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## Calculating Power Draw when sizing Ball Mills (16 replies and 1 comment)

The discussion you have initiated is very interesting indeed. I too am not an expert in ball mill sizing but from what my general understanding goes, method to calculate Bond's Work Index (WI) takes into consideration a 250% circulating load and ball mill sizing is based on the WI. In other words a 250% circulating load is already factored while calculating the WI. So, if the actual circulating load in an operating mill goes above 250% then obviously, as you say, the residence time in the mill will correspondingly decrease and vice versa but I am not clear about your comment "if we engineer too much risk into capital equipment". Are you implying "over designing" to include too many safety factors?

The actual lab experiment in finding the BWI has a 250% circulating load, is done dry and involves reducing the ore from a p80 of 2mm to 100 microns. If you size a ball mill based on Nordberg; you use the hardness to derive the needed power to reduce to a target size at a particular throughput. From that "power draw" you calculate a shell size from 4 parameters: diameter, effective length, wet or dry? %loaded and % of critical speed. You also size an appropriate motor to turn the shell from the original "power draw" you calculated.

The most important work in the ball mill sizing IMHO is sizing based on the orebodies feeding it, taking into consideration the entire mine plan, desired throughput and giving yourself a bit of extra "breathing room" in case there's a slump in prices, new production capacity or synergies created and you want to ramp up production.

The circulating load is a result of the ore hardness, mill power, power efficiency (i.e. size of balls, slurry density, etc), classification efficiency, and product size. The power draw is driven mainly by mill diameter and length, ball and slurry charge level, and rotational speed. But the slurry charge in an overflow ball mill doesn't change very much because most of the slurry occupies the void space in between the balls, so as the circulating load increases, the discharge rate also increases. This means the residence time goes down but the power doesn't really change that much. On the other hand, for SAG mills with grate discharge, the charge level is a bit more variable, so you do sometimes see higher SAG mill power or mill load levels at higher circulating loads. This why the cyclone feed pump or cyclone cluster is often the bottleneck in capacity-constrained ball mill circuits, but mill load or power draw is often the bottleneck in capacity-constrained SAG mill circuits.

Regarding the other comment about risk, I'd say that there is no universally agreed upon perception of risk, and what is risky for one engineer is not for another (and vice-versa). As Jonathan notes, modern geometallurgical techniques are a great way to manage and mitigate risk associated with the ore body's hardness properties. Model validation and error propagation studies are effective for reducing risk on the scale-up side.

I don't know how to design a ball mill. I am an operator. I can discuss about operation problems in grinding.

About OPERATIONS:

Power calculation is done by 100% power consumed to do a job divided by throughput. We say KWhr / TON FEED. It is the power consumed by input feed to achieve a grind of mesh say 200# 80%.

HOW THIS IS AFFECTED:

Feed size: As feed size increases consumption will also increase as, larger feed size reduces input rate to achieve 200# 80%.

Ball Charge: If you reduce ball charge ---same effect as feed size.

Ball Mix of different sizes: ------do-------

Largest ball size charged daily------do-------

Wt% Solids: ---------------do--------------

RECIRCULATING LOAD:

This is never achieved as per design. It always varies on higher side. As today we are use Hydro-cyclone whose apex gets worn out soon. Old days we used Classifiers.

Wear of Apex will cause high recirculating load. It goes along with feed. Finally feed to ball mill should be same. But it never happens. After 1st day of operation it gets reduced due to this problems. Fresh feed is reduced.

Pumps: If not operated efficiently cyclone will have surging effect and more RCL.

While designing a ball mill are all these operating parameters are taken care?

Ball Charge: Size, Ball Hardness, composition also play a major role. Ore is never same while designing and after 10 years.

If you are using rubber spigots, switch over to wear resistant ceramic or polyurethane ones. To address the surging effect, you may either use an efficient sump level control or variable speed sump pumps. Any good text book on ball mills will give you a formula to calculate the ball top size for your operation. The ball type is also a subject of economics as well as technology. Cast alloy steel balls are cheaper than the forged variety, but the latter is always better. Forged balls have no internal defects such as cavities, blow holes etc and therefore wear out evenly, a factor that is essential for high ball mill efficiency.

When sizing a mill the dimensions are specified to draw the power required to produce the hourly rate of finished product, circulating load is not finished product, it is a convenient way to achieve a continuous operation instead of a batch operation.

The power requirement is based on the Bond Work Index test result. The test provides the energy required to reduce a known mass of material from a F80 to a proposed P80 as stated above, nominally 106um (though specific tests may even go down to 75um if further accuracy is required), depending on the product size design basis being considered. The resultant is in kWh/t.

