Hello everyone,

I would like to ask if anyone could please help me with a design I am
struggling with due to space constraints. I have a Rapidshare link
listed below where you can download CAD and JPEG images of the cam and
follower, along with output from my cam design software, for
clarification of the problem.

This is related to my post regarding finding a cam material that can
withstand high contact stress. I would like to try to attack this from
another angle and try to find a cam curve that will have a lower
maximum contact stress than the Parabolic curve I am now using.

The cam is a very small radial disk cam with an oscillating roller
follower that has high contact stress between the cam and roller.
Everything on the design is "locked in" i.e., I cannot make the cam or
roller larger (except for cam thickness & roller length), I cannot
increase cam versus follower displacement, or decrease follower versus
cam displacement. This is a very slow moving cam oscillated manually by
hand, so I don't have to worry about the dynamics of the curve,
vibrations, etc..

I am presently using a Parabolic curve because it has the largest
minimum radius of curvature and lowest contact stress of all the
standards curves my cam design software can produce, i.e., Harmonic,
Modified Sine, Modified Trapezoid, Cycloidal, and the "standard"
Polynomials (3-4-5), (3-4-5-6), (4-5-6-7), etc..

At the link below you can download DWG and duplicate DXF drawings,
along with duplicate JPEG images of the cam, from Rapidshare. The CAD
files have layers you can turn on that show more curve detial than the
JPEG's. I also included output text files from my cam design software
and a text file with all dimensions, angular displacements of the cam
and follower, and roller forces and spring rates ...

http://rapidshare.de/files/16364719/...-Tips.zip.html

This is a dual roller conjugate rib or blade cam that uses two cam
follower rollers. The outer roller pushes into the outer profile (the
profile furthest away from the cam rotation axis) and inner roller
pushes into the inner cam profile (the profile closest to the cam
rotation axis). The two rollers have different springs and spring
rates.

The arrangement is fully explained in the Read-Me Microsoft Word file
included with the drawings.

The inner profile is the profle with the highest contact stress due to
its smaller radius of curvature. Even with the existing Parabolic
curve, the outer profile of the cam has much more reasonable maximum
contact stress at about 181,000.00 PSI using a 3/8" thick cam, which
seems acceptable to me.

I would like to keep the maximum cam thickness at 3/8" as it may be
difficult to increase thickness beyond that.

It seems it might not take much of a change to reduce the contact
stress on the inner curve, perhaps at the expense of a larger pressure
angle or some other trade off. The inner and outer profiles have to be
the same curve type, so whatever changes I make to the inner profile, I
will have to make to the outer profile.

Perhaps a cubic curve, elliptical curve, or a special Polynomial curve
is the solution. Dynamics and vibrations are not an issue since the cam
is so slow moving. I would have liked to explore the Stoddart, Duddley,
Berzake, Thoren, Cycloid first half, and Harmonic first half curves,
but my software won't produce those curves.

If there is a curve that produces a lower maximum contact stress and I
could get a CAD file of the curves I could superimpose over the
Parabolic curves for comparison in AutoCAD, that would be a very big
help. Cam design software output for the curves would also be a very
big help. If I know the cam angular displacement versus follower
angular displacement for each degree or preferably each 0.25 degree of
cam rotation, I can put that in my spreadsheet and double check the
maximum contact stress & other things.

I wish my cam design software were not so limited, because I could then
just experiment and zero in on the best compromise.

I would really appreciate any feedback or help anyone can offer.

Thank you.

Sincerely,
John

Is springbreak over?

Sounds like homework to me.

If not, do we get to share in the royalties?

TMT

Too_Many_Tools wrote:

Is springbreak over?

Sounds like homework to me.

If not, do we get to share in the royalties?

TMT

John2005:
This is not homework, I am not in school & there are no royalties to
give. It's a problem I am stumped with and I am trying to get some help
or advice.

The cam is completely designed, I just need to "plug in" another curve
in place of the existing Parabolic curve that will have a lower maximum
contact stress. If my software would allow me to add the required
changes to the standard Parabolic or other standard curves, it would
take about three minutes for me to do or to at least find out if it's
possible or practical.

