Request for help with spring design

[John2004]

Hello,

I would like to ask if someone could please provide some feedback on a unique spring design problem.

Thanks
John

PROBLEM:

I have a radial plate cam, with an oscillating roller follower. The small cam is oscillated manually by hand, via a 6" long lever. At the neutral or resting position, the roller follower is in contact with the approximate center of the cam curve or profile. From the neutral position, the cam can be rotated clockwise, (by pushing the 6" activation lever down) or counter-clockwise (by pulling the activation lever up). The maximum angular displacements of the lever and cam are 16 degrees clockwise from the neutral position, and 14.5 degrees counter-clockwise from the neutral position.

When the cam is rotated clockwise from the neutral position, the force the roller follower exerts on the cam curve decreases, but when the cam is rotated counter-clockwise, the force the roller follower exerts on the cam profile increases.

At the neutral position, the roller follower is in contact with a "dwell" portion of the cam profile, and as such, the force the roller exerts on the cam profile does not create any torque on the cam at the neutral position. However, when the cam is rotated from the neutral position in either direction, the roller force then creates a torque on the cam.

When the cam rotates clockwise from the neutral position, the roller moves towards the cam rotation axis. When the cam rotates counter-clockwise from the neutral position, the roller-follower moves away from the cam rotation axis.

When the cam rotates clockwise from the neutral position the cam follower roller force goes down. When the cam rotates counter-clockwise from the neutral position, the roller force goes up.

I have springs connected to the cam in a series parallel array, i.e., 4 springs on each side of the cam, which hold the cam at, and return the cam to, it's neutral position, when the activation lever is pushed down or pulled up from the neutral position, and then released. The opposing springs are pre-stretched at the neutral position with equal forces on each side of the cam. This provides a "balanced feel" in the activation lever, which is important for the design.

My problem is, when the cam rotates clockwise from neutral 4.637 degrees, the un-balanced force of the springs needs to be about 50 pounds to overcome the force of the follower roller and return the cam to the neutral position when the activation lever is released. Since the force of the follower roller and the force of the springs are nearly balanced at this point, it is easy to push the lever down from the neutral position. The roller follwer force "helps" to push the activation lever down.

However, when pulling the lever up from the neutral position, not only does the force of the follower roller increase, but the force of the opposing return springs also increases (i.e., the un-balanced force will also be 50 pounds at 4.637 degrees counter-clockwise).

Also, the roller follower force works against the activation lever when pulling the lever up from neutral.

I need a system that provides a "balanced feel" in the activation lever at the neutral position, but allows the force to pull the lever up from neutral, to be small, like it is when pushing the lever down.

I tried using different (lower) rate springs on one side, but when I layed it out in my CAD system, and did the math, I could not get everything to work out.

It seems the opposing spring forces must be balanced at neutral, and the unbalanced force of the springs must be 50 pounds at 4.637 degrees of clockwise cam rotation, but somehow smaller when the cam is rotated counter-clockwise 4.637-degrees.

I basically want the force to pull the lever up from neutral to be as small as possible through the entire 14.5 degrees of counter clockwise rotation. It’s desirable to keep the forces necessary to move the lever as low as possible in either direction, either clockwise or counter-clockwise from neutral. The forces look good for pushing the lever down from neutral, but I would like to see lower forces for pulling the lever up from neutral.

I cannot really increase the length of the activation lever, since I am using a stock lever and want to keep using it. The space I have to work in is very small and constraining. The entire cam is also adjustable up and down by a total travel of 5 mm, which complicates things further.

The springs I am using now have about a .390" OD, a 1.8" free length, and a 115 lb/in rate. It would be difficult to increase the OD of the springs very much do to limited space.

Please let me know if anyone has any suggestions for a type of spring, spring system, or design that my work.

Thanks for your help.

John

 

[zekeman]

After further review, my idea won't work.

Could you impose an opposite spring at the point of application of the linear spring that produces 115 lb? If so, that could be a starting point. Otherwise, a spring solution under the parameters set forth would be very difficult, since you must know that the fundamental energy equation:

T*Dtheta=F*Dx

where:

T= torque on your hand
Dtheta = the incemental angle in radians that your hand moves on the lever
F is the applied force 115lb at the linkage
Dx= the incremental motion of the force applied to the link
So you see,it is obvious that by using the opposing springs for the neutral "feel" you have added a strong energy absorber that your hand must deliver at increased angle, especiallyfor springs with a high spring rate.

Under the circumstances, I wonder whether you could just state the basic problem and if whether you are locked into this configuration. If not, you might be better served by this forum if you could convey what you want to do and then kick around ideas that might lead to a satisfactory solution, but that might mean scrapping your cam and linkage.

