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Request for material recommendation for cam and follower 1

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John2004

Mechanical
Mar 29, 2004
237
Hello everyone,

I would like to ask if anyone could please help me with the following situation.

I have 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, and I am using a Parabolic curve, which should give the best minimum radius of curvature and lowest contact stress of just about any curve that is located between two dwell points. 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..

The maximum contact stress between the cam and roller using a 3/8” thick cam & 3/8” long roller is 331,228.24 PSI. I used the formulas in the cam design manual by Clyde Moon to calculate the contact stress along the curve, with the aid of a spreadsheet. I downloaded the design manual from
It’s difficult to make the cam thicker than 3/8” due to various design constraints, but there is a small chance I could go to a thickness of 7/16” or possibly ½” at the very extreme. This would give a maximum contact stress of 306,657.76 PSI & 286,852.07 PSI respectively.

The maximum contact stresses occur at the point of maximum angular cam displacment, and 90% of the time the cam is not rotated that far. The average maximum contact stress that the cam sees 90% of the time is probably in the range of 220,000 to 252,000 PSI depending on cam thickness. Still, it seems I should design for maximum stress along the entire cam profile.

If the device fails there is a zero percent chance that anyone would get hurt or injured. I don’t think I have the luxury of working with normal safety factors (if any), since the design is on the edge.

My main concern is that I need to avoid plastic deformation, and I need to be reasonably sure that any elastic deformation of the cam or roller will not cause the roller to roll rough or slide, i.e., if the pressure causes a large enough flat spot on the roller, there would be sliding or rough rolling. I am more concerned about these two factors than wear or fatigue, since the cam rotates so slow and intermittently.

Can anyone please recommend a material and hardness combination for the cam and follower that would withstand this type of contact stress? I want to use something that is as cost effective as possible to machine, heat treat, and work with. What metal properties do I need to be most concerned with ? I would think compressive yield and shear strength would be the two most important properties to consider, along with how easy the material is to work with.

I found the following materials listed below on that have compressive yield strengths of over 300,000 and 400,000 PSI, depending on how hard they are (usually between 60 & 64 Rockwell C). However, I am not sure how difficult they are to machine and work with prior to heat treatment. The site gave no machining rating, but said the ASTM 897 grade 5 machines well.

The cam is a very small “rib” cam that has two rollers. One roller works on an inner profile and one roller works on the outer profile. The stresses listed above are for the inner profile, since it has the highest stresses. The cam rib gets thin right at the cam high point (about a .120” wide rib over a short span) in case this could be a problem during heat treatment.

Materials Found on
UDDEHOLM VANADIS 6® Hot Work Tool Steel
Carpenter Speed Star® High Speed Steel (Red-Hard) (AISI M2)
Spray Formed Grade ROLTEC SF Cold Work Tool Steel
Spray Formed Grade WEARTEC SF Cold Work Tool Steel
ASTM 897 Grade 5 (230-185-00), Austempered Ductile Iron
UDDEHOLM ELMAX® Powder Metallurgy Stainless Mold Steel

Regarding the cam follower roller, I will be pressing the .1875” OD roller onto a 2mm OD hardened steel dowel pin so the roller “rotates with” the dowel/ shaft. Each end of the shaft is then supported by a low friction self lubricating bushing. I think this arrangement will allow the roller to roll well without sliding between the roller OD and cam profile. I was going to use stock tool steel (i.e, A2, D2, 0-1, W-2 etc.) drill rod for the roller since it already comes in the OD I need and is held to close tolerances. There will be no lubricant between the cam profile and roller OD. I have also considered glass bead blasting the cam profile to increase friction between the cam profile and roller OD, to help insure that the roller always rolls well with no sliding between the cam and roller OD.

My concern with the roller is finding stock round 3/16” OD bar that can handle the high contact stress. It seems to me that it probably needs to be hardened to handle this type of stress. However, when the center of the 3/16” OD rod is drilled out so that it can be pressed onto the 2mm OD dowel, it leaves a thin wall. I am concerned that the roller will distort or crack during heat treatment. I need to make the rollers as cost effectively as possible, and due to the way they are assembled, I cannot make the roller and shaft as one piece.

