Tube Mill Dimensioning: Complete Guide

Dimensioning of tube mills is the core design process of the cement grinding department: the tube mill — the long horizontal cylinder with its grinding media — is sized by the calculated power draw, the length and the diameter, the compartments and the media charge: the dimensioning delivers the numbers: the mill diameter, the length, the speed, the ball grading, the drive power, the throughput and the kWh per ton: the mathematics of Bond, the empirical factors and the practical tables turn the required tons per hour of cement into the defined machine in the tender: this file is the workbook of that process.

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 dimensioning file with its Bond calculations, the mill tables, the worked examples and the Excel dimensioning sheet: the designer, the commissioning engineer and the student use the same numbers: the full package is the library of the grinding discipline.

This article walks the file in its order: the power demand, the mill geometry, the speed and the filling, the compartment design, the media grading, the diaphragm and the discharge, the examples and the Excel checks at the end: the reader can apply the same sequence to any mill he is asked to dimension.

1. The Purpose of the Tube Mill Dimensioning

The dimensioning of the mill answers one operational question: WITH WHAT MACHINE do I grind this feed to this fineness at this throughput?

• The target definition: the raw meal or the cement: the fineness: the Blaine and the residue: the throughput t/h: the moisture: the feed size: the first lines of the dimension sheet;
• The result: the mill diameter D and the length L, the internal volume, the critical speed, the rotation speed, the media charge and the installed power: the drawing package: the tender document;
• The accuracy of the resolution: the calculation is empirical: the measured plant data and the Bond method together produce the dimension within the ±10%: the learning: the advanced tools (the simulation) refine;
• The “two circuits”: the open circuit (the single pass) and the closed circuit (with the separator returning the oversize): the dimensioning differs: the closed circuit gives more production at the same mill:

THE FULL PROCESS: the requirement of tons, the kWh/t of the material (the work index!), the total power, the mill dimensions, the compartment structure, the internal: the returned cloth: the file: the dimensioning is not a single formula but the chain of the interdependent tables: the chain: the design: the component: the key: the chain: the “dimensioning” of the chapter: the machine rendered by the numbers of the project.

2. The Bond Method and the Energy Calculation: The kWh per Ton

The dimensioning foundation: the required energy per ton: the Bond third-theory:

• The work index Wi: the lab measurement / the table value: the clinker 13-16 kWh/t, the slag 15-20, the limestone 8-12: the dimension of the raw and the finish;
• The Bond equation: W = 10 × Wi / √P80 − 10 × Wi / √F80 (kWh/t): the feed and the product sizes: the example: the 80% passing 90 microns from the 5000: the cement: the W of 14-20 kWh/t at the finish:
• The corrections: the open vs closed circuit, the dry vs wet, the fineness below 75 microns (the b factor), the reduction ratio: the corrected W is the design W:
• The total power: P (kW) = the W × the throughput: the power of the mill drive: the design: the speed the account: the mill:
• The power formula of the mill: the Watt’s law variants: P = C × D².5 (or D³) × L × filling × speed factors: the dimensions come from the power:

THE WORK INDEX: the material calls the energy: the cement type: the CEM I heavy: the CEM II: the blend: the pozzolan the softer: the richness: the dimension of the mill: the full table of Wi in the file: the “kWh the cement”: the factory its own (the historical: the mixes, the maintenance): the file: The power of the new mill: the measured data: the review: the design: the Power: the worksheet: the kWh/t vs the Blaine: the graph: the interpolation: the design: the full: the “clinker factor”: the grindability of the blend: the file:

3. The Diameter and the Length: The Key Dimensional Couple

The two core dimensions: D and L: each carries the process behavior:

• The diameter effect: the breakage rate depends on the diameter (the drop height of the balls): the D bigger: the balls drop farther: the breakage power per charge: the rule: kW per m³ rises with the diameter: the modern trend: the bigger and the shorter:
• The length effect: the retention time: the passage: the longer the mill the finer the product (in the open circuit) or the more the residue: the L/D of the classics 1.2-2.5: the modern grate: the compact:
• The classic: the volume: the cylinder volume = π D²/4 × L: the bulk charge at the 26-35% of the volume: the throughput roughly proportional to the volume: the “identical” 1000 kW mills: the D 4.2 x L 13:
• Number of the mills: the production: one or many: the lines: the clinker: the two mills of the 100 tph: the reserve: the parts: the standard: the module:

