232 posts

### vibrating screen efficiency calculation

dear all

how to calculate the efficiency of vibrating screen .

the input to the screen 2900 tpd , oversize 2412 tpd , undersize 488 tpd.

- 30mm in oversize is 8% & +30mm in undersize is 6% .

can we calculate the eff. without knowing the input & output tpd or tph.

raj

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536 posts

### re vibrating screen efficiency calculation

Hello Raj,

Screen efficiency is obtained using different equations, depending on whether your product is the oversize or undersize fraction from the screen. The following information is required to calculate the two screen efficiencies;-

- Qms(f) = Mass flow rate of solid feed.
- Qms(o) = Mass flow rate of solid in the screen overflow.
- Qms(u) = Mass flow rate of solid in the screen underflow.
- Mu(f) = Mass fraction of undersize in the feed.
- Mu(o) = Mass fraction of undersize in the overflow.
- Mu(u) = Mass fraction of undersize in the underflow.

The screen efficiency based on the oversize (Eo) is then given by the equation;-

Qms(o) * [1 - Mu(o)]

Eo = ----------------------------- ( Equation 1)

Qms(f) * [1 - Mu(f)]

and the screen efficiency based on the undersize (Eu) is then given by;

Qms(u) * Mu(u)

Eu = ------------------------------- ( Equation 2)

Qms(f) * Mu(f)

Overall screen efficiency is then calculated by multiplying these two efficiencies together ie;-

E = Eo * Eu ( Equation 3)

In your case the following values are given;-

- Qms(f) = 2900 t/d
- Qms(o) = 2412 t/d
- Qms(u) = 488t /d
- Mu(o) = 8% = 0.08
- Mu(u) = 94% = 0.94

(Where oversize = +30mm fraction and undersize = -30mm fraction.)

However we need to also know the mass fraction of undersize in the feed, Mu(f). This can be calculated from the values already given by a simple mass balance based on the undersize, ie;-

Mu(f) * Qms(f) = Mu(o) * Qms(o) + Mu(u) * Qms(u)

or...

Mu(o) * Qms(o) + Mu(u) * Qms(u)

Mu(f) = ---------------------------------------------

Qms(f)

therefore,

[ (0.08 * 2412) + (0.94 * 488) ] (192.96 + 458.72) 651.68

Mu(f) = -------------------------------------------- = --------------------------- = ----------- = 0.2247

2900 2900 2900

So now we can calculate your screen efficiency based on oversize (+30mm), according to Equation 1;-

2412 * (1 - 0.08) 2412 * 0.92 2219

Eo = ------------------------------ = ---------------------- = ---------- = 0.987 = 98.7%

2900 * (1 - 0.2247) 2900 * 0.7753 2248.4

Similarly, using Equation 2, we can calculate the screen efficiency based on undersize (-30mm);-

488 * 0.94 458.72

Eu = ----------------------- = -------------- = 0.704 = 70.4%

2900 * 0.2247 651.63

Therefore, using Equation 3 we can calculate the overall efficiency of your screen based on the given data;-

E = 98.7 * 70.4 = 69.5%

Regards,

Ted.

80 posts

### re vibrating screen efficiency calculation

**Dear Raj**

**Mr Ted is right to find the actual efficiency of any vibrating screen.**

**but if TPH is not known than feed material undersize, product undersize and overproduct undersize % can be used to find the efficiency. I am giving an example below for your understanding.**

**In limestone separation for (-) 30mm .**

**The Feed material to the screen contains 60% (- 30mm).**

**After screening the oversized fraction contains 10% (-30mm)**

**undersized contains 95% of (-30mm).**

**Calculation: **

** Let us find the Values of A,B and C for calculating Efficiency,**

**A= 60/100 , B = 95/100 , C = 10/100**

**Efficiency -1 = (A-B)/(C-B) = (0.6-0.95)/(0.1-0.95) = 0.411**

**Efficiency -2 = (C-A)/(C-B) = (0.1-0.6)/(0.1-0.95) = 0.588**

**Efficiency -3 = (1-C)/(1-A) = (1-0.1)/(1-0.6) = 2.25**

**Efficiency -4 = B/A = 0.95/0.6 = 1.587**

**Overall efficiency = Eff 1 x Eff 2 x Eff 3 x Eff 4 x 100
**

**Overall all efficiency = 0.411 x 0.588 x 2.25 x 1.587 x 100 = 86.3%**

536 posts

### re vibrating screen efficiency calculation

Thanks Chari,

You are quite correct. The equation you provided can be derived fairly easily from the basic screen efficiency equations. I can post this derivation if anyone is interested in the mathematics behind it.

Regards,

Ted.