The parts are so small I don’t think material cost is a big issue, I am worried that the high strength materials will be hard to work with. I would appreciate any recommendations on the most cost effective materials (easiest to work with) I could use for the cam and follower, and the best heat treatment method for small parts that have thin walls.

Thank you for your help.

Sincerely,
John
 
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I just finished a roller system very much like a car roller lifter but much smaller. I had to stick with stainless steel for use in the food industry. I think you could use tool steel for the roller and a needle bearing as I did. You need the largest diameter needle bearing you can fit in and the widest. If you look around INA bearings you can buy just the roller needles alone. You could possibley optimize the design this way. I used 440 c stainless steel for the shafts and retained them with TRU Arc retaining rings. I durability tested this unit for over 2.5 millinon cycles and it was still going strong. I only lubed it once a day with food grade gear lube which is nothing as far as good oil. The test cam which in reality represented the fixed machine cam was 6" in dia and the roller had constant contact under load so it was far in excess of what real life was. The machine currently has 1/2 million cycles on this system now and runs 24/7
 
I don’t know of any materials that can stand up to these stresses reliably. Gears and rolling element bearings see the highest contact stresses of any application I am aware of, and the stresses are not as high as yours, but not too much lower.

Conventional highly loaded gearing is carburized, case hardened, and ground. Commonly used steels for this are SAE 9310, SAE 8620, and 17CrNiMo6. In manufacturing, 8620 is not controlled for toughness, so good performance for gears requires special metallurgical controls. This may not be an issue in your application. 17CrNiMo6 is popular in Europe, but not in the states.

Nitriding is another possibility. It creates an extremely hard case, but the case is relatively thin and brittle, and not at all good for impact loading (which may not be an issue for you). The thinness of the case may be a problem, though, with those very high contact stresses.

Another possibility is 52100 bearing steel.

Timken makes a wide range of bearing and tool steels and probably could steer you in the right direction.
 
Hi Bentwings1 & Philrock,

Thanks for your replies,

Philrock, you mention my contact stresses are a little higher than those seen in rolling element bearing and gearing applications.

What type of high side contact stresses are generally seen with gearing and rolling element bearings ? This may give me an idea of what to shoot for, as I try to make the best compromises for the design.

The contact stresses are probably going to be high no matter what I do, but perhaps I could get them down to the high side of contact stresses seen with gearing and rolling element bearings.

The Parabolic curve gives the lowest contact stress of most of the standard curves, i.e., Modified Sine, Cycloidal, Harmonic, Modified Trapezoid, and most of the standard Polynomial curves.

I got a demo of the cam design program Dynacam, and it had a few curves that seemed to produce much lower stresses (179,000 to 181,000 PSI). The curves were Thoren, Stoddard, Duddley, Berzake-e, Berzak-d, and "Cycloid first half" & "harmonic first half".

Responsiveness between cam versus follower movement after leaving the dwells is important on the design. The demo program won't let me export anything, so I cannot really compare the responsiveness of the above mentioned curves with the Parbolic. At the very least I would like to superimpose the curves over the Parbabolic & standard curves in AutoCAD, just to get a feel for them.

If I had a displacement output file showing cam angular displacement versus follower angular displacement for each degree of cam rotation, that would tell me what I need to know.

At a price of over 2,000 the Dynacam program is a little pricy for one job.

I wish I had some way to explore the Thoren, Stoddard, Duddley, and Berzake curves, before making a final decision on material. The cam design software I have, won't produce these types of curves. It could be that the Parbolic is already the best compromise, but it would be nice to be sure.

Thanks again for your help,
John
 

Have you condidered the torque it will take to turn the cam? Sooner or later, this seems like it would be a problem area being of such small diameter.

Is lube striclty out of the picture? At such slow speeds, I'm not so sure a non-lubricated rolling element assembly can take more pressure or last any longer than a lubricated non-rolling single-piece follower.

 
Hi Fabrico,

Thanks for your reply.

The torque required to rotate the cam is fine. The cam follower rotates on low friction self lubricating bushings, but there will be no lube between the cam profile and roller follower OD. I could use something if I had too, only once at assembly, but the device needs to be maintenance free.

I don't want lube between the cam profile and roller OD because I think it will just lead to more sliding between the cam and roller OD.

I have actually considered ways to increase friction between the roller OD and the cam profile, such as using a coating of "belt dressing" on the cam profile and possibly glass bead blasting the cam profile, to help insure the roller always rolls without sliding.