 

[John2004]

Hi Zekeman,

Thanks for your message.

I think I have found a solution to the problem. I did not want to use a "track cam" that could both push and pull the roller, because I was worried about the roller binding in the track, since close clearances would be necessary between the roller and the curved track.

However, I found that I can use a "rib cam" i.e., a curved rib with a follower-roller on each side, which will make the cam double acting so that it can both push and pull the roller, and eliminate any roller binding problems.

I had previously thought the maximum pressure angle of the inner rib curved profile would be to high, but I found a way to decrease it to acceptable levels.

With this arrangement, I can put a spring on the roller, which opposes the roller load at neutral. The rib cam with dual rollers, will still be able to move the follower in each direction from neutral, even though the counter spring is connected to the roller to offset the roller force onto the cam.

I will still have opposing springs connected to the cam to provide a balanced feel at neutral, but they can be smaller than with the previous arrangement.

I think this will make the activation lever easy to move whether rotating the cam clockwise or counter-clockwise from neutral. Please let me know what you think.

I am still interested in any alternatives if anyone thinks of anything. It's a close fit, but so far, this seems like a very viable option.

Thanks
John

 

[zekeman]

John,
Your solution looks ok but I don't understand why you couldn't oppose the 115 lb input spring force with an almost equal inline opposite spring force (or torsion spring in the follower axis) such that there is a slight force inbalance assuring contact between the roller follower and the cam. Then, you could have the lower inline "feel" springs, as you point out, with much smaller spring rates. This would be about the same as your proposed solution, but obviously much simpler.

Zeke

 

[desertfox]

Hi john2004

Looking at your drawings it would appear to me although it
depends on how accurate the drawings are, that your largest
resistance to lever movement is governed by your balance springs. Now if you can't increase the length of your lever
how about reducing the 'moment' the balance springs exert on the cam by moving them vertically upwards closer to the centre of cam rotation, this would have the same effect as increasing the lever length.
Alternatively could you turn the balance springs through 90 degrees and have it pulling vertical through the cam rotation centre, if you could do this you may be able to reduce the number of balance springs. Although you would have no 'moment' exerted in the neutral position any movement clockwise or anticlockwise would stretch the balance spring and generate a balancing moment.

regards desertfox

 

[zekeman]

I posted a reply but Isee it did not go through. Repeating:
I think if you would add a soft spring force {or soft torsion spring in the follower pivot) in line with the input 150 lb spring force stretched to slightly smaller magnitude in order to maintain roller contact, you could do exactly as you describe at a fraction of the complexity.

 

[John2004]

Hi Zekeman and desertfox,

Thanks for your messages.

Due to design constraints, I cannot put an opposing spring "above the follower pivot" the spring that opposes the follower load must go below the follower pivot point. I know that may be hard to understand without seeing the whole mechanism, but that is one other design constraint I have. A torsion spring underneath may be viable, but I will have to check into it.

However, what is the main advantage of using a torsion spring to oppose the follower load, as compared to a couple of extension springs? I also need to be able to adjust the spring load, against different follower loads. I can't put the torsion spring right on the pivot point i.e., follower pivot point in center of torsion spring.

If I were to reduce the moment that the balance springs exert on the cam, I would then have to also increase there strength and/or rate, and I would not gain anything. This is because the unbalanced spring force needs to be 50 pounds when rotating the cam 4.632 degrees clockwise from neutral with the present return spring moment arm. If the spring moment arm is shortened, then the spring strength must be increased to provide more than 50 pounds of unbalanced spring force at 4.632 degrees clockwise cam rotation from neutral, in order to create the same torque on the cam as with longer spring moment arm.

Putting the springs in line with the cam rotation axis, would require a very high rate stiff spring, since the moment arm of the springs would go from zero to only a very small length, as the cam is rotated from neutral.

Considering the maximum spring force is needed at only 4.632 degrees clockwise cam rotation, the spring rate may need to be over 1,000 lb/in if the extension springs were located right in the center of the cam rotation axis.

With the solution I mention in my previous post, I will just put a couple of extension springs on the "yoke" that holds the roller, and this will oppose the roller load onto the cam. At neutral, the "spring assist" will have a force almost equal to the roller force at neutral.

Thanks for your feedback.

John

 

[zekeman]

2nd attempt to reply.
John,
I believe that you can accomplish the same thing with the initial am configuration by placing an opposing spring at the point of application of the 150 lb soft spring input load (or follower torsion spring), slightly less in force so that you maintain contact of the roller with cam.Then you could then add your lower force "feel springs as you describe.

 

[John2004]

Hi zekeman,

Thanks for your message.