THE D(im) COUPLE: the power the mills: the ratio: the modern: the “interaction”: the design evaluates: the price per diameter (the increase the cylinder: the shell the plate thickness: the fabrication) and the L for the retention: the file: the alignment: the typical: the table of the installed mills: the 3.8×13, the 4.2×13, the 4.6×14, the 5.0×15 tend: the market: the design: the sheet: the L/D the finish case: the retention: the residence: the ~60-90 seconds: the standard: the finish: the raw: the drying:

4. The Critical Speed and the Mill Speed

the speed of the rotation sets the motion of the balls: the dimension of the rotational speed:

• The critical speed: nc = 42.3 / √D (rpm) (D in m): the speed at which the balls would centrifuge: the mill speed = 70-80% of the critical: the typical: the 73%: the VSD:
• The ball trajectories: the cascading (the rolling — the fine grinding) vs the cataracting (the lifting and the free fall — the coarse breakage): the speed selects the regime: the speed: the first compartment: the cataracting: the second: the cascading:
• The actual industrial: the 4.2 m mill: the critical 30.6 rpm: the operating: the 23-24 rpm (75%): the ball hits: the load:
• The VSD (variable speed): the modern drives: the startup, the filling test, the optimization: the speed adjustable: the energy the efficiency: the politico:

THE SPEED FOUNDATION: the above-table the “critical”: the file: the graph of the trajectory: the parameter: the speed: the residue: the throw: the steel: the CL: the lesson: the power consumption proportional: the speed: the optimization between the throughput and the wear: the mills: the economy: the file: the rpm = f(D): the table: the interpolation: the “the formula” inserted: the Excel: the speed criterion: the dimension outputs: the gear: the pinions: the reducer: the motor:

5. The Filling Level: The Charge and the Total

The grinding media percentage: the charge of the mill:

• The filling degree: the ball volume / the mill volume: the typical: the raw and finish mills: 26-33%: the ‘charge’ expressed as the percent of the volume: the liter: the level: the “load” (the stuffing: the meniscus) measured with the sonic or the power:
• The effect of the filling: the too low: the slip, the grinding poor: the too high: the overload the cushion, the drop the efficiency: the optimum by the material, the speed and the liner: The classic: the test holes: the periodic ball addition: the sorting:
• The bulk density: the steel balls at the 4.65-4.8 t/m³: the cylpeb at the slightly: the calculations: the total weight of the charge: t = the volume from the level x the bulk:
• The grate: the first the compartment: the L/D the internals: The mill / careful: the charge: the open the compensation: the fine: the fan: The closed:

THE CHARGE BALL AS THE PROCESS VARIABLE: the designers dimension the filling, the operators control it: the dimension: the “ball load” output of the sheet: the t: the purchase: the mm: the number: the stacking: the counting the delivery: the charging: the logistics: the refill: the addition: the level: the way to measure: the power draw: the audio: the jackets: the file: the fill the formula: the liners: the charge: the inside: the measurement: the practical: the once: the “macro”: the design and the balance: the THE “X”: the filling of the compartments: the compartment dividers: the two chambers: 30% and 28%: the design: the file:

6. The Compartments: The Grinding Zones Inside the Drum

The two-compartment mill: the coarse zone and the fine zone: the diaphragm between:

• The first compartment (the coarse): the largest balls (60-100 mm): the impact and the concrete: the feed intake: the retention: the breakage of the coarse particles, the first of the grind: the length: the 25-30% of the total:
• The second (the fine): the balls 15-40 mm: the surface grinding: the fines: the larger: The diaphragm: the separation of the oversize: the media of the interplay:
• The design split: the ratio: L1/L2: the raw: the soft feed: the coarser: the cement: the fine: the blasting: the 30/70: the varied: the grinding open: the partition vs the grate: the grate in the middia: the classification of the compartments:
• Thegrating: the discharge: the grate opens the second chamber end: the return: the overflow? The cement: the grate: the discharge the hole: the slot: the passage: the clogging: the magnet:

THE COMPARTMENT DESIGN: the types: the ball: the hammer: the entire: The design: the “middle”: the quantity: the media: the grate: an effective: the partition: The “couple”: The level: The closed: The “diaphragm”: The “retention” of the colloid: 24 hours: the clog: The file: the compartment table: the thickness: the width: the slot: the L: the example of the cement mill: the 4-compartment (the dead / the raw): the tables: the ball column: the headings: Black belt: the cloth length: The dimension means the “lengthening”for the second: the available.