If I knew what curve has a lower maximum contact stress than the
Parabolic, and how to define it graphically or mathematically, perhaps
I could create it as a set of points, and then run a spline curve
through the points with AutoCAD.

In any event it's not homework, just a request for help and/or advice.

Best Regards,
John

In article .com,
says...


I am presently using a Parabolic curve because it has the largest
minimum radius of curvature and lowest contact stress of all the
standards curves my cam design software can produce, i.e., Harmonic,
Modified Sine, Modified Trapezoid, Cycloidal, and the "standard"
Polynomials (3-4-5), (3-4-5-6), (4-5-6-7), etc..

Since this is a low speed mechanism and you don't need to worry about
acceleration, jerk, etc., I'd forget about all the standard cam
profiles. Isn't the curve with the largest minimum convex radius a
constant radius? The minimum concave R only needs to be larger than the
follower. I'm talking about the outer cam here.

Like this...
http://www.suscom-maine.net/~nsimmons/news/Cam.jpg

The .379 radius, which is what you need to maximize, is dependent on the
angle between the dwells (the shape of the cam is fully defined without
the .379 dimension); 20 degrees in this example. Making the radius of
the convex part of the rise smaller lowers the contact stress.

But maximizing the radius will probably not result in the lowest stress,
since it appears the force on the follower varies quite quickly with
displacement. Is that correct?

Ned Simmons

Hi Ned,

Thanks allot for your reply & the drawing.

I agree with you that I should forget about the standard profiles, it's
just that my software won't let me change the standard profiles to my
liking (or at all, other than for the Symmetry / Asymmetry factor of
the curve, i.e., make the follower start faster and stop slower, or
start slower and stop faster after leaving the dwells). However, I can
create a profile like the one you showed in AutoCAD.

Ned Simmons:
Isn't the curve with the largest minimum convex radius a
constant radius?

Yes I think so, and probably the smallest pressure angle as well.
Perhaps a "modified constant velocity curve" where you take a constant
velocity curve and then smooth the ends where it meets the dwells, with
a radius, (Just like the drawing in your previous message, but with a
..188" radius at each end of the curve) is the best that can be done to
reduce stresses in my case, I am not sure.

I checked with my spreadsheet program and using a constant velocity
curve for the inner cam profile gives a maximum contact stress of
around 145,000 PSI which seems great, but I did not check where the
curve blends with the low dwell. This will depend on what size radius
is used there i.e., at least .188 but I would probably try to go a
little bigger.

The guys at www.camcoindex.com told me you should always make the
minimum radius of curvature of the pitch curve (path of the roller
center) at least equal to the roller radius plus .0625". It only needs
to be equal to the roller radius to theoretically avoid undercutting,
but Camco says to add at least .0625" to this, minimum. I think this is
most important with a convex radius. I was able to get close to Camco's
recommendation with a Parabolic curve, but not quite there. Perhaps I
could use a modified constant velocity curve, shoot for .25" end
radii, and see what that does.

Ned Simons:
But maximizing the radius will probably not result in the lowest stress,
since it appears the force on the follower varies quite quickly with
displacement. Is that correct?

John2005:
Yes, the roller force varies according to the spring rates listed on
the drawings. The inner an outer rollers have equal forces at the
neutral position, but different forces at the cam low and high point
dwells. If I can just get the stresses to a reasonable or acceptable
level for the inner curve, I will be happy. I would like to just make
the cam and roller out of either hardened tool steel or 4140, instead
of something more specialized or exotic.

Ned Simons:
Making the radius of the convex part of the rise smaller lowers the contact stress.

John2005:
I am a little confused at this part. Don't I want to make the minimum
convex radius as large as possible to make the contact stress lower ?
Referring to your drawing, where the .379" radius blends in with the
..188 radius is a concave sharp point (if this were the inner curve it
would be a convex sharp point). It seems I need to find the optimum
size of the .188" radius to get the best contact stress. I'm thinking
in terms of the inner curve since that is the one with the highest
contact stress.

I'm not sure if I would want a 0.188" (or larger) radius at each end of
the curve, i.e., at both the low and high dwells. I may want to do this
just to keep a decent responsiveness between the cam and follower when
leaving the dwells. That is, I want the follower to start moving a
reasonable amount withing a reasonable time after leaving the dwells
and it may also be desirable if the follower was halfway to it's
maximum angular displacement when the cam is halfway at it's maximum
angular displacement. I might be able to do it either way though.

I just wonder if there is something that would produce lower contact
stress than a modified constant velocity curve having adequate size
radii blended at the curve ends.

Thanks again Ned, I really appreciate your help.

John

On 26 Mar 2006 11:01:40 -0800, "John2005"
wrote:
snip
If there is a curve that produces a lower maximum contact stress and I
could get a CAD file of the curves I could superimpose over the
Parabolic curves for comparison in AutoCAD, that would be a very big
help.
snip

Try a tautochrone or cycloid curve. You can use excel to
generate the coordinates, and export these to a text file. There
are many lisp programs that will import the text file and create
the curve. Use polyline to generate an actual curve if required,
then use scale and rotate as required. Send me a good email
address if you need the coordinate import lisp program.

see http://en.wikipedia.org/wiki/Tautochrone_curve and about
17,000 more google references.

Hi Everyone,

Thanks Nick & F. McDuffee,

F. McDuffee, I had not heard of a tautochrone curve, I will try to
check into it further. A regular cycloidal curve has a higher maximum
contact stress than a Parabolic, but perhaps a tautochrone will be
better, if I can create it in autocad and/or excell. If excel will
create the points with a formula, I can run a polyline or spline
through the points with AutoCAD.

If you could please send that coordinate import lisp program you
mentioned to the email under my profile at this site, it would be much
appreciated.

Nick, the closest I can get to a straight line is to use a modified
constant velocity curve, which is basically a straight line with a
radius added where the straight line blends with the dwell. I think I
may be limited on how large of a radius I can put at the curve ends,
possibly it can't be much larger than the rollers, if any.

Presently, with the Parabolic curves, the minimum radius of curvature
of the actual inner cam profile is .020" where the curve meets with the
low point dwell. The outer profile minimum radius of curvature is .086"
at about 8.2 degrees CCW from the neutral position (between the mid and
high point dwell) . To get the pitch curve radius of curvature, you
just add .09375" to the aforementioned figures.

If I can blend the ends of the straight line with the dwells using a
radius at least as big as my roller (which is a radius of .09375") I
may get reasonable stresses. The maximum stress on the outer Parabolic
profile, with it's .086" minimum radius of curvature already looks
acceptable at about 181,000.00 PSI, maybe not great, but acceptable.
The stresses on the inner profile are what I am worried about.

I should have no problem with getting radii at least as big as the
roller, which should get the stresses down to the 181,000.00 PSI range
or maybe a little better if I'm lucky (I hope). The high stress will
only occur at the end radii blend points and be about 145,000.00 PSI
for the straight line portion of the profile.

I have heard of a "modified harmonic" curve, but I don't know how it
differs from a standard simple harmonic curve. I don't know if this is
similar to the Tangential lobe you mentioned or not.

Any drawings, diagrams, and/or math you can send to my email address on
the tangential lobe would be a great help, and much appreciated.

Thanks again guys I sincerely appreciate it !
John

John2005 wrote:

I have heard of a "modified harmonic" curve,

Not really. But maybe the modified (standard has only 3 radii) has one
additional that is between the base circle and the chest circle (hope
you understand my nomenclature). That additional radius is to smoothen
the "slap" when the roller (that has some play/swing) hits the chest
circle. But I wouldn't bet my head for that.


I don't know if this is similar to the Tangential lobe you mentioned or
not.

No, the tangential is the most primitive lobe that exists. And it was
used until maybe the 20th of the last century. It is noisy.


