Screening, screen analysis and screen effectiveness

Screens and screen analysis (mesh, Tyler series), the overflow/underflow material balance and screen effectiveness E = E_A·E_B with worked numericals.

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Why it matters

Screening is the cheapest way to split a granular solid by size, and screen analysis is the standard way to measure the size distribution of anything coarser than about 75 µm. Crushing circuits, fertiliser and cement plants, catalyst handling and food processing all rely on screens; the material balance and effectiveness calculations here tell you how much product of the right size you actually recover.

Key ideas

Screening. A screen is a surface with uniform openings. Particles smaller than the opening can pass and form the undersize (fines, underflow, minus material); larger particles are retained as the oversize (tails, overflow, plus material). A single screen makes one cut; a stack makes several fractions. The cut diameter D_pc is the size at which the separation is intended; for an ideal screen it equals the aperture.

Real screens are not ideal. Some undersize is carried over with the oversize (insufficient residence time, particles riding on top, blinding of openings by near-size particles or moisture), and broken or elongated particles can let some oversize slip into the underflow. Screen performance therefore needs a measure that penalises both errors.

Screen equipment. Grizzlies (parallel bars) for coarse scalping; trommels (rotating cylindrical screens); gyratory and vibrating screens for most medium and fine work. Vibration and gyration keep the bed stratified so fines reach the mesh and they reduce blinding. Capacity rises with open area and feed rate, but effectiveness falls at high feed rates because the bed becomes too deep for fines to reach the openings.

Standard screens and screen analysis. Test sieves are woven wire. Mesh is the number of openings per linear inch, so aperture ≈ 25.4 mm/mesh minus the wire diameter; mesh number is not itself a size. In the Tyler standard series the base screen is 200 mesh with a 74 µm aperture, and the aperture ratio of successive screens is √2 (the area ratio is 2); intermediate screens with ratio 2^(1/4) are available for finer resolution. A screen analysis stacks the sieves, shakes a weighed sample and records the mass retained on each screen. The fraction retained between two screens is assigned the arithmetic mean of their apertures, which feeds directly into the mean-diameter formulas of the previous topic. Results are reported as differential or cumulative (undersize or oversize) analyses.

Material balance. Let material A be the "should be oversize" material (coarser than D_pc). Let F, D and B be the mass flow rates of feed, overflow and underflow, and x_F, x_D, x_B the mass fractions of A in each. Total and component balances fix D and B from the three analyses.

Effectiveness. The recovery of oversize in the overflow E_A, times the recovery of undersize in the underflow E_B, gives the overall effectiveness E. An ideal screen has E_A = E_B = E = 1.

Formulas

F = D + B, F·x_F = D·x_D + B·x_B D/F = (x_F − x_B) / (x_D − x_B), B/F = (x_D − x_F) / (x_D − x_B)

  • F, D, B: feed, overflow and underflow rates (kg/s or t/h); x: mass fraction of oversize material A (−).

E_A = D·x_D / (F·x_F) (oversize recovered in overflow) E_B = B·(1 − x_B) / (F·(1 − x_F)) (undersize recovered in underflow) E = E_A·E_B E = (x_F − x_B)(x_D − x_F)·x_D·(1 − x_B) / [(x_D − x_B)²·(1 − x_F)·x_F]

  • All E are dimensionless fractions between 0 and 1.

aperture ≈ 25.4 mm / mesh − wire diameter; Tyler series: aperture ratio between successive screens √2, 200 mesh = 74 µm.

Worked examples

Example 1 (standard). A screen receives F = 10 t/h of feed containing 40% oversize (x_F = 0.40). The overflow contains 85% oversize (x_D = 0.85), the underflow 5% (x_B = 0.05). Find D, B and E.

  1. D/F = (x_F − x_B)/(x_D − x_B) = (0.40 − 0.05)/(0.85 − 0.05) = 0.4375, so D = 4.375 t/h and B = 10 − 4.375 = 5.625 t/h.
  2. E_A = D·x_D/(F·x_F) = 4.375 × 0.85 / (10 × 0.40) = 0.930.
  3. E_B = B(1 − x_B)/(F(1 − x_F)) = 5.625 × 0.95 / (10 × 0.60) = 0.891.
  4. E = 0.930 × 0.891 = 0.828.

Example 2 (GATE level). 20 t/h of crushed ore is screened at a cut of 2 mm. Screen analyses show the fraction coarser than 2 mm is 0.30 in the feed, 0.90 in the overflow and 0.04 in the underflow. Find the overflow rate, the underflow rate and the overall effectiveness.

  1. D = F(x_F − x_B)/(x_D − x_B) = 20 × (0.30 − 0.04)/(0.90 − 0.04) = 20 × 0.26/0.86 = 6.05 t/h.
  2. B = 20 − 6.05 = 13.95 t/h.
  3. E_A = 6.047 × 0.90 / (20 × 0.30) = 5.442/6.0 = 0.907.
  4. E_B = 13.953 × 0.96 / (20 × 0.70) = 13.395/14.0 = 0.957.
  5. E = 0.907 × 0.957 = 0.868. Check with the closed-form expression: (0.26)(0.60)(0.90)(0.96)/[(0.86)²(0.70)(0.30)] = 0.13478/0.15532 = 0.868.

