reduction in vibration

[mark1505]

Hi, i am looking at reducing the overall vibration in a wildcat helicopter for my university course. Obviously, due to the cost, i am unable to utilise a real life wildcat so am looking to use a radio-controlled helicopter to prove my concept works. I need to measure the phase of the main rotor head so i can then ensure the dc motor i will use as a "shaker" will be 180 degrees out of phase. due to the size of the RC helicopter, i am unable to use an accelerometer to pick off the required information. i have looked at lasers but they are too expensive and accelerometers but they are cumbersome My question is what component would be best to use and is this even feasible? Thank you in advance for your expert opinion and input.

[nfmax]

I'm not quite sure what you are asking for here - a measurement of the 1R/NR vibration velocity amplitude & phase, or simply a tacho that gives you a 1R reference signal. If you want to measure vibration, I think an MEMS accelerometer is probably your best bet. For a reference tacho, I suspect a Hall effect magnetic sensor will be the optimum choice.

Do you have size, weight, and power limits in mind for the sensors? Obviously, cost is an issue, but these sensor types can be very cheap, small, and light.

[mark1505]

Thank you very much for taking the time to reply to my question, it is very much appreciated.

I intend to input vibration into the radio controlled helicopter by adding tape to one of the main rotor blades, (the helicopter will be strapped to the deck) When the vibration is visible i will use a rotary to linear "shaker" (dc motor)  to reduce the vibration. What i need to do first is to ensure the helicopter and dc motor are out of phase with each other to prevent magnifying the vibration and causing damage.  This is where im struggling as i am unsure of how best to achieve the phase information,

best regards
mark

[CatalinaWOW]

You might want to think through your whole system, not just concentrate on the measurement of vibration.

Helicopters vibrate a lot, but there are many source of this vibration other than imbalance of the rotor head.  Have you verified that this is actually the dominant source in the wildcat helicopter you are aiming at?  Other common sources include, but are not limited to blade slap do to varying lift between advancing and retreating blades, vortexes shed from the rotor interacting with the tail boom, inertial loads from all the moving and whirling parts in the head and similar reactions in the tail rotor.  Some in the industry say that helicopters are really not aircraft, but a collection of parts flying in formation.

In your case, where you have deliberately imbalanced the head of a model, measurement of amplitude and phase of the the resulting motion requires you to define a reference frame.  The centerline of the helicopter is often used.  Now you need to measure where the rotor head is relative to that reference frame.  As others have mentioned hall and optical sensors are common choices.  Place a contrasting paint patch or magnet on one of the blades, or on the shaft and sense it each time it goes past.  A magnet can also be sensed by a coil as easily as using a Hall sensor. 

In any case you will now have a signal with pulses or peaks once for each rotor turn that provides a reference signal.  The easiest next step is to mount an accelerometer (mems ones are tiny, only a mm or so on a side) to sense the motion due to unbalance.  This motion could also be sensed by a vision system, an LVDT, an interferometric system or other choices, but there are significant additional complexities to all that I am aware of.

Where you mount the accelerometer requires a lot of thought, both from a sensing standpoint, and from the point of view of your overall objective.  A helicopter airframe is not a rigid body, and the motion induced by the rotor head may change in both phase and amplitude at various points.  Do you want to measure motion at the location of some vibration sensitive instrument, the pilots seat, or at the source?  The answer depends on what you are trying to achieve, and where your compensator will sit.

In many ways mounting at the shaft close to the rotor head is a good answer.  It measures the source of the vibration driving the rest of the system.  If you can model the rest of the system, it provides the appropriate input and you may be able to derive the answers you need elsewhere in the helicopter.

The output of your accelerometer will be a hash of all the various vibrations that come from being a helicopter.  If you are lucky the dominant signal will be a rough sinusoid at the rotor frequency.  If you pay attention to the phase shifts in the filters you can even filter the signal to make this more true.  The phase you are looking for is the phase between this signal and the reference discussed earlier. 

You will now have to come up with a control system to drive your compensator.  If your compensator is located at the rotor shaft near where the accelerometer is mounted you have another interesting development - the signal you are using to control the compensator goes away if the compensator is successful.  There are ways to deal with this, but as you start to work through those complexities you will start to really appreciate the simplicity of balancing the rotor in the first place.  If you are mounting your compensator elsewhere the dynamic model of the airframe discussed earlier will become very important.

[nfmax]

There are ways to deal with this, but as you start to work through those complexities you will start to really appreciate the simplicity of balancing the rotor in the first place.

