Sliding Velocities Of Gears

"While the geometry of a screw rotor profile is not that of an involute, it is similar enough at the pitch line for standard gear theory to apply."

If you take a perpendicular cross section of one of the lobes or 'rollers' of a rotary screw compressor, will you not get an involute gear form with the same lubrication requirement(s) as standard involute gears?

When all else fails consult with the manufacturer's technical support. Could the wear be attributed to dust or other foreign material passing thru the compressor? Sounds like a very unusual case.

Just one knight behind the pawns - that looks a very aggressive game. Does the picture show the beginnings of the board being overturned?

no. I usually lose more gracefully than that.

I'd assumed it was your opponent you were photographing...

Only in my dreams.

Just found my 'working' model (desk toy) of a "Sullair" rotary screw. Id not appear to conform to my earlier 'off the top of my head' analysis as the profiles of each rotor are different and mating but are not gear teeth as such.

There does appear to be sliding friction at work and if you are operating and maintaining the machine to manufacturer's recommendations then the manufacturer is the part to consult with at their customer service department if you are still encountering problems.

ss

Hi Stan

I am the factory tech support. The issue has more to do with pushing the technology envelope a bit than knowing what the cause is. The condition we are experiencing is properly identified as "scuffing" which involves exchange of material between gears or rotors through a "micro-welding" process (my description) where average surface temperature exceeds 360F and highly localized surface temperature is high enough for material from one rotor or gear can adhere to the other rotor or gear. This is different from "scoring" which usually involves debris passing through the rotor or gear set. My knowledge of gear technology is largely through self-education and experience. I believe that minimizing the sliding velocity of the rotor set will help eliminate the wear we are experiencing. As such, I need to be able to calculate it and don't have any guidance for how to calculate it.

If your screws have parallel axes (as I suspect), there can be no point on the surfaces where they can contact without at least a radial velocity mismatch during engaging and disengaging*, and only one radius at which the circumferential velocities match at any time.
If you don't need the ultimate output pressure, you can use slightly undersized screws that never actually contact. The gaps can in principle be made very small, but operation at 360 degF means that you would not only need very high precision machining, but also to select low-expansion materials whose expansion must also match - and this includes the drive train for the spiral gears, as these determine the relative positions of the threads. Maybe this is just a way of saying that it sounds pretty intractable (to me) to modify an existing design for long life in this application. I hope you can come up with a solution - you will have a humdinger of a product

*Unlike standard gear trains, there is no possibility to disengage before this at least starts.

Yes, these are parallel axis rotors. The 360F temperature is due to excessive friction and is local to the contact zone. The bulk metal temperature is closer to 200F as is the bulk oil temperature. The backlash of the set is between .004 and .006 inch. Profile clearances and tip clearances are of similar size except at the contact zone due to crowning of the main rotor.

As I understand the geometry, a perfect spur gear set using an ideal involute profile will have pure rolling contact throughout the contact zone ocurring along the line of action. A helical gearset, on the other hand, has some sliding due to the helical form of the gear teeth.

I intend to try to solve the problem by using a larger contact zone which keeps the teeth in contact for a greater angular displacement, spreading the load over a larger contact zone and reducing the pressure in the contact zone. Hopefully, it will prevent the breakdown of the oil film which will eliminate metal to metal contact and eliminate the wear problem. I would like to calculate the sliding velocity to guide me in this approach.

Please, if you think any of my assumptions are flawed, let me know.

Won't the worst-case sliding velocity increase as the square root** of the radial extent of the contacting region? That gives you a trade off between reduced contact pressure and increased sliding velocity - and I don't know whether that will be beneficial.

You probably already thought of everything that follows - if so, please regard it as my way of framing questions so that they are clear, rather than trying to teach you to suck eggs...

If you have design freedom, you will reduce both sliding velocity and pressure (assuming the system is spring loaded?) if you can use larger diameter gears.

Are you already using the lowest contact pressure that meets the pumping requirements?

What freedoms do you have regarding gear materials and oils? Can one of the gears retain some magnetic properties at the operating temperature, and allow you to use a lubricant with some magnetic properties? Do_you/can_you use a pair of gears of different materials that are non-binding?

**I think that is what happens to the sliding velocity as the worst part of the gear is just separating

Regards

Fyz

Regarding the worst case sliding velocity, I don't know. I don't know how to calculate it. The more I reduct contact pressure, the better able I am to maintain an oil film. As long as I maintain an oil film, the friction due to sliding should be significantly lower than metal to metal.

Don't worry about how you are framing your questions - I do the same thing as you can see from above. I do that so I don't miss something obvious and it doesn't always work so I appreciate what you are trying to do.

Larger diameter rotors are out of the question because I am trying to fix an existing compressor design with many installed units.

The contact pressure is determined by the pressure differential across the compressor, the density of the gas undergoing compression and the surface area of the contact zone, as I understand the physics. Please correct me where you find errors.

