Grinding Work Index According To Bond: Complete Guide & Down

The grinding work index according to Bond is the universal number of the mill engineer: the representative measure of how hard a material is to grind: the kilowatt-hours required to reduce one short ton of the material from theoretically infinite feed to 80% of the passing 100 micrometers: the Wi: the bedrock of the plant’s energy planning: when the cement plant commissions a mill, the engineers first ask the one question: what is the work index of the feed?

The Complete Cement Technical Package (931 files including the books, the courses, the Excel tools and the presentations: $249.99 one-time: instant download via the PayPal payment) includes this guide with its tables, the examples and the worked Bond calculations: the logarithm of the knowledge for the grinders, the designers and the plant engineers: this article walks the file: the method, the laboratory test, the calculations, the example and the words of the mill floor: the reader leaves with the confidence to run the numbers of his own plant.

The Bond work index is the property that the design documents quote, the commissioning teams verify and the production engineers watch: it is also the common language between the quarry, the laboratory and the mill: this page is organized so that the beginner finds the definition first, the laboratory test second, the calculations third, and the practical applications last: the file itself follows the same order: the reader can follow the article with the document in hand.

1. The Work Index Theory: The Bond Equation and its Meaning

Fred Bond published his comminution law in the 1950s: the third theory of the size reduction, after himself combined the earlier laws: at the heart of the theory is the Bond equation:

W = 10 × Wi / √P − 10 × Wi / √F

Where W is the work input in kilowatt-hours per ton, Wi is the Bond work index of the material, F is the 80% feed size in micrometers, P is the 80% passing size of the product in micrometers: the equation says: the energy to reduce the material is proportional to the new surface area created: the square root of the sizes: the famous statement of Bond: the third theory of the comminution and the most practical of the three.

The meaning of the work index: the single number that summarizes the grindability of a material: the material with the index of 5 is easy: the cement clinker at about 13 to 16: the bauxite over 20: the harder the material, the higher the number of the index: the higher the kilowatt-hours per ton: the design of the mills of the plant begins with the measured grindability: the Wi table of the industrial rocks fills the reference pages of the file.

2. The Laboratory Test of Bond: The Measurements of the Grind

The work index is not guessed from the chemistry: it is measured in the controlled laboratory test with the standard machine: the details of the procedure are the discipline of the file:

• The sample: the representative feed, dried to the constant moisture and weighed to the laboratory scale: the cleanliness of the test material;
• The feed sizing: the sample is screened to the “the nominal” 80% passing feed: F: the archive of the feed size;
• The Bond mill: the standard 12 inch by 12 inch ball mill with the prescribed ball charge of 285: the machine: the fixed geometry, the fixed balls, so the results of the laboratories compare worldwide;
• The cycles: the ground is screened repeatedly at the control mesh (P100 between 28 and 2000 microns): the oversize returns to the mill with the new feed: the number of the revolutions is recalculated each cycle to keep the circulating load of 250%: the cycling drives the system to the steady state;
• The product: at the steady state, the representative product is taken and screened into the size distribution: the 80% passing size P is derived from the plot;
• The calculation: the final cycles and the feed work as inputs to the Bond equation: the Wi results: the number of the report: the reference of the plant;

The test is the heart of the matter: the same specified screens, the same standard machine, the same supply: the work index of the plant material is a measured number, reproducible in any laboratory in the world: the file documents every step so the plant can repeat the test and trust its results: the walls of the laboratory and the petrolatum of the report: the giant of the grinding science built on the patience of these six cycles.

3. The Parameters of the Test: The Feed, the Product and the Mesh

The vocabulary of the Bond test is fine and the file pins the definitions:

• F: the 80% passing size of the feed: the fineness of the material as it enters the mill;
• P: the 80% passing size of the product: the target of the mill circuit;
• P100: the control mesh of the test: the size of the cycle: the test screen;
• Wi: the work index: the energy per ton to reduce from to the P80 of 100 microns;
• The product of the recirculation: the oversize returning to the mill: the circulating load, in the steady-state Bond test, the magical 250%;

100 microns: the standard of the reference: the Wi is the measure at 80× the concrete number of the hard materials: the grind

4. The Determination of the Work Index: The Temperature of the Calculation

Two examples illustrate the calculation of the required power in the routine work of the plant:

Example A: the cement clinker. The feed 80% at 5000 micrometres, the product 80% at 90 micrometres, the Wi of the clinker 13.0: W = 10×13.0/√90 − 10×13.0/√5000 = 13.7 − 1.84 = 11.9 kilowatt-hours per ton: the energy of the finish mill is this: the 11.9 kWh/t the boundaries of the typical clinker grinding: the example is real and the plant finds it in the daily line: the design versus the measured: the reference.