Simplicity!?
I spent a tidy chunk of my career designing and building rotor track & balance systems: I don't think I've ever heard it described as 'simple' before

[CatalinaWOW]

It's all relative.  You better than most should understand the relative ease of what you did to trying to do the same thing from a remote location of the helicopter.  But still worthy of a careers worth of effort.

[tecman]

Your biggest problem is that there are multiple modes of oscillation occurring.   Add to that the fact that the amplitude of the modes varies with the cyclic inputs.  So your rotary balancing weight may cancel one or two modes, but may also enhance other modes and actually make matters worse.  Active damping measures work best when there is one dominant mode of vibration.

paul

[max_torque]

it's also worth noting that it will be impossible to apply your 'balance correction' force to exactly the same place as the out of balance force is created.  Hence you end up with a force couple.  Whilst it may be possible to get to an overall state of balance for the whole device, internally, the un-balanced forces must be carried by something, and as helicopters are not, generally, that robust (due to having to be low mass to fly) you may find the airframe cannot actually provide the necessary load paths!  (it's always better to remove the source of the out-of-balance, than try to negate it!

An interesting project however, may be to use a 3 axis accelerometer, sampled at a decent rate (say 10 Khz) and to do a 3d vector analysis of the vibrations.  You could also use a powerful micro to calculate the various vibration energies in the frequency domain, compare that to the fundamental frequency for various shafts and gears in the transmission (the main rotor is typically around 300rpm (5 Hz), but things like tail rotors and shafts significantly higher) and come up with a warning system that spots an out-of-balance event in real time, before something breaks!

[nfmax]

For a real helicopter the main rotor frequency (1R) is of the order of a few Hz. The blade-pass frequency (nR) will be two, three, four, or five times higher, depending on the number of blades. The components of interest for RTB are the vertical and lateral vibration at each frequency, generally expressed as a vibration velocity, even if measured as acceleration. A tri- or bi-axial accelerometer mounted on the airframe somewhere near the gearbox mounting is used, often in a location specified by the aircraft manufacturer. Obviously this picks up a lot of other vibration sources, from the tail rotor/fan, tail drive shaft, engine shaft, gearbox, etc. There's a lot of vibration about.

To get rid of this stray vibration, synchronous averaging is used. A pickup on the main rotor shaft gives an impulse, for example each time the master blade is over the nose. This is used to synchronise the data acquisition system so that it samples the accelerometer signals at equal increments of rotor angle, rather than equal time periods. Obviously in a full size helicopter the rotor speed is nearly constant: but not exactly. You only need a few samples for each period of the blade-pass frequency. Sixty samples per revolution is a good choice, because 60 divides by 2, 3, 4, 5, & 6 exactly. Back in the old days we generated a variable-frequency ADC sample clock using a PLL off the main rotor tacho, but then moved on to constant-frequency ADC operation and variable-ratio resampling.

The corresponding resampled sample points from successive rotor revolutions are averaged together, over maybe 30 seconds or so, while the pilot holds a steady flight condition. The averaging acts as a bandwidth-narrowing operation, filtering all signals which are not rotor harmonics, and accumulating those which are. This measurement & averaging is applied to each of of the two or three axis signals simultaneously. Then you take the FFT of each averaged signal (not the power spectrum) and extract the amplitude and phase of the 1R and nR bins. So each flight condition gives you 4 measured numbers, per axis. Note that the FFT phase is the phase relative to the rotor shaft tacho impulse - effectively the rotor shaft angle.

You repeat this process over a set of flight conditions - FPOG, hover, and various forward speeds. Sometimes extra conditions such as autorotation or HOGE are used as well. You then have to make adjustments to the rotor system to reduce the amplitude of 1R & nR in each axis at each test condition (generally you don't care about the phase). The available adjustments are the adjustable pitch links in the control system; one or more weight pockets at each blade tip; sometimes one or more tabs on the trailing edge of each blade; and possibly also lag dampers (though these are generally a case of replace rather than adjust).

At the same time, in each flight condition, you measure the tip-path of each rotor blade. In theory, they should all follow each other exactly moving in the same plane, but in practice some blades fly high and some low. Similarly, some blades may lag more than others (i.e. arrive slightly early or late at the reference position compared to the ideal). This measurement is generally done optically. This gives you another set of numbers at each flight condition, all of which need to be minimised. I spent years working on optical blade tracking devices!

