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Revised analysis of propeller gap: reduced safety factors



Original poster: "Scott Hanson by way of Terry Fritz <teslalist-at-qwest-dot-net>" <huil888-at-surfside-dot-net>

Terry B. -

I finally had a few free minutes to look at your analysis of the forces
acting on the press fit of the tungsten rod into the hub of your "propeller
gap", and I think there may be  a few errors that created the impression of
a large safety factor. The actual loads are much greater (~100X) than your
calculations indicate.

The most significant error is in the velocity of the tip of the rod. Your
calculations show a velocity of 7 meters per second, about the speed of a
ping-pong ball. Actually, the velocity should be 70 meters per second (250
kilometers per hour, or 157 MPH). This is very significant, as this value is
squared to find the centrifugal load. Your velocity value of 7 meters per
second squared gives a multiplier of 49, instead of the correct value of 70
squared, for a multiplier of 4900.

Also:
your 4mm diameter rod is .004 meter, not .0004 meter;
the rod radius is .002 meter, not .0002 meter
the rod length is .18 meter, not .018 meter

If we plug these corrected values into your examples, we get the following
results:

1. For an admittedly large rod offset of .5 cm, the centrifugal load on the
rod is 15 lbs, not 1.48 lbs. Since the frictional restraining force securing
the rod in the hub is around 20 lbs, the safety factor is only 1.3X, not
13X. This gap has a very high probability of failure after a short period of
operation.

2. For the second, more realistic case of a rod offset by 1mm, instead of
.03 lbs the centrifugal load is about 3 lbs. Instead of a 67X safety factor,
you have a 6.7X safety factor, which is marginal in my opinion.

3. For your last example of a 3750 RPM operating speed at a 1mm offset, the
velocity is 35 meters per second, not 3.5. Instead of .073 lb, the real load
is .73 lb, so the safety factor is 27X, not 274X. This is the only
arrangement that shows any real chance of not eventually self destructing,
but there are other effects not taken into consideration in this exercise
that would further reduce the safety factor.

(Hopefully, someone will review these numbers and provide corrections for
any errors. By the time I get home & check my e-mail, it's well after 10:00
PM, and my brain is working at about 35% efficiency).

Again, please consider this a realistic review of safety issues, not
destructive criticism.

Regards,
Scott





----- Original Message -----
From: "Tesla list" <tesla-at-pupman-dot-com>
To: <tesla-at-pupman-dot-com>
Sent: Thursday, January 23, 2003 5:58 PM
Subject: Re: My first ARSG, or a Dangerous Design? Terry Blake speaks