As far as using a non-rotating follower, I thought of using a 3/16" OD hardened chrome plated steel pin, but I am afraid there will be sliding or rubbing noise. Plus, I don't want the user to have to worry about re-lubricating the cam profile.

Thanks again,
John

 
Nominal allowable contact stress for carburized steel is 225 ksi, per AGMA 2001, but for gears this is further reduced by many factors which don't have equivalents in your application.

When I first responded to your question, I overlooked the point that there will be no lube in the contact zone. Gear calculations assume adequate lube. I see this as hopeless without lubricant. You might be better off using lubricant and letting the roller slide if it wants to.

Lubed or not, I think longevity will be a problem.

FYI, what makes elastohydrodynamic lubrication (as in gears and rollng element bearings) work, is the fact that the viscosity of oil increases sharply under great pressure. The consistency of oil in the contact zone of heavily loaded gear teeth is roughly that of solid nylon.
 
Torque to turn the cam is very real!!! Just as a side note in the old days of top fuel drag racing it used to take about 50 ft lbs to turn just a loaded roller cam over when assembling a motor. This is about what it took to turn the crank and pistons too.
MY test noted above started out with a 1/2 hp ac motor and controller. It could not rotate the cam profile roughly 6.0 inches in diameter and .75 lift at 120 rpm smoothly. In fact it woudn't run at all. Even a 1/2 hp dc motor wouldn't do it. We finally set the whole thing up in a Bridgeport and ran it there with out problems. I ran as long as 18 hours with any lube other than what was applied by hand. The entire test lasted about 4 weeks and I only used about 4 oz of food grade lube.
To address your question. The roller won't have a problem rotating against the cam if there is even a little pressure.
In my initial test with the roller, I had only a used roller and we had to get something going quickly. This ran about a million cycles before it failed. It happened on a weekend so how long it ran with the bearing destroyed is unknon but I would guess at least 50,000 cycles without lube. It did tear up the cam some but we didn't have time to replace it so I simply cleaned it up and put the new roller assembly on and reset the counter. The cam was just soft 1020 steel and there was 80# spring pressure on the roller. The pin was 17-4 ph stainless and about rc40 so far from very hard. My new ones are much harder and smoother. There really was not much wear onthe cam itself. The machine cams have no visible wear after 500k cycles.
Plastic bushings in the rollers lasted less than 4000 cycles but the needle bearings were still running way after 2 million. I just checked with my customer and they are at 500,000 cycles now and still running with out problems.

99 Dodge CTD dually.
 
As I mentioned before, you must explore other profiles. The parabolic is not the best for situation and you must remember, most cam programs are more concerned with dynamic forces which are virtually zero in your case. Again give us a sketch of your system and let us see what we come up with to minimize the stresses which are statically induced. You may not need a fancy program to ascertain a better design curve.
 
Hi Bentwings1,

Thanks for your additional feedback.

Bentwings1 wrote:
>Torque to turn the cam is very real!!!<

John2004:
I did not mean to imply torque was not something to consider. I just meant that I have calculated it, and it is not a problem at all in my application.

Do you have a rough idea of what the contact stresses were for the cam and roller used in your test ? Just curious.

My cam follower roller normal force goes from about 97 to 130 pounds Maximum, but the cam and roller are so small, it's causing high contact stress. Just to look at this thing, you would think a 3/8" thick cam or at least a 1/2" thick cam would support a roller normal force of 130 pounds without failure or any problems, especially hardened.

Here are all the specs on the cam which gives you an idea of how small it is...

This is a rib or blade cam with an outer cam follower roller that works on an outside cam profile and an inner cam follower roller that works on an inside cam profile. The inside cam profile is the profile with the high contact stress, due to its smaller radius of curvature.

The inside cam profile is the profile closest to the cam rotation axis, the outside profile is the profile furthest away from the cam rotation axis.

The outside cam follower roller pushes towards the cam rotation axis (like most normal cams) and the inside cam follower roller pushes away from the cam rotation axis, into the inside cam profile. The rollers create opposing torques on the cam.

Inner Cam Profile:

Curve types between dwells = Parabolic / constant acceleration
Inner profile base circle radius (cam rotation axis to low-point dwell) = 0.8527"
Cam rotation axis to mid-point dwell = 0.9959"
Cam rotation axis to high-point dwell = 1.0949"
Follower swing arm pivot point to roller center = 0.8221"
Cam rotation axis to follower pivot = 1.1475"
X,Y, coordinates of follower pivot = X = 0.8616 and Y = 0.7579 (with cam rotation axis x,y = zero)
Cam follower Roller OD = .1875"
Follower Swing arm start angle at cam low point = 41.33647 degrees(angle between line of centers of the roller center and swing arm pivot, and the line of centers between the cam rotation axis and follower pivot).

Outer Cam Profile:

Curve types between dwells = Parabolic / constant acceleration
Outer Profile base circle radius (Cam rotation axis to low-point dwell) = 1.0117"
Cam rotation axis to mid-point dwell = 1.1332"
Cam rotation axis to high-point dwell = 1.2142"
Follower swing arm pivot point to roller center = 0.7417"
Cam rotation axis to follower pivot = 1.1475"
X,Y coordinates of follower pivot = X = 0.8616 and Y = 0.7579 (Cam rotation axis x,y = zero)
Cam follower roller OD = .1875"
Follower Swing arm start angle at cam low-point = 67.73626 degrees (angle between line of centers of the roller center and swing arm pivot, and the line of centers between the cam rotation axis and follower pivot).

Cam & follower angular displacements from low-point to high-point:

Cam & follower displacement (Low point to Mid-point dwell)
CCW cam rotation of 18 degrees = CCW follower displacement of 10 degrees

Cam & follower displacement (Mid-point dwell)
Follower dwells for one-degree of CCW cam rotation at mid-point

Cam & follower displacement (Mid-point to high point dwell)
CCW cam rotation of 14 degrees = CCW follower displacement of 7 degrees

Cam and follower displacement (high point)
Follower dwells for 3 degrees of CCW cam rotation at the cam high point.

The cam oscillates between the start of the low and high point dwells. The dwells at the cam low-point and high-point are just there for safety, and are not really used. At the resting or neutral position, the rollers are in the center of the one-degree mid-point dwells. Most of the time, the cam is oscillated about 8 degrees CW from the mid-point dwells and back to neutral, or 8 Degrees CCW from the mid point dwells and back to neutral. The high contact stress occurs on the inner cam profile near the cam low-point.

At the mid-point dwell or resting position, the inner and outer rollers have equal forces. The spring rate for the outer roller force is 8.67 pounds per each degree of follower swing arm pivot. The spring rate for the inner roller force is 4.072 pounds per each degree of follower swing arm pivot.

Inner roller force goes up with CW cam rotation and outer roller force goes down with CW cam rotation. At the cam low-point, the inner roller force is at maximum and the outer roller force is at minimum. At the cam high point, the outer roller force is at maximum, and the inner roller force is at minimum.

I chose the Parabolic curve because it had the largest minimum radius of curvature and lowest contact stress of the standard curves. However, the Thoren, Stoddart, Duddley, Berzake-e, Berzak-d, "Cycloid first half" & "harmonic first half" may produce lower stresses, but my software does not produce those curves.

Thanks for your help.
John
 
Hi Zekeman,

Thanks for your post, I did not see your reply as I was posting may last reply.

Please let me know if the additional information on the cam geometry, displacements and dimensions in my last post helps. I can give more information or provide a CAD drawing along with my cam design software ouptut if this can help.

I would appreciate any advice you or anyone else can give on a profile that may yield lower contact stresses than the parabolic curve.

Thanks again,
John
 
Hi everyone,

Zekeman, I just uploaded some DWG and duplicate DXF drawings, along with duplicate JPEG images of the cam, to Rapidshare. I also included output text files from my cam design software.

You can download the files from the link below...


I would appreciate any advice from you or anyone else on finding a cam curve that will have lower maximum contact stress than the Parabolic.

If there is a curve that will produce lower contact stress, it would be very very helpful to get a CAD file of the curves that I could superimpose over the parabolic curves in AutoCAD for comparison.

Software output showing cam angular displacement versus follower angular displacement for each degree or preferably each 0.25 degree of cam rotation would also be very helpful as I could use this with my spreadsheet to compare responsiveness of the follower to cam displacement, after leaving the mid-point dwell, to the parabolic curve.

Thanks again, I really appreciate your help.

Sincerely,
John
 
Hi everyone,

I think that one way to solve this problem may be to start with the Parabolic curve (since it produces a farily large minimum radius of curvature), and then increase the minimum radius of curvature further by decreasing both acceleration and deceleration of each curve segment. This would be done at the expense of creating a larger maximum pressure angle, but as long as it's reasonable for an oscillating follower that's no problem.

Even with the existing standard parabolic curve, the outer profile has a maximum stress of around 181,373.00 PSI with a 3/8" thick cam, which is much more reasonable than the inner profile. I would like to shoot for a cam no thicker than 3/8" if at all possible.

I would not want the curve to accelerate and decelerate any slower than necessary to achieve acceptable maximum contact stress, since this decreases responsiveness between cam rotation and the start of follower motion after leaving the mid-point dwell, which is on thing I need to consider on the design. It seems to me a small decrease in the acceleration / deceleration of the curve may do what I need.

Unfortunately, I presently see no way to do that with my cam design software.

Well, this was one possible solution that came to mind I thought I would mention.

Thanks again guys, I appreciate your help.
John
 
Regarding my comments on the Parbolic curve in my previous post, I forgot it already has the lowest possible peak acceleration / deceleration for a given motion, I suppose reducing it further won't be possible.

Perhaps it's still possible to somehow increase the minimum radius of curvature of the cam profile at the expense of a higher maximum pressure angle or some other trade off, I'm not sure. Hopefully there is some curve that will give lower contact stress.

Thanks
John

 
Hi everyone,

I wonder if a "modified constant velocity curve" might be the best solution for this problem.

With this curve you take a constant velocity curve and then put a radius on the ends of the curve where it blends with the low and high dwells. It will have to be at least equal to the roller radius to avoid undercutting, but I will make it as big as I can.

After leaving the dwell, I want the roller to start moving a reasonable amount within a reasonable time. It may also be desirable to make the follower halfway to its' maximum angular displacement at the same time the cam is halfway to its' maximum angular displacement(like a standard curve).

I checked with my spreadsheet and using a constant velocity curve for the inner cam profile produces a maximum contact stress of about 145,000.00 PSI at the cam low point, but I did not check right where it blends with the dwells. This will depend on what size radius is used. There is a 0.195" minimum radius of curvature on the existing outer parabolic profile(which has a maximum contact stress of about 181,000.00 PSI) so perhaps I could shoot for a little bigger than this.

Perhaps blending a constant velocity curve between the low and high dwells, with a .250" or so radius, is the way to go.

I just wonder if there is a better option.

Thanks
John
 
I think that using an asymmetric constant acc/dec curve might be of some consequence. You start with a higher acceleration for more than half the period followed by a higher deceleration, the second half for openers but you must look at the reduction in concave curvature at the start.Now that I think about it, you already have a radius of curvature of -.11 at the start, so that suggestion won't work.
I am looking into this problem and I must agree that 2000 bucks for that program is not worth it (unless you can get the government to pay). For this problem, it should be fairly staightforward. I will post the equations you need,shortly.
Also you might think of reducing the spring forces where they are significant at the start of the inner segment. As a suggestion, what about constant force springs?
 
I have run some calculations and cannot corroborate your 300,000 psi stresses.
I get around 200,000 psi at the first curve based on your tabulated data on a cam radius of curvature of .114 and a cam diameter of 0.1875" and width of 3/8".
The Hertz stress should be
sqrt(.35P[1/(rc-rf)+1/rf)]/(2*.375}/E
=sqrt(.35PE[1/(.114-.0937)+1/rf])/(2*.375)
P=130*.419/1.1475=47.5 lbs normal force (noting that cos of small pressure angle is nearly unity.
I got 199,000 psi. at that point which I think is near the max stress.
If you think that is not the max stress, please post otherwise.
 
Hi Zekeman,

Thanks allot for your reply, I appreciate it.

>Zekeman:
>I think that using an asymmetric constant acc/dec curve >might be of some consequence.

John2004:
I tried an asymmetric Parabolic profile, problem is, I have a small radius of curvature at each end of the curve, so if you change the symmetry factor to make the radius of curvature better at one end, it gets worse at the other end.

