Vibrating Screen G-Force, Bed Depth & VSMA Ratio Formula

Flooding a 16 mm vibrating screen deck to an 8.5x bed-to-aperture ratio (136.5 mm thick!) traps undersize fines on top so clean spec gravel rides straight to the oversize pile!

**Circular-Motion Inclined Vibrating Screens** (`Eccentric Counterweight Radius r` mm -> **Peak-to-Peak Throw `S = 2 * r`** mm at Shaft Speed `N` RPM) stratify crushed stone only inside a narrow mechanical window: **Centrifugal Throw Index `K_v = ((r / 1,000) * ((2 * pi * N) / 60)^2) / 9.80665`** (`G-units`, kept inside **`3.5–5.5` G** so rock launches clear of wire mesh without cracking side-plates!), while **Discharge-End Oversize Bed Depth `d_{bed} = (((Q_{over} / 60) / rho_b) / (W * v_m)) * 1,000`** (`mm` across Effective Deck Width `W` m, Material Travel Speed `v_m` m/min, and Bulk Density `rho_b` t/m³) MUST satisfy the **Vibrating Screen Manufacturers Association (`VSMA`) Rule `d_{bed} / a <= 4.0`** (`<= 3.0` for sticky damp `100` kg/m³ clay/sand)! Exceed `4 * a` (`where a` mm is square mesh opening) and near-size particles never percolate down to touch the screen cloth!

Verify on a `1.8` m (`6`-ft) Wide Secondary Aggregate Sizing Deck—Eccentric_Amplitude `r` = 4.50 mm (B2), Vibrator_Speed `N` = 920 RPM (B3), Effective_Deck_Width `W` = 1.80 m (B4), Oversize_Discharge_Tonnage `Q_{over}` = 145 t/h (B5), Conveying_Speed `v_m` = 22.0 m/min (B6), Loose_Bulk_Density `rho_b` = 1.55 t/m³ (B7), and Wire_Mesh_Aperture `a` = 16.0 mm (B8): Peak-to-Peak Stroke equals `9.0` mm (E2), Centrifugal Acceleration `K_v` equals `4.26` G (E3), Discharge Lip Bed Depth equals `39.4` mm (E4), giving an ideal **`2.46x` Bed-to-Aperture Ratio** (`<= 4.0` VSMA limit! E5)!

VSMA Vibrating Screen Centrifugal G-Force & Discharge Bed-Depth Formula

Validate `Eccentric_Radius r` in `[1.0, 12.0]` mm, `Vibrator_RPM` in `[500, 1,800]`, `Deck_Width W` in `[0.6, 4.5]` m, `Oversize_Load` in `[5, 2,500]` t/h, `Travel_Speed v_m` in `[6, 45]` m/min, `Bulk_Density` in `[0.8, 3.2]` t/m³, and `Mesh_Aperture a` in `[1.0, 150]` mm!

=LET(er_m, B2, nr_p, B3, dw_m, B4, qo_t, B5, vm_m, B6, rb_t, B7, ap_m, B8, bd_m, (((qo_t / 60) / rb_t) / (dw_m * vm_m)) * 1000, IF(OR(er_m < 1, er_m > 12, nr_p < 500, nr_p > 1800, dw_m < 0.6, dw_m > 4.5, qo_t < 5, qo_t > 2500, vm_m < 6, vm_m > 45, rb_t < 0.8, rb_t > 3.2, ap_m < 1, ap_m > 150), "Invalid Screen Input", ROUND(bd_m / ap_m, 2)))

Reversed Counter-Rotation + Surge Feed (`Q_over = 320` t/h, `v_m = 14` m/min) Deck-Flooding Check

Wire the drive motor backward into uphill counter-rotation (`v_m` slows to `B6 = 14.0` m/min) during a `B5 = 320` t/h primary surge: Discharge Bed Depth E4 swells `3.5x` to **`136.5` mm**, blowing VSMA Ratio E5 to **`8.53` (`> 4.0`!)**—blinding apertures and dumping saleable `< 16` mm chips into the crusher recycle loop!

=IF(ISTEXT(E5), E5, ROUND((((B5 / 60) / B7) / (B4 * B6)) * 1000, 1))

Further reading

• Arte Sheets Lesson — Rotary Trommel Critical Speed, Residence Time & Bed Depth
• Arte Sheets Lesson — Cone Crusher CSS, Eccentric Throw & Parallel-Zone Capacity