehicle in the premix flows preferentially through the large gaps; where, as we said before, the shear force is not high enough to do any deagglomeration. As a result, mill efficiency suffers. This is the reason for using the roundest possible media…to improve the uniformity of the gaps between the media.
For years, it was thought that denser media worked better than lighter media across the board. This is a misapplied theory from vertical mill days, because denser media was necessary to avoid media float in high viscosity premixes. In a horizontal mill, however, density is not nearly as important because gravity is not a major factor in their operation. Going back to the model above, we see that the media is homogeneously distributed in the shell by nature of the energy level imparted by the agitator shaft, irrespective of gravity. As the media circulates in the mill, the only parameter that is affected by density is media acceleration and the retention of energy in the media after it has been energized by the disk. Denser media is accelerated more slowly than less dense media. In other words, it has more inertia. Once energized, it also loses energy more slowly. The effect of these properties in a horizontal mill is that the media will impact the grinding shell wall and sink energy to the mill wall before being drawn into the recumbent flow area between the disks. This is undesirable in a horizontal mill because it causes grinding shell wear and puts undue stress on the mill cooling system. The bottom line is that you are probably better off using glass and Zirconium Silicate (inexpensive) media in your horizontal than the more exotic (expensive) types.
Media Surface Effects
In addition to these properties, media also exhibits different levels of surface activity which is directly attributable to the type of surface finish which is on the media. Porosity or pock-marked, irregular surfaces on the media has an additive effect on the milling process caused by surface cavitation as the fluid under process is forced around the bead. Beads with the most surface effect are of the pressed and sintered variety, as sprayed or rolled media ends to develop a smooth, shiny outer surface. The effect of surface cavitation on mill efficiency is minor, but the downside of using this type of media is accelerated mill wear because of the increased abrasion of the irregular surfaces. Also remember that denser media is usually made by the press and sinter method, and it is more prone to unwanted mill impact in the first place, so the effect is additive.
Finally on the horizontal, there is the effect of media size. We touched on this earlier, but it is good to restate it now. As most of the work in a horizontal mill is done by squeezing the material through the gaps between the media, it makes sense that the more the gaps, the better the milling. In order to increase the number of gaps, one needs to increase the number of beads. Assuming that the percentage media loading is maintained as a constant then the only answer is to decrease the diameter of the beads. Some constraints need to be placed on the application of this theory, however. Initial premix particle size has a considerable bearing of its effectiveness. If the intermedia space in the operating mill is smaller than the incoming particle size of the premix, the mill becomes a filter, and the mass of the particles tends to push the media to the discharge end of the mill. In mills that are designed for this type of operation, very small particle sizes can be had. However, standard horizontal mills will grind themselves up in this type of duty, much as they will if the mill is packed-out hydraulically. In order to use very small media, (0.50 mm or smaller) you must have a very good premix indeed.
The bottom line in media selection for a horizontal mill is to use the smallest, roundest media that you can afford, irrespective of the density and material type of the media.
Vertical Mills – The Basics
A vertical mill is a similar, and in some ways more complex device than the horizontal mill, with a much different set of media concerns, owing to the fact that it works completely differently from a horizontal mill. In a vertical mill, one must deal with gravity, hydrodynamics and media flotation which are not a concern with the horizontal mill.
The average vertical mill comprises a large vertical grinding chamber with a centrally located agitator which has a number of grinding disks mounted on it. On the bottom of the shaft is a massive balance pulley which serves to help center the shaft and to a certain extent direct the flow of the product from the inlet, which is at the bottom of the vessel. The premix material is introduced at the bottom of the mill, is sheared in the various shear zones caused by the rotation of the disks, and exits through a separation device at the top of the grinding vessel. The hubbed disks impart a peculiar flow characteristic in the mill which causes actual media impingement in the high energy area of the mill. This is the major way in which the vertical mill is different from the horizontal. As it is generally not be loaded with as much media as a horizontal mill (as a percentage of the total void volume), this wiping action between the disk flow patterns allows the vertical mill to pick up some efficiency. Your average vertical mill can only be loaded to a 50-60% media load for several reasons. First, due to the negative effects of gravity, it is likely that the agitator shaft drive horsepower will be insufficient to start the media bed in motion and fluidize it completely. Second, if more media is loaded, it is likely to rise when fluidized to the discharge device and either blind or wear it.
