Mill Dimensions: Sizing & Design Guide

The mill is the biggest rotating machine of the cement plant and its size is the first question of every project: the length and the diameter of the steel cylinder: the two numbers that the drawings show on the first line: the two numbers that decide the tonnage, the fineness and the power of the grinding line: the dimension of the mill is not a matter of taste: it is the consequence of the tonnage, the fineness and the material that the plant must grind: and the file of the package teaches exactly this sizing.

The Complete Cement Technical Package (931 files including the books, the courses, the Excel tools and the presentations: $249.99 one-time: instant download through the PayPal payment) includes this dimensioning file with its formulas, the reference tables of the installed mills and the worked sizing examples: this article walks the file: the diameter and the length, the volumes, the speeds, the power and the process of the dimensioning: the reader leaves with the ability to read the mill data sheets of his plant and to check the dimensions of a proposed machine.

The dimension is the foundation of the mill: the diameter governs the power, the lift and the ball trajectory; the length governs the residence time and the smoothness of the grind: the file treats the two dimensions as the system: this page follows the document chapter by chapter and the engineer of the package can open the PDF next to this article.

1. The Dimensions of the Mill: The Two Numbers of the Cylinder

The file opens with the object of the study: the rotating cylinder of the grinding and its defining numbers:

• The diameter (D): the inside diameter of the shell, the dimension measured across the interior of the lining: the typical cement mills from 2.5 to 5.2 meters: the number that decides the cascading power of the charge;
• The length (L): the length of the grinding chamber shell: the typical finish mills from 8 to 17 meters: the unites that decide the residence time of the material in the grinding zone;
• The L/D ratio: the quotient of the length over the diameter: the character of the mill: the short mill of 1.5 to 2.0, the long mill of 2.5 to 3.5: the first diagnostic number of any mill;
• The shell volume: the internal volume of the cylinder: the cubic meters that carry the charge and the material: the basis of the all filling calculations;
• The technical data: the weight of the shell, the trunnions, the bearings and the gear: the manufacturer’s number: the dimensions only start the file:

The two dimensions are the identity of the mill: the plant engineers speak of “the 3.8 by 13” and every process man of the industry recognizes the machine: the diameter and the length of the data sheet pair with the tonnage and the power on the nameplate: the engineer of the grinding who reads the history of his own machines begins to see the patterns: the ratio of 3.0 for the fine finish, the 2.5 for the coarse: the language of the dimension becomes the language of the plant conversation: the cylinder, named.: the file teaches the language of the dimensions first so the technical chapters read naturally: the cylinder, named.

2. The Diameter: The Master of the Power

The diameter is the dimension that drives the power: the file states the relation and explains the physics:

• The charge of the fall: the balls in the rotating shell climb the liners and fall: the height of the fall grows with the diameter: the bigger the mill, the higher the cascade and the greater the energy per fall;
• The power equation: the internal power of the mill follows the diameter to the power of roughly 2.4 to 2.5 in the classical formulas: the mill of the double diameter draws many times more power: the growth of the dimension is not linear;
• The friction of the torque: the motor overcomes the weight of the charge and the inertia of the cylinder: the torque of the mill and the power diagram: the gearbox of the 1,000 to 5,000 kilowatts: the muscle of the dimension;
• The absorption capacity: the maximum charge that the lining can lift: the bigger shells hold the greater percentage of the media: the practical power of the machine:
• The scaling: the designers scale the power between the plants of the similar material with the ratio of the diameters: the file teaches the scaling of the kilowatt: the basis of the estimates:

The diameter is the political choice of the mill: the largest machines of the industry reach the 6.2 meters in the trunnion mills and the 7 to 8 meters in the the (dry) ball shells of the raw: the dimension records: the file maps the sizes with the powers: the engineer of the project reads the diameter and immediately the order of the power of the machine.

3. The Length: The Chamber of the Residence

Where the diameter gives the power, the length gives the time: the second dimension of the file:

• The residence time: the minutes that the material spends inside the mill: the typical finish grinding of the 20 to 35 minutes: the length that the finer grind needs: the time is the quality of the fineness;
• The compartments: the mill is divided by the internal diaphragms: the first compartment grinds the coarse, the second the fine: the length of each refers the stage: the proportion of the two chambers;
• The residence and the fineness: the longer the path, the smaller the product: the target Blaine expresses the required work: the length and the power together yield the fineness of the design;
• The L/D ratios of the practice: the ball mills of the cement: the 2.5 to 3.5 for the finish: the raw mills 2.5 to 3.0: the single chamber: the rod mills with the ratio of 1.5 to 2.0: the reference brackets of the file:
• The power per meter: the units of the specific power of the mill: the kilowatt per length unit: the proportions of the cylinder of the existing mill: the audit of the capacity:

The length is the answer to the fineness: the plant that increases the product Blaine extends the residence needs or raises the power: the file teaches the arithmetic and the physical meanings: the length of the mill of the plant and the minute in the cylinder: the time of the grind.

4. The Volume and the Fillings: The Percentage of the Steel

The mill is not a hollow cylinder: it is 28 to 36 percent full of the steel: the file computes the internal volume and the fill:

• The internal volume: the product of the cross and the length minus the voids: the classic volume: the mill of the 3.8 by 13 has the shell volume of about 130 cubic meters: the plant volumes of the line:
• The filling degree: the share of the volume occupied by the charge at rest: the 28 to 32 percent for the fine cement, the up to 40 for the coarse: the optimum of the power: the parameter of the ball loading:
• The bulk density: the charge mass: the steel balls: the 4.5 tons per cubic meter of the voided volume: the ball charge of the typical mill: the 50 to 200 tons: the weights of the crane load:
• The charge level measurement: the sound method and the power method: the resonance of the mill: the level of the media inside: the modern acoustic sensors: the online of the plant:
• The additions and voids: the interstices of the balls hold the material and the powder: the void fraction of the load: the 40 percent of the bed: the grinding in the interstices: the working volume:

The quantitative chapters of the file give the engineer the arithmetic of the charge: the volume, the density, the steel mass: the design of the fill is the basis of the power calculation: the file teaches the frozen filling degree that the formula assumes and the practice maintains: the fill of the mill: the heart of the load.

5. The Speed of the Mill: The Spin of the Dimension

The dimensions interact with the rotation and the file introduces the critical speed:

• The critical speed: the rotation at which the centrifugal force holds the ball against the lining: the formula: the 42.3 divided by the square root of the diameter in meters: the revolutions per minute of the critical:
• The limit of the physics: at the critical speed the grinding stops: the charge sticks and rotates with the shell: no cascade, no break: the critical defines the ceiling of the operation:
• The the operating speed: the 70 to 80 percent of the critical for the ball mill: the cascade of the cataracts: the balance of the breakage: the speeds of the plant: the 13 to 17 rpm of the typical cement mills:
• The length influence: the same critical formula depends on the diameter only: the length does not change the speed: the speed of the plant fixes first the diameter: the dimension of the speed:
• The actual setting: the gear box ratios and the pinions: the motor speed conversion: the VFD of the modern: the operator dials the operational speed: the % of the critical: the screen set point:

The speed is the partner of the dimension: the same diameter can run the mill at the different speeds and the plant does: within the limits of the physics: the file provides the table of the critical speeds for the range of the diameters: the dimension of the mill: the spin of the cylinder: the balance of the cascade. The operator meanwhile watches the actual revolutions on the tachometer and the power drawn by the motor: the measured combination of the speed and the load: the optimum of the plant finds its own working point between the cascade and the cataracts: the file marks the zone of the operation: the 70 to 78 percent of the critical for the finish lines, where the grinding momentum balances the wear of the lining.

6. The Power of the Dimension: From the Filling to the Motor

The central calculation of the file: the demand of the dimension: the electrical power that the motor must supply:

• The grinding media mass: the product of the volume, the filling degree and the bulk density: the tons of the steel that the mill rotates: the first term of the power;
• The power formula: the classical: the internal power: the constant of the grinding high: the diameter to the 2.5 to 3: the length: the speed ratio: the media mass: the classical mill calculation: the numbers of the file: the example: the mill 3.8 by 13: the power: 2,500 to 2,900 kW:
• The drive losses: the gear, the friction: the amperage of the motor: the efficiency of the drive: the billing: the 93 to 95 percent of the modern reducers:
• The 80% passing check: the bond W of the material: the kilowatt-hours per ton: the throughput of the design: the multiplication: the cross-check of the power estimation: the two methods of the professional:
• The installed motor: the chosen power with a margin: the 1,000 to 5,000 kilowatts of the cement mills: the spec: the motor of the order book: the dimension of the design law of the mechanical:

The power is the summary of the dimension: the file trains the engineer to compute the motor demand of the mill from the dimensions and the charge: the spreadsheet of the package does the same in seconds: the design of the power line: the measured electrical audits of the existing mill establish the truth: the file: the power of the dimension, calculated.

7. The Compartments and the Diaphragm: The Internal Architecture

The dimension of the plant is not uniform: the chamber of the mill builds the inside: the file explains the architecture:

• The two compartments: the classical ball mill: the first chamber with the big balls and the coarse grinding: the second chamber with the small balls and the fine finish: the two rooms of the grind:
• The chamber lengths: the proportion: the 1st chamber at the 25 to 35 percent of the length: the feed end: the coarseness: the balance of the morphology of the charge:
• The diaphragm: the perforated plate between the chambers: the aperture: the material advances: the holder: the outlet: the diaphragm controls the material transfer and the ball retention:
• The grinding of the chamber: the material flow is squeezed between the balls: the coarse of the water: the film of the powder: the media size of the chamber: the design of the second chamber: the fine media:
• The retention: the powder clings to the media: the dead: the Dev the overfill: the clean the diaphragm slots: the sample of the plant: the clogging the power: the file warns:

The compartments convert the single cylinder into the series of the machines: the file teaches the layout of the chambers, the design of the diaphragms and the adjustment of the partition: the same dimensioned shell can be optimized by the internal architecture: the dimension of the mill: the interior that counts as much as the exterior.

8. The Dimensioning Worked Example: The Two Mills of the Plant

The meat of the file: the worked sizing of the equipment: the examples of the two plants:

• Example A: the raw mill: the specification: the 1,500 tons per day of the raw meal, the feed of the 25 millimetres, the product of the 90 micron at the 12 percent residue: the designer: the Bond index 11, the diameter: 4.2 m, the length: 12.5 m: the volume: 173 m³: the ball charge at 30%: the 160 tons: the power: 3,300 kW: the motor installed: 3,600: the verification:
• Example B: the finish mill: the cement 42.5 at the 4,000 cm²/g: the 110 tons per hour: the W 30 kWh/t: the drawn power: the 3,300 kW net: the mill: 4.0 m x 14 m: the L/D 3.5: the two compartments: the balls of the 60 mm in the 1st, the 17 to 30 in the second: the dynamic separator: the back the 250%: the file:
• The iterations: the estimator rises the diameter, weights the power, checks the residence: the second iteration: the iterations of the design spreadsheets: the manual checks of the file: the development of the dimension:
• The limits: the increasing of the diameter damages the lining? the manufacturer’s limit: the practical max: the transport of the sections to the plant: the logistics of the dimension: the site: the crane of the large:

The examples show the methodology: the tonnage and the fineness fix the energy; the energy and the internal synergy fix the dimension: the file exercises the reader with the real numbers of the two plants and the spreadsheet repeats the job: the reader of the file designs a mill on paper after the chapter.