>Zekeman:
>I am looking into this problem and I must agree that 2000 >bucks for that program is not worth it (unless you can get >the government to pay). For this problem, it should be >fairly staightforward. I will post the equations you >need,shortly.

John2004:
I would sure be grateful for anything you can do, and I appreciate what you have done so far. Thanks !

>Zekeman:
>I got 199,000 psi. at that point which I think is near the >max stress. If you think that is not the max stress, please >post otherwise.

John2004:
That is surely the point on the profile of maximum stress, however, after checking my spreadhseet, I may have made an error entering the sign of the radius of curvature in the spreadsheet but using either + or - sign the calculations are still different than yours. This brings about several important questions listed below. Please see below and let me know what you think.

Regarding your calculations, the 130 pound inner roller force at the low point of the cam is created by a linear extension spring. It's not a torque force like the force shown on the outer roller. Therefore it would not be multiplied by the .419" spring moment arm distance.

The .419" distance is the moment arm that the outer roller spring force acts through for the "outer roller only", and is only applicable to the outer roller. As noted in the drawings, the inner and outer rollers use different springs, spring forces, and different spring rates, but I should have noted that the inner roller force is purely linear and does not act through a moment arm, whereas the outer roller force is a torque force acting through the .419" moment arm. The outer roller force is still generated by an extension spring, but it acts through a moment arm. The inner roller is mounted on a slider, but the slider pivots about the follower pivot point with the follower / swing arm.

This is one reason why your contact stress calculations were different than mine.

The inner and outer roller forces are exactly as shown in the drawings. Please note that the drawings show the different spring rates for the rollers, and show the roller forces at the low, mid, and high point dwells. These are the actual roller forces, and the normal force is the roller force divided by the cosine of the pressure angle, but it usually only adds a few pounds. At the .114" radii point, normal force and roller force are basically the same since the pressure angle is only 2.98 degrees.

Even if the force of the inner roller were a torque force, I am not quite sure why you are using the 1.1475" dimension for roller force calculations, since this is the distance from the cam rotation axis to the follower pivot point. You would actually use the distance from the follower pivot to the roller center, in place of the 1.1475" dimension, but again, for the inner roller, the spring force does not act through a moment arm, only the spring force for the outer roller acts through the .419" moment arm, which is then divided by the .742" length of the outer roller swing arm, to get the force of the outer roller.

The formulas I used for contact stress were from the cam design book by Clyde Moon. You can download a PDF file of the book for free here...


I think the contact stress formula is on page H-1.

I checked my contact stress calculations at the dwell positions with the values given by the program Camtrax and they were the same. The Camtrax program will not make a Parabolic curve for an oscillating follower, and that's why I made the spreadsheet to calculate the contact stress for that curve. They will give you a 10 day trial of Camtrax if you want to check it out, It's fully functional for 10 days, then stops running.

I used the same formula for the entire profile in the spreadsheet, (adjusting it for a positive or negative radius of curvature)so I figured that since I got the same contact stress as the camtrax program at the dwells, my formula was "probably" valid. Now, I'm not sure.

The contact stress formula (in it's simplified form) according to the Moon manual is...

Contact stress = (10)^3 * the square root of (Pn * C) / (L * M)

Where...

Pn = Normal force
C = Radius factor
L = length of cam and roller contact
M = Material Factor = 0.190 for steel according to Moon

For a convex surface...

C = Rc / ((Rc-Rf) * Rf)

For a concave surface...

C = Rc / ((Rc + Rf)* Rf)

C = 1/Rf for a flat surface

Where...

Rc = Radius of curvature of the pitch curve
Rf = Radius of roller foller (.09375)

From the moon book...

"If the radius of curvature (Rc) and the normal force (Pn) are the same sign (Positive or negative) the surface is convex; if they are of opposite signs, the surface is concave. If Rc is infinite, the surface is flat".

Regarding my software output, it appeared to me that for the outer profile the negative radius of curvature is concave, and the positive radius of curvature is convex. I assumed this would be the same for the inner profile. So I used the above (C) formula for a convex profile when I had a positive radius of curvature and the (C) formula for a concave profile when I had a negative radius of curvature. This also seemed to be consistent with a diagram in the Moon PDF file, but the diagram did not seem 100% clear to me.

