Courbe De Tromp Ii: Complete Technical Guide

The second part of the Tromp curve course takes the curve out of the laboratory and into the control room: the first part taught the construction of the classification curve of the separator: the cut size, the bypass and the imperfection: this second part teaches what the numbers mean, how the separator produces them, and how the operator and the engineer move them: the bypass down, the sharpness up, the circuit output up: with the worked case studies of the real plants and the tuning sequences the operators apply on the shift.

The Complete Cement Technical Package (931 files including this Tromp II file, the separator handbooks, the Excel tools and the training courses: $249.99 one-time: instant download via the PayPal payment) hosts the two-part Tromp course with the case studies, the tuning tables and the calculation sheets: this article walks the second part: the physics behind the curve parameters, the optimization sequence, the before-and-after cases with the numbers, and the integration of the curve into the circuit control: the reader leaves able to run a separator improvement campaign.

The logic of the second part follows the logic of the clinic: the diagnosis first (the curve measured and read), the treatment second (the physical adjustments), the follow-up third (the curves re-measured): the file insists on the discipline of the before-and-after: every optimization is a small experiment with the measured start and the measured finish: the plant that follows the discipline converts its separator knowledge into the permanent circuit gains, and this article explains the sequence with the same numbers.

1. The Recap: The Three Parameters and Their Physics

The curve of the separator carries three numbers, and the physics behind each one dictates the treatment:

• The bypass (the floor of the curve): the fraction of the finest particles that follow the coarse stream: the physical causes: the mechanical short-circuit through the seals and the gaps, the air drag of the coarse stream, the overload of the classification zone: the bypass is the parameter with the largest energy cost and the clearest mechanical fix;
• The cut size d50 (the position of the curve): the size at which half of the material goes each way: set by the rotor speed, the air flow and the feed concentration: the d50 is the operator’s daily tuning knob for the fineness;
• The imperfection I (the slope of the curve): the sharpness of the cut: set by the flow uniformity, the turbulence and the classifier geometry: the low I needs the healthy internals and the well-distributed air: the I is the project parameter of the shutdown, not the knob of the shift;

The hierarchy of the file: the bypass first (the leak, the quick money), the sharpness second (the geometry, the project), the d50 last (the daily trim): the operator who keeps this order fixes the machine before he tunes it: the same order structures the whole second part of the course.

2. The Circuit Model: How the Curve Shapes the Circulating Load and the Output

The curve parameters act on the circuit through the circulating load, and the file develops the circuit model quantitatively:

The model: the mill discharge distribution is approximated by the Rosin-Rammler curve with the characteristic size and the distribution exponent: the separator curve splits each size class: the fines fraction of the feed Ff = Σ(fi × (1 − Ci)): the circulating load = (1 − Ff)/Ff: the circuit output = the mill throughput × Ff:

• The bypass effect: each 10% of the bypass raises the circulating load by roughly 15 to 25 points and lowers the circuit output 5 to 10% at the equal fineness: the bypass is the silent tax on every ton;
• The sharpness effect: the I at 0.35 against 0.25 at the same d50 produces the 4 to 8% lower output because the near-cut material recycles: the sharpening of the cut is the second tax relief;
• The d50 effect: the d50 down 20% (the finer cut) raises the Blaine 60 to 120 cm²/g at the constant mill conditions, at the price of the circulating load up and the output down: the d50 is the fineness exchange rate of the circuit;
• The example of the file: the 100 t/h circuit at the 2% residue: the bypass cut from 25 to 12% raises the output to 108 t/h at the equal product: the sharpness improved from 0.35 to 0.25 adds another 4 to 5 t/h: the total 12% of the free capacity: the numbers justify the whole second part of the course;

The model in the spreadsheet: the package’s circuit calculator takes the mill discharge distribution and the separator curve and prints the circulating load, the output and the energy at the target fineness: the engineer plays the scenarios (bypass down, I down) and sees the t/h before the shutdown is even scheduled: the model is the planning tool of the optimization.