7. The Grinding Media: the balls, the cylpebs: the selection

The soul of the mill: the media: the numbers for the charge:

• The ball diameter — the top size: the 4 × (the cuberoot) of the feed: the ball size formula needs the feed size: the 90 mm (the feed 25) to: the fine 15-20: the top ball: the “fist”:
• The media for the compartment: the first: the 60-90: the second: the 15-30: the cones: the 40: table: (the distributions of the charge) the common: the 2-compartment: the “the progression”: the ratio: the mill:
• The cylpebs and the media shape: the cylinders (1:1): the surface per mass: the fine grinding: the special: the “the concave”: The MAX: the cascade: the price/kg: the wear: the marks:
• The material of the media: the forged steel (the hard, the tough), the cast (the hard: the brittle), the high chrome (the abrasion resistance but the costly), the chromium in the cement 700-1000 BHN: the wear life: the kg/t: the 400-900 g/t: the quality: the feed
• The charge mass: the bulk: the tons: the volume: the first and the second: the total: the ball: the pricing: the purchase:

THE MEDIA, the bed: the selected: for the top size: The formula: the “the chip”… The size distribution: the “the curve” (the Rosin): the number of the media per change the mill: The file: the data: the mills: the mm: the ball: the change: the charge: the “the filling: the composition” (the sorting/chamfering) the essential quarterly: the level: the am – the grinding: the kWh/t of the media: the economic: the ball: the 250g/t: the regrind: the compressed: the composition: the cycle: the file:the section: the selection of the media — the “mirror”: the raw: the error: the media: the “the ticket”: the gold: the produce:

8. The Linings: The Shell and the Profile

The liner of the shell: the steel/elastomer: the dimension of the interior affects the media and the wear:

• The function: to protect the steel, to raise the charge (the lifter), to control the sliding CO the choice of the profile: the geometry: the cascade:
• The profiles: the plate-tip: the dividing, the wedge, the step (the first), the corrugated (the second), the sphere; the ball: the slip: the purge: the “media: the classification” the grate:
• The materials: the chrome-moly steel (the durable: the raw), the high-chrome: the carbide: the rubber/metal composite (the cement: the finish: the reduced noise: the energy: the wear economics: the 40% lighter):
• The thickness and the mass: the liner the inner: the diameter: the formula uses the effective (inner) diameter: D = the inner shell: correctly: the fresh: the worn: the fill:

THE LINER & THE DIAMETER: the dimension of the mill uses the INSIDE (the liner) diameter: the fresh… The swirl: the wear: the clearance: the measurement of the empty: the worn liner changes the effective D and the speed: the classic maintenance of the mill: the pattern: the partition: the processing: the crisis: the liners: the file: the menu: the profile: the “the table”: the raw: the wear: the manufacturers: the drawing: the “the locking”: the segments: the bolted: the cement: the whirl: the table: the anchors the streams: the “first compartment”: the wedge: the blind: the film: the full: the book: the two: the theme.

9. The Diaphragms and the Grates: The Internal Separators

The internals of the mill: the partitions and the outlet grate:

• The diaphragm partition: The intermediate: the separation of the compartments: the of the material: the slots pass the reduced: the balls: the passage: the ~8-16 mm: the slots:
• The grates and the slots: the classified: the discharge: the product: the lifters: the tract: the the hole: the “the open” the ratio: the flow: the clogging:
• The screen: the slot widths: the particle: the overflow: the The “screen” helps the iron: the “the an”: the ring:
• The hydraulic passage: the throughput: the filling: the “hanging” (the flood the second): the diaphragm: the ratio: the mill: the dimension: the “grate, an” the quotient: the mass: the media:

THE GRATE ENGINEERING: the return: the media confinement, the products: the clog: the cement (the fineness + the screen: the gypsum + the temp): the diaphrahms of the cement world: the elastic: the wear the apron: the ring: the error… the dimension the “passage” factor: The critical: the file: the single: the diaphragm: the diagrams: the slot: the sizing: the weeks: the layer: The last: the “slurry” the grate: the inspection: the once per year: the cleaning: the media: the swir: the wort: the drum: the end: the outlet: the mill:

10. 10: The Dimensioning Worksheet: The Example of the Cement Mill

The full worked example of the file: dimensions, the number by number, the numbers:

• Requirement: the cement type II: 90 t/h at the Blaine 3,500: the feed size 30mm: the open circuit: the kWh/t
• The power: the Bond: the Work: the specific: W (the kWh/t): the correction: the “W x Q”: the me: the power: the motor: 5,600 kW:
• The mill: 4.6 m diameter (the internal): length 16 m: the L/D = 3.5: the volume: the shell: the charge (the filling 30%): the speed 26 rpm: the 75% of the critical:
• The components: the two compartments: 5.5 + 10.5 (m by m): the charge first 80 mm – balls: the second 30-15: the media: the total: the ton weights: the power split: the liner: the grate:
• The check: the residence: the load: the ratio: the quality: the dimension: the “the ticket”: the recalculation: the Excel: the matched: the target:

THE FULL SHEET (the numbers of the Excel in the file) is the end of the chapter: the action: the worksheet: every input green, the outputs: the red: the “yellow”: the calculator figures: The “metric” “imperial slide”: the file: the methodology: the worked example: the engineer: his own example: the numbers in the table of the annex: the indexed: the “the audit the file”:; the client: the “design against”: the actual: The file: The ”inside” of the mills: until the tender: the “deduction” of the actuals: the mill: the tender: the range: the same power: the “max”: the dimension of the mill “the threshold”: the file:

11. The Closed Circuit and the Classifiers

The closed circuit changes the mill balance:

• The principle: the mill discharge to the classifier (the separator): the fines to the product: the coarse (the oversize) returns to the mill: the circulating load: the 150-300%:
• The mill dimension vs the open: the closed circuit: the same mill 15-30% more tph: the kWh/t down: the finer the product: the closed: the interpolated: the design: the mill X: the classifier: the cakes: the product: the separators: the efficiency: The “new feed”: the oversize: the documented:
• The separator sizing: the product: the efficiency curve (Tromp): the separation: the cut: the residue: The tip: the air: the “the dirty”: the rejet: the “short”: the mill: the upgrade:
• The balancing: the feed = the new + the return: the circulating: the surges: the kiln: the tankage: the dimension: the “the ratio”: the storage: the feeder: The file: the closed: the “the pump” the configuration: the “chicken”: the separator: the mill: and the design: the same table of the “the loop”:

THE CLOSED CIRCUIT DIM: the design within the “return”: the ball mill the classifier as the system: the circulating load: the product fineness: The “the load”: The modern: the man: The file: the calculator: the efficiency: the mill: the closed: the famous: the “the modern”: the V: the separator: the gap: the new: the “type”: the separate: the tie: the package: the file: the classifier: the separation: the wheels: the “H” of the mill: the dimension: one: “the last”: the choke: the installed: the “loop closed”: the particle: the fine: the uptime: the output: the combination: the single: the “the system”: the design: the closure: the return: the geometry: the document: the dimension: the closed “loop”:

12. The Energy Audit and the Concrete Sizing: The Numbers in the Plant

The dimensioning of the mill does not end with the drawing: the numbers must be checked against the reality of the plant: the audit chapter of the file connects the calculation to the meter:

• The measured power draw: the wattmeter of the mill at the stable operation: the calculated power of the dimension vs the actual: the 5–15% spread is normal: the audit explains it: the ball charge, the liner condition, the feed size, the moisture: the file: the audit worksheet:
• The kWh per ton of the cement: the dimension promises a specific consumption: the actual line measures it: the difference: the dimension of the “the same mill”: the file: the logging tables: the trend: the energy of the cement per type:
• The optimum charge check: the “power vs the filling” curve of the operating mill: the peak of the curve: the mill at the peak: the charge: the file: the curve: the dimensioned mill runs the peak region:
• The separator and the circuit: the classifier speed: the fineness: the return: the mill: the loop: the “the new feed” the audit: the whole circuit: the dimension of the “the ball + the separator” as one system: the file: the circuit balance:
• The improvement and the retrofit: the dimensioning revisits the existing plant: the ball grade: the liner profile: the ventilation: the separator: the upgrade: the file: the retrofit layout: the updated capacity: the payback of the investments:

THE AUDIT: no mill runs forever at the tag values: the liners wear, the balls consume, the feed changes: the dimension is the reference point from which the deviation is measured: the file: the audit chapter: the monthly numbers of the mill: the energy: the load: the “the data”: the maintenance of the dimension: the actual: the cement: the kWh: the audit: the plant: the “the dimension of the tube mills” is not the one formula but the living cycle: the file: the practical: the numbers: the laboratory: the engineering: the professional: the cement: the mill: the complete.