When Clyde Moon made the comment quoted above about the normal force being positive or negative, I assumed that since the roller is always pushing into the cam profile, the normal force must always be positive. I am not quite sure what he meant by a "negative" normal force. I felt negative must mean the roller is pulling away from the profile, which is never the case with this cam.

At the negative 0.114" radius of curvature point (this is right where the inner curve meets the low point dwell), I calculated a radius factor of -.114 / ((-.114 + .09375) * .09375) = 60.049

C = 60.049

So, using the simplified formula given by Clyde Moon above...

130 * 60.049 = 7806.42 / (.375 * 0.190) = 109563.78

The square root of 109563.78 = 331.004

10^3 * 331.004 = 331,004.00 PSI .

Should I have used the absolute value of the radius of curvature in the formula, and ignored it's sign ? If so, then the contact stress (using a concave radius factor) would be...

.114 / ((.114 + .09375) * .09375) = 5.853

C = 5.853

(130 * 5.853) = 760.91 / (.375 *.190) = 10823.76

The square root of 10823.76 = 104.04

10^3 * 104.04 = 104,040.00 PSI

It seems a little low to me though, given the small cam radius of curvature at that point, and a fairly high load of 130 pounds for a 3/16" OD roller.

I need to be exactly sure when to use the convex or concave radius factor (C) in relation to a + or - radius of curvature listed in my software output, and whether I should use the signed radius of curvature, or ignor the sign and use the absolute value of the radius of curvature in the formulas. Can anyone please shed some light on these issues ?

The formula Moon gives for the material factor (M) is...

M = ((Ec + Ef)/(0.35 * Ec * Ef)) * 10^6

Where Ec is the modulus of elasticity of the cam and Ef is modulus of elasticity of the follower (I used 30,000,000). This worked out to .190 just like Moon said.

Moon also gives a longer formula where Sc^2 = contact stress...

Sc^2 = (0.35 * Pn) * ((1/Rc ± Rf) ± 1/rf) / L * (1/Ec + 1/Ef)

I am assuming that both cases of the ± signs in the formula above are + for a concave profile and - for a convex profile ?

I have a couple other books on cam design by Rothbart and Reeve and they seem to use slightly different contact stress formulas.

Now I'm really getting confused.

Regarding the dwells, the outer profile dwells would surely be convex, but what about the inner profile dwells? The software output lists both inner and outer dwells as a positive radius of curvature.

If Moon's simplified formula is valid, it seems best to use it to avoid the chance of error with a more complex formula.

I would like to reduce the contact stress as much as possible in any case, but perhaps the situation is not as bad as I thought. I can't be sure until I can find out more about the validity of the calculations.

Can anyone please help us verify contact stress for the following scenario ?

Inner cam profile as shown in drawings, roller at cam low-point
Pressure angle = 2.98
follower Pitch curve radius = negative 0.114"
Roller radius = .09375"
Normal force = 130 pounds
Cam thickness and roller length both = .375"

I can email the spreadsheet I created to calcualate contact stress to you. I would also try to copy the page from the moon book related to contact stress.

You can email me at (johnjmechanical @ Yahoo.com) lose spaces before and after @ sign. This is the email I use for forums, online, etc..

I sure hope I can get straightened out on this problem.

Thanks again Zekeman, I really appreciate your help.

Sincerely,
John
 
John,
1)You are quite right. I goofed on the cam force by using the wrong dimension-should have used the arm length which is academic to your problem.
2) The fact that ( I missed it) you already give the force at 130 lbs on the cam and by my calculation, I used about 49 lb is the cause for the whole discrepancy, since the hertzian stress is proportional to the square root of the force. Therefore, your stress should be sqrt(130/48)*199,000, confirming your numbers.
3)You are correct in assuming that the point in question has a convex curvature and when that occurs, the cam radius of curvature( at the cam, not the pitch curve,rc) is equal to the pitch point radius of curvatue minus the roller follower curvature rf, or rc-rf.Please note that rc is not the radius at the cam.
4)So, you have a large force pushing on the cam with a radius of about 0.02 inches, prctically a pencil point, and therefore the stresses you get are correct and very large.
5) Why can't you do something about this 130 lbs spring force-- or can't you?
6) If you were to make the cam nose radius of curvature .05", yielding a pich cam radius of 0.14, it might get the job done, but the acceleration in the first phase wouls have to be reduced. I will look into this shortly and post back.
 
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