# Brick Pressing Rate Calculations

# Introduction

Under the assumption of incompressible flow and fixed hydrauilic cylinder volume, the brick pressing rate of The Liberator can be calculated for a given hydraulic flow rate.

CEB Press v16.09, 2016 machine build. Machine is shown without hopper for manual loading with soil buckets. Used during the 2016 Seed Eco-Home Build. See CEB Press Genealogy.

# The Liberator II - 2018

- 18 hp engine, DuroMax, 77 lb dry weight
- Hydraulic Calculations state that HP required to drive a pump is HP = PSIxGPM/1714. Thus - for 2200 PSI - GPM=HPx1714/PSI=18x1714/2200=14.0 gpm. For 16 hp it is 16x1714/2200=12.5 gpm. Or, if we press at 2400 PSI - we have GPM=18x1714/2400=12.9 GPM
- Take 14 gpm pump -

## Main Cylinder Volume, D= 5 inches, D_rod=2.5 inches

**Expansion Volume**: Cylinder volume = 157 cu in (8" stroke)- Rod volume = 39.3 cu in
**Retraction Volume**- Cylinder volume-rod volume = 117.7 cu in**Full cycle volume**- (expansion volume + contraction volume) = 275 cu in

## Secondary Cylinder Volume, d=2.5 inches, d_rod=1.25 inches, 14" long

**Expansion Volume**: Cylinder volume (expansion volume) = 68.7 cu in- Rod volume = 17.2 cu in
**Contraction Volume**: Cylinder volume-rod volume = 51.5 cu in- Drawer cylinder multiplier = contraction to expansion time ratio (used in control code) = 51.5/68.7 =
**0.75** **Full Cycle Volume**: (expansion volume + contraction volume) = 120 cu in

## One complete cycle volume

One cycle volume = 395 cu in

1 gallon = 231 cu in

1 cycle = 1.7 gallons of fluid

**Thus - 14 GPM should produce 8.2 full (4") block per minute (2200 PSI). 12.9 GPM should produce 7.6 block per minute (2400 PSI).'**

That is quite attractive for an 18 hp as opposed to 55 hp engine of 2009

Design consideration: Blockage condition is defined as the condition when machine motion stalls when an impenetrable object, such as a rock, blocks the machine from moving. If one examines the motion cycle - this is possible ONLY during the pressing chamber closure motion after loading soil. The machine can be designed to stall upon a blockage condition, or it can be designed to keep bypassing at a blockage condition. Ideally, the algorithm allows a blockage condition to resolved automatically. If it can't be - there is no real disadvantage of 'design for engine stalling' in the blockage condition - ad a higher GPM pump should be used. Ideally, the control algorithm does not allow dwelling in a blockage condition.

## Ratio of Main Cylinder Drift Velocity to Drawer Closure Velocity

- Main - 2.5" radius squared = 6.25 sq in
- Secondary - 1.25 raidius squared - rod .625 squared = 1.17 sq in

Velocity ratio of 6.25/1.17 = 5.3

Thus, during 7" drawer travel, main cylinder will move up 1.3".

Thus, need to keep main cylinder down for 1.3"

Main cylinder motion from above - 17.7 motions per minute x 8" = 141 inches per minute or 2.4" per second. Need to keep main cylinder down for 1/2 second to allow closure of drawer.

# The Liberator - 2009

Let's take 25 gallons per minute for the design flow rate of The Liberator Beta v2.0.

The Liberator uses a 5x8x2 inch cylinder (diameter x length x rod diameter) for pressing, and a 2.5x14x1.125" cylinder for the soil loading drawer.

The effective volumes for both cylinders differ. This is because the cylinder rod takes up some volume - thereby reducing effective volume and force for the contraction part of the stroke. The expansion part of the stroke uses the full cylinder volume.

## Main Cylinder Volume, D= 5 inches, D_rod=2 inches

- Cylinder volume (expansion volume) = 157 cu in
- Rod volume = 25 cu in
- Cylinder volume-rod volume (contraction volume) = 132 cu in
- Volume filled for a complete cycle of the cylinder (expansion volume + contraction volume) = 289 cu in

## Secondary Cylinder Volume, d=2.5 inches, d_rod=1.125 inches

- Cylinder volume (expansion volume) = 69 cu in
- Rod volume = 14 cu in
- Cylinder volume-rod volume (contraction volume) = 55 cu in
- Volume filled for a complete cycle of the cylinder (expansion volume + contraction volume) = 124 cu in

## One complete cycle volume

One cycle volume = 413 cu in

1 gallon = 231 cu in

1 cycle = 1.8 gallons of fluid

## Pressing Rate Results

The results above yield 14 brick per minute results.

We need to consider 10% inefficiency in the CEB hydraulic system (-1.4), intermittent operation of the soil grate shaker (-.5), and reduction of the main cylinder speed towards the end of the compression stroke (-1). This slowdown at the end of the compression stroke has been calculated as the condition where the last 1/2" of compression is slowed down by a factor of 4.

**With these considerations, we obtain 11 bricks per minute for 4" thick bricks.**

**Similar calculations and reasoning for 2.5" thick bricks yield an overall results of 13 bricks per minute.**