Dissimilar materials may help. At this point, we recommend that our customers use good quality synthetic oils, which they usually do. We have not tried any anti-wear additives, mostly due to the logistics of doing so. It is still on the table. The rotors are currently ductile iron so magnetism is not an issue. My concern is what the magnetic particles in the oil would do to the roller bearings.

Let's keep talking.

thanks for contributing.

The only thing I think I can directly help with is the theoretical value for the peak sliding velocity. But that occurs where the surfaces are joining and separating - i.e. where the pressure is lowest, and so this may not be the most important region. If the gears have radius R, the contacting region extends dR on either side, and they turn at W cycles/second, the peak sliding velocity (at closure and separation) will be 2.pi.W.R.2.sin(arccos(1/(1+dR/R)). That is approximately 2.pi.W.R.2.sqrt(2.dR/R), or 17.8*W*sqrt(R*dR).
BTW, I suspect that the problem with sliding is not just the damage it does when the oil is missing - it could also contribute to local heating of the oil and thinning of the film.

I don't even know enough to anticipate a problem with the roller bearings - I suggest you contact the technical help desk of the appropriate lubricant company about the effect of the oils on the roller bearings - I've always found technical experts to be very helpful once you've got some idea what you're asking for (maybe it's such a relief when someone has taken the trouble before asking??)

I know nothing about the way the contact pressure is generated in these machines - and I've never even seen one. So I shall doubtless expose my complete ignorance here. My assumption was that the manufacturer or the user sets the contact force to a sufficient level for the application, and the oil coverage would improve as the operating pressure increased and the oil was forced into the gears. The other possibility that I hadn't considered would be some sort of hydraulic feedback mechanism that generated the roller force from the pressure of the pumped fluid. If the latter, it might simply be that the arrangement is providing slightly too high a roller force for these operating conditions (for example not taking into account that the viscosity of the oil reduces as it heats).

Your comments might stimulate additional ideas - there's even a remote possibility that one of them could be useful.
(It sounds a challenging problem, to say the least.)

Regards

Fyz

This is a sketch of the offending components ( I just figured how to paste a picture in here). The intersecting circles are the pitch diameters of the respective rotors. The rotor on the right turns in a clockwise direction and is driving the rotor on the left. As I understand the equations you posted, the peak sliding velocity is for a gear whose pitch radius is R turning at w revolutions per second. Therefore the peak sliding velocity of the gearset is the combined peak velocities of each gear at their respective rotational speeds (not sure I worded that well).

Regarding the oil thinning, you and I are in agreement that localized heating is taking place, thinning out the oil. My working hypothesis is that the contact zone is too narrow for the contact pressure, squeezing the oil film to a point where contact between rotors ocurrs. Metal to metal contact generates more heat than otherwise is generated where a good oil film exists. That heat is then transferred to the oil which thins further. This leads me to believe there is a threshold where a sufficiently wide contact zone will promote a good oil film. The sliding velocity is working against me in that the higher the velocity, the more heating due to internal friction in the oil. However, (as I think about this some more) it may be possible to shape the leading edge of the right hand rotor to promote a hydrodynamic oil film as is done in fluid film bearings. This way, instead of fighting against the sliding action, I may be able to take advantage of it.

In this particular rotor set, the addendum of the right hand rotor is about 1 mm and the dedendum is about 1 mm. I can't do much with the addendum but I can extend the dedendum to about 5 mm. Since the rotor tip extends beyond the pitch circle by about 2 to 3 mm, I may be able to shape tip appropriately by putting a wedge shaped "ramp" which the oil film would act upon to force more separation between rotors and maintain a thicker oil film. Does that make sense?

The contact forces in a rotary screw compressor are generated in much the same way as in a gear pump where the differential pressure and the driving torque combine to create a reaction force at the line of contact between gears.

Regarding oil additives, I do talk to the lubricant manufacturer about the antiwear additives and other such questions. They are the oil gods, I am but a lowly serf. They are the ones that told me about the detrimental effects of the antiwear additives to the bearings. I am still considering it though.

Thanks. I had (as I three-quarters feared) completely misunderstood.

First, if (?) I've got it right now, the basic principle is different from what I had guessed: I now assume that the pumping action is identical to a standard gear pump, and the purpose of the helix is to minimise the vibrational effects of discontinuities in the driving arrangements. That could mean that the helix is rather slow?

Then, your radial contact position changes along the length of the helix. That makes for a different cause and amplitude for the sliding than I had assumed. Is the drawing to scale? If (??again) I read the text aright, that would correspond to something like a 6-mm separation of the axes. If so, the approximations that I made to calculate the sliding velocity would be invalid.

If I'm now holding the stick by the correct end, I'll have another go at a more appropriate calculation.

Fyz

No they are not to scale. the pitch diameter of the right rotor is 101.64 mm and the pitch diameter of the left rotor is 67.76 mm. The separation distance is 84.701 mm.