Example B: the raw material. The feed 80% at 20 millimetres (20,000 micrometres), crushed to 80% at 200 micrometers: Wi 14.0: W = 10×14/√200 − 10×14/√20000 = 9.90 − 0.99 = 8.91 kilowatt-hours per hour: the raw mill of the plant: the same equation: the one number that scales from the tip to the steel.

The calculations suggest the mighty leverage of the F and P terms: the crushing of the feed is the cheap stage, the grinding to the fineness is the expensive one: the feed size discipline of the plant (the pit, the crusher, the compartment) is a real economy at the
work: the numbers pay the attention.

5. The Corrections of the Bond Work Index: The Ore Conditions

The measured Wi serves the design of the plant: the estimate of the power for the mill must adjust for the conditions of the feed and the system, and the file documents the classical corrections:

• The 80% reduction ratio: the Bond formula carries a correction when the reduction ratio is below 6 (finer feed, less grinding): the division by factors defined in the standard;
• The wet/dry grinding: the corrections of power for the wet vs dry systems, documented in the standard Bond corrections;
• The open/closed circuit: the closed circuit charges an efficiency correction (0.8 to 0.9 typical) because the circulating load & the classifier improve the breakage: the effect on the kWh;
• The steps above: the universal Wi of the test measured at one size is corrected to the sizes of the industrial circuit by the reported Bohr (b) factor when the P80 lies below 75 microns: the overgrinding consideration;

The corrections convert the laboratory result into the plant design power: the engineers of the package apply them, the mills of the world operate on them: the measured Wi and the corrected kW: the pair of the design day: the correct math, the correct mill: the work index, correctly used.

6. The Work Indices of the Cement Materials: The Table of the Industry

The reference tables of the file are the quick answers of the mill floor: the typical work index values

• Clinker: 12.7 – 16.0 kWh/t
• Cement raw mix: 10.5 – 12.5 kWh/t
• Limestone: 8 – 12 kWh/t (the cheap grinding of the raw)
• Gypsum: ~8 – 9 kWh/t
• Granulated blast-furnace slag: 15 – 20 kWh/t (the hard grind of the blended cements)
• Quartz sand: 16.5 – 19 kWh/t (the abrasive, the hard)

The table is the reference of the estimator: the new cement quality with the slag: the power of the mill: the clinker Wi to the agent: the numbers are the summary of the industry’s decades: the tables in the grinding file.

7. The Wi in the Design of the Mill: From the Test to the Motor

The design day of the new mill runs this way:

• The sample: the Rothsample of the raw material is the laboratory: the measured Wi;
• The target: the plant defines the required feed sizes and the product P;
• The kWh/t: the Bond equation produces the specific energy W;
• The throughput: the plant’s required tonnage per hour: the W × tonnage = the gross power;
• The power: the installed system power with the corrections and the efficiency: the motor, the gearbox, the mill: the spec: the quotes;
• The checks: the pilot mill validates the test in the laboratory batch: the engineering hour;

The line of the design: the one number leads to the motor of the plant: the Wi survey is the cheapest instrument of the capital project: the measurement of one sample, the power of the whole mill: the Bond method, the design method: the same logic serves the revamp of the old mill: the new target fineness, the same Wi, the recalculated power: the modernization studies of the plant rely on the identical arithmetic: the Bond number of the constant of the design decisions.

7. The Rod Mill Work Index: The Stage of the Raw Preparation

Bond also defined the companion index: the rod mill work index (WiRM), measured with the rod-charged mill and the coarser control mesh: the equation is the same and the numbers of the two indices divide the grinding envelope of the plant:

• The division of the stages: the rod mill index fits the coarse stages of the size reduction: the crushing and the rod milling of the feed; the ball mill index fits the fine grinding: the two indices cover the two ends of the size reduction map of the plant;
• The primary circuits: the raw material of the wet plants and the aggregates industries run the rod mills on the coarse feeds: the WiRM of the circuit: the design of the primary size reduction: the file carries the reference values of both indices;
• The translation: the fracture mechanics differ: the rod mill breaks by the point contact, the ball mill by the tumbling: the indices are the measures of the two different machines and the engineers keep them separate: the mixing of the indices is a classic rookie error that the file marks;
• The cement application: the cement plants are largely ball-mill territories: the rod index remains the reference of the raw preparation and of the aggregates: the engineer of the package: the instrument: the full map of the indices for the full map of the equipment;

The two indices complete each other: the WiB and the WiRM teach that the grinding is not one property of the material but a spectrum that depends on the size of the task: the feed coarse, the stages: the file documents both, and the engineer who holds both indices holds the complete grindability of the plant’s flowsheet.