Any drawings, diagrams, and/or math you can send to my email address on
the tangential lobe would be a great help, and much appreciated.

Could you please send me an eMail? Or I will forget to scan the pages
for you, as I don't have the time right now. Thanks.


Nick
--
Motor Modelle // Engine Models
http://www.motor-manufaktur.de
DIY-DRO // Eigenbau-Digitalanzeige
http://www.yadro.de

In article . com,
says...


John2005:
Yes, the roller force varies according to the spring rates listed on
the drawings. The inner an outer rollers have equal forces at the
neutral position, but different forces at the cam low and high point
dwells. If I can just get the stresses to a reasonable or acceptable
level for the inner curve, I will be happy. I would like to just make
the cam and roller out of either hardened tool steel or 4140, instead
of something more specialized or exotic.

I mentioned 52100 bearing steel in an earlier post and still think it's
worth considering.


Ned Simons:
Making the radius of the convex part of the rise smaller lowers the contact stress.

John2005:
I am a little confused at this part. Don't I want to make the minimum
convex radius as large as possible to make the contact stress lower ?

Sorry about that, too many concaves and convexes for me to keep
straight.g What I meant is the stress will be lowest when the follower
nestles in a concavity in the cam with the cam and follower radius
equal. As you said earlier, you do want to leave a little clearance, but
I wouldn't be afraid to go a little tighter than Camco's recommendation.
I'd imagine 1/2" diameter followers are more typical of their smaller
indexers, so an allowance of 1/4 the roller diameter seems consistent
with their advice and reasonable to me.

Referring to your drawing, where the .379" radius blends in with the
.188 radius is a concave sharp point

No, the two radii are tangent so there's no bump or point. In my layout
the small radius is .094 (3/32).

(if this were the inner curve it
would be a convex sharp point).

On the inside cam the small R would be tangent to the high dwell rather
than the low dwell as shown for the outer cam - again no bumps. The cams
aren't required to be true conjugates are they?

Ned Simmons

In article ,
says...

The profile with the lowest pressure (with the same load) is a straight.
If you can do that, do that. This is a tangential lobe you will seldom
find in literature, because they are noisy, have huge acceleration and
even more "Ruck" (don't know your technical term, "Ruck" is differential
of acceleration).

Jerk.

Displacement Velocity Acceleration Jerk Snap

I've also seen discussions of Crackle and Pop, the 5th and 6th
derivatives of displacement, but have enough trouble wrapping my head
around the physical effects of jerk without worrying about snap, crackle
and pop.

Ned Simmons

Hi Ned,

Thanks for your reply. I will keep your suggestion about 52100 bearing
steel in mind. It makes sense since rolling element bearings experience
high contact stress. I have no experience working with it, and was
thinking tool steel might be easier to work with, but perhaps not that
much different. I also have some thin walls, so I need something that
deforms as little as possible during heat treatment.

Ned Simmons:
The cams aren't required to be true conjugates are they?

If by true conjugate you are asking if the inner and outer curve needs
to be of the same type, I think it should. The way I have everything
set up, I can have a reasonable manufacturing tolerance on the rib
width, but I think it will work best if the inner and outer curves are
the same type. However, as long as the two rollers have the same
angular displacement about the swing arm pivot point, at any given
angular displacement the cam, it should be fine. That's the only reason
I say the curves should be the same type.

Ned Simmons:
On the inside cam the small R would be tangent to the high dwell rather
than the low dwell as shown for the outer cam - again no bumps

I think the main difference between the curve you show and a constant
velocity or straight line curve is that the center of the arc radius
(the large .379" radius) for a constant velocity curve would be the
rotation axis of the cam. Then you put a radius on each end of the
straight line ramp. Would the curve you show produce a "near" constant
velocity. It almost looks like it would produce an eccentric type
motion somewhat like a harmonic curve.

