Dimension Of Mill: Complete Technical Guide

The dimension of the mill is the first decision of the grinding engineering: the diameter, the length and the proportion of the shell define the power, the capacity, the fineness and the availability of the whole grinding department: the correct dimensioning of the tube mill follows the physics of the tumbling media: the energy of the drop, the residence time and the internal classification: the file of the package is the design manual of the dimension, with the formulas, the tables and the worked sizing of the real mills.

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 mill dimension guide with its dimension tables, its power formulas and its design procedures: the document serves the plant designer, the mill engineer and the student of the grinding theory: this article walks the file section by section: the shell geometry, the power laws, the media charge, the compartments, the scaling rules and the optimization of the existing shells.

What the reader gets: the ability to judge the dimension of any mill at a glance, to calculate the power and the capacity of the shell, to understand why the cement mills have their characteristic L/D ratios and to check the vendor designs against the classical tables: the page follows the same order as the file: the definitions, the diameter, the length, the power, the media, the compartments, the L/D, the comparisons and the practice: the reader works through the article with the formulas printed in the document.

1. The Geometry of the Mill Shell: The Vocabulary of the Dimension

The tube mill is a rotating cylinder: its two dimensions are the diameter D (the inside diameter of the shell) and the length L (the distance between the end walls): the ratio L/D is the classic proportion of the shell: the mechanical details complete the geometry:

• The diameter: the internal diameter of the lining: the true grinding diameter: the reference of every formula: the plant compares the mills by the nominal diameter of the shell blank;
• The length: the internal length between the heads: the residence volume of the charge: the L with the D: the compact drum of the raw mills and the long drum of the classic finish mills;
• The L/D ratio: the proportion of the shell: the small ratio 1.5-2: the wide-short mills of the first generation: the ratio 3-4.5: the long classical: the ratio 1-1.3: the ideal of the modern verticals; the ratio governs the residence time and the classification;
• The chambers: the internal partitions: the diaphragms: divide the shell into the compartments: the first the coarse, the second the fine: the doubling of the residence per chamber;
• The speed: the rotational speed as the fraction of the critical speed: the 65-75 percent for the ball mills: the speed and the diameter determine the drop path of the charge: the dimension and the motion are one design;

The dimension of the mill is the physical book of its identity: the engineers of the world recognize a mill by its diameter and length written on the data plate: the dimension of the mill is not a simple pair of numbers: it is the envelope of the whole grinding process: the file gives the standard dimensions of the industrial mills in the tables of the products.

Mill type	Inside diameter (m)	Length (m)	L/D	Power (kW)
Small raw mill	2.4 – 3.0	7 – 10	2.8 – 3.5	500 – 1,500
Medium finish mill	3.4 – 4.0	10 – 13	3.0 – 3.8	1,800 – 3,200
Large finish mill	4.2 – 4.8	13 – 16	3.0 – 3.5	3,500 – 5,500
Two-compartment	4.0 – 5.0	14 – 17	3.2 – 3.6	4,000 – 7,000
Gearless ball mill	5.0 – 6.2	16 – 20	3.0 – 3.3	6,500 – 12,000

The industrial reality of the table: the wheel mills of the world have converged on the narrow band of the L/D between 3.0 and 4.0 for the cement grinding: the decade of the experience shows why: the shell must be short enough to grind the material through in the controlled residence time and long enough to fit the charge of the two chambers: the numbers of the table are the consensus dimension.

2. The Power Laws: From the Diameter to the Kilowatts

The power drawn by the mill is the product of its dimension and its charge: the classical empirical relationships relate the installed power to the diameter and the length: the file derives the famous equations of the mill power used by every sizing engineer of the industry order:

• The volume and the power: the large the mill, the more the media, the more the useful weight raised and dropped: the power is roughly proportional to the volume times the density of the charge:
• The diameter exponent: the classical rule: the power varies as the diameter to the power 2.5 to 2.7 (the exponent of the bath behavior): doubling the diameter multiplies the power by about 5.5 to 6.5: the big diameter is the exponential advantage;
• The length line: the power is linearly proportional to the length: the doubling of the length doubles the installed kilowatts: the length is the simple arithmetic and the diameter is the radical;
• The filling degree: the percent of the mill volume occupied by the balls: the optimum filling of 28 to 35 percent: the power curve rises to the maximal filling and decays after: the optimum of the charge ratio;
• The speed fraction: the power peaks near the 72-75 percent of the critical speed: the file shows the curve of the power versus the speed: the location of the maximum is the automatic choosing:

The important relationship of the design: the power of the mill is proportional along to the 2.5-2.7 power of the diameter: the consequence: the modern large mills of 5-6 m diameter reach the megawatt powers of the 8-12 MW and the single mills of the cement plant today produce what the battery of the small mills of the 1980s produced: the file gives the tables of the installed power and the examples of the calculations: the practical reading of the law: the difference between the 3.0 m and the 4.5 m mill is not 50 percent but a factor of about three in the power: the investment in the larger diameter pays the energy saving per tonne over the life of the decade: the dimension formula is the economic law of the grinding plant as much as the physical one.