9. The Extensions and the Modifications: The Dimension Changes

Not every mill is new: the file covers the changes of the existing machines: the elongation and the modernization:

• Adding the length: the extension of the shell: the classical revamp of the old plants: the new section of the cylinder: the assembly of the plant: the length increase the residence and the fineness: the project of the elongation: the cooler the 10 meters:
• Increasing the diameter: the rare and the complex: the liner and the shell changes: the wheel of the trunnion: the bearing: the speed needs rethinking: the cost of the diameter: the new mill is the same: the file of the investor:
• The power increase: the motor swap: the gearbox and the new drive: the 10 to 20 percent power step: the existing shell: the new lining: the mixture: the gain of the throughput: the revamping economics:
• The internal revamp: the new line: should the diaphragm: the mill of the classifier outside: the separation: the energy savings of the classification: the dimension remains, the process changes:
• The calculation of the duration: the civil structure: the foundations: the revital of the machine: the machine and its own foundation: the file: the project call of the existing plant:

The file covers the revamps with the same rigor as the new: the audits of the dimension of the old mills: the properties: the possible: the file of the promise: the engineering: the dimension of the existing mill: the measured and the improved: the two speeds of the plant modernization: the file: the step of the capacity. The great majority of the plants of the world do not order new machines: they improve the existing ones: and the dimensioning knowledge of this file is exactly the language of that improvement: the elongation studies, the drive upgrades and the internal re-lining proposals all start from the measured dimensions and the calculated limits: the engineer of the package holds the method of the revamp as well as the method of the new machine.

10. The Comparison Table: The Mill Data of the Industry

The reference of the file: the table of the installed mills and their dimensions:

• The finish mills: the 3.5 x 12: the 2,000 to 2,400 kW: the 75 to 90 t/h at the 3,500 Blaine: the workhorse: the most installed of the world:
• The 3.8 x 13: the 2,500 to 3,000 kW: the 90 to 110 t/h: the most quoted in the tenders is a legend of the industry:
• The 4.2 x 14: the 3,500 kW: the 130 t/h: the big ring of the cement:
• The 4.6 x 16 and the giant: the 5,400 kW: the 200 t/h lines of the 42.5: the single drive and the dual drive: the mechanics: the distribution:
• The reference of the vertical: the VRM: the table and the rollers: the 5,000 kW class for the raw: the tables of the Lfe: the different geometry, the same job:

The table of the industry gives the engineer the feel of the dimension: the size, the power, the tonnage: the reference brackets: the estimation of the project: the file compares the installed machines with the formulas of the chapters: the proportions of the plant: the table of the file: the catalog for the designer and the benchmark of the operator.

11. The Errors of the Dimension: The Classic Mistakes

The honest file warns against the errors of the sizing that cost the plants dearly:

• The over-dimensioning: the mill too big for the material: the capital wasted and the efficiency low: the motor hums at the 60 percent: the customers: the temptation of the reserve: the normal usage 80 to 95:
• The under-sizing: the mill too small: the tonnage impossible: the overfills: the failure: the corrective purchase: the worst of the two:
• The standard mix-up: the use of the work index of the other material: the clinker index for the slag: the power error: the samples: the lab values, correct at the start:
• The speed misuse: the critical formula with the outer diameter; the double counting: the interior of the lining is the dimension of the calculation: the check of the numbers:
• The ignorance of the circuit: the dimension of the only mill without the separator: the open versus the closed: the classifier: the duty of the mill: the closed loop power: the file: the full view of the system:

The mistakes of the file: the lessons of the industry: the failures of the past teach the new: the file names the three classical errors and the method to avoid them: the engineer of the projects: the checklists of the dimension: the double testing of every design before the order.

12. The Excel Tool of the Dimension: The Calculator of the Package

The dimension chapters convert the theory into the spreadsheet: the package includes the sizing tool and the file describes it:

• The inputs of the tool: the material, the tonnage, the feed size, the product P80, the work index, the circuit: the half page: the quick: the spreadsheet: the cells:
• The power of the mill: the tool calculate: the diameter, the length, the volume, the fill, the cabaa: the % of the critical: the installed power: the outputs; the table of the design:
• The circuits: the open/closed choice changes the results: the tool handles the circulation and its influence: the classifier and the feed: the design of the closed loop:
• The scenarios: the several dimensions: the comparative table: the cost estimate: the power consumption and the annual kWh: the deciding of the options: the project:
• The examples complete: the template of the file: the two plants of the chapter: open: the sanity checks of the sliders: the training of the spreadsheet: the mastery of the round:

The Excel of the file: the tool among the 931: the dimension: the routine shall be in the hands: the many scenarios of the project: the estimators: the built-in: the file describes the tool entirely: the downloader: the package: the calculator: the dimension of the mill, the value in the sheet.