Thanks again,
John

In article . com,
says...
Hi Ned,

Thanks for your reply. I will keep your suggestion about 52100 bearing
steel in mind. It makes sense since rolling element bearings experience
high contact stress. I have no experience working with it, and was
thinking tool steel might be easier to work with, but perhaps not that
much different. I also have some thin walls, so I need something that
deforms as little as possible during heat treatment.

The Metals Handbook groups 52100 with 4140 for machinability. It's use
in bearings requires stability in hardening, so I don't think that would
be a problem.


Ned Simmons:
The cams aren't required to be true conjugates are they?

If by true conjugate you are asking if the inner and outer curve needs
to be of the same type, I think it should. The way I have everything
set up, I can have a reasonable manufacturing tolerance on the rib
width, but I think it will work best if the inner and outer curves are
the same type. However, as long as the two rollers have the same
angular displacement about the swing arm pivot point, at any given
angular displacement the cam, it should be fine. That's the only reason
I say the curves should be the same type.

By conjugate I mean that the relationship between the followers is
constant. Conjugate cam/follower systems don't require springs to
preload the follower. Desmodromic valve trains are an example. If I
understand, you'd like the relationship between the followers to remain
approximately the same, not necessarily exact.


Ned Simmons:
On the inside cam the small R would be tangent to the high dwell rather
than the low dwell as shown for the outer cam - again no bumps

I think the main difference between the curve you show and a constant
velocity or straight line curve is that the center of the arc radius
(the large .379" radius) for a constant velocity curve would be the
rotation axis of the cam. Then you put a radius on each end of the
straight line ramp. Would the curve you show produce a "near" constant
velocity. It almost looks like it would produce an eccentric type
motion somewhat like a harmonic curve.


When I get a few minutes I'll try another CAD (Inventor) layout of both
the inside and outside cams. I assume your acad .dwgs are to scale?

Ned Simmons

Hi Ned,

Thanks for your reply.

The AutoCAD drawings are all to 1:1 scale. I always draw everything in
model space just like it is in the real world. I never really
understood why some people draw things at odd scales in model space
when designing. I only use scales when printing in paper space if I
have to get something large to fit on a certian size paper, or blow
something small up so it can be seen better. I have not had the
pleasure of trying Inventor yet, but it looks like a neat program.

Regarding your question about the conjugate nature of the design, the
relationship between the rollers is constant, but I guess it's not a
true conjugate in the sense that the inner roller is mounted on a
slider that allows the roller to move linearly if needed, and the
slider "pivots with" the follower about the pivot point.

There is no real sliding of the slider, any sliding would only be a few
thousandths of an inch, equal to manufacturing tolerance variances on
the width of the cam "rib" that would tend to cause the rib to bind
in-between the two rollers, if both rollers were rigidly fixed. I could
not find such small rollers that would be accurate enough to use with a
very accurate ground cam, which would allow both rollers to be fixed
without any binding of the rib between the two rollers as the cam is
rotated.

Referring to the drawings, the two rollers create opposing torque's
on the cam after leaving the centered dwell position. After the cam has
been manually displaced Clockwise from the mid-point neutral position
dwell via a lever connected to the cam, and then the lever is released,
the sole purpose of the inner roller force is to return the cam to it's
centered neutral position dwell.

After the cam has been displaced Counter-Clockwise from the centered
neutral position dwell via a lever, and then the lever is released, the
force from the outer roller returns the cam to its centered neutral
position dwell.

I had thought of using a single roller in a cam track or groove, but
decided against it because I thought I would have problems with
clearances between the roller OD and the track. That's usually not a
big issue, but on this design I thought I might have problems.

The roller forces actually bring the cam back to the start of the
one-degree mid-point dwell and then opposing extension springs
connected to the cam return the cam for the .5 degree distance to the
center of the one degree mid-point dwell. This is done since the roller
forces can't create any torque on the cam once they are in contact with
the dwells.

Note that the drawings show different springs, spring forces, and
spring rates for the inner and outer rollers. The outer roller force is
generated through a .419" moment arm. However, the inner roller force
is created solely by extension springs and the force is not acting
through a moment arm, it is strictly linear. In the drawings, I listed
the actual inner and outer roller roller force at the cam low, mid, and
high point dwells and listed the spring rates.