The critical speed deserves its own paragraph: the critical speed of the mill is the rotation at which the centrifugal force holds the balls against the shell at the top of the travel: n_c = 42.3 / the square root of the diameter D (in meters): the mill speed for the grinding is 65 to 75 percent of that critical: the modern design of the big mills runs the 72-74 percent with the finer charges: the dimension and the speed: the two variables that shape the drop of the charge: the file’s tables: the mill diameter, the critical speed, the industrial speed and the corresponding drop profile of the charge: the reader of the file practically composes the motion law of every shell with the numbers.

3. The Worked Sizing: The Example of the Finish Mill

Let the numbers speak: the file takes the reader through the complete sizing of the finish mill with a real target: the example below is the classical one, the size of the finish mills of the world:

• The requirement: 250 t/h of the CEM I 42.5N at 350 m2/kg Blaine: the annual operation 7,500 hours: the specific energy 30 to 35 kWh/t of the system: the total power requirement of the grinding about the 8,000 to 9,000 kW installed;
• The candidates: the single large mill of 5.0 x 16.5 meters (the L/D 3.3) against the two mills of 4.2 x 13.5 (the 3.2): the number of the lines, the layout and the availability: the single mill the big, the twin the flexibility:
• The media: the charge of the 5.4-meter mill: the 30% filling: about 300 t of the grading balls: the ball charge per meters: the two chambers of the rough and the fine:
• The separator loop: the third generation separator of the 9,000 t/h circulating, the product of the Blaine and the rejects: the closed circuit the dimension of the mill alone does not:
• The motor: the gearless ring motor of the 8,500 kW at the 11.0 r/min of the shell: the flint of the modern order the direct drive: the dimension of the shell the lock-step:

The complete calculation of the file: the specific power from the Blaine curves (the kWh/t) times the tonnage: the gross power 8,500-9,500 kW: the volume of the shell from the dimension: the filling and the speed: the media weight and the motor: the result is the size of the standard modern line: the reader performs the same with the workbook of the package: the special input the size.

The detailed arithmetic of the example is instructive: the shell of 5.0 m inside diameter and 16.5 m length has the internal volume of about 320 cubic meters: at the 30 percent filling with the 4.5 t/m3 balls the charge weight is approximately 430 tonnes: the power consumed lifting this charge: about the 8.5 MW at the 10.8 revolutions per minute: the specific load of the mill: the 43 tons of balls per megawatt: the balance of the modern designs: the kilogram of media per kilowatt makes the charge manageable and the liner pressure acceptable: the file’s cross-check tables allow the designer to verify the vendor numbers: the media weight per MW: from the 38 to the 48 t/MW for the standard cement mills: the industry’s fingerprint of a well-balanced dimension.

4. The Optimum Dimensions: The Historical Rule Books

The dimensioning of the cement mills follows the historically proven rule books: the classical literature of the industry (the Handbooks of the Duda and the engineering classics) tabulates the optimum shell dimensions for every tonnage target: the file reproduces the essential tables:

• The capacity tables: the installed power per the tonnage of clinker: the 0.1-0.15 MW per ton per hour: the design guideline of the finis lines: the tables of the file list the silicone:
• The L/D rules: the finish mill classic of the closed circuit: L/D = 3.0 to 3.8: the open circuit requires the longer 3.8-4.5 to grind without the classifier: the raw mill of the pre-grinding: the modifications:
• The shell speed: the speed of the shell: the 74 percent of critical classic: the rule of the percent: the mills with the large diameter run the higher critical fraction: the file explains the why: the drop height:
• The ball grading: the max ball diameter from the feed size: the classical formula the ball: the width of the compartment versus the gradation: the dimension the shell and the media together:
• The concurrent tables: the recommended mill sizes for every capacity of the raw and the finish grinding: from the 10 t/h pilot to the 300 t/h giant:

The rule books are the distilled experience: the author of the file does not ask the engineer to reinvent the dimension: the tables give the starting point and the physics: the ball of the file: the special case: the design formulas of the yield and the proven trim: the optimum of the rule books is the band, not the point.