 > Original poster: "Terry Blake by way of Terry Fritz <teslalist-at-qwest-dot-net>"
<tb3-at-att-dot-net>
 >
 > Who could argue with safety.  An enclosure of some type (plywood) is a
"must
 > have", to block the arcs' UV and to stop flying shrapnel.  Heck, something
 > could fall on the spinning rotor and cause all hell to break lose.  DO NOT
 > RUN WITHOUT ONE.
 >
 > But just how big a deal is the friction fit?  Let us not fear the unknown,
 > but embrace it.
 >
 > Let's do some calculating based on a 5/32" x 7" Tungsten rod.
 >    D = 5/32 * 2.54 = 0.40 cm
 >    L = 7 * 2.54 = 17.80 cm
 >
 > Mass of the 5/32" x 7" Tungsten rod:
 >    Tungsten density: 19.35 g/cc
 >    Volume of a cylinder: Pi * r^2 * h = Pi * (0.2)^2 * 17.80 = 2.24 cc
 >    M = 19.35 g/cc * 2.24 cc = 43.25 g
 >
 > Velocity at the end of the rod at 7500 RPM (1000 BPS on my ARSG)
 >    Circumference = Pi * D = 3.14 * 17.80 cm = 55.89 cm
 >    V = 7500 RPM / 60 * 55.89 cm = 6986 cm / S = 7 m / S
 >
 > Now we have some numbers to work with.
 > D = 0.0004 M (diameter)
 > R = 0.0002 M (radius)
 > L = 0.0180 M (length)
 > M = 0.043 Kg (mass)
 > V = 7 M / S      (velocity)
 >
 > Suppose the rod was slid off center by 0.5 cm (which is huge), there would
 > be an extra 1 cm of mass on one side and not the other.
 >
 > M (1 cm) = 43.25 g / 17.80 = 2.43 g = 0.0024 Kg
 >
 > The centrifugal force pulling on the rod would be
 > F= MA = MV^2/R = 0.0024 Kg * (7 M/S)^2 / 0.018 M = 6.6 N (Newtons)
 >
 > 1 lb = 4.448 N
 >
 > Soooo, 6.6 / 4.448 = 1.48 pounds of force pulling on the rod.
 >
 > Sounds like a lot, but when I go check one of my rotors, I find that I
have
 > to
 > push on it with over 20 pounds of force (using my bathroom scale), to get
 > the
 > rod to move.  So my safety margin in that situation is about 20 / 1.5 = 13
 > factors, or 1300 %.
 >
 > So what about a more likely scenario.  The rod is off-center by 1 mm,
there
 > would be an extra 2mm of mass on one side and not the other.
 >
 > M (2mm) = 0.2 * 43.25 g / 17.80 = 2.43 g = 0.00048 Kg
 >
 > The centrifugal force pulling on the rod would be
 > F= MA = MV^2/R = 0.00048 Kg * (7 M/S)^2 / 0.018 M = 1.3 N (Newtons)
 > Soooo, 1.3 / 4.448 = 0.3 pounds of force pulling on the rod.
 > My safety margin in that situation is about 20 / 0.3 = 67 factors or
6700%.
 >
 > What if we only spin around at 3750 RPM (500 BPS on my ARSG)
 > F= MA = MV^2/R = 0.00048 Kg * (3.5 M/S)^2 / 0.018 M = .33 N (Newtons)
 > Soooo, .33 / 4.448 = 0.073 pounds of force pulling on the rod.
 > My safety margin in that situation is about 20 / 0.073 = 274 factors or
 > 27,400%.
 >
 > It looks pretty safe to me, but could someone check my math, to see what I
 > messed up on.
 >
 > I cannot address the plastic cold-flow issue, but to say that the rotor I
 > just checked (with the 20 pounds of grip), was assembled 9 months ago.
 >
 > As far as heat isues, my rotors have been checked numerous time after TC
 > runs and were found to have cool rods near the center.
 >
 > If you are overly concerned, I would suggest scraping up the rod (with
 > sandpaper) and putting a dab of epoxy on either side of the rotor (next to
 > the poly) to hold the rod in place.  That should be helpful.
 >
 >
 > Terry Blake
 > Coiling in Chicago.
 >
 >
 >
 >
 >
 > ----- Original Message -----
 > From: "Tesla list" <tesla-at-pupman-dot-com>
 > To: <tesla-at-pupman-dot-com>
 > Sent: Thursday, January 23, 2003 9:00 AM
 > Subject: Re: My first ARSG, or a Dangerous Design?
 >
 >
 >  > Original poster: "Scott Hanson by way of Terry Fritz
 > <teslalist-at-qwest-dot-net>" <huil888-at-surfside-dot-net>
 >  >
 >  > Some time ago, when I saw the first proposal for a rotary gap based on
 > this
 >  > design, I cringed but refrained from making any comments.
 >  >
 >  > However, I feel that I must warn anyone who would consider this
 > "makeshift"
 >  > type of rotor that it is unquestionably the most dangerous design
concept
 >  > that I have ever seen proposed on the TCML. Please understand that this
is
 >  > not a personal attack on anyone who has conceptualized, designed, or
built
 >  > such a device; its just that this design is intrinsically incredibly
 >  > dangerous, and is contrary to all conventions and design standards that
 > have
 >  > been established for high speed rotating machinery.
 >  >
 >  > The single greatest weakness in this design is in the attachment of the
 >  > rotating electrode (tungsten rod) to the "hub". The only thing
retaining
 > the
 >  > rod in the hub is friction, whether it is obtained from a press fit of
the
 >  > rod into the hub, or side load provided by a set screw, etc. The
 > coefficient
 >  > of friction between any plastic and a smooth tungsten rod is very low.
 >  > Theoretically, if the hub and rod were somehow assembled with such
 >  > perfection that they were in a condition of perfect dynamic balance,
the
 >  > centrifugal forces acting on each leg of the rod would cancel each
other,
 >  > and there would be no load on the rod trying to move it axially through