13. The Dimension and the Modern: The Mills of the New Century

The last industrial chapter positions the dimension of the classic ball mills against the modern machines:

• The vertical roller mill: the raw grinding: the table of 4 to 6 meters and the rollers: the geometry of the machine: the dimension of the vertical: the height of the machine: the 20 to 30 percent energy savings of the raw:
• The roller press: the rolls of the 1.2 to 2.4 meters: the bed of the material crushed: the pre-grinding: the energy of the finish: the dimension of the press: the combination of the plants: the cakes: the subsequent ball:
• The stirred mills: the small bodies: the fine: the consumer of the dry: the industrial: the fine cement: the stirring: still an exception in the cement, common in the mines:
• The hybrid plants: the ball plus the press and the classifier: the dimensions of the ball: the smaller: the circulating: the complete: the design of the modern line: the mixture of the machines:
• The business case: the energy price: the modernization: the upgraded mill continues: the file: the modern dimension of the grinding rooms of the industry: the past, the present and the century:

The file closes the machines with the honesty: the ball mill remains the mainstream but the competitors shorten the processing: the dimension of the total plants: the modern: the engineer: returns: the territorial: the dimension of the mill: from the cylinder to the cloud: the file of the state of the art: the mill: the learning: the plant of the future.

14. Conclusion

The dimension of the mill: the diameter and the length: the power and the residence: the numbers of the cylinder: the first lines of the tender and the first measures of the plant: the file teaches the totality: the volume, the fill, the speed, the power, the compartments: the user of the package finds the tables of the reference and the worked examples: the art of the sizing, the tool of the Excel: the knowledge of the cement grinding: the dimension is the language of the mills: the engineer speaks it, the plant listens: the actual dimension is the dimension of the machine, respected: the package.

The Complete Cement Technical Package includes this file of the mill dimensioning with the formulas, the tables of the real mills and the Excel calculator: the one-time $249.99: the instant download: the library of the archives: the dimension: the tool: the professional: the mill: the engineer: the design capacity: the ground: the cement right.

The Frequently Asked Questions

What is the first thing we calculate for a new mill?

The tonnage demanded and the material: the design hourly mass and the work index of the material: the specific energy kWh per ton and the total power of the mill: then the dimension: the diameter from the power and the length from the effect: the file guides the sequence: the first number: the tonnage of the line.

What does the ratio L/D of 3.0 mean for me?

The mill is long relative to its diameter: the material spends a long time inside the chamber and the fine grinding dominates: the long mills make the finer Blaine: the shorter mills the coarser cement: the ratio of the plant: the profile: the ratio drives the character and the application of the machine.

Can I enlarge an existing mill?

Yes: the elongation by adding the shell section is a proven revamp: the new section, the new bearing positions, the re-application: the extension adds the residence and the fineness: the diameter increase is by far rarer and more expensive: the elongation, the classic revamp: the file documents both with the cost thinking.

Why do the dimensions of the cement mills use the metres?

The original standardization of the suppliers: most of the machinery of the industry is described in the metres (diameter by length): the Bond tradition aside: the metrics of the plant: the plants of the US use the feet in the reports: the file uses both in the appendix of the conversions: the same machine, the two numbers.

Does the file give the numbers of my existing mill?

The table of the file gives the benchmarks of the typical installed machines: the recognition of every large application: the power bands: the exact tonnage of a specific mill comes from the nameplate of the plant and the site measurements: the file provides the framework and the Excel of the check: the identification by the package.

Is the mill dimensioning an art or a science?

Both: the science of the volume, the power and the residence of the formulas: the art of the final adjustments with the classifier, the moisture and the operating speed: the file turns the art into the method: the grid: the engineer: the diameter of the finishing: the confidence of the design: the two, the science then the art.

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.