5. The Compartments and the Internal Dimensioning

The internal dimension of the mill is the division of the shell into the grinding chambers: the first chamber for the coarse breakage and the second for the fine finishing: the compartment lengths relative to the total: an optimization variable of the mill:

• The two-compartment mill: the first chamber with the large balls (60-90 mm) and the lifting liners; the second with the small balls (15-40 mm) and the classifying liners: the length ratio of the first to the total 25-40 percent: the classic finish mill:
• The three-compartment mill: the older and the longer tradition: three chambers with the graded media: the ratio of the total length divided into the fine stage: the two-compartment replaced most: the file: the alternatives:
• The diaphragm design: the intermediate diaphragm: the retention of the media, the passage of the materials: the lower the screen openings, the finer the classification: the internal recycling rings:
• The classifying liners: the progressive liners that push the small balls toward the outlet: the axial classification of the charge: the product and the fineness: the new liner designs:
• The weight balance: the charges of the chambers: the filling of the first 30-32%, the second 28-30%: the balance of the power and the sum of the cooperating chambers:

The internal dimensioning is the art of the mill: the same shell of the D x L can behave as the rough mill or the fine mill according to the internals: the test of the plant: the total charge and the ratio of the first chamber media: the audits of the file show how the correct internal redistribution improved the existing shells by 5-12% without changing a single millimeter of the shell: the cheap upgrade is inside.

6. The Scaling of the Mills: From the Pilot to the Plant

The dimensioning of the new mill usually starts from the pilot or the lab tests: the scale-up laws translate the small results to the industrial size: the file describes the models:

• The Bond scaling: the specific energy from the lab work index: the pilot mill data at the fixed diameters: the energy per ton is the scaling variable: the kWh/t is the bridge of the sizes:
• The throughput scaling: the plant capacity scales with the power: the installed kilowatts divide the environment: the dimension of the shell follows from the power table:
• The media and the material: the batch data: the circulating load: the production of the whole circuit: the scaling of the closed circuit: differs from the single shell:
• The residence and the sizing: the same kWh/t produced at the longer residence (the longer mill) and the lower power: versus the shorter mill and the higher: the L/D decision: the available classification:
• The empirical correction: the pilot corrections for the feed size, the grindability, the density and the moisture: the closed loop of the scaling: the safety margin of the 5-10%:

The scaling is where the confident engineer and the gambler separate: the file teaches the systematic scaling with the worked case: from the 30 cm pilot to the 5.4 m industrial: every factor is traced, every assumption declared and the final design rechecked against the database of the known mills: the reader of the file learns to lead the scale, not to pray for it.

7. The Shell Thickness and the Mechanical Design of the Dimension

The dimension of the mill is not only the internal geometry: the shell must be strong enough to carry the billion of the charge drops and the weight of the liners: the mechanical design of the shell thickness follows the structural rules of the rotating cylinders:

• The shell plate: the welded steel plate of 50 to 120 mm thickness for the large mills: the plate quality of the fine grain steel: the fatigue of the welds: the X-ray of the girth at the fabrication:
• The stress system: the bending stress from the weight between the bearings, the shear at the ends, the torsion from the drive: the combinations of the stresses: the fatigue factor of the rotating machines;
• The fatigue of the ring: the circular weld seams and the openings are the stress raisers: the design rules put the openings away from the stress zones: the file: the inspection points;
• The journal heads: the mill heads with the hollow trunnions: the bearing seats with the grinding: the head geometry spreads the load: the mill of the gear ring mounted at the shell middle:
• The foundation loads: the mill on the slide shoe and the bearing schools: the dynamic loads of the rotation: the foundation stiffness and the damping of the supports: the vibration control of the mill train:

The mechanical design of the dimension is the seat belt of the whole process: the mill shell has a fatigue life, typically beyond 25 years with the correct maintenance: the file gives the stress tables, the material specifications and the inspection schedules of the shells: the mechanical dimension is as critical as the grinding dimension and the two are taught together in the file.

8. The Comparison of the Dimension of the Vertical and the Ball Mills

The dimension of the mill appears again in the comparison of the technologies: the tube mill and the vertical roller mill are the two giants of the finish grinding: the file compares their dimensions quantitatively:

• The ball mill footprint: the tube of the 5.4 x 16 m on the floor of the plant: the support of the building, the crane and the hoist: the compact vertical of the 12 m height with the built-in classifier:
• The installed power: the ball mill 30-38 kWh/t, the vertical 22-28 kWh/t of the comparable cement: the vertical is the energy leader of the last decades: the ball mill remains for the special qualities:
• The flexibility: the ball mill handles the different materials, the moisture grudges the vertical, the grinding of the slag and the special: the dimension of the two machines follows the different physics:
• The maintenance: the ball charge replacement: the long shutdowns of the ball: the vertical: the rolls and the table rebuilt in the hours: the availability of the plant:
• The modern dimension: the ball mills kept for the low Blaine and the high energy, the vertical mills: the two world sizes of the plants: dimension’s own:

The comparison table of the file places: the ball mill of 4.2 x 13 m at 3,600 kW and the vertical of 420 t/h at 2,800 kW: both in the same lines of the big plants: the file explains what each dimension wins and loses: the engineer of the dimension decides the technology before the shell, and the tables of the file make the decision honest.