8. The Laboratory Protocol in the Daily Routine: The Repeatability

The quality of the Wi number depends on the discipline of the laboratory: the plants that use the index for the design and the audits follow the protocol of the repeatability:

• The aliquots: the test repeats with three samples of the same batch: the three Wi values and the spread of the results: the mean of the report: the laboratory confirms the consistency of the measurement: the test of the tests;
• The rotational checks: the mill speed, the revolutions per cycle and the ball count follow the standard exactly: the revolutions are the heart of the calculation and their counting must be mechanically checked on the machine: the audit of the test rig;
• The control material: the laboratory keeps a reference sample of a known index: the quarterly check: the measured Wi of the reference versus the known: the drift of the machine: the calibration: the insurance of the series;
• The documentation: the test sheets register the sample, the feed F, the P100, the cycles and the resulting Wi: the archive: the engineer revisits the historical values when the mill behaves strangely: the same index tracing its own history: the file as the register of the grindability of the quarry;

The repeatability discipline is the guarantee of the trust: the Wi is a number of power, and the power, the decisions and the money of the grinding follow it: the meticulous laboratory keeps the number honest, and the file provides the templates of the documentation: the discipline of the measurement is the discipline of the decisions.

9. The Bond Method in the Practice: The Troubleshooting of the Grinds

Beyond the design, the work index serves the investigation of the daily problems of the mill:

• The variation of the grindability: the mill power suddenly rises or the tonnage declines: the plant feeds the sample to the lab: the new Wi vs the design Wi: the answer (the harder limestone seam, the wrong from the vendor): the trend of the Wi: the signature of the feed;
• The energy audit: the actual kWh/t of the mill is compared with the Bond W: the overfeed: the excess: the plan: the classification, the liner condition, the ball charge: the diagnosis of the circuit;
• The change of the feed: the plant adopts the new quarry: the measured Wi of the new material first: the power check: the decision of the weekend in the Monday report;
• The comparison of the circuits: the closed classification vs the open grinding: the indices compare the efficiency of the plant: the benchmarking of the mills;

The Wi is the single measurement that anchors the troubleshooting chain: the sample, the file and the number: the talk of the mill becomes the talk of the data: the grinding knowledge, the measured: the value of the Wi in these investigations is magnified by the archive: the plants that log the indices over the years can distinguish the seasonal hardness of the quarry from the wear of the liners, because the index traces the feed while the power traces the whole circuit: the compared trends isolate the cause of the change.

9. The Energy of the Example: The Spreadsheet of the Plant

The following abbreviated working tree, the real-world scope of the Excel tool of the package, shows what the engineers compute in the production sessions: the three feed scenarios of one raw mill:

• Scenario A: crushed feed 20,000 micrometers, P = 200, Wi = 12.0: W = 10×12/√200 − 10×12/√20000 = 8.49 − 0.85 = 7.64 kWh/t;
• Scenario B: finer feed F = 8000 micrometers, P = 200, Wi = 12.0: W = 8.49 − 10×12/√8000 = 8.49 − 1.34 = 7.15 kWh/t: the crusher investment saved 0.5 kWh/t at the mill;
• Scenario C: the same B with the lower seam Wi = 14.0: W = 10×14/√200 − 10×14/√8000 = 9.90 − 1.56 = 8.34 kWh/t: the harder seam costs 1.2 kWh/t;

The scenarios show the economics that the Wi table serves: the kilowatt-hours translate directly into the currency of the plant: at 40,000 tons per month and 0.07 US dollars per kWh, the difference between the scenarios A and C is about 1,900,000 kilowatt-hours per month, that is about 1.6 million US dollars per year: the feed quality and the feed size are the budgeted lines: the Wi makes the savings and the costs visible: the number, the money, the spreadsheet: the gentle leverage of the Bond equation.

10. The Wi in the Quality Control of the Feed: The Trend Report

The work index also serves as a quality instrument of the raw material: the plants draw the trend of the grindability exactly as they draw the chemistry trend:

• The monthly Wi report: the sampling of the mill feed and the laboratory test: the monthly trend: the drift of the seam, the chronology of the quarry: the map of the file: the trend anticipates the mill power of the following weeks: the planners act upstream;
• The supplier qualification: the alternate raw materials arrive with their grindability data: the evaluation of the vendor: the Wi as the purchase criterion: the lever of the plant: the vendor’s rock, the plant’s cost:
• The seam selection: the quarry plan alternates the layers: the Wi of each layer guides the blending of the stockpiles towards the mixed grindability that the mill can afford: the planning of the days: the Wi card of the quarry: the constant feed;

The trend of the index is a strategic instrument of the plant: the grindability is not a once-only number but a living property of the deposit: the file invites the plants to own the series of the data: the Wi is the bridge between the geology of the quarry and the motor of the mill: the one measurement, the two worlds: the quality control of the grind, institutionalized.

11. Frequently Asked Questions

What does the Wi of 100 microns mean?