3. The Bypass Reduction: The Mechanical Campaign

The bypass is the first target of the optimization, and the campaign follows the fixed order of the file:

• The seal audit: the separator casing, the feed and the rejects air locks, the product outlet seals: the leaks are found by the pressure tests and the dust observations: the worn seals replaced: the bypass drop of 3 to 8 points is typical from the seals alone;
• The air lock check: the rejects air lock (the flap or the rotary valve) must hold the differential pressure: the leaking air lock drags the fines down with the coarse stream: the rotary valves with the worn tips leak the air and the fines together: the tip replacement restores the separation;
• The louvre condition: the worn and the eroded louvres replaced: the new louvres restore the air guidance and the uniform distribution: the bypass another 2 to 5 points down;
• The loading check: the separator feed at or below the design: the overloaded separator loses the classification: the feed concentration above the design doubles the bypass: the debottlenecking of the elevator or the mill upstream is sometimes the real bypass fix;
• The verification: the new curve after each step: the plant measures the step gains separately to know which investment paid: the file’s campaign sheet logs the step, the cost and the measured bypass delta;

The worked case of the file: the 150 t/h circuit with the bypass at 28%: the seals (1,500 USD), the air lock tips (2,800 USD) and the louvres (18,000 USD) brought the bypass to 14%: the output rose 9 t/h, the energy fell 2.3 kWh/t: the payback under 3 months: the case is the standard story of the bypass campaign, and the file repeats it in the three plant variants so the reader recognizes his own machine.

4. The Sharpness Improvement: The Geometry Project

The imperfection drops through the aerodynamic health of the classification zone, and the project list follows the file:

• The air distribution: the uniform air velocity across the annulus between the rotor and the louvres: the velocity profile measured with the pitot traverses: the deviating profile (the ±30% across the annulus) smears the cut: the straightening devices and the adjusted vanes even the profile: the I typically falls 0.05 to 0.10;
• The rotor condition: the cage blades with the erosion and the deposits: the deposits on the blades disturb the flow: the cleaning and the reconditioning restore the sharpness: the rotor re-balancing completes the job;
• The particle dispersion: the feed must be dispersed before the classification zone: the feed chute and the spreading plate at the top of the separator: the clogged or the worn spreaders let the particles fall in the streams: the dispersion restoration improves both the I and the bypass;
• The fine material re-entrainment: the turbulence at the fines outlet re-drags the settled fines into the coarse stream: the flow baffles and the calm zones at the bottom of the separator body: the I of the bottom zone measured separately in the detailed campaigns;
• The geometry upgrades: the modern separators offer the retrofit kits (the rotor extensions, the vane rings) that the manufacturers validate with the curve before and after: the kits are the middle ground between the tune-up and the full replacement;

The discipline of the sharpness project: the I is measured with the full campaigns, not the single samples, because the flow fields are sensitive to the operating point: the file’s rule: the I comparisons need the equal d50, the equal feed rate and the equal product fineness: the curve of the before and the after printed with the conditions on the corner, the delta of 0.05 or more counted as the real change.

5. The d50 Tuning: The Daily Knob of the Operator

With the bypass and the sharpness healthy, the d50 becomes the operator’s instrument for the fineness, and the file teaches the tuning relations quantitatively:

The practice: the operator holds the product residue with the speed loop: the +5% speed drops the residue about 0.3 to 0.6 percentage points on the 45 µm in the typical circuits: the air flow trimmed by the fan damper for the fine corrections and the seasonal ambient changes: the file warns against the simultaneous changes: one knob at a time, the 30-minute stabilization, the laboratory check: the discipline that makes the tuning reproducible.

6. The Case Study A: The Modernization of the Second-Generation Separator

The file’s first full case is the retrofit of the 120 t/h circuit with the whizzer separator, and the numbers are worth reproducing:

• The starting point: the whizzer separator at the bypass 30%, the I 0.42, the d50 68 µm, the product at 3,300 Blaine and 4.2% residue on 45 µm, the circuit output 118 t/h, the specific energy 34.2 kWh/t;
• The project: the in-place retrofit with the dynamic cage kit, the new louvres, the seals and the air lock upgrade: the shutdown of 10 days, the investment 480,000 USD including the drives and the control;
• The result: the bypass 11%, the I 0.26, the d50 34 µm at the same product: the output rose to 132 t/h at the equal 3,300 Blaine, the energy fell to 30.4 kWh/t: the gain 14 t/h and 3.8 kWh/t;
• The quality side: the PSD sharpened: the 3-32 µm fraction up 5 points, the 28-day strength up 2 MPa at the same Blaine: the concrete water demand down: the sales argument of the mill built in the shutdown;
• The economics: the 14 t/h at the 200,000 t/y extra capacity and the 3.8 kWh/t at 1.9 million kWh per year: the payback under 2 years at the 0.10 USD/kWh and the market price of the cement: the case closes with the curve before and after printed side by side;

The case is the standard modernization story of the industry, and the file presents it as the template for the feasibility study: the plant measures its own curve, prices its own retrofit, runs its own model: the file supplies the spreadsheet of the case so the numbers can be edited with the local values.

7. The Case Study B: The Tuning of the Modern High-Efficiency Separator

The second case is the different animal: the already modern separator that drifts, and the tuning that restores it without the capital:

• The symptoms: the product residue creeping from 2.0 to 2.8% at the constant Blaine 3,800, the circulating load up from 220 to 280%, the output down 6 t/h over the six months;
• The curve campaign: the curves showed the bypass up from 10 to 19% and the I from 0.24 to 0.31: the d50 unchanged: the classic drift profile of the aging internals;
• The investigation: the internal inspection found the worn seal strips of the rotor, the eroded louvres at the feed side and the deposits on the fan blades: the wear accelerated by the returned dust of the filter bag leaks discovered in the same campaign;
• The fixes: the seal strips (3,200 USD), the louvre section (21,000 USD), the fan reconditioning (5,500 USD), the bag filter repair (12,000 USD): the shutdown of 6 days;
• The result: the bypass 11%, the I 0.25, the residue back to 2.0% at the 3,800 Blaine, the output back to the design plus 3 t/h: the curve of the after matched the baseline archive of the separator’s first year;

The lesson of the case: the modern separator is not the set-and-forget machine: it wears exactly like the old ones, only faster because the air speeds are higher: the quarterly curves of the plant that caught the drift in the sixth month instead of the eighteenth saved itself the year of the losses: the archive discipline of the first part pays here in the second.

8. The Control Integration: The Curve in the Process Automation

The advanced plants do not stop at the monthly curves: they embed the classification logic into the process control, and the file describes the practical systems:

• The fineness loop: the product residue (or the online Blaine analyzer) controls the separator rotor speed: the PID loop trims the speed to the target residue: the loop handles the feed variations within the minute scale: the curve parameters set the loop’s working range and its constraints;
• The circulating load protection: the load of the elevator or the separator motor watches the circulation: the load above the setpoint trips the mill feed cutback before the separator floods: the curve of the campaign defines the safe envelope of the load;
• The air flow control: the separator fan damper follows the product and the mill ventilation setpoints: the damper positions come from the tuning table of the file: the automated split keeps the d50 inside the envelope while the operators manage the mill;
• The model predictive layers: the advanced plants run the circuit models with the inferred separator curve parameters from the online measurements: the model retunes the setpoints against the drift before the quality pays: the file describes the architecture without overpromising: the foundation is always the good curve data;

The control message: the automation multiplies the tuning, but it inherits the machine: the bypass and the sharpness are the mechanical realities that no software can tune: the plant that automates the d50 while the mechanicals decay merely automates the loss: the curve campaigns keep the machine real, and the control keeps the machine accurate.

9. The Optimization of the Whole Circuit: The Mill and the Separator Together

The separator is half of the closed circuit, and the file devotes its integration chapter to the mill-and-separator pairing:

• The mill discharge as the input: the separator curve works on the discharge of the mill: the coarser the discharge, the harder the separator works: the mill internals (the charge, the liners, the ventilation) set the discharge distribution: the separator optimization and the mill optimization are the two halves of one project;
• The joint tuning: the classic sequence: the mill ventilation and the charge restored first, the discharge coarsens optimally, the separator cuts it with the low bypass and the sharp curve: the result is the highest output at the target fineness: the order matters: the separator tuned against the sick mill locks the error in;
• The energy split: the circuit energy = the mill energy + the separator and the fan energy: the sharp separator at the higher fan power can still save the total: the file’s example: the +15% separator power (0.4 kWh/t) bought the −3 kWh/t of the mill: the total falls 2.6 kWh/t: the system thinking beats the component thinking;
• The quality loop: the product PSD targets from the laboratory: the curve envelope that produces the target PSD: the quarterly joint review of the mill audit, the separator curves and the cement quality trends: the review agenda of the file: the three reports on one table;

The integration message: the closed circuit is a system, and the Tromp curve is the measurement that makes the system visible: the plant that runs the joint reviews with the curve data every quarter operates its grinding on the evidence instead of the habit: the discipline is the real competitive edge.

