My rotor hub design continues to evolve as I learn more about the complex forces and motions of a rotor system.
One of my goals of this project was to keep it simple. Ideally as simple mechanically as a small electric quad, but as discussed in a previous post, that is not the desired approach, so I'm designing a "collective only" variable pitch rotor head, not unlike what might be found on a conventional helo's tail rotor. As you can see from the image, I'm trying to leverage stock structural materials such as standard architectural aluminum channel and square tube.
The design above consists of a "double wishbone" (for lack of a better term) composite strap made of approx 11 layers of 6 oz. plain weave fiberglass fabric with about 50% by weight of Series 2000 epoxy resin with 2120 slow cure hardener (FiberGlast Resin). This should give a tensile strength of about 5500 Lbs which is almost 4x the anticipated centrifugal blade tension of 1500 Lb.
My big challenge here was to come up with a way to attach mechanical structures to the composite flex-element without weakening the composite. My approach here is to use a large number of small diameter "shear pins" which will pierce through a sandwich of aluminum plates and the composite. The idea is to spread the load across a large area of the composite and avoid force concentrating geometries which will exceed the local strength of the fibers.
A simple test of a 1/16" diameter nail through 2 layers of this composite matrix is surprisingly strong.
A variation of that test was to line up 4 nails in a line (spaced about 1/4" apart) along the axis of tension, and even though these nails were all aligned, the strength went up sufficiently that it was able to support my full weight (~160 Lbs).
This tells me that the composite matrix is doing a good job of spreading the load to neighboring fibers.
So, back to the rotor design....The vertical shaft is the main rotor mast. The channel and plate at the upper end of the mast comprise a sandwich which holds the composite "wishbone" on center, and receives upward forces from the thrust generated in the blades (not shown).
The wishbone shape is a copy of a shape observed in several articles I've read. The idea is to give flexibility for the rotor blades to flap (up and down due to dissymetry of lift), lead/lag (oscillate forward and backward in the plane of rotation) due to correolis forces generated as a result of flapping, and pitch (or feather) the blade to increase/decrease the angle of attack of the blade to control the lifting thrust of the rotor.
Based on this flat geometry, this particular design will not have a tremendous amount of flexibility in the lead/lag direction, however, I am hoping this is ok because of the measures I am taking to limit flapping.
The pitch control horn protrudes forward of the blade leading edge, and a rod extends this toward the center of rotation a bit. The idea here is that I will connect my pitch control links to the rod at a point which is outboard of the effective flapping hinge point. In this way, when the blade flaps up, it's angle of attack will be reduced (because the pitch control link won't flap up), and will tend to limit the amount of blade flapping. Now I've been around control systems long enough to know that if I get too aggressive with this (by making the pitch control horn too short, or by connecting the pitch link at a point that is too far outboard) the system could become unstable and the flapping could actually be exaggerated to the point of destruction.
Another interesting observation relating quad copters to single rotor copters:
On a single rotor copter, the cyclic forces cause the rotor disc to tilt, and this is transferred to the helo airframe through the rotor hub and mast. The airframe FOLLOWS the rotor disc.
On a quad copter it is quite the opposite. The difference in thrust of the 4 rotors causes the airframe to tilt, which causes an effective "flapping" of the rotor discs relative to their masts new position. Moments transferred through the mast and hub then bring the rotor disc axis into alignment with the mast. The rotor disc(s) FOLLOWS the airframe.
This is one reason I'm so excited to try this flapping compensation technique with the forward extending pitch control horn as it promises to greatly reduce cyclic bending stresses on the mast, rotor, and blade roots.
Comments
No different than a helicopter's tail rotor hub. If you examine some of the tail rotors of the world, some have hingeless designs, and some have the full onslaught of hinges that the main rotor hubs can. Hard to tell the rhyme or reason as to why some have it and some don't. Seems the more complex designs come with the larger rotors, which I can only assume come with larger forces. There must be a certain point as the rotors get larger when it becomes lighter to add the hinges than to create a single structure large enough to handle the stresses from loading without the hinges.
