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What is the required volume ratio (compression ratio) for free piston stirling engine ? Whether is it lower or higher than kinematic stirling engines ?

-Satyavijay

When I make a free piston engine, I assume that the volumes will be the same as a similar engine with a crankshaft, the piston and displacer find their own stroke, the displacer needs cushoning at each end of its strokeso that it does not hit the ends, my first one knocked the hot end right off, the stroke, as in a ringbom engine varies according to the load. As far as the displacer rod diameter goes, I'v not found what the ratio should be to the diameter of the displacer, so I'v just guessed, and seems to work. The rod is actually another piston that drives the displacer, it sometimes needs a spring to assist it, or two magnets, like poles facing each other, same works on the power piston. I'v got one here awaiting completion of a rebuild, and when I get it done I'll post a photo. Ian S C

Dear Colleague,
Your question is interesting,Same Stirling let us simple ratios around,
but I´ll retransmit a recently posted ratio based on piston work swept vol cylinder,
x 1.5=swept vol. of Displacer, some simple mathemathics establish the optimum
ratio between piston radius and displacer radius and displacer length cylinder,
regarding piston work dia. = stroke.

V=height x r exp2x pi.VOLUME AS GEOMETRY.KEEP IN MIND SWEPT VOLUMENS.
1.5 x h(piston)x r(piston) exp 2=h(displacer)x (r displacer exp 2),PI CANCELED BOTH SIDES.

Compromising between HP and rpm implies h(p)=D(piston)

3xr(p)exp3=h(displacer)xr(displacer)exp2.i HAVE ALREADY OPTIMIZED PISTON DIA.
AGAINST STROKE, ROD LENGTH/STROKE LENGTH=1.5

sTIRLING WROTE,
Displacer chamber L =3x dia.
Heater chamber length=2/3 L
L of cooler=1/3 L

Cordially yours, in Google, search, Stirling Engines Theory.
My study on optimizing best ratio=Piston Dia./Piston stroke, is controvertial with
equalizing DIA=h square current american racers.
Johann wegmann, do not hesitate to contact me again.

Dear Colleagues,
I read in this Forum something exiting, in gamma this ratio can be handled fron 1 to 10!!!
I have an enthusiastic friend fan of SE, he doesnt know,by the rule of thumb and space his gamma,2 displacers vertical and 2 free small pistons rubber sealed, is running quite well.
Lets find out criteria to move this ratio, of course I see electromagnetic transducer linear needed to complet the equation, we can control frecuency then resonance and good coupling with displacer.
Excuseme to be so complex,in displacer users,keeping square pistons,stroke=dia.
the ratio between radios displacer /piston=cubic root(1.5)=1.145.
American racers ratio bet ween stroke and piston dia. reaches 1/2 I guess.
Last reflexion,the point to start easy an engine design, is to know the max. speed acceptable between piston and liner, according materials 8.5 to 14 m/s as reference.

I think the thing is to keep the power stroke as short as practical, this way the frequency can be kept as high as possible, you really would be best with a minimum of 20Hz, up to 60Hz, if you want to generate electricity with a linear alternator. I made the mistake with my free piston motor, of making the power piston a little small on diameter, causing the stroke to be a little long, and its speed is between 15Hz, and 20Hz, the motor is built as a GAMMA motor, my first attempt was a BETA type, it worked, but not too well, some time later I found the reason, all the frame work, the power cylinder etc., were made of steel, and the magnets of the alternator were interfering with the running of the motor. The second motor, and now its rebuild were/are built mainly of aluminium, and the power cylinder is bronze. Ian S C

Dear Ian,
Please accept my apologies for so colloquial reply on your enquiry.We have dynamic linked pistons based on fluid mechanics and Inertial dynamics only.If you apply Lagrange mechanics,for ex.solving all eq. simultaneaously,regardin compressible eq. of working fluid, then you´ll be in displacer and piston resonance,max power.Sadly only one linking frecuency.When we make a free piston with electromagnetic coils,I have reports,is not sufficient to reach required power,then with a frecuency variator and mass inertia,you can add resonance,natural vibration=forced vibration,not easy.This solution is properly edited in Google,dont forget that Ringbon is magnetic Driven displacer,my friend this is the most clear example that Theory and Practice must walk together,its easier make a few calculations in a computer,and start the aproach closer,you cannot be randomly fixing frecuencies by the rule of thumb,it´ll be much longer.Good Health Ian,the ratio of volumes ranges from 10/1 to 1/1.The cuesion is where we gwt optimum power output?????Forget all about beta and gamma, and see the double acting in line alpha,4 cyl,world champion SE.I also love free pistons and prefer dynamic linkage, except linear elec. transducer drive to move the piston,if Lagrange mechanics is heavy for you,do not think that,contact a professor Univ.
Regards Johann.sometimes I seem to be an ignorant.No I have a brain damage,an accident.