The life of the vertical began in around 1950, when several engineers at E. I. DuPont de Nemours and Company, Inc. developed a design and a specification for a vertical mill with multiple agitators that combined shear and attrition to do the grinding. A manufacturing license was granted to Chicago Boiler in the USA, and the Red-Head was born. The mill was comprised of a tall, vertical chamber, with a top-entering agitator shaft oriented in the center of the vessel. Pinned or set screwed to the agitator shaft are multiple hardened spoked disks of specific design. The exterior flat disk area id used to accelerate in the mill into multiple layers of fairly orderly laminar flow. These zones are arranged the whole way up the shaft tot he discharge device. The spoked open center of the disk allows the media which is carried up to the top of the mill to flow back down to the bottom in the low energy area close to the shaft. Unlike the horizontal mill, these tori intersect, causing considerable attrition in a fairly high energy area of the mill, where the two flow patterns “wipe” across one another. This is what causes the characteristic “herringbone” media flow pattern in a vertical mill.
In order to more completely appreciate the significance of the disk design in the operation of the mill, and your choice of media, let’s explore the physics of the mill more carefully. As the agitator disk spins, the energy state of the mill is transformed from low to high in relationship to the peripheral speed of the grinding disk across a line bisecting it at its axis. The area between the grinding disk and the shell, then, is the area of highest kinetic energy in the mill. The disk itself couples to the media. The product is accelerated away from the inner ring diameter of the disk toward the grinding vessel wall, and the media goes along for the ride, displaying a finite impedance to motion, or inertia, determined jointly by the force of gravity, the “stickiness”, or viscosity of the material under process, and the density of the media. Thus is formed two energy tori for each disk, one “doughnut” above, and one below each disk. The flow inside each torus is ordered from high next to the disk to low in the area of recumbent flow between the disks. The vessel wall forces a transform of velocity which causes the material to lose considerable energy induced by the disk. It is in this area of recumbent flow that media is allowed to move from torus to torus up and down the mill. Compared to a horizontal mill, the recumbent flow area of a vertical mill contains more potential energy, due to the design of the disks. It is for this reason that physical attrition in a vertical mill is an important component in the work that it does.
As the media tumbles from its most highly energized state to its most benign state, it is likely that it will be drawn into the high energy area of another disk, jumping randomly between energy tori, allowing overall random media flow within our laminar flow model. Even though the media flow through the mill is random, the product flow is highly ordered and highly predictable. None of this physical activity would be possible without this peculiar disk design, which maximizes shear within the framework of an inefficient model of shear generation. Remember, this was ground-breaking research in the 1950’s, and the world have never seen the like of even this level of efficiency in the grinding process.
What we have created with the mill disks is a fluidized bed of highly energized media, just like in a horizontal mill. Unlike a horizontal, however, gravity causes the media to return to the bottom of the mill when it loses energy. The space between the media is influenced by the percent media charge in the mill, since the energized beads seek a homeostatic spacing scheme, influenced by the level of energy transfer from the fluid under process. The closer the spaces between the media, the higher the level of shear developed in the mill. Also, the closer the beads are spaced, the more likely they will be to be involved with the wiping impact (causing physical attrition) that is characteristic of vertical mills.
If a vertical mill were to be fitted with a glass shell so that you could see the media flow while the material is under agitation, you would see an even, herringbone pattern of motion, as the media lines up into shear layers and begins to do work. If you were to load two colors of media lines into the mill in two distinct layers, you would see that the two colors would mix and become ostensibly homogenous in the first few seconds of operation. This indicates that the mill will wear the media uniformly, and that the load is fluidized properly.