James,
I had not seen THAT human powered video, but a similar one. This one was quite impressive.
I remembered that another (maybe invalid) reason for me designing "flap compensation" (or delta hinge, or whatever you want to call it) was because of the way a quad is so different from a standard helo. In a standard helo, the rotor tilts due to cyclic control, then the mast and airframe follows due to moments transmitted through the rotor hub. In a quad it's exactly the opposite. imbalances in lift of the various rotors causes the frame to tilt, then moments transmitted through the hubs cause the rotors to tilt.
Because of the large moment of inertia of my rotors (with the tip weights) I am concerned about trying to use the rotor hub to transfer moments from the shaft to the hub/rotor to make the rotor pitch/roll with the airframe. So, my thought is to use this "flapping compensation" technique to help the rotor tilt in the direction of the airframe. My BIG concern is that I don't fully understand the dynamics of these torques. I know that gyroscopic precession causes there to be a 90 degree offset between the torque applied and the movement of the gyro momentum vector. Also other factors too complex to discuss here. So my approach will be trial and error to some extent. I will build a test stand that can tilt, so I can see how the rotor system responds to changes in airframe pitch and roll. Thanks for link to youtube video.
Ah yes you're right about flapping compensation - its even less of a factor than I had stated before. I had momentarily forgotten about the CW vs CCW effects counteracting each other. To me, your main goal for your hub should be to make something strong enough to be able to withstand the alternating stresses, not necessarily to allow the blades freedom to move as they wish.
Have you performed a fatigue calc for your flex element using a goodman line or ASME elliptical? The alternating stresses seem like they would be a big factor in your element's fatigue. Not only do you have the tensile stresses, but you have bending in two axes and torsion to also take into account, that's a lot of additive stress.
I understand why you're using variable pitch rotors instead of direct drive individual motors. I agree with the argument that the response time with a rotor with high rotational inertia could be too slow.
In my experience, strength/weight is one of the most basic challenges to any sort of mobile machinery, especially those that fly. My industry is road legal cranes, and strength to weight is always one of the top concerns in our designs. In some of my prior exposures within the aircraft industry, nearly everything inside an aircraft is subjected to very strict weight requirements. As an extreme case, have you seen any of the human powered helicopters (they are really quadcopters). You might find their structures of interest, not for a practical solution to your structure, but simply as an interesting study on extreme strength to weight ratios on a similar application to yours: https://www.youtube.com/watch?v=P843wHX3n28
James, Thanks for the comment. Yes, this project started out "simple", and now is anything but. I guess it might help to understand that I view this whole endeavor as a personal journey, not necessarily a race to accomplish a specific task. So as long as I'm learning, and having fun in the shop, and staying out of trouble (wink) it is very satisfying for me personally. All of your concerns are valid, and I sometimes wonder if I should just go out and buy a toy quad-copter and have fun flying it. But it's more about a creative process for me. I appreciate your concerns about untested systems in human carrying aircraft. I am a long long way from that point, and may never get there. I'll have to be pretty darned confident with hours and hours of flight with full payload in drone remote control flight before strapping in. I'll be shopping for a kevlar flight suit too. :)
Regarding the flapping compensation, you bring up a valid point about it maybe not being necessary. In fact I believe all of the forward flight effects cancel out on a quad, as the rotation alternates from CW to CCW around the quad.
I certainly could build a set of rotors without flapping cancellation, or with very little. I'm in that area of the design right now, and it's not too bad. Just trying to get the droop stop design incorporated into the upper "swash plate" (for lack of a better term).
If I wanted to design this as a drone only (unmanned) aircraft, I could design with 4 motors and save a lot of headache on the power transmission design too.