You say Ringbom displacer is magnetically operated, but this is not correct, the displacer is operated by a subpiston, in the form of a large diameter displacer rod, ie., somewhere about 1/4 to 1/3 the diameter of the displacer, the varying pressure caused by the power piston moving in its cylinder, moves the displacer. If you don't get the maths right, or the displacer rod gland is a little tight, a spring can assist the movement. I have built three of them. Ian S C

Hi Ian SC,
I do agree with anybody that free piston can be dynamically linked to displacer,with a Scotch Yoke you have an easy drive for trials.Thankyou for explaining me the ringbon mechanism,you do not say why the electromagnetic field to move the displacer by outside coils?then probably Beale said why dont we make a working piston induction magnetism actuated?As always the last eminen report is that induction itself is not sufficient to reach a reasonable force,then they added resonance besides and increased required force if displacer Inertial values together with working free pistons fitted to make forced vibrations=natural vibrations.Do not be afraid, any FEA code,with the geometry and fysical properties and boundary condittionss will give you at least the 7 first natural frecuencies of the gamma or any other machine.The advantage of free piston electrically controlled is control function,starting with frecuency, at the end any SE with a free piston can be programable with inteligent procesors ar handy,dear Friend, why not to buy an linear actuator in USA,is an standard, linear, speed controlled, frecuency controlled, power controlled , cheap,I quoted it,is revesible motor or generator very light.The drawings I have from Free pistons are not very simple,Is it also reliable.For you to know, to day reports in Yahoo probably,a good and auspicious new to you, Free piston will be integrated to Alpha cycle.Have you measure how many watts does a free piston,induction type,needs in percentage of Energy input?
My Friend Sergio Ossa worked a long time to run its beautifull gamma,2 liters in displacer chamber,and 2 kinematically linked work pistons 1/5 of total Disp.Volume, I meant before that the author of optimum volume of free piston respect to Displ.Vol ranges freo 1/10 to 1/1.Apologize me pease.
My deep concern, I share with you, was alpha, beta or gamma is the best otion to compete with IC engines!!!Adding Free Piston for all of them.
I confess that in the net, many statements are just oppinions, without fundamentals,without experience as you have,So I am reluctant to speak only with one reference,I hear all the bells and then I draw ,make good drawings, good scale, and measure relevant variables,the basis of engineering is Technical Drawing, if equations fail the drawing will show you whats is mistaken.
The world ranking,lost in the Internet, but I took hadwritten notes on the four engines,if you are interested is a good reference,I was in love since the beginning with V Alpfa,90 degrees.
After many drawings sep by step positions I discover a kinematic error,shortly when I said why not open 180,flat configuration the pistons positions TDC and BDC for expansion and compresion just converged to that of PV diagram intersections,
Regarding the mechanical point of view on thin and light displacer with a strong rod,Id like to tell you, shell on Elasticity(Timoshenko professor)is the highest order partial diferential equation I saw, after Navier Stokes eq.Its order is 8th.The shell discretization and degrees of freedom the most delicate,and the discontinuity of stiffeness matrix between rod and drum of displacer cannot be worse.Conclusions not mine,the torque,power limit, perhap 100 kW?Is it worthwhile? I read for Vamoose,one Greman report a double acting,Siemens)alpha,4000 kW.Ian I changed my mind,I have studied double actings diferent variations,they are the champions, one piston is expansion one side and compression other side.One working stroke per revolution so 2 stroke engine,V alpha is a 4 strokes,one working stroke per 2 revolutions,I introduced a small device in circuits,for your oppinion, the expansion valve throtle,used in refrigarators,capillars are also used,you can get a drop in pressure,dissassembly an old refrigerator, and check the drop in temp,heavy,meaningfull.
Forgiveme to bore you, I am entirely at your disposal,for SE sharing experience.johann

Unless you have won Lotto, or something similar, a few hundred Watts is a good target to aim for. Don't get too fixed on replacing an IC engine with a Stirling Engine. For the greatest power to weight ratio, I think the ALPHA type would be the best.
I use a magnet under the magnet of the linear alternator on my free piston GAMMA motor. The bottom fixed magnet has the poles arrainged to be like with the ones above, ie., N facing N, this acts as a spring to bounce the power piston. Before I rebuilt that engine, I used mechanical springs. I have not got the displacer rod quite the right diameter(it should work the same as a Ringbom), so it has a light spring under it, the displacer cylinder is vertical, with the hot end at the top, and a ring type LPG burner. Ian S C