There are more things to be minimised than available adjustments, i.e. the system is under-determined, meaning that a perfect solution may not exist. We used to treat it as a constrained linear least-squares system, since in many cases there are absolute limits to be observed. There may be alternatives techniques these days.

The first RTB system I was involved with used a Rockwell 6511 to control the data acquisition and a National NSC800 to crunch the numbers (both 8-bit microprocessors!). This was possible because you have to land & shut down before the ground crew can make the rotor adjustments, so there is always a delay of a few minutes. Then we moved on to a pair of 68000 16-bit micros. That system went out to the first Gulf War almost before we had got it into production. Then we moved on to HUMS systems, where the RTB function was secondary to monitoring the gearbox & engines.The first one of these used Inmos Transputers (yes, really!) after which I left the company and moved on to other things.

I remember shortly after the collapse of the Soviet Union, flying in Switzerland in a Kamov coaxial-rotor helicopter while we were measuring the effect of introducing specific rotor system adjustments on the measured vibration - effectively calibrating our least-squares solution. We were accompanied on one flight by a senior Kamov engineer, who was very old school. He didn't like the level of vibration he was feeling in one of our tests, and decide to check it out. He produced a piece of card and a pencil. Then he leant against the airframe with the arm holding the pencil, and moved the card down past it with the other hand, drawing what could have been, but was not, a straight line. He then measured the peak-to-peak amplitude of the wiggles, and used his slide rule to convert from displacement to velocity. I don't speak Russian, so I don't know what his measured value was - a pity, as it would have made an interesting comparison.

----

For an active vibration control system such as the one you are proposing, you will need to generate a force which is ideally equal and opposite to the force from the rotor imbalance at each flight condition, and apply it at the same point, i.e. the gearbox output shaft. The force must have components at the 1R and nR frequencies with independently adjustable amplitude and phase, controllable separately in the vertical and lateral axes. Obviously you can't do this with a single motor. However, you can in principle at least, cancel out one component - I suggest the 1R vertical. You will need to measure the phase angle of the rotor both so that you can isolate & measure the 1R vertical, and so that you can control the motor speed so that it rotates synchronously with the main rotor - effectively a PLL where the 'voltage controlled oscillator' is your DC motor variable speed control. Once this loop is in lock your motor should behave as though it was coupled directly to the rotor shaft. Then you need (somehow) to make this motor generate a variable periodic force as it rotates - effectively you want an adjustable imbalance in the motor shaft. Your control system must adjust both the imbalance and the phase of the motor shaft relative to the main rotor shaft so as to cancel out the chosen component. Tricky!

One way to make a varying imbalance might be to use a flexible shaft with a weight attached to it, between a the motor an a moveable bearing. By moving the bearing, you could introduce a misalignment in the shaft so that the weight would generate an out-of-balane force that would be (nearly) zero when the bearing was aligned with the motor shaft, and increases as the angle between the two bearing increases. Maybe - I haven't worked this out in detail.

Good luck!

[CatalinaWOW]

I didn't think we had any fundamental disagreement.   

[EEVblog]

There are some pretty tiny accelerometers available:
http://www.pcb.com/TestMeasurement/Accelerometers/mini/Miniature_Single_Axis_Accelerometers/352A9x
http://www.akron.be/pdf/endevco/7264D.pdf

[mark1505]

Thank you for your reply, a very interesting and informative piece. I am concentrating on the Vertical axis and will (hopefully) carry out the reduction in vibration whilst the helicopter is strapped on the deck.  The area in which i am finding extremely difficult to come up with a way forward is exactly how i am going to achieve the phase information from the main rotor head and also the dc motor i intend using as the "shaker" to be honest i didn't think it would be so difficult to get a definitive answer but it seems its more obscure a question than i thought and not something that is common in the radio controlled helicopter world

[nfmax]

Suppose you have a rotating shaft with a small magnet mounted on it. As the shaft rotates, it carries the magnet with it and once each revolution it passes in front of a magnetic detector. This gives a short pulse signal, which we take as our 0? phase reference. If the shaft tuns at a constant speed, the pulses repeat each time the shaft reaches the 0? point, at a constant frequency (1/60th the speed in rpm).

Now suppose we have another such magnet and detector arrangement attached to the shaft of the DC motor. This will give a similar pulse each time the motor shaft passes its 0? point. The speed of the DC motor, and hence the frequency of the pulses from this detector, will depend on the voltage applied to the motor. What we want to achieve is for the motor speed to be exactly the same as the shaft speed, so that the two sets of pulses occur at the same frequency, and that the two pulse trains have a fixed phase difference between them. It might be that we want the DC motor to be 72.3? ahead of the shaft angle, for example.

We can do this by using a phase-locked loop (https://en.wikipedia.org/wiki/Phase-locked_loop). The signal from the pickup on the rotating shaft is the 'reference' input to the phase comparator; the 'VCO tuning voltage' is the motor supply voltage; the VCO is the DC motor itself; and the magnetic pickup on the DC motor is the feedback input to the phase comparator. The action of the PLL is to vary the motor supply voltage so that the phase difference between the two inputs to the comparator is zero, at which point the DC motor is turning in lock step with the rotating shaft. When the PLL is in lock, it will keep this synchronisation even though the shaft speed may change (within limits).

In your application, you want to have a controllable phase angle between the DC motor and the rotating shaft. You can modify the PLL to achieve this. So long as its two inputs are at the same frequency, the phase comparator gives an output voltage which is proportional to the phase difference between the two. For example, you might get 1V output for pi radians phase difference. The PLL operates to reduce the phase comparator output voltage to zero, and, so long as the loop filter contains at least one integrator and the shaft speed is constant, the phase comparator output voltage will be zero when the loop is in lock. If we add an extra DC voltage to the output of the phase comparator, and feed the sum of the two voltages into the loop filter, the PLL will act to make the sum of the two voltages equal to zero. Which means the output from the phase comparator will be equal and opposite to the voltage we applied, which means the phase difference between the two inputs will not be zero, but rather a constant set by the control voltage & the sensitivity of the phase comparator.

Now, by varying the extra DC voltage, you can control the phase angle between the DC motor shaft and (in your application) the rotor shaft.

I hope this gives you some ideas!

[Henrik_V]

I attached an idea for an actor.
Two motors run two unbalanced wheels, where the exenter masses are choosen that way, that in 180° position the system is balanced.
Rotor shaft and both wheels have a position sensor (hall, optic..) and are run in sync with the rotor (PLL)
Phases are set by PLL and controller (see post from nfmax)
Max compensation (at rotor rotation R)  is reached when both masses rotate at same phase.
By controlling the phases of the two wheel one should be able to compensate R unbalance .
Even certain other vibrations should be able to compensate by modulating the wheel phases.

Henrik

[mark1505]

You will need to measure the phase angle of the rotor both so that you can isolate & measure the 1R vertical, and so that you can control the motor speed so that it rotates synchronously with the main rotor -

I appreciate this hence why it was my original question. How do I measure the phase angle?.

[CatalinaWOW]

You will need to measure the phase angle of the rotor both so that you can isolate & measure the 1R vertical, and so that you can control the motor speed so that it rotates synchronously with the main rotor -

I appreciate this hence why it was my original question. How do I measure the phase angle?.

Quoted from my previous post.

... measurement of amplitude and phase of the the resulting motion requires you to define a reference frame.  The centerline of the helicopter is often used.  Now you need to measure where the rotor head is relative to that reference frame.  As others have mentioned hall and optical sensors are common choices.  Place a contrasting paint patch or magnet on one of the blades, or on the shaft and sense it each time it goes past.  A magnet can also be sensed by a coil as easily as using a Hall sensor. 

In any case you will now have a signal with pulses or peaks once for each rotor turn that provides a reference signal.  The easiest next step is to mount an accelerometer (mems ones are tiny, only a mm or so on a side) to sense the motion due to unbalance.  This motion could also be sensed by a vision system, an LVDT, an interferometric system or other choices, but there are significant additional complexities to all that I am aware of.

There are four angles of interest for the simplest version of your problem.  First the angle between the rotor phase sensor and your reference plane.  If you place your rotor phase sensor on the reference plane this angle is zero and can be neglected.  Second, the angle between the rotor unbalance  direction and the direction of your rotor reference.  The rotor reference is the magnet, white stripe, LED or whatever you put on the rotor to provide a reference.  Third, the angle between your unbalance compensator reference and the reference plane.  Again, if you put the sensor in the reference plane this angle becomes zero and can be neglected.  Finally, the angle between your compensator's unbalance and the magnet, white stripe, LED or whatever. 

Draw all of this from the top of the helicopter looking down and it should become obvious to you.  At worst you will need to draw pictures of a couple of rotor positions and compensator positions and sketch out a time sequence of the signals from your sensors.