If I add a spring to oppose the the follower load onto the cam, (i.e., a spring force almost equal to the follower load at neutral), then I must use a cam that can both push and pull the roller. If I use the original cam, when the cam is rotated clockwise from neutral, the added spring that opposes the follower load will not allow the roller to follow the decreasing radius of the cam curve. This is why I must use a cam that is double acting, i.e., the rib cam with a roller on each side of the rib.

Thanks
John

 

[zekeman]

John,

Testing!! I've been trying to get thru for some time.

 

[zekeman]

John,

If you balance out the follower moment at the extreme clockwise position of the follower (and cam) with a soft spring on the follower link, and then add your balancing springs on the cam for the neutral, I think you can materially reduce the crank arm forces with the existing cam design. It would depend on the nature of the input 115 lb spring force, the equalizing spring and their spring rates.

In that connection it would be helpful if you could furnish the nature of the input force and some dimensions of the folower linkage and cam,

Zeke

 

[John2004]

Hi Zeke,

Thanks for your message.

I am pretty sure I need a double acting cam that can both push and pull the follower. I am not sure that counter-balancing the follower forces at the extreme clockwise position of the cam and follower, would be sufficient, since the roller forces are fairly low at that point. I think it is probably necessary to counter-balance the follower spring force at neutral.

Please take look at the following information and let me know what you think.

The spring that exerts the 118 pound force at neutral, (which creates the roller follower load onto the cam), has a rate of 1,390.42 lb/in. As the cam rotates clockwise from neutral, the 118 pound linear spring force at neutral (which creates the roller follower load onto the cam) decreases by about 8.34 pounds per each degree of clockwise cam rotation from neutral. The maximum clockwise cam rotation from neutral is 16 degrees, but the first 0.5 degree is a dwell, and therefore the follower load does not decrease at all, for the first 0.5 degrees of cam rotation from neutral.

When the cam is rotated counter-clockwise from neutral, the 118 pound spring force (which creates the roller follower load on the cam) increases by about 8.34 pounds per each degree of cam rotation. The maximum counter-clockwise cam rotation from neutral is 14.5 degrees, but the first 0.5 degree is a dwell, so the follower does not move for the first 0.5 degree of counter-clockwise cam rotation from neutral. The roller is in contact with the center of a one-degree dwell at neutral, and as such, the roller does not move for the first 0.5 degree of cam rotation either CW or CCW from neutral.

The perpendicular distance from the follower arm pivot point to the center of the roller at neutral "linear dimension" is 0.6". The length of the follower arm (follower pivot to roller center "aligned dimension") is 0.625". The distance from the cam rotation axis to where the opposing "balancing" springs connect to the cam, is 0.672". The diameter of the follower-roller is .1875".

The distance from the cam rotation axis to the dwell at the cam neutral position is .955". The distance from the cam rotation axis to the dwell at the cam low-point is .851". The distance from the cam rotation axis to the dwell at the cam high point is 1.03".

The maximum clockwise follower-arm rotation from neutral is 9.5 degrees. The maximum counter-clockwise follower-arm rotation from neutral is 7 degrees.

If you draw a line from the follower arm pivot point, to the cam rotation axis, and you draw a line from the follower arm pivot point to the roller center at neutral, the angle between the two lines is 64.9264 degrees.

Thanks
John

 

[John2004]

Hi Zeke,

I wanted to add one more detail to the dimensions given in my last message.

The perpendicular distance from the line of action of force, of the 118 pound linear spring load (the spring force that causes the roller to push into the cam) to the follower arm pivot point, is .419"

Thanks
John

 

[zekeman]

After looking at your final proposed design, I am in agreement with it- double acting cam and balancing the follower link at neutral.
Assuming the follower balancing spring has the same spring rate as the force spring and is located, as you mention, near the roller center, I get a maximum force of about 8 lbs on your 6 inch arm to move the cam manually plus the added amount you need for the balancing springs which should be quite small. I still don't appreciate the need for this since the follower balancing spring should bring the double acting cam almost back to neutral from either direction, although at exactly neutral, of course, there would be a 1 degree dead zone.
As a further note, in reading your posts, you seem too concerned about pressure angle, to the detriment of the rib wall thickness. You can easily get away with a pressure angle of 70 or 80 degrees for a pivoting follower (your case). The problem of high pressure angle and binding is treated in the literature for translating systems where they usually keep the angle less than 60 degrees. If you need a reference on this I could furnish one.

Good luck on your design. I think you have a good solution.

Zeke

 

[John2004]

Hi Zeke,

Thanks for your message. I really appreciate all your input and help with this problem, and all the input of the other forum members that posted replies.

