It’s been a while since I added anything to this growing encyclopaedia of Math channels! Like my previous article, this one also focuses on hydraulics.
Unlike other machinery, which can be connected to a dynamometer, mobile construction equipment that uses hydrostatic transmission without a PTO output makes it tricky to determine the engine power output.
However, in the majority of cases, the hydraulic pumps required to operate the machine are directly connected to the engine and so in effect we have our own built-in dynamometer.
In order to determine the engine power required, we first need to obtain the hydraulic fluid power. The formula for this is:
As you can see, this formula requires both hydraulic pressure and flow. For this reason, the Pico hydraulic flowmeter is required and in order to load the hydraulic system, it is necessary to have a flow meter with a built-in load valve.
This valve applies a restriction to the hydraulic flow rate and so increases the pressure within the system. Much like electricity with voltage and current, pressure and flow are linked. As a restriction is applied to the system, the hydraulic pump has to be able to maintain a flow rate despite the pressure increasing due to the restriction. As seen in Maths is cool part 10, understanding the relationship between pressure and flow is really important in determining pump health.
Safety is paramount, of course here when dealing with any hydraulic system. Please ensure you have adequate training and PPE prior to any hydraulic measurement. Much like high-voltage systems, we have to respect this system and the potential dangers it contains.
When using a flow meter, be mindful of the preferred installation flow direction, fittings, pipe rating, temperature, etc. Loading a hydraulic system without any work being done generates a lot of heat and the flowmeter will start to get hot, including the pipes. Do also ensure that you minimise any possible chance of contamination entering the system. The last thing you want to do is introduce more problems!
Ideally, in order to load the pumps, you want to place the flowmeter in a position near the outlet of the hydraulic pump. This carries some risks, as you would not be protected by the relief valve. However, as you are graphing data live with PicoScope, you can add on some visual and audible tools to warn you when the pressure is getting too high. Actions on measurements could be one way to ensure you don’t go over a safe working pressure by setting a limit and adding a sound action.
For example, I’ve added a limit of 340 bar to the below capture, which is the PQ guided test in the heavy-duty and off-highway section, should you wish to try any of the following techniques.
Here you can see an alarm symbol and the measurement is in red.
Back to the maths!
With pressure and flow captured, we need to insert our formula for the hydraulic power. This can be shown with the formula (B*C)/600 and setting the units to kW.
Once you click finish, you will now see a Math channel that appears to follow the pressure curve fairly closely. This is to be expected, given that the pressure is changing the most compared to the hydraulic flow.
So, we could stick with this, add some measurements and get our peak hydraulic power, which is around 40 kW. However, we can also work out the engine power required to make 40 kW of hydraulic power.
To do this, we need to add an additional factor for pump efficiency. Now, we could be clever here if we knew the displacement of the pump, as we have the engine speed. We could therefore calculate the theoretical flow rate as per Maths is cool 10 and work out the efficiency based on the actual flow rate. However, for this example, we don’t know the pump displacement.
As a general rule of thumb, gear pumps are around 70-85% efficient, variable displacement pumps between 90-95% and vane pumps around 80-90%. In the example we are using, this was captured from a variable displacement pump, so we are looking between 90 and 95% efficient. As this isn’t a new pump, I will use the lower end of this and opt for 90%.
The formula now is as follows:
Where pump efficiency is written as a decimal, so if we are using 90% this will be 0.9. In the Math channel, we need to enter it as follows: (B*C)/(600*0.90).
As you can see, there is now quite a lot going on with these Math channels, but there is a better way to visualise the engine power and that is to plot it alongside the engine speed.
To do this, we will make use of the XY view, much like we have done with the pressure and flow curve.
In the bottom left corner, we can see a relatively straight line. This highlights how the engine speed changes relative to the hydraulic load placed on the engine. If the engine starts to ‘lug’ down due to the load from the hydraulic system, the line will start to lean further over to the left. This is often referred to as Governor droop.
If the engine is in good health, then this line should be pretty straight, indicating that the engine speed is maintained despite there being a hydraulic load being added to the engine.
By combining 4 signals, crankshaft position sensor, hydraulic pressure, hydraulic flow, and hydraulic oil temperature, there is a huge amount that can be unveiled by harnessing Math channels.
Going the extra step
I mentioned earlier that we could be clever and use a math channel to calculate the pump efficiency and this could be used inside the engine power formula.
Using the psdata file from the Maths is cool part 10, we know the displacement of the pump is 51cc. As we have the theoretical flow rate and the actual, we can create the pump efficiency math channel as follows, where B = hydraulic pump pressure and D = hydraulic pump flow.
(D/(51*(1.616*LowPass(freq(A),4))/1000))*100
This does give us the efficiency in %, so we need to drop the 100 from the end of the formula, so we end up with a decimal as required in the engine power maths. The formula would now be
(D/(51*(1.616*LowPass(freq(A),4))/1000))
Using this formula, we can insert this in the engine power formula so it will read as follows:
(B*D)/(600*(D/(51*(1.616*LowPass(freq(A),4))/1000)))
Using the time rules, we can now add measurements at the point the pump is put under load and we can observe the output.
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