Some paint manufacturers over the years have charged their mill with two different sizes of the same or different density media. The object here was to use the larger media (often more dense) at the bottom of the shell, and the smaller (often lass dense) media at the top. As you know, the efficiency of media varies with its size ratio to the particles being ground. Some have reported picking up some efficiency, since the larger, denser media will tend to segregate to the bottom of the mill where the larger particle size exists. As the product grinds and is moved up the mill, it is worked on by the smaller media, which more nearly mates with the smaller product particle size. There are certain practical limits to this, however. The density and size difference must be kept to a minimum, and this is a largely dependant on the shear viscosity of the premix. In addition, there will be a certain loss of efficiency in the area where the media will mix, as it invariably will. This media mixing causes two problems. First, the larger media will cause a “windage” area on either side of the smaller media, decreasing the actual amount of shear surface in the mill. Also, the denser media, irrespective of size, will tend to wear the less dense media at an accelerated rate. If the larger, denser media is too much of either, it will not fluidize correctly, grinding away the bottom of the grinding chamber.
Go, No-go Shear Model
As opposed to the horizontal mill, not all of the work done in a vertical mill is attributable to shear. For this reason, density makes a little difference when choosing media for a vertical mill. Denser media stores more energy, and when it runs into pigment particles and other media, it releases more energy, generally providing more of a “whack.” However, an indication of the efficiency of attrition in a vertical mill is shown by the fact that this extra energy would be liberated into the mill upon impact as heat. Vertical mills are not known as being product heat control problems, in fact, they are know as being somewhat less of a problem than horizontals in this regard. The indication, then, is that very little of the work done is by attrition. All other things being equal then, most of the work is still done by shear. But this puts the vertical mill at an extreme disadvantage, since common knowledge says that you charge a vertical mill to only a 50 or 55 percent media load. Having said this, then, it is obvious that the media will be more distantly spaced in a vertical mill, and less shear will be exerted on the product. Why is it necessary for a vertical mill to run at this lower bead charge?
The primary reason for this is media float and the resultant screen blinding that occurs. If you are one of the intelligent who converted your open vertical mills to run with packing glands, effectively sealing them, you have received a secondary benefit. Your primary benefit is that your open mill is no longer belching VOC’s into your manufacturing area. The secondary benefit is that you can now jack up your media loading and completely flood the screen area with media and product. The increase will not be a milestone, you are safest to start at 65%, but it will yield you considerable increased efficiency where some is sorely needed. All of the other old rules also apply:
For this sphericity discussion, I would like to propose an experiment. As we all know, oblateness, or “eggyness”, causes media tumbling in the mill. The reason for the tumbling is that the oblate shape causes inconsistent distribution of energy on the bead’s x, y and z axes. For the moment, we’ll spare you the vector physics that proves this, but it can be demonstrated easily. Find a shop vacuum. Install the hose on the discharge of the vacuum, and put the discharge nozzle in a vice to stabilize it. Locate a child’s play ball about 3 ½ to 4 inches in diameter. Lighter is better, and the best weight is about 3 ounces for most shop vacuums with ½ HP motors. Also secure an oblong object about the same weight and diameter – a L’eggs container that has been glued together will work well. Make sure that the nozzle is plumb and level in the vice. Turn on the vacuum, so that a stream of air is blowing out of the nozzle. Ever so gently, suspend the ball in the air stream. It will find its own level on the column, then stay suspended at the same place, seemingly levitated on the column of air. Now try this with the oblate spheroid. It will be suspended for a short while on the air column, but it will then begin to tumble and gyrate, eventually falling off of the column.
This is the effect of media tumbling in the mill. With the ball and the vacuum cleaner, we are concerned with aerodynamics. In a mill, we are concerned with hydrodynamics. CD (or drag coefficient) is the important variable with the vacuum. CD’s hydrodynamic analog, viscosity, is the important variable in the mill. The surface area of a pure sphere is the same in the object’s x, y and axes. An oblate spheroid, on the other hand, has different exposures in the x, y and axes, which causes the energy to be distributed disproportionately across the body, creating dynamic instability. Having media displaying tumbling behavior in an enclosed space causes many problems, but explains one peculiar problem. It explains the phenomenon of all media shapes wearing round. In case you never noticed, all media tends to wear into a spherical form, rather than wearing uniformly so that the original oblate media ends its life as a smaller analog of itself. Media tumbling exposes the pointy ends to more abrasion, since the pointy end tends to whack into other media as it tumbles. For this reason, media always tends to wear round no matter what shape it starts out as. This same tumbling causes the space around the media to be different form bead to bead, creating wide and narrow passages in the media bed. Product will flow preferentially through the wide spaces, considerably lowering the composite shear in the grinding chamber. So, get the roundest, most uniformly sized media you can afford. As we mentioned before, density does make a difference here, so factor this into your decision.
