Commentary on the apparatus of the Bond rod mill Work Index
by Alex Doll
December, 2015
alex.doll@sagmilling.com
The Bond “Third Theory” of comminution was originally divided into three size classes reflecting the varieties of comminution equipment common during the time period when Bond (and his collaborators) were gathering the information to calibrate comminution models. The middle size class, represented by rod milling, is fitted to a tumbling test, referred to as the Bond rod mill work index (WiRM, or RWi). The apparatus used to determine this work index was described in 1943 by Bond & Maxton. The author has noted there are some laboratories that have deviated from the apparatus specified by Bond & Maxton and there are modern comminution models that are calibrated to this non-standard mill geometry.
Introduction
The specification for the apparatus to determining a “Bond” rod mill work index is first described in Bond & Maxton (1943). It states that the apparatus is a tumbling rod mill to be operated in a locked cycle test at a fixed circulating load. The geometry of the grinding chamber is described as:
- mill inside diameter of 12 inches
- mill grinding chamber length of 22 inches (later revised to 24 inches in SME Mudd Series handbook)
- rods of two size classes, 21 inches long
- mill rotation speed of 46 revolutions per minute (approximately 60% of critical speed)
- a wave liner
The test procedure also describes a “rocking” of the mill every 10 revolutions to avoid coarse particles collecting in the empty space between the end of the grinding rods and the end of the grinding chamber.
The author is aware of three issues with this specification and the actual implementation of the test in commercial laboratories world-wide. Specifically, the meaning of “mill inside diameter” in the context of a wave liner, the use of a smooth liner in some laboratories, and the consistent implementation of the rocking behaviour. Of these three issues, the Author believes use of a smooth liner is the biggest issue with respect to standardization of the test.
Rocking of the laboratory mill
The length of the grinding chamber is longer than the rods, resulting a void space at the ends of the mill where little or no grinding happens. To avoid the collection of coarse material in this space, the test procedure includes “rocking” the mill every 10 revolutions through a 10° rotation “forward” for one revolution and then “backward” for one revolution, after which the mill is returned to a level position for the next ten revolutions before being rocked again.
The laboratory rod mills common in North and South America are all configured to be rocked, and this is believed to be a standard procedure in all the laboratories that the Author is familiar with (one laboratory presently lacks the rocking mechanism but is working towards implementing it).
Issues with a smooth liner
A “Bond” rod mill work index is to be determined in an apparatus with a wave liner. The author is aware of four laboratories that offer a rod mill work index test where the lining of the mill is either smooth, or smooth with a small number of primitive lifters that do not constitute a wave liner (one of the four laboratories is known to be investigating replacing the liner with a wave). Work index values determined by this alternative geometry should not be marketed as “Bond” work index values because they deviate from the specification and calibration of a proper “Bond” rod mill work index.
There are two problems with the smooth liner:
- The energy per revolution is different to the calibration data set used by Bond in his derivation of the Third Theory fitting of the work index formula to the rod mill apparatus.
- The nature of the breakage will be skewed towards abrasion breakage in the smooth liner designs, whereas the wave liner will have more attrition (and possibly crushing) breakage.
The first problem comes from the equation derived by Bond to calibrate a rod mill work index to the parameters of the rod mill tumbling test. The term in the calibrated formula that is affected by the liner is the grams (therefore, the energy) evolved per revolution of the laboratory mill. Since the equation expects a certain amount of energy (Joules) per mill revolution, the equation for a laboratory mill with smooth liner must re-calibrate Bond’s empirical equation (below, converted to Wi metric units) to the Joules per revolution generated in a machine with a smooth liner.
The second problem is related to how a rock breaks inside the apparatus. There are generally three mechanisms of breakage recognized as significant in milling: crushing, attrition and abrasion. A particular ore in a particular mill will have a characteristic combination of these three mechanisms that describes both the breakage energy consumed and the size distribution of the mill product. The action of a wave liner in a rod mill is to lift the mill charge and “spread” the charge as the mill rotates. This causes both crushing and attrition action by trapping particles between the rods as they are alternatively lifted and dropped. This lifting action is greatly diminished in a mill with a smooth liner, meaning that the relative amount of crushing and attrition will be less in the smooth liner design; most of the breakage will instead consist of abrasion.
Attempts to “convert” work index determinations from one mill geometry to the other must account for this difference in breakage mechanism. It is not enough to say “deduct 2 kWh/t from the smooth liner result” and expect an equivalent work index for a wave liner design. An empirical conversion determined for a particular type of ore (eg. Paleozoic meta-granitoids) is only valid for rock types that have similar ratios in the resistance to abrasion, attrition and crushing. A completely different rock type (eg. Tertiary andesite) will have a completely set of ratios, and therefore will likely require a different empirical calibration between the two styles of mill liner.