 > the
 >  > hub. In reality, the balance will never be perfect, and the unbalance
 > forces
 >  > will try to fling the rod out one side of the hub. Now as soon as the
rod
 >  > slips a few thousandths of an inch, the unbalance forces will increase
 >  > greatly. In a few microseconds, the rod is shot out of the hub at very
 > high
 >  > velocity. The tungsten rod has scores or even hundreds of times the
 >  > sectional density, and penetrating power, of a nut and bolt or short
 > section
 >  > of tungsten rod that might be shed by a conventional disk-type
rotary-gap.
 >  > While a heavy Lexan shield can usually contain electrode parts from a
 >  > conventional gap, there is a much higher probability of penetration by
a
 >  > projectile with high sectional density (that's why almost all
 >  > current-technology gun-fired anti-tank projectiles are long, thin
 >  > high-density kinetic energy "penetrators" of tungsten carbide or
depleted
 >  > uranium).
 >  >
 >  > By itself, that's bad enough. But there's much, much more wrong with
this
 >  > design. First, all plastics "creep" to release internal stresses. A
good
 >  > "press-fit" of the rod into the plastic hub the day its made will be
 > looser
 >  > next week, and even looser next month as the plastic "cold-flows" and
 > loses
 >  > its grip on the rod. If a set screw is used, the threads in the plastic
 >  > slowly deform and creep, and the clamping pressure of the screw against
 > the
 >  > rod decays with time. In the end, no matter how tight a fit the rod is
in
 >  > the hub initially, it will inevitably get looser with time.
 >  >
 >  > Now, add the potential problem of heat conduction through the rod to
the
 >  > plastic hub, either causing the plastic to heat up and expand very
 > slightly,
 >  > or in more severe cases to start to melt. Again, the rod is in danger
of
 >  > being shot out of the hub as if from a gun.
 >  >
 >  > Further, all these considerations are also applicable at the attachment
of
 >  > the hub to the motor shaft, which is also very weak in this design.
 >  >
 >  > The bottom line is that this type of rotor construction may run for
 > several
 >  > hours, or it may self-destruct before the motor ever reaches operating
 > speed
 >  > the first time it is powered up. The probability of failure, and the
 >  > consequences of failure, are much more severe with this type of rotor
 >  > construction, compared to a conventional disk rotor with multiple
flying
 >  > electrodes.
 >  >
 >  > Unfortunately, the construction requirements for a high speed rotary
gap
 >  > (1,000 RPM or greater) are not easily improvised in a home workshop. If
 > you
 >  > lack the right equipment (lathe, milling machine & precision rotary
table)
 >  > to make a high quality disk-type rotor with multiple flying electrodes,
 > you
 >  > will not be able to make a safe "propeller" type rotor either.
 >  >
 >  > Dan, the construction quality and attention to detail in your rotary
gap
 > is
 >  > apparent from your photos. Unfortunately, the basic design is severely
 >  > flawed. If you actually intend to power this rotor up, PLEASE equip it
 > with
 >  > a multi-layer safety shield/enclosure of Lexan,  3/4" plywood, or steel
 >  > pipe, etc that can stop the rod when it separates from the hub.
 >  > Additionally, I'd orient the gap vertically, and stay out of the plane
of
 >  > the rotor when its operating.
 >  >
 >  > As for others contemplating the construction of this type of gap, I'd
 >  > emphatically urge "DON'T DO IT". The risks are just too high.
 >  >
 >  > Regards,
 >  > Scott Hanson
 >  >
 >  >
 >  >
 >  >
 >  >
 >  > ----- Original Message ----- type
 >  > From: "Tesla list" <tesla-at-pupman-dot-com>
 >  > To: <tesla-at-pupman-dot-com>
 >  > Sent: Wednesday, January 22, 2003 7:50 PM
 >  > Subject: My first ARSG - Tribute to Terry Blake !
 >  >
 >  >
 >  >  > Original poster: "by way of Terry Fritz <teslalist-at-qwest-dot-net>"
 >  > <dhmccauley-at-spacecatlighting-dot-com>
 >  >  >
 >  >  > I just finished my first ARSG and to my knowledge, I think I am the
 > first
 >  > to
 >  >  > follow in the footsteps of Terry Blake's Propeller-Rotor design.
 >  >  > Thanks to Terry Blake's ingeniusness, we individuals who lack the
 >  > machining
 >  >  > equipment to make a precision balanced rotor can now have a
 >  >  > top quality rotary spark gap.
 >  >  >
 >  >  > Here is a picture of my ARSG:
 >  >  >
 >  >  > http://www.spacecatlighting-dot-com/images/arsg01.jpg
 >  >  >
 >  >  > Here is the complete webpage:
 >  >  >
 >  >  > http://www.spacecatlighting-dot-com/teslacoil9.htm
 >  >  >
 >  >  > And here you can see the genius himself at work creating a wide
variety
 > of
 >  >  > different Propellar-Rotor sparkgap designs:
 >  >  >
 >  >  > http://www.tb3-dot-com/tesla/sparkgaps/index.html
 >  >  >
 >  >  > Thanks again Terry for the help!!!  Lets hope it works as good as it
 >  > looks!
 >  >  > Better wear those safety glasses!
 >  >  >
 >  >  > Dan
 >  >  >