Thanks again Ned, I really appreciate your help.

Sincerely,
John

Nick Müller wrote:

Could you please send me an eMail? Or I will forget to scan the pages
for you, as I don't have the time right now. Thanks.

Now I have put that on my home page.
Find it at:
www.motor-manufaktur.de/temp and get the files s0.jpg ... s5.jpg.
Each file about 1MB. I'll remove them in a week or so.


As you can't German (I guess) here some words to get a bit of
orientation in the text and formulas:

Nocken = lobe
gekrümmt = curved
Stössel = lifter (roller)
Kipphebel = rocker arm
Erhebung = lift
Gewschwindigkeit = speed
Beschleunigung = acceleration
Winkel = angle
Kreis = circle
Kreisbogen = partial circle
hohl = concave
eben (ebene) = flat
gewölbt = curved (round)
Ventil = valve

Hope that helps,
Nick
--
Motor Modelle // Engine Models
http://www.motor-manufaktur.de
DIY-DRO // Eigenbau-Digitalanzeige
http://www.yadro.de

Nick Müller wrote:

Gewschwindigkeit = speed

Guess you won't find that typo in the book. :-)

read "Geschwindigkeit"

Nick
--
Motor Modelle // Engine Models
http://www.motor-manufaktur.de
DIY-DRO // Eigenbau-Digitalanzeige
http://www.yadro.de

Hi Nick,

Thanks for your message.

I tried to click on the link you gave,
http://www.motor-manufaktur.de/temp but it just said

"Forbidden

You don't have permission to access /temp/ on this server.
Apache/2.0.53 (Linux/SUSE) Server at www.motor-manufaktur.de Port 80"

I also looked around your main site http://www.motor-manufaktur.de/ but
I did not see the info.

I sent you an email if you could please reply at your convenience (I
have not checked it for a day or so, in case you already sent it there
as well as putting it on your site) .

Thanks again,
John

On 29 Mar 2006 13:11:14 -0800, John2005 wrote:
Hi Nick,

Thanks for your message.

I tried to click on the link you gave,
http://www.motor-manufaktur.de/temp but it just said

"Forbidden
You don't have permission to access /temp/ on this server.

Nick, at the risk of telling you the blisteringly obvious, that if
you're the Nick I think you are you already know, this is either a
DocumentRoot problem, or a "disallow directory listings" problem.
I'm guessing the latter.

BTDT...

John2005 wrote:

I tried to click on the link you gave,
http://www.motor-manufaktur.de/temp but it just said

Not everything that can be clicked should be clicked without thinking
and reading. Blind clicking is the reason for all the viruses running
around.

OK, no virus, no more barking.

If you take the link I gave and the files I gave and make one path out
of them like with:
www.motor-manufaktur.de/tmp and s0.jp -
www.motor-manufaktur.de/tmp/s0.jpg you got one valid link. Do that for
the other files.


Nick

--
Motor Modelle // Engine Models
http://www.motor-manufaktur.de
DIY-DRO // Eigenbau-Digitalanzeige
http://www.yadro.de

Dave Hinz wrote:

Nick, at the risk of telling you the blisteringly obvious, that if
you're the Nick I think you are

I am the Nick I am, not the one you think. I think. :-)


you already know, this is either a DocumentRoot problem, or a "disallow
directory listings" problem. I'm guessing the latter.

Disallow directory listing is no problem.


Nick
--
Motor Modelle // Engine Models
http://www.motor-manufaktur.de
DIY-DRO // Eigenbau-Digitalanzeige
http://www.yadro.de

Hi Nick,

Thanks for your help. I tried what you suggested with the link but it
still did not work for me. Here is the mesage I got...

"Not Found

The requested URL /tmp/s0.jpg was not found on this server.
Apache/2.0.53 (Linux/SUSE) Server at www.motor-manufaktur.de Port 80"

Same thing with s5.jpg as well.

John