This value is then multiplied with the throughput to get the kW requirement.

ie BWi x t/h = kW

(though this would be considered a worst case number)

The mill designer then takes that kW requirement and evaluates the numerous parameters, as all above have stated, to determine the energy transfer requirement from the mill motor to the particle surfaces to achieve the size reduction in the continuous operation.

So with increasing throughput you increase the power requirement.

In relation to the circulating load this is really a function of what is needed to achieve the size reduction, for a continuous operation. But at the end of the day the total energy is the same it is just with increasing circulating load you are changing the transfer particle size distribution, hence the portion of material that is removed to the product stream on each circulation.

The system eventually reaches an equilibrium, for each circulating load considered. Provided you adjust operating parameters of mill and cyclone systems to still achieve the product size distribution proposed.

I hope that answers your question. Do not look too closely at the internals as that will make things look confusing, step back and look purely at the feed in and the product out.

I am not a designer but had been in operation for more than 20 years. In my experience the mill size calculated from Bond's index is not sacrosanct as per as capacity is concerned. Significant increase in new feed capacity can be effected by control of classification efficiency. This increase can be as high as 30% in smaller mills. The consideration should be mill & the classification system together and not mill alone in isolation.250% circulating load is not to be treated as something "holy" but it should be managed for the best or to say loosely the optimum output. And output is not grind size alone but also the % solids of the mill circuit output. Many times optimum % solids required in the beneficiation circuit dictates the requirement from the grinding circuit. Selection from Bond's law is the starting point for mill sizing but needs to be corrected with many factors as the law holds for 8' by 8' mill only.

Of course no one, including myself, have addressed the original question posed by Mr. Keith and what we are writing are the actual observations in operation. I guess the answer would require a population balance of each fraction and how that changes with increase or decrease of circulating load or increase of fresh feed. Difficult to put the details here but may be someone could do it.

Very good dimension; as said, do not try to analyse a ball mill performance in isolation; the hydro cyclone which looks so small in size in comparison to the mill and which does not make much noise nor heat has a major say in understanding gridding circuits.

I am not an expert but am into basic sizing of mills. I agree to the answer given by Peter above hold good because mill power is calculated for power drawn by the cylinder (mill) considering media and slurry loading. Any excess feed in terms of fresh or recirculating for that particular mill power drawn will not affect. However, lesser feed will definitely draw lesser power.

If you run a ball mill in open circuit the chance of large particles surviving the trip is low but they do break into medium sized particles. At the discharge end the outflow is a sample of the slurry there. There will be way too many oversize particles for most intended applications. The solution is to classify the discharge by size and return the oversize to the feed. Bonds work assumed a circulating load of 250% so that a reference set of conditions could be met for testing. By removing particles that were already smaller than the desired size this both prevents overgrinding (grinding too small) and frees up volume for the larger particles that are returned.

Bond says that a work index is the measure of the energy to reduce from a feed to a product size under these conditions. This is energy per tonne of raw feed, the higher the recirculation the lower the residence time, but the power draw of a mill is a fixed number. It is, simplistically, the energy required to lift/tumble a ball charge that occupies 40% of the volume.

Efficiency is another story. Bond's equation has several factors related to the physics of the mill and the desired reduction. These are used with the Work Index to estimate the capacity of a given mill. Another factor that, IIRC, Bond did not investigate is the percent circulating load. Studies have demonstrated what is intuitively obvious, that the higher the CL the more efficient the circuit. This is because particles of acceptable size are being removed faster, preventing the wastage of energy to make them even smaller and freeing up energy to use on the oversize. A 400% circulating load will allow more tonnes per hour of on-specification product that does 250%, and even higher re-circulation is better. The trade-off becomes the cost of the pumps and the classifying equipment.

Cyclones are not efficient classifying devices but they are cheap and low maintenance compared to the spiral and rake classifiers that preceded them, and require less water. An alternative to them is wet screening which can be done down to around 100 microns if the solids volume exceeds 50%. The solids returning to the ball mill contain lower amounts of fines, zero being ideal. This can add another 10 percent or more capacity while reducing the amount of undersize that might not concentrate. There are a couple of hundred circuits on the planet that use screens. Derrick Screens are specialists at this.

The limited tests in lab work index on some iron ores indicated that varying test sieve and circulating load [CL]indicated that the work index value increased with increase in finesse of MOG [ increase in sieve number] and decrease in circulating load. The increase in work index value may be due to finer product [P80] and decrease in net grams produced per mill revolution [GBP]. The decrease in GBP is a result of requirement of more number of revolutions required for producing more finished material as weight of finished material is inversely proportional to [1+CL]. However in practice the use of 2 stage classification and use of Derrick stack sizer is believed to increase mill throughput and reduce the grinding cost maintaining the MOG. Probably, the increase in mill throughput is due to prevention of over grinding finished material. However detailed test data sharing by lab test people, mill designers and classifiers designers is solicited to understand the phenomenon.

I believe that as circulating load in a ball mill increases beyond a critical point the mill power draw begins to fall so there is an adverse effect on grinding efficiency (apart from the obvious physical problems it causes like high scats rates, balls discharged from mill, sumps overflowing, cyclones clogging up etc.). But getting back to the basic question, if circulating load is too high, then it really is saying the mill (or calculated power) is too small, therefore beyond a critical CL an allowance should be made in sizing a mill, question is what is the critical CL?

The energy draw in a ball mill is friction plus the work to lift the load of balls and slurry, mostly balls, up the wall so that it can free fall and create grinding. It has absolutely nothing to do with rate at which the slurry is being replaced by new or recirculating feed. How in the world can a ball mill motor know the rate at which the slurry is passing through body of the mill? Your list of negative effects is hard to comprehend. Higher scat rates are good for the operation. Good balls can be sorted easily and recycled, and no good engineer would try to operate a mill at a CL that is not compatible with the available classification equipment, both being chosen at the same time.

The really good paper that I have describes test results from 100 to 500% CL on several minerals including coal. Above that the incremental gains were much diminished. 500% would require about twice the pumping and classification capacity vs. the reference 250% and the laws of CAPEX and OPEX apply. It may not make economic sent to use anything higher than 250%. It should, though, when overgrinding causes significant recovery reduction.

Sizing a mill is straightforward. If the rock needs 10 kwh/t which is based on a CL of 250% and the plant requires 150 tph, then the mill must deliver 1,500 kw at steady state. That will not be the size of the attached motor which must be capable of starting the mill, up to twice as much nameplate power. Power draw is basically related to volume after all the efficiency factors are put in.

The reference CL is 250% and as far as I know there is no physical upper limit until the feed chute plugs. The premise of this thread, that power draw and CL are related, is wrong to begin with. And for what it's worth, I only do these calculations for a small operation.

I agree with Mr. Enzo that higher circulating load is not necessarily healthy. In closed circuit operation of any mill, the mill discharge has a higher % of intermediate particles than the finished size range. The hydrocyclones separate the desired size and circulates back the coarse. Due inefficiency (cyclone efficiency is never more than 60-70% at 200 mesh separation) of the hydrocyclones a good amount of liberated fines also circulate back to the mill. In a normal operation the cyclone underflow contains anywhere between 25-35% of the liberated fines. And that is considered a good operation. Higher circulation would essentially mean, for a particular mill, more of such fines circulating in the system. Even if the feed chute does not get choked, which is an extreme situation, there will be more slurry in the system than the pumps or cyclones can handle and thus the new feed will have to be reduced to bring back the flows to normalcy. This situation is very often faced when the spigots/apex of the cyclones wear out and are not replaced in time. Double stage classification increases classification efficiency and reduces recirculation of fines and thus enables increased new feed from the same mill than designed. Same is the case with Derrick screens which are very efficient. Ease of installation or cost is another matter. A simple mass balance calculation considering different circulating loads can explain this.

I would also like to emphasise that a particular mill-cyclone combination cannot be used to achieve a wide range of grind requirements. It can be done only within a limit that too at the cost of new tonnage unless care is taken to maintain the classification efficiency. Agreed 250% circulation is only a base but that does not mean that that the mil could be run with 400% circulating load without affecting new feed tonnage or output quality both terms of size & pulp density. Similarly mills cannot be operated at too low a circulating load either, it will grind too coarse and the mass balance will go awry.

Circulating load has to be brought back to around 200-300% by increasing new feed to stabilise the circuit. To me it is a mystery how Mr. Bond had hit upon 250% circulating load which seems to be optimum for most of the normal grinding requirements.

GOOD MORNING SIR/MADAM,

Am working in Mineral processing designing field, as a fresher i don't have much idea about sizing equipment's...please tel me how can i calculate ball mill size ?

I’m interested to know when sizing a new ball mill, as to why recirculating load has no effect on the power calculation, although it will have effect on volumetric capacity naturally. For instance a mill of 300tph with a 300% recirculating load would have 1200 tph going through effectively, but if we reduce the recirculating load to 200% at 900 tph it will not change the power calculation. However if we increase the fresh feed by 100 TPH the power calculation goes up as does the size of mill required.

Not being a comminution expert by any means, I wonder if we engineer too much risk into capital equipment these days, or am I just working with the wrong calculations.