## CWi vs DWi

What is the difference between CWi and DWi: WiC measures fracture strength in coarse rocks, DWi measures matrix competence in medium-size rocks.

What is the difference between CWi and DWi: WiC measures fracture strength in coarse rocks, DWi measures matrix competence in medium-size rocks.

**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 (Wi_{RM}, 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.

Unrelated ‘entertaining’ image

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 ….Read more

These notes are based on observations made while on a recent trip through the West, for the purpose of studying the practical operation of the ball-mill. The writer takes this opportunity to express his thanks for courtesies extended at the many plants visited as well as for the valuable data received.

While there are several types of ball-mill on the market, particular attention will here be given to the diaphragm type (Peripheral Discharge Ball Mills ), as the open-trunnion type, especially the conical mill, has been thoroughly discussed here.

There is a prevailing impression that the ball-mill is a recent development; however, ball-mills were used extensively in Montana and other western states for crushing ores for concentration. Its present prominence is due in part to its recent successful application by one of the large copper companies. Without any reference to dry grinding, the first successful ball-mill for wet crushing, which is still in operation, was built 10 years ago. This mill, designed by Erminio Ferraris for crushing Sardinian ores for concentration, is of more than passing interest. It embodies the peripheral discharge with grates, large forged-steel balls, and the principal features of the modern ball- mill. The results approach present-day practice, ….Read more

Rittinger’s theory and law of the energy expended in crushing of rock is that the work of crushing is proportional to the reduction in diameter; or, as I have more fully expressed it:

“The work done in crushing is proportional to the surface exposed by the operation; or, better expressed for this purpose, the work done on a given mass of rock is proportional to the reciprocal of the diameter of the final product, assuming that all the mass has been reduced to one exact size, which is only theoretically possible.”

**Kick’s law is: “The energy required for producing analogous changes of configuration of geometrically similar bodies of equal technological state varies as the volumes or weights of these bodies.” In other words, the energy expended is porportional to the volume reduction, instead of the diameter reduction.**

That these two laws would give widely different results may be shown by a simple imaginary case. A ton of 16-in. cubes is broken to 1-in. cubes at the first operation, and these are broken to 1/16 -in. cubes at a second operation. Since the first operation produces only one-sixteenth as much new surface as the second, the ratio of energy expended in the two operations ….Read more

I happen to be one of those who believe that Rittinger probably meant what he said when he wrote what Stadler has quoted, “the increase of the surfaces exposed is directly proportional to the force required for reducing” “and therefore also to the work absorbed in effecting the separations.” (The italics are now mine instead of Rittinger’s or Stadler’s.)

Our difficulty lies in not understanding just what occurs at the so called “elastic limit.” Up to this point the energy applied to the body is absorbed by it uniformly in proportion to volume. At the so-called elastic limit the first break occurs some place within the body, releasing the energy locally absorbed at the point and allowing a further deformation without a proportional amount of energy being absorbed. The cause of the first break within the body is that the ultimate strength of a single crystal, or of the bonding material between crystals, was exceeded. A series of these “ local” breaks occur in sequence throughout the body until at some point several of these breaks lying close together so weaken it that the remaining crystals and bonding material are unable to resist further and the section fails, a fracture being ….Read more

The drop weight test is a common laboratory measurement used to determine the comminution characteristics of rock samples. A common metric derived from a drop weight test is a value “A×b”. Another common metric that is derived from the SMC Test™ variant of a drop weight test is a “Drop Weight Index”, abbreviated as DWi. This work looks at a public database of test results to determine a relationship for DWi as a function of A×b.

by Alex Doll @ SAGMilling.com

A database of publicly published grindability test results has been collected by the Author. This database includes just over two hundred instances of a DWi and A×b being published for the same rock sample. A series of equations were fitted to this database with the goal of finding the best fitting equation.

An equation published by Lane *et al.* (2015) gives a relationship, equation [1], that includes the density of the coarse particles (ρ, or SG for “specific gravity”) and two fitted constants, *c* and *d*.

….Read more

Here is the old Allis-Chalmers Bond Work Index Grindability Test Procedure.

The standard feed is prepared by stage crushing to all passing a 6 mesh sieve, but finer feed can be used when necessary. It is screen analyzed and packed by shaking in a 1000-cc graduated cylinder, and the weight of 700 cc is placed in the mill and ground dry at 250 per cent circulating load.

The mill is 12 in. x 12 in. with rounded corners, and a smooth living except for a 4 in. x 8 in. hand hole door for charging. It has a revolution counter and runs at 70 rpm.

The grinding charge consists of 285 iron balls weighing 20, 125 grams. It consists of about 43-1. 45- in. balls, 67-1. 17 – in. balls, 71-0. 75-in. balls and 90-0. 61 in. balls with a calculated surface area of 842sq. in.

Tests are made at all sieve sizes below 28 mesh. After the first grinding period of 100 revolutions, the mill is dumped, the ball charge is screened out, and the 700 cc of material is screened on sieves of the mesh size tested, with coarser protecting sieves if necessary. The under size is weighed, and fresh unsegregated ….Read more

A linkedin.com group was recently discussing this by asking: I’ve tried to **estimate AG/SAG Mill power requirements** using several different **methods**:

(1) Using the results of SMC data

(2) Using SAG Power Index (SPI) data

(3) Using the 1989 Barratt method updated on Alex Doll’s Web site (February 16, 2015)

(3) Using Don Burgess’ method (11th Mill Operators Conference 2012)

They seem to give very different predictions for guiding the selection of SAG mill sizes.

I tend to favor the updated Barratt method in terms of the rationale behind the approach, but I don’t have access to a database to really check it out. The Burgess method gives predictions that seem to be over-sensitive to the transfer size. I recently attended a Global Mining Standards and Guidelines Group workshop that focused on the Bond Work and SMC methods; they seem to be the most popular methods, but are they the best?

Many answers went as follow:

- The spark test is not actually a test but a red light for a consultant. The sparks are caused by the fight between the rock and the machines. It is an indication of high rock competency. Hence competency tests should be developed.

I agree with your observation, consultants and engineering ….Read more

The Bond Abrasion Test determines the Abrasion Index, which is used to determine steel media and liner wear in crushers, rod mills, and ball mills. Bond developed the following correlations based on the wear rate in pounds of metal wear/kWh of energy used in the comminution process.

Determining rock abrasivity in the laboratory

https://www.911metallurgist.com/equipment/abrasion-index-tester/

Here is an illustration of the typical relationship between the Mohs Mineral Hardness Scale and their corresponding Bond Abrasion Index.

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