9. The Audit of the Existing Mill Dimension: The Retrofit Cases

Most of the plants work with the existing mills designed decades ago: the audit of the dimension evaluates whether the shell still serves the production: the file describes the audit work:

• The current balance: the actual t/h, the kWh/t, the Blaine, the rejects: the rating of the shell against the book curves: the deviation from the optimum: the audit baseline:
• The feed change: the pre-grinding installed (the roller press and the fine crusher) shifts the load to the mill: the mill may be oversized for the coarser feed: the revamp options:
• The compartment: the revamp: the first chamber shortened, the second extended, the intermediate diaphragm replaced: the internal changes that rebalance the old shell at the low cost:
• The lining period: the new generation liners with the classifying wave profiles: the same shell, the lower kWh/t: the case study of the file: the 5-12% improvement:
• The full tan: the separator upgrades and the static/dynamic: the shell dimension with the better classification: the modern classification: the 10-20% capacity at the same shell:

The dimension of the mill is a conviction, not a destiny: the audits of the file show the cases across the industry: the existing 4.0 x 13 m mill with the new internals at the same installed kW produced 15% more at the 2% lower kWh/t: the numbers of the retrofits in the file: the dimension: the design and the redesign: the file is the toolbox of the dimension change.

10. The Frequently Asked Questions About the Mill Dimension

What is the best L/D ratio of the cement ball mill?

The closed-circuit finish mill: L/D of 3.0 to 3.8 is the proven band of the industry: the open circuit requires the longer 3.8-4.5: the raw mill with the drying: the ratio 2.5-3.5 with the larger diameters: the optimum is decided by the separator, the feed and the target fineness: the file tables give the full mapping.

Why does the power of the mill grow with the diameter to the power of 2.5?

The media charge mass grows with the volume of the shell (the D2), and the drop height of the charge grows with the diameter (the D): the combined effect gives the exponent of the bath behavior around 2.5-2.7: the practical consequence: the larger mills are per-kilowatt more economical and the modern plants prefer the single large units.

Can the existing mill be lengthened?

The lengthening of the shell is possible with the new segments and the re-welding, but the cost of the modification approaches the cost of the new mill: the more common path: the internal rebalancing, the pre-grinding and the separator upgrades: the file compares the lengthening against the alternatives with the economics.

What is the relation between the dimension and the Blaine?

The fineness of the product demands the energy per ton: the higher Blaine raises the kWh/t and the fracture of the shell dimension: the final product of 3,000 vs 6,000 cm2/g: the specific energy increases roughly from 25 to 60 kWh/t: the dimension design starts from the target Blaine exactly: the tables of the file.

Does the package include the dimension calculators of the mill tools?

Yes: the Complete Cement Technical Package includes the Excel tools of the mill dimension: the power formula, the media charge, the compartment balance and the scaling spreadsheets: the engineer enters the targets and the tools deliver the dimension: the 931 files of the package: the mill design made practical.

11. The Mill Dimension and the Future of the Grinding

The dimension of the mill will not stop evolving: the file closes the technical chapters with the directions of the grinding technology:

• The HPGR circuits: the high-pressure grinding rolls pre-crush the feed to the mill: the dimension of the ball mill reduces while the total system reaches the 17-20 kWh/t of the whole finish process: the dimension of the future: the circuit more than the shell:
• The large verticals: the 500-800 t/h vertical mills with the compact dimension: the new plants of the world choose the vertical: the mill buildings become the small and the electrical:
• The digital dimension: the dimension decisions made from the models: the digital twin of the shell with the wear and the vibration: the predictive design: the dimension as a data object:
• The modular manufacture: the modular design and the reduced manufacturing: the shells of the container modules: the plants assembled in the weeks: the future construction of the cement:

The dimension of the mill: the numbers of the shell, the physics of the charge and the centuries of the practice: the future continues to use the law of the diameter power: the file of the package: the dimension the knowledge and the future: the engineering of the grinding: the exact size of the cement of tomorrow.

12. Final Words of the Guide

The dimension of the mill: the diameter, the length, the L/D, the power, the compartments, the scaling, the mechanics and the audits: the single most consequential numbers of the grinding department: the engineer of the file reads the size of a mill and reads the history of its plant: the designer, the operator and the buyer all live in the same dimension: the correct mill, the dimension done right, the cement ground well.

The Complete Cement Technical Package includes this mill dimension guide with the tables, the formulas, the worked sizing and the Excel tools: the one-time price of 249.99 via PayPal: the instant download: the 931 files: between them the dimension file: the exact size of the mill: the engineering: the complete library of the cement: the knowledge of the correct dimension of the grinding machine.

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.