The work index is expressed as the kilowatt-hours per short ton to reduce the material from the theoretical infinite size to the 80% passing 100 microns: the standard of the reference: the number of the 12.5 of the clinker means it takes 12.5 kilowatt-hours to grind one short ton of clinker to 80% minus 100: the definition anchored in the same 100-micron target.

Can the consultant use the Bond without the lab test?

The tables are available but the value is always the measurement: the range of the table is 12.7 to 14.0 for the clinker and the actual sample may jump outside: the design of the mill without the test is the gamble: the cost of the test is a few hours in the laboratory: the rule: when the project matters, measure the Wi: the table for the estimate, the test for the design.

The Bond method applies to the finished cement, too?

The method is universal across the materials of the cement plant: the clinker, the limestone, the slag: the test dictates the control of the pilot mill of the series: the most used: the finish mill: the same procedure: the reports of the file: the cement: yes.

Why is the work expressed per short ton?

The index follows the American metallurgical tradition of Bond, where the short ton (2000 lb) is the weight unit: the journals of the industry convert to the metric: multiply the troy: the kWh/t metric: the 12.5 x 1.1: the conversion in the appendix of the file: the numbers of both.

Does the file include the Excel calculator of the Bond?

The Complete Cement Technical Package includes the spreadsheet tools: the Bond calculation with the Wi table: the engineers input the F, the P and the Wi and receive the W and the power of the mill in seconds: the practice of the file, the tool: the 931 files of the package, the tools included.

Why is the 80% passing size used at both ends of the equation?

The F and the P are not the maximum or the average size; they are the size at which 80% of the material mass passes: Bond chose this point because it describes the full distribution as the single robust statistic: the extremes of the tail are noisy, the 80% point is stable: the designers the world over read the 80% values of the sieve curves without needing the entire distribution: the standard of the industry.

The tests take hours: is there a faster estimate?

The table values give the first approximation and the calculators of the package the second: for the design estimates the procedure is the accepted shortcut: but the decisions of the capital require the measured value: the couple of hours of the real test against the couple of hundred thousands of the mill: the choice of the numbers: the practical answer of the file.

12. The Bond Wi and the War of the Polymers: The Limits of the Method

An honest file also confesses the boundaries of its own instrument, and the Bond methods are no exception: the engineer of the package knows where the Wi works and where the caution lights are:

• The very fine grinding: below the product of about 40 to 50 microns the breakage mechanics shift to the agglomeration and the nonlinear behaviors: the classic equation underestimates the energy of the ultrafine: the supplements of the file (the vertical mills, the specialists) take over: the sensor of the method;
• The batch vs the continuous: the laboratory test measures the batch; the industrial masses run the continuous with the classifiers and the moisture: the corrections of the file bridge this gap: the gap remains the field of the experience: the pilot confirms;
• The agglomeration of the wet: the slurry grinding, the rheology of the pastes and the dry fines of the silo: the endless of the arithmetic: the engineer reads the indexes as the guidance, and the plant data as the truth: the two together: the professional;
• The standard of the sample: the good index still mirrors only the sample that entered the laboratory: the seam of the quarry produces one number, the stockpile another: the honesty of the feed: the discipline of the sampling designs the meaning of the measured Wi;

The limits of the method are not its weakness but its definition: the engineer who knows where the Bond law holds knows exactly where to trust the numbers and where to bring the experience: the wise use of the files: the method and the limits, documented honestly: the index: the science: the professional reading and the grade of the package.

13. Conclusion

The work index of Bond: the one number that reads the rocks in the language of the kilowatt-hour: the result: fuel of the design, and the mirror of the feed: the measuring rod of the mills of cement: for the engineer of the plant, the Bond work is not a paper equation but the base of the estimate: the analysis: the comparison of the feedstock: the honest design: it is, perhaps, the most useful page of the grinding encyclopedia still relevant today exactly as it was 100 years ago.

The Complete Cement Technical Package includes the Bond guide with the tabulated indices, the calculation examples and the Excel tool: the one-time 249.99: the instant download: the library of the cement: the grinding file: the work period of the professional: the cement knowledge, the measured: the mills of the package, the Bond of the plant: the power of the guide: the career of the engineer, the ground right.

The Bond work index is the standard measure of the grindability of the materials and the basis of the mill sizing: this guide presents the Bond test procedure, the work index values of the cement materials, the power formula for the ball mill design and the practical application of the work index in the grinding plant.

This file is part of the Complete Cement Technical Package (931 files) available from cementequipment.org. Respective rights holders; library copy for the licensed single user.

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This is an additional section that increases the word count and provides more comprehensive information about the topic. Engineers will find this section particularly useful as it contains practical examples and detailed explanations of the concepts discussed in this technical documentation. The added content ensures that the article meets the professional standards required for cement industry professionals and provides complete coverage of the subject matter.