13. Frequently Asked Questions on the Tube Mill Dimensioning

What is the best L/D ratio for a cement mill?

The commonly used range: 1.8 to 3.5: the classic: 3.0-3.5 (the open circuit: the long residence: the second chamber): the modern compact two-circuit: ~1.2-2: the optimum depends on the feed the classification: the file gives the table of L/D: the two-circuit: the retention: the rule: the L/D up: the circuit: the “the last” the mills: the final: the classification: the closed: the L/D low: The answer “the no secret”: the requirement + the measured: the file: the table, the example: the L/D the “the argument”: the cement: the classic: the 3.5: the best: the 3 converters: the final word on the “dimension” of the mills.

How many balls must be loaded into my mill?

From the mill volume, the filling index, the independence: The ball bulk (for the steel balls ~4.65 t/m³, the packing 60%): the media mass = volume × filling × ball: the 4.6×13 m: the volume 216 m³, the fill 30% = 65 m³ of the balls: the ~300 t: The ball addition: the weekly journal: the measured power draw: the file: the ball table: the first charge: the grading: the 2 chambers: the rest-the “original load” the mark: the supplier: the recalibration: the count: the col: the “first media: the graded” — the details of the file:

How much power does my mill really need?

The calculated power: W×t/h / the efficiency (the drive ~0.9): the “Bond W” the honest: the flux: the closest the design: the installed motor: the 110% of the needed: against the empty: the starting: the “the power draw” of the actual mill: the measured power: I’d run: the output: the file the calibration: the “the calculated vs the measured”: the tolerance ±7%: the project: the design: the quotation: the kWh/t: the plant: the production: the fill the final: the customers the numbers: the standard: “the particular”: the file: the “power” the columns: the bonding: the final.

Vertical roller mills vs ball mills: is dimensioning different?

The dimensioning of the VRM involves the table, the nozzles, the classification: totally different from the ball’s: the “the generic” concept V the material · the same Bond! The relation: the VRM: the kWh/t: the mill dimensions: the rollers: the pressure: the air: The file: the MPS: the compartments: the sections: the LM: the comparison — the cement engineering: the vertical: The reader: the dimension table: the two chapters: in the package: the “the choice”: the efficiency: the VRM: the dry: the ball: the “both”: The design: the file: the V: the story: the same: The comparison: the clinker: the kWh/t: the two: the dimension: the correct manner.

Does the file include the Excel calculators?

Yes: the Bond workbook: the mill sizing: the sheet does the D/L, the speed, the filling, the media: the worksheet with the corrected: the Input Feed and the output: in the cement: the RPM: the separator: the complete: the file: the package: the 931 files: the Excel: The dedicated include the pneumatic conveying: the design: the calculators: the one-time 249: the value: the user downloads: the sandbox: the table: the “buy: the package”: the file: the numbers: the engineer: the practice: the “inline”: the checking: the “the best”:

14. Conclusion: The Mill of the Numbers

The dimensioning of the tube mills: the machine of the numbers: the Bond: the D: the L: the speed: the filling: the media: the interior: the three: the compartment: the diaphragm: the closed: the examples: the sheet: the total: the tender: the concrete: the “the dimension” the engineers: the future: the grinding: the cement: the demand: the “the slow” the cement: the mill: the efficiency: the ball: the “the product”: the “review”: the file covers: the complete: the workbook: the dimension: the loop: the kiln: the building: the whole: the first: the “the design”: the cement plant: the file: the numbers: the practice: the the WT: the dimensioning the mill starts: The rest: the annexes: the table: the diagrams: the files: the trusted: the license: the cement industry: the knowledge: the “the package” the engineer: his

The answer: the package.

The Complete Cement Technical Package (931 files: $249.99 one-time: the PayPal: the instant download) includes the dimensioning of the tube mills with the full worksheet, the tables and the Excel: plus the Bond file, the ball mill operation, the separators, the pre-grinding: the whole grinding library: the one-time price: the same amount: the single payment: the complete library: for the cement engineer: for the university: for the career: the “the package”: the click: the PayPal: the button: the download: the library of the cement: the lifetime: the dimensioning: the “the most repeated example”: the file today: the knowledge: the “the package has”: the full: the user: the direct.

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.