10. The Pitfalls of the Curve-Based Optimization: The Honest Warnings

The file confesses the limits of its own method, and the second part lists the pitfalls the practitioners must respect:

• The curve of the unstable circuit: the curve measured during the drifts is the average of the changing states: the interpretation leads astray: the stability discipline of the campaign is not the formality but the validity condition;
• The single-parameter chasing: the bypass forced below the physical floor of the machine by the extreme speeds: the d50 chased without the product check: the plant optimizes the curve and ruins the cement: the product laboratory data must close every optimization loop;
• The over-instrumentation: the inferred curves from the online sensors are the estimates, useful for the trend and dangerous for the precision decisions: the full sieve-based campaigns keep the ground truth;
• The sample representativeness: the corners of the streams sampled instead of the full cross sections: the curve of the biased samples is the illusion: the sampling protocol of the first part re-read when the results look too good;
• The equipment age: the old separator with the worn body cannot match the curve of the new machine: the optimization has its ceiling: the curve shows the ceiling and the cost of staying below it: the replacement decision follows the numbers, not the pride;

The warnings keep the method honest: the curve is the scalpel, and the surgeon respects the tissue: the file’s closing advice of the chapter: when the curve contradicts the plant, re-measure; when the plant contradicts the curve, believe the plant: the instrument serves the process, not the other way around.

11. The Economics of the Curve Campaign: The Money of the Optimization

The second part closes its technical chapters with the money, because the curve projects compete for the capital with the whole plant:

• The value of the output: the +10% circuit output at the 1 Mt/y plant is 100,000 tons per year: at the 40 USD/ton margin, the value 4,000,000 USD per year: the bypass campaign at 30,000 USD pays in the week;
• The energy value: the −2 kWh/t at 0.10 USD/kWh is 200,000 USD per year on the 1 Mt/y: the sharpness project at 250,000 USD pays in 15 months;
• The quality value: the strength and the water demand improvements support the premium pricing and the customer retention: the softer to quantify, the larger in the end: the file prices the quality conservatively to keep the feasibility honest;
• The sequence of the paybacks: the seal and the louvre maintenance first (weeks), the retrofit second (2 years), the replacement last (3 to 6 years): the plant funds the quick wins and builds the case for the capital with the measured results;

The economics chapter is the boardroom translation of the curve: the engineer presents the bypass in the percent, the manager hears the dollars: the file’s one-page summary sheet converts every parameter delta into the annual value at the plant’s own numbers: the summary sheet of the campaign, ready for the management review.

12. The Standard Operating Procedures of the Campaign

The whole method is useless without the execution discipline, and the file ends with the campaign SOP that the plants copy into their systems:

• The campaign plan: the scope (the curves to measure, the steps to execute), the schedule (the sampling weeks, the shutdown window), the responsibilities (the process engineer, the operators, the laboratory) and the budget: written before the first sample;
• The baseline: the curves and the KPIs of the current state: the output, the energy, the residue, the Blaine, the circulating load: the baseline report signed by the plant management: the before number is the contract of the campaign;
• The execution: the step-by-step changes with the measurements after each: the step log with the date, the change, the cost and the measured result: the deviations from the plan approved through the change procedure;
• The final report: the after curves, the KPI comparison table, the economics, the new standard settings and the new baseline for the archive: the report closes the campaign and feeds the quarterly reviews;
• The handover: the new separator settings documented in the operation manual, the operators trained on the new tuning ranges, the control loop parameters updated: the campaign is finished when the plant runs the new state, not when the report is written;

The SOP message: the optimization is a project like any other: the plan, the baseline, the execution discipline, the report and the handover: the plants that run the campaigns with the SOP discipline repeat the gains; the plants that improvise learn the lesson once: the file provides the full SOP text and the forms, ready for the adoption.