Bailey et al. (2009) described a rod mill work index round-robin program between different international laboratories with a normalized standard deviation of 12%. It is believed that the round-robin is a mixture of smooth and wave liner designs. The Author is aware of three Australian laboratories have have smooth designs, and these are expected to give higher work index determinations than the wave designs. The paper reveals that the two maximum values are Australian laboratories (therefore, smooth liner designs). If one excludes them and re-calculates the statistics, then the normalized standard deviation drops to 6.3%.
The wave liner specification
The Bond & Maxton specification gives no guidance to what constitutes a properly designed wave liner. The geometry of a wave would correctly require specification of:
- the wave height from crest to trough, and
- the number of waves.
The author is aware that most laboratories with wave liners have settled on designs involving eight waves with ½ inch wave height. Minor variations in height mostly affects the mill inside diameter calculation (discussed in the next section) and the Author expects the wave height will not otherwise affect the validity of the rod mill work index calculation (for reasonable heights where the rod trajectories are normal). If the lifting action of the rods is reasonably similar to what Bond calibrated his equations to, then the geometry is valid.
The meaning of inside diameter
The specification of the inside diameter is not specific about how to measure the diameter in the situation of a wave liner. Three possibilities are:
- measure the 12 inches from the top of a wave to the top of an opposite wave (crest-to-crest),
- measure the 12 inches from the bottom of a wave to the bottom of an opposite wave (trough-to-trough),
- measure the 12 inches from some middle or average point in the liner.
The Author is aware of laboratories who have implemented different versions of these options. It is reasonable to ask what is the expected difference in each situation, and is it significant?
The Nordberg rod mill power draw model (Outokumpu, 2002) is an easy way to check the effect of diameter by comparing the Factor A in the power model against three potential mill diameters. In all cases, assume a ½ inch lifter height. The “middle” measurement case will be a 12 inch effective diameter; the “trough-to-trough” will be 11½ inches; and the “crest-to-crest” design will be 12½ inches.
Calculating the Nordberg Factor A for all three liner cases and assuming that all other parameters are the same (Factor B, filling; Factor C, speed; ore density), then the difference in the Factor A should equal the difference in the power draw of the laboratory mill (this is over-simplified because the Factors B and C will change slightly). Assuming the “middle” measurement is a base case, the predicted variation in a work index determination due to measurement position is indicated in Table 1.
Table 1: Effect of mill nominal diameter on power draw
|
Diam, inch |
Diam, mm | Factor A |
Difference |
|
11.5 |
292 | 0.160 |
-10% |
|
12 |
305 | 0.178 |
0% |
|
12.5 |
318 | 0.197 |
11% |
The ambiguous definition of Bond & Maxton’s specification of the inside diameter of a wave liner can reasonably result in up to 20% variation in the results of a Bond rod mill work index. Which of the definitions is “correct” depends upon which definition was used in the Allis Chalmers laboratory where Bond and his collaborators calibrated the original work index equations. The Author is not aware of any publication that describes these details of the apparatus used at Allis Chalmers.
Final thoughts and recommendations
The Author is aware that other comminution consultants will have different opinions. Comminution is not climate science – consensus among practitioners is not mandatory. There are comminution models calibrated to use the smooth liner test results, and it is completely appropriate to use a smooth liner apparatus when using such a model. Calibration is more important than dogma.
- Ask a laboratory what type of liner is in their apparatus as part of a request for quotation. Also ask about the procedure used to rock the mill.
- If you are using a particular consultant for your project, then use the type of testing apparatus suitable for that consultant’s model.
- If it is necessary to convert work index results between the wave and smooth liner types, then rely on your consultant to decide how to transform test results.
- Laboratories using a smooth liner should not be marketing their test as a “Bond rod mill work index”. It is reasonable to call such tests a “rod mill work index”, but they should not be using the name “Bond” unless fully compliant with Bond’s specification, notwithstanding the ambiguities discussed in this commentary.
- If you use two consultants, expect three opinions.
More generally, the Industry needs a more exact definition of the specification of a Bond rod mill for work index determination. There is presently (2015-2016) a drive underway to better standardize the use of Bond work indices and testing procedures under the auspices of the Global Mining Standards Group (GMSG), and this may be a reasonable venue to better standardize the specification of the rod mill apparatus and the test procedures.
References
- Bailey, C., Lane, G., Morrell, S., and Staples, P. (2009) `What can go wrong in comminution circuit design?`, Tenth Mill Operator’s Conference, Adelaide, Australia, pp. 143–149
- Bergstrom, B.H. (1985) `SME Mineral Processing Handbook`, ed. Weiss, N.L., Society of Mining Engineers of AIME, New York, USA, pp. 30-65 – 30-71
- Bond, F.C. and Maxton, W. L (1943) `Standard Grindability Tests and Calculations`, Society of Mining Engineers, Vol 153, pp. 362–372. http://www.onemine.org/
- GMSC Bond Standard Working Group,
- [in progress]
- Outokumpu Mills Group (2002), `The Science of Comminution`, technical publication p. 39