Slider Crank Motion Profiles

[ThePerk]

Hey all,

I'm working with a slider crank configuration that is actuated by what is essentially a spring piston, think single cylinder engine with a spring force rather than gas force. The "crank" is rotated to an arbitrary position in turn compressing the spring. Upon release of the crank the spring energy provides a driving force for the system. I'm trying to determine the velocity and acceleration profiles for this system. Any ideas?

I have complete kinematic relations for the system, all pertinent mass properties, and the spring properties. Following this I intend to complete a full dynamic force analysis. I've referenced many texts on the subject, the problem is, I haven't come across any that deal with determination of velocity and acceleration based on the driving force only. Most topics only cover a steady-state analysis, like that of an engine assumed to be rotating at a constant rpm. I'm seeking the most general solution possible, you know, the gooey ones full of Greek letters, as I intend to manipulate various parameters to analyze the effect on the system in an Excel sheet.

Any help is much appreciated! I'm not looking to be spoon fed the answer, rather in need of a push in the direction of the proper method.

Thanks!

 

[MiketheEngineer]

build one??

 

[btrueblood]

Did you throw away your Dynamics textbook? Might be worth a trip to a used bookstore near a university, and pick up a used text.

Or here:

http://www.amazon.com/Engineering-M...7919/ref=sr_1_1?ie=UTF8&qid=1335378730&sr=8-1

 

[zekeman]

Oh, so you want us to do the math for your project and then what?

I'll give you a hint

At any angular position of the crank, the spring force is F and it is depressed x, F=kx
Next you write the torque equation on the crank set equal to
I@''. Get the geometric relationship between crank angle and x to eliminate x in the dynamic equation.
You now have a single 2nd order equation in @.initial conditions are @(0), @'(0)=0

As a further hint

Td@=Fdx; T=Fdx/d@

Should be fun.

 

[ThePerk]

Mike, it's an existing design that I am analyzing now with pure numbers.

Btrueblood, in case you didn't read my second paragraph, I stated that I've referenced many texts.

Zeke, as I mentioned, I don't want to be spoon fed an answer, just looking for a smidgen of guidance. This is a personal exploration, not a school project that I'm trying to cruise through. I was in the process of constructing my differential equation prior to this thread, I'll continue on that path. Thanks for the input.

 

[btrueblood]

Yes, you said:

" I've referenced many texts on the subject, the problem is, I haven't come across any that deal with determination of velocity and acceleration based on the driving force only."

And so, I posted a link to a sophomore-level engineering Dynamics textbook.

 

[GregLocock]

You may find that performing a work calculation for small time steps is easier than an F=ma approach, if you choose to simulate it rather than deriving an analytical solution.

The analytical problem is relatively straightforward first or second year dynamics problem, as it is, when all is said and done, a single degree of freedom system (hint, write all your equations of motion in terms of theta). That is why you are getting a bit of teasing.



Cheers

Greg Locock


New here? Try reading these, they might help FAQ731-376

http://eng-tips.com/market.cfm?

 

[ThePerk]

Greg,

Thanks for the help.

I initially worked on a solution from an energy standpoint, equating the spring energy to the sum of the energy of each component for small steps. Not knowing any of the velocities, I wrote each components energy as a function of the crank speed, which had been determined from a velocity analysis so I only had 1 unknown in the equation. I wasn't 100% confident in my results so I was seeking out an alternative approach.

Sadly, little of my experience in undergrad dynamics courses involved differential equations so I'm admittedly weak in that respect. Hence, why I posed the question here before I buried my nose in a differential equations text for a refresher course.

I had previously been laying out a differential equation in terms of theta, so it sounds like I was on the track, I'll continue in that direction.

Thanks!