13. The Characterization of the Separator Faults by the Curve Shape

The experienced engineer reads the shape of the curve like the doctor reads the ECG: the anomalies of the classifier write themselves in the geometry of the plot, and the file dedicates its fault-characterization chapter to the shape lexicon:

• The high floor (the elevated bypass): the whole curve shifted up at the fine end without the slope change: the mechanical short-circuit: the seals, the air locks, the loading: the fix the bypass campaign: the floor above 30% with the modern machine also suggests the internal dust accumulation bridging the classification zone;
• The shallow slope (the high I): the flat S-curve spreading over the decades of the size: the poor aerodynamic dispersion: the worn louvres, the deposits, the asymmetric air: the fix the geometry project: the slope flatter than the type curve at the equal d50 flags the machine before the sieve data even confirms it;
• The double-stepped curve (the plateau): the curve climbing, flattening, then climbing again: the two different classification mechanisms acting in parallel: the classic signature of the internal leaks and the secondary air paths: the fines dragged down one route, the coarse carried up another: the inspection finds the broken baffles or the opened recirculation:
• The shifted slope (the d50 drift): the whole curve translated along the size axis without the shape change: the operating point drift: the speed, the air, the feed: the operator’s daily tuning territory: the correction one knob at a time;
• The rising tail (the coarse contamination): the curve approaching 100% too slowly at the coarse end: the oversized particles leaking into the product: the worn screens of the air-swept circuits or the damaged rotor blades: the product residue on 45 µm and the >90 µm fractions show the contamination before the curve:

The shape lexicon converts the subjective look of the plot into the objective fault list: the file pairs every shape with the confirmation checklist (the inspection points, the measurements) and the treatment reference: the operator who masters the shapes reads the separator’s health from the quarterly curve before the bypass number alone would reveal it: the lexicon page is the most consulted page of the file in the plants that adopted the method.

14. Frequently Asked Questions

Which parameter should be optimized first: the bypass or the sharpness?

Always the bypass: the leak is the mechanical condition that wastes the energy on every ton and the fix is the cheap maintenance (the seals, the air locks, the louvres): the sharpness improvement follows with the geometry project: the d50 tuning comes last, because the operator’s knob only works well on the healthy machine.

What bypass can the modern separator achieve?

5 to 15% in the healthy high-efficiency separators: the values above 20% in the modern machines demand the investigation of the seals, the air locks, the louvres and the loading: the campaign of the file typically recovers 8 to 15 bypass points with the payback of the months.

Does the sharper classification always improve the cement?

Up to a point: the sharp cut raises the 3-32 µm fraction and the strength, but the extreme sharpness narrows the PSD beyond the concrete needs and can raise the early-heat issues: the target PSD comes from the laboratory and the customer feedback: the curve serves the target, it does not set it.

How long does a separator optimization campaign take?

The bypass maintenance campaign fits the normal shutdowns and runs 2 to 6 weeks including the measurement cycles: the retrofit project runs 3 to 6 months with the engineering and the delivery: the full replacement 6 to 12 months: the file’s SOP structures each duration with the realistic checkpoints.

Can the curve be measured while the mill runs?

Yes, the sampling campaigns run on the operating mill: the mill continues, the samples are taken from the fines and the rejects streams, the sieving in the laboratory: the shutdown is only needed for the internal inspections and the physical fixes: the curve is the operating instrument, not the shutdown ritual.

Is the Tromp method valid for the vertical roller mills?

Yes, with the adaptation: the VRM has its own internal classification with the dynamic classifier at the top: the same sampling and the curve construction apply to the VRM classifier, and the same parameters (the bypass, the sharpness, the cut size) describe its quality: the VRM file of the package covers the machine; the Tromp method covers the measurement.

15. Conclusion

The second part of the Tromp course converted the curve into the action: the bypass campaign, the sharpness project and the d50 tuning: the case studies with the real numbers, the control integration and the campaign SOP: the reader finishes with the complete toolkit of the separator optimization: the measurement of the first part, the treatment of the second, and the money of the economics chapter: the closed circuit of the plant, opened and healed.

The Complete Cement Technical Package includes both Tromp parts with the calculators, the case studies and the SOP forms: the one-time $249.99: the instant download: the 931 files of the cement library: the classification engineering of the industry, organized: the curve measured, read and healed: the grinding circuit of the plant, optimized: the engineering career, advanced.

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.