Common mistakes

  • Writing E = (feed − undersize)/feed or "mass passing / mass fed". That is just a split ratio and says nothing about separation quality.
  • Mixing up which material is A. Be consistent: if x is the oversize fraction, E_B uses (1 − x).
  • Treating mesh number as a size. 100 mesh is not 1/100 of anything in metres; look up the aperture in the sieve table.
  • Assigning the fraction retained on a screen the aperture of that screen instead of the mean of the two bounding apertures.
  • Expecting effectiveness to rise with feed rate. Capacity rises, but effectiveness falls as the bed deepens.

For GATE CH

Expect material-balance numericals: given three screen analyses and a feed rate, find the overflow or underflow rate and the effectiveness. Conceptual questions cover the Tyler series ratio, the meaning of mesh, blinding, and the capacity–effectiveness trade-off. Practise the D/F formula and the E_A·E_B product until you can do them in under two minutes.

Quick check

  1. What is the aperture ratio of successive screens in the Tyler standard series?
  2. Write D/F in terms of x_F, x_D and x_B.
  3. What is the overall effectiveness of a screen with E_A = 0.9 and E_B = 0.85?
  4. Why does effectiveness fall at very high feed rates? Answers: 1. √2 (about 1.414). 2. D/F = (x_F − x_B)/(x_D − x_B). 3. 0.765. 4. The bed becomes deep and fines cannot reach the openings before leaving the screen.

Interview questions

All Mechanical Operations interview questions

Try answering each one aloud before you open it.

  1. 1.What is screening in the context of mechanical operations?Concept

    Screening is a mechanical operation used to separate particles based on their size. It involves passing a mixture of particles through a screen or mesh, where smaller particles pass through the openings while larger particles are retained. This process is commonly used in industries such as mining, agriculture, and pharmaceuticals to classify materials.

  2. 2.Explain the term 'screen analysis' and its importance.Concept

    Screen analysis is the process of determining the particle size distribution of a granular material by using a series of screens with different mesh sizes. It is important because it helps in understanding the size distribution of particles, which can affect the efficiency of processes like grinding, mixing, and chemical reactions. Accurate screen analysis ensures optimal performance in industrial processes.

  3. 3.What is screen effectiveness, and how is it calculated?Concept

    Screen effectiveness measures how cleanly a screen separates material coarser and finer than the cut size. With x the mass fraction of oversize material in feed (F), overflow (D) and underflow (B), the recovery of oversize in the overflow is E_A = D·x_D/(F·x_F) and the recovery of undersize in the underflow is E_B = B(1 − x_B)/(F(1 − x_F)). The overall effectiveness is E = E_A·E_B, which is 1 only for a perfect screen. D/F itself comes from the material balance, D/F = (x_F − x_B)/(x_D − x_B); the mere fraction of feed that passes through is not an effectiveness.

  4. 4.Why is a vibrating screen used in industrial screening processes?Application

    Vibration keeps the bed on the screen loose and stratified so that fine particles migrate down and get many chances to meet an opening, which raises both capacity and effectiveness compared with a static screen. It also shakes near-size particles out of the apertures and so reduces blinding. Vibrating screens handle medium to fine dry solids well; very wet or sticky feeds still tend to blind them and may need wet screening or sprays.

  5. 5.What happens if the screen mesh size is too large for the material being processed?Application

    If the screen mesh size is too large for the material being processed, smaller particles that should be retained may pass through the screen, leading to poor separation efficiency. This can result in a product that does not meet the desired specifications and may require additional processing steps to correct.

  6. 6.How does the angle of inclination of a screen affect its performance?Application

    The angle of inclination of a screen affects its performance by influencing the speed at which particles move across the screen surface. A steeper angle can increase the speed, leading to faster processing but potentially lower separation efficiency. Conversely, a shallower angle may improve separation efficiency but reduce throughput. The optimal angle depends on the material characteristics and desired outcome.

  7. 7.What is the purpose of using multiple screens with different mesh sizes in a screening operation?Application

    Using multiple screens with different mesh sizes in a screening operation allows for the classification of particles into several size fractions. This is useful for producing products with specific size distributions and for separating unwanted fines or oversized particles. It enhances the overall efficiency and effectiveness of the screening process.

  8. 8.200 kg of feed containing 25% oversize is screened. The overflow contains 75% oversize and the underflow 5% oversize. Find the overflow mass and the overall screen effectiveness.Numerical

    From the balance, D = F(x_F − x_B)/(x_D − x_B) = 200 × 0.20/0.70 = 57.1 kg, so the underflow is 142.9 kg. E_A = 57.1 × 0.75/(200 × 0.25) = 0.857 and E_B = 142.9 × 0.95/(200 × 0.75) = 0.905. The overall effectiveness is E = 0.857 × 0.905 ≈ 0.776, about 78%.

  9. 9.A screen recovers 90% of the oversize material in the overflow and 85% of the undersize material in the underflow. What is its overall effectiveness, and what does the number mean?Numerical

    Overall effectiveness is the product of the two recoveries, E = E_A·E_B = 0.90 × 0.85 = 0.765, or about 77%. It penalises both kinds of error: undersize carried over into the overflow and oversize slipping into the underflow. A screen that sent all the feed to one stream would have one recovery equal to 1 but the other equal to 0, so its effectiveness would be zero, which is why the product is used rather than either recovery alone.

  10. 10.What factors can affect the efficiency of a screening process?Application

    Several factors can affect the efficiency of a screening process, including the particle size distribution of the feed, the moisture content of the material, the screen mesh size, the screen's angle of inclination, and the type of screen used (e.g., vibrating, rotary). Additionally, the feed rate and the presence of any blinding or clogging of the screen can also impact efficiency.

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