rotational stiffness of a constant torque spring hinge

[WildBlueMtn]

I am trying to estimate, ultimately, the natural frequency of a mass attached to a hinge which is driven by a constant torque spring motor (negator). More specifically this is a deployed solar panel that rotates about the hinge axis with a known, constant applied torque.

Normally, if the hinge were driven by a standard torsion spring I would know the Krot spring constant (in-lbf/rad)of the spring. Knowing the mass moment of inertia (I) of the panel being deployed, I can get a theoretical estimate of the natural frequency:

fn= 1/(2pi)*(Krot/I)^0.5

But with a constant torque, the spring rate Krot would be zero. What am I missing?

Thanks.

 

[GregLocock]

Nothing

Cheers

Greg Locock

Please see FAQ731-376 for tips on how to make the best use of Eng-Tips.

 

[sms]

Stiffness and load are two different things...Constant torque is the load, the mechanical stiffness of the system is (semi) independant of load..

-The future's so bright I gotta wear shades!

 

[WildBlueMtn]

I take that to mean you agree that Krot=zero.

I guess the more direct question is what is the relationship between drive torque about the hingeline and the natural frequency of the driven mass?

Thanks.

 

[WildBlueMtn]

sms, I guess I did mix terminology in the subject line and body of the post. Krot, rotational spring constant is also refered to as the rotational spring stiffness. May not be technically correct though.

 

[GregLocock]

A constant torque produces a constant acceleration, in the absence of anything else, and so it is a zero Hz motion.

There are other springs in the system which will define the frequency. These may or may not be obvious, foundation stiffness, gas pressure stiffness, and shaft stiffness might all contribute, for example.



Cheers

Greg Locock

Please see FAQ731-376 for tips on how to make the best use of Eng-Tips.

 

[israelkk]

Constant torque spring never in practice gives constant torque. It is alway near constant. It can change up to +/-10% of the torque depends on the number of rotations, friction between the coils etc. The reason is simple because the metal strip radius on the drum is changed by the strip thickness with every complete drum rotation. Add to this the fact that the natural strip curvature in free state is not constant. If you are relying only on the torque in the spring to hold the solar panels in the deployed position then you will have a very low natural frequency.

 

[WildBlueMtn]

lsraelkk-that is exactly some of the points i have been coming up with. Thanks.

I am still curious to know of a better formula than the original one i posted to relate that holding torque to fn. It makes sense to me that the greater the holding torque applied against the hardstop at full deployment, the greater the fn. I just don't know how to back it up with the math. for now I am relying solely on the spring holding torque. Any further insight would be helpful, thanks!

 

[GregLocock]

By waht mechanism does your actuator create its 'constant' torque?

Cheers

Greg Locock

Please see FAQ731-376 for tips on how to make the best use of Eng-Tips.

 

[WildBlueMtn]

Greg,

There is a set of flat negator springs stacked on one another to provide a quoted minimum torque ~6in-lbs. These are integrated into the hinge mechanism directly at the hingeline. Hardstop at full deployment puts the 2 halves of the hinge 180 deg apart. Stowed position in my application is at 120 deg, so 60 deg travel when deployed. It doesn't take much torque to deploy in a zero-G environment but I do care about maintaining the natural frequency of the deployed system to be greater than 3 Hz. Panel itself is much stiffer than this so the "weak link" will be the hinge holding torque.

Thanks, again.

 

[GregLocock]

Well, I more or less failed to understand that, but supposing you were to plot torque v deflection. Does it have a slope?

Would say a rayleigh approach help (ie KE at zero dsplacement =PE at max displacement)?



Cheers

Greg Locock

Please see FAQ731-376 for tips on how to make the best use of Eng-Tips.

 

[WildBlueMtn]

Greg, sorry if I'm confusing matters further. Simply stated, lets say I have a door on a hinge that is allowed to swing from initial position thru 60 degrees at which point there is a hardstop which prevents further swing. A spring is inside that hinge providing torque to swing the door and the torque of that spring holds the door against the hardstop.

The Rayleigh method is what is used to derive the equation in my original post, which is typically used in this situation. fn= 1/(2pi)*(Krot/I)^0.5

Problem I am having is that this equation assumes that there IS a slope to the Torque v Deflection curve (Krot>0). This works for traditional wire torsion springs that have increasing torque with greater deflection. But with these constant-torque springs there is NO slope, T doesn't increase with increased deflection, K=0 (or at least very close to it as israelkk pointed out).

I think I am at least convincing myself further that I have to approach it from more of a statics point rather than a kinetic one...just assess what holding torque does it take to dis-allow motion given my mass at the given moment arm. So if i know the torque that mass/arm combination exerts about the hingeline, then I know the minimum torque output needed for the spring to maintain equilibrium. So as long as I am under that point, the frequency is not going to vary with the holding torque, the many other joints and panel properties are going to be the weaker links...something I assumed incorrectly.

Thanks for all your time, its good to get feedback and I think I am on a better track at least.

J

 

[sreid]

Maby frequency is not what you are looking for. Isn't rotational acceleration under constant torque the same as linear acceleration under constant force?

F=ma

T=J x Alpha

 

[WildBlueMtn]

True, but what I am calculating is natural frequency of the system (resonance).

 

[sreid]

But to have resonance wouldn't the torque have to change direction at some point? For example, constant torque with a torque reversal at "Zero Position." You could easily calculate a frequency for that (at a given amplitude).

 

[israelkk]

WildBlueMtn

I am not sure that you are correct. If an external harmonic steady excitation applies to the structure at a frequency identical or close to the natural frequency the structure will gradually gain increasing amplitudes and will go into a resonance even if it is held by the torque. As far as I remember the stored energy in the torque even feeds the energy to increase the amplitudes. Can somebody clarify this issue?

 

[WildBlueMtn]

sreid, the holding torque is not a source of vibration here, I am looking to calculate the natural frequency of that spring if it were excited by some outside vibrating source. It is important to know this natural frequency so as to avoid exposing the system to sources which might excite it, since the greatest deflections and therefore greatest mechanical stresses occur at this natural frequency.

 

[sreid]

Perhaps you answered the question with your original post; if Krot = 0, fn=0. But fn=0 can have a value (amplitude) which is a constant. This is, of course, exactly what a constant force spring has.

There is an amplitude of a sine excitation force required to just lift the panel off its hard stop. This force requirement would be the same at all frequencies.

 

[GregLocock]

Let's consider a slightly simpler case - two equal weights hanging off a rope over a pulley, in an idealised world.

Where is the equilibrium position of the system?

There are infinitely many. The system does not have a preferred position, there is no force encouraging a return to the preferred position.

If there is no energy advantage in returning to a given position then the system won't go there without external motivation.








Cheers

Greg Locock

Please see FAQ731-376 for tips on how to make the best use of Eng-Tips.

 

[WildBlueMtn]

thanks folks, but all i am trying to do is find the Natural Frequency of the system. Just like a tuning fork, the system has a first fundamental frequency which produces the greatest deflections. This is a Modal Analysis to discover the natural frequency of this system. Once it is built I can test it by putting the system on a vibration table and installing accelerometers to measure the modes...Fudamental Modes are independent of external inputs.

thanks for your time.