From your comment it sounds like you expect my major challenges to be structural strength/weight. That is interesting to me. Because I am on a very tight budget, I'm not yet playing with carbon, but only fiberglass. I have a weight analysis spreadsheet but it's full of assumptions and also is incomplete. For the collective arm (that reach out 14" from the swashplate to the pitch control horn) I'm looking at a custom composite moulding which includes a tubular beam (or CHS- circular hollow section) to act as the arm and droop stop all in one. Playing with different designs to get the absolute most out of a tubular beam to avoid stress concentrators and to avoid buckling. Since I'm not in a race, I'm perfectly ok with a bit of tinkering to optimize, or at least improve the design over a simple straight tube. I'll blog about that at another time. BTW - I have seen the videos of copters experiencing ground resonance. This gives me tremendous respect for the myriad forces, moments, inertias, gyros, vibrations, resonances, etc. etc. etc that could reduce this project to a scattering of fiberglass slivers in the blink of an eye. Thank you for the time you took to comment. Please "follow" me if you can. I value the input from other conscientious enthusiasts.
Randy, I was reading back through your blog to try to understand the rest of your design.
While I understand the desire to keep your design simple, I think you and I have different definitions to the word simple. While mechanically your idea of the bearingless rotor is simple, there are so many hurdles that you need to jump over before you can really get down to the meat and potatoes of your full size quadcopter design. This may be the practical nature of my engineering career talking, but it feels like you're hinging a very large workload (designing the entirety of the quadcopter to be light enough and strong enough) on the design of a fairly novel and unproven design. So while mechanically it's simple and has less moving parts, design-wise your bearingless design itself is very complex, being furthermore complicated by using a composite material of relatively unknown fatigue strength.
My point is only that there are so many other challenges to be had in designing a ground-up copter, why not use a more proven or more off-the-shelf design for your rotor head? By itself, the head you have laid out could be a multi year design project to fully analyze and test for human carrying. A bearing design like you laid out originally seems like it would be worth the extra complexity just to help the project move forward.
From my understanding, the whole flapping issue becomes a bigger issue in single rotor or tandem rotor designs due to its tendancy to roll the plane. With a quad, you may already have the systems in place to remain fairly unaffected by increased lift (and flapping) during lateral flight. The only real affect will be that the center of lift on one side of the quad will move away from the CG some, and the center of lift on the opposite side will move in laterally towards the CG (I guess a similar affect to a single rotor, but I would imagine the effect is less). This can be easily remedied by the brains of your system (APMs deal with this in every quad they are installed in), so having a rotor design that allows flapping like yours does and mechanically reduces the AOA during the up flap seems like a potential recipe for disaster without the appropriate tools to fully analyze the nuances of the mechanics and aerodynamics together (IE an FEA and fluid dynamics simulator).
Doesn't the flapping only become a big deal with increasing forward/horizontal flight speeds? I'm not sure what the ratio of rotor speed to forward flight speed it becomes critical, but I would imagine that at the speeds in which you will be flying, the flapping will be minimal. That is - unless your rotor speed is so slow that any lateral speed would put it into a critical flap-potential scenario (of which that ratio is, I don't know).
Don't take my post wrong, obviously if I wasn't intrigued by your design, I wouldn't have delved into your blog and done my own research in order to sound smarter while writing my reply to you. I am only voicing my concern that you're limiting your progress in other challenging arenas of your design (structural strength/weight) by getting mired up in the nuances of the rotor hub in which it normally takes teams of engineers and years to design. Regardless, I'm looking forward to reading more from you.
We call this compliant mechanism in the university. It has a lot of possibilities but sometimes it's tricky to have a good design.
I think is quite feasible to have such mechanism for our rotor system, we just need some nice design for it. Looking forward for your upcoming results Randy.
Jerry, Not sure I understand your comment (bearing sprint spring?), but thanks for looking. FYI my application is full size quad. Thanks for your interest.
rigid rotor is popular in full size high-end helis. people fly heli models are looking for even more rigid contronl (3d) , so bearing sprint might not be a good idea
Here is a more complete picture. I will need to do some work on the pitch link connection. I will probably need to add another link to couple the upper swash rotation to the rotor rotation, and let the pitch links have ball joints at both ends.
something similar http://www.higheye.nl/airboxer/
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