Most of the books I have on cam design, say to keep the pressure angle of a cam with a translating roller follower at 30 degrees or less for optimum performance. The book "cams for industry" by John Reeve, says that anytime you go over a 45-degree pressure angle, you must consider the consequences of the high pressure angle very carefully.

However, none of the books I have give pressure angle recommendations for oscillating or pivoting roller followers like the system I have with this design. They simply say that oscillating roller followers can tolerate a higher pressure angle than translating roller followers, (which one would expect) but they do not tell how much higher.

The two main references on cam design I use are "Cams for Industry" by John Reeve, and "Cams, design, dynamics, and accuracy" by Harold A. Rothbart.

I would be interested in learning of any other references you can provide on cam design. In addition to being a help with this project, I just have a general interest in cam design and I am always interested in books, articles, or software related to the design of mechanical cams.

One thing that I found out is that I will need to put the inner roller on some type of slider and spring load the slider and/or inner roller into the inner profile, to offset the force of the outer roller onto the outer profile.

I found that only .002" of clearance between the rollers and the rib curve, will cause 1/4" to 1/2" of backlash in the end of the lever at neutral, i.e., the end of the lever will move for 1/4 to 1/2" before the inner curve touches the inner roller, if there is .002" clearance between the inner roller and the inner profile at neutral.

The force of the outer roller pushing into the outer profile causes the cam to rotate clockwise, but the force of the spring loaded inner roller pushing into the inner profile, causes the cam to rotate counter-clockwise. I think this will still take care of the force problems, and also eliminate the roller clearance and lever backlash problems mentioned above.

The arrangement above is very similar to what Nick suggested with the mirrored profile arrangement. However, It did not occur to me to do it quite like this before.

Otherwise, considering manufacturing and assembly tolerances, I think it would be very hard to hold acceptable clearances between the rollers and the rib, which would not cause a backlash problem in the activation lever.

Now, I just need to come up with some way to mount the inner roller on some type of a slider, which is connected to the same "yoke" that holds the outer roller, and connect a couple of extension springs to the slider that the inner roller is connected to, in order to push or pull the inner roller into the inner profile, and offset the spring force of the outer roller. I need to do this in a "very" confined space.

Please let me know if you have any other comments or suggestions.

Thanks again,
John

 

[zekeman]

John,
The numbers I threw out on pressure angle are for low speed, low friction systems.The lower numbers that are recommended are predicated mostly on a substantial safety factor and for reduced wear in high speed systems.

The limiting pressure angle for oscillating follower is governed by the friction in the system. As you point out the literature doesn't come up with a number. However, Rothbart and others state that it is very difficult to create a binding condition for this configuration.

I worked out a limiting number based on a solid roller (i.e one that is bound and will not roll for a worst case)

cot(alpha)> mu

where
mu= friction coefficient
alpha= pressure angle

If you take a pretty severe case of static fricton,namely
mu=0.4, I get
alpha < 62 degrees

If you can use needle bearings, this number gets higher,
approaching 90 degrees, although you obviosly wouldn't design to that.

As far as refernces, Rothbart is good, but the most comprehensive treatment that I have seen is
Mechanics and Design of Cam Mechanisms,F.Y. Chen,Pergamon Press, 1982. It is a little mathematical at points but is very thorough.

Best Regards,

Zeke

 

[John2004]

Hi Zeke,

I wanted to add one more comment, regarding the following comment you made in a previous post:

Your comment:

"I get a maximum force of about 8 lbs on your 6 inch arm to move the cam manually plus the added amount you need for the balancing springs which should be quite small. I still don't appreciate the need for this since the follower balancing spring should bring the double acting cam almost back to neutral from either direction, although at exactly neutral, of course, there would be a 1 degree dead zone".

My reply:

Actually, the opposing springs also serve another purpose, which is to hold the cam at the neutral dwell point. I don't know if you have ever rotated a cam by hand when the roller follower is in contact with a dwell, but the force required to rotate the cam at the dwell point is practically zero, even with a high follower force.

With this design, the lever is only 6" long and about 1/4" diameter. However, even with a 200 pound follower roller load pushing into the cam dwell, just the weight of the small lever will rotate the cam off the dwell, after the lever is released(I have done this with prototypes). The force required to rotate the lever and/or cam when the roller is in contact with the dwell, is so small, I doubt you could hardly even measure it.

This is because the force from the rollers, (no matter how great) will not create any torque on the cam, or cause it to rotate in any way, when the rollers are in contact with the cam dwell.

So, something is needed to hold the cam at the neutral dwell point, and the small opposing springs connected on each side of the cam work very nice for this purpose.

Thanks again for all your help and feedback.

John