Remember…tumbling (or non-spherical) media displays non-homogenous inter media spacing, which allows the product to bypass the high shear (smaller) gaps and pass through low shear (wider) gaps. As a result, composite mill efficiency plummets. Although this effect in a vertical mill is far less debilitating than in a horizontal, the benefits of round, uniform media are noticeable and worth striving for.
Media float and the screen blinding that it causes are the worst enemy of the vertical mill. This is a phenomenon where the media is carried to the top of the grinding cavity by the product flow. In a horizontal mill, this would be called hydraulic packing. There are several ways to solve the problem of media float, so the mill user is not without options. The first and easiest way to solve the situation is to use media of higher density, which will have less of a tendency to float in the first place. The next thing to do is to lower the product pump speed, as the velocity of the millbase through the grinding cavity can also cause the media to rise in the chamber, much as increasing the volume of air being discharged in our vacuum cleaner model a few topics ago caused the ball to rise higher on the column of air. If you decide to solve your media float problems through going to denser media beware of several complicating factors. A denser media, because it is “heavier”, will tend not to fluidize as easily, and will tend to take more power to start up. This is normally not a problem, but it does exacerbate an existing problem with vertical mills. That is that they are not as energy efficient as horizontals. When they are started, they must overcome the force of gravity. Normally, a vertical mill will require between 95% and 115% of rated agitator horsepower to start, and then fall back to 50% - 70% to run. Many older plants are close to their maximum power grid usage, and may not have enough power to start a really dense media load. Of course, most people do not start all of their mills at one time, even if they are cascaded. Loading an electric motor to over 115% of its rated shaft horsepower for more than a few seconds is pure folly. Before changing to denser media, make sure you have the power to start it. In addition, if you have sealed your mill, you can enjoy the benefit of loading a greater media volume. This can make startup horsepower problems much more sticky.
By way of practical example, a typical “sandmill” of the 30 gallon size generally comes equipped with a 40 HP motor, which is fine for a 50% charge of silica or glass. It is even O.K. for a 50% load of zirconium silicate or oxide. 40 HP is marginal for a 65% load of these denser medias, however. It will also absolutely not work with steel shot. For steel shot or hardened stainless balls, 50 HP is required.
Surface effects are influential in vertical mills much as they are in horizontals. One must be wary, however, especially when switching to a denser media with increased surface effects. A example of this would be switching from glass to zirconium oxide. Your grind will surely improve in most cases, however zirconium oxide is several orders of magnitude more abrasive than glass because of its “nooks and crannies.” Being denser, it will tend to stay in the bottom of the mill, particularly with a low viscosity premix with hard-to-grind components, like a waterborne airdry or electrophoretic primer. This will cause accelerated lower shell wear as well as reducing your balance pulley to the size of a hockey puck in no time. Be careful. In general, the less viscosity exhibited by the premix, the lower density and lower surface effect you want from your media. There are, however, several manufacturers who provide zirconium silicate which is only slightly denser and has much greater surface effect than standard. This gives you the best of both worlds.
Media size is less important in a vertical mill than in a horizontal, but does have an effect on the final grind. It follows form what went before that smaller, denser media, in keeping with the premix viscosity is the best way to charge vertical mill. Most vertical mills can easily be adapted to run media down to .7 mm and above. Again, size consistency is most important here. The narrower the size range of the media, size for size, the better the mill will perform.
You should select the media for a vertical mill in much the same way that you do for a horizontal. Be aware that media density can either be your best friend, or your worst enemy depending on your premix viscosity. Your vertical mill has some performance limitations caused by the mill’s orientation but in the real production-floor world, these can be easily overcome by various means.