I think I have a better idea - but by no means comprehensive.

Right rotor diameter: 101.64mm
Left rotor diameter: 67.76-mm

It leaves the following initial uncertainties (many more about the specific shape of the gears to ensure continuous contact along the length of the spiral - but I think we can get some way without that detail of information)
Are there just four teeth around the circumference of the smaller rotor, or is that also a drawing simplification (if not, how many)?
What is the gear pitch along the axis? (for each gear separately - I think they should be in the ratio 2:3 to minimise unintended sliding)
Do both helices have the same handedness?

Thanks

Fyz

The left rotor has 4 teeth and a right hand helix with a 45 degree helix angle at the pitch diameter while the right rotor has a left hand helix with a 45 degree helix angle at the pitch diameter. Hand calculation verifies a 2:3 ratio of pitch diameters.

6-mm peak-to-peak height with a pitch of 50-mm. To my mind, that scary - probably my inexperience in the area. The principles I used for sliding velocity should still work in principle - but I'll think about the detail over the weekend. (Personally, I'd be quite concerned about the pressures at the localised driving points as well - I suppose that is why the long-life vacuum "roughers" I used drove both of the screws.

Best regards

Fyz

John

Now I have a slight understanding: can you increase the dedendum by those amounts without significantly increasing the pumped volume? If not that would increase the total pump force that you have to provide from the contacts; combined with the inevitable increase in the sliding velocity, it seems unlikely that increasing the depth would be productive.
There are conditions that could make this statement incorrect - such as there being significant losses that are independent of flow rate - in which case the increased throughput might assist with cooling. But I think you would have all sorts of other problems already if this was significant.

To my mind, the best way to increase the contact area is to reduce the pitch - say twice as many teeth around the circumference. You could then modify the dedendum to maintain the existing pumped volume.

Spiral gears generate significant axial forces, and it wasn't clear whether the bearings are designed for the increased level of force under these more severe operational conditions. It is also conceivable that you are exceeding the axial forces that the bearings are capable of sustaining before encountering problems. One way to avoid this would be to increase the axial pitch relative to the circumferential pitch (so that the angle was say 26.6 degrees instead of 45)

Regarding the temperature - have you been able to check whether the system is more durable if/when you provide cooler the inlet gases? If so, another lubricant manufacturer might be able to provide an oil that is more viscous at the operating temperature.

A final note for now - have you been able to check that the contact locations (where the wear occurs) are exactly where you would expect radially - and that they are the same throughout the length of the spirals? It may be that the various forces are moving or bending the gears - in which case you could perhaps either modify the dimensions or the shapes to recover the intended location. (It's not strictly relevant, but I believe that compressional rollers are often mounted with their axes slightly skewed to allow for bending effects. I suspect that this is neither practical (because of the support system) nor desirable (because of the operational range you need to cover).

Sorry this is a bit stream-of-consciousness - I'm just hoping something rings the correct bells

Regards

Fyz

In this case, I am defining the addenda and dedenda as the active or contacting parts of the profiles above and below the pitch diameters. On the right hand rotor, I can exted the dedendum up to about 7 mm and extend the addendum of the left hand rotor to match without significantly affecting the pumped volume. If I can maintain a hydrodynamic fluid film, the increased sliding velocity may be beneficial. I would need to shape the right rotor addendum and tip relief properly to prevent shearing away the boundary layer.

"To my mind, the best way to increase the contact area is to reduce the pitch - say twice as many teeth around the circumference. You could then modify the dedendum to maintain the existing pumped volume." I agree. The increased machining time makes this a less than desireable option due to the increased cost, 1 1/2 to 2 times greater than current plus retooling, a set of four cutters being about $100,000.00, so not a trivial option.

In a rotary screw compressor, the axial force due to the torque loads between rotors is not the primary axial load on the bearing set. The differential pressure between inlet and discharge acting on the transverse plane of each rotor is due to the large surface area of the transverse plane presented to the pressure. I have calculated thole loads for the worst case operating conditions and sized the bearings accordingly. The wear patterns on the bearings are normal for lightly to moderately loaded taper roller bearings.

We have insufficient data to prove or disprove sensitivity to inlet gas temperature. Reliable field data is hard to get and good engineering tests take 6 months for accurate results.

The wear patterns are generally evenly distributed along the pitch line and exactly where we expect them to be until they have been run for a couple thousand hours. After that, they become excessively wide and the crown is eventyally completely worn away.

That was one way to check that I was understanding the terms as they are properly used (I wasn't): as you doubtless deduced, I'd assumed addenda and dedenda to be the full depths of the pumping grooves.

Presumably your change means that the 'driving' region will become asymmetric wrt the zero-sliding point? (Or can you also move the bearings)

Regarding axial forces - I wasn't worried about strain on the bearings so much as side effects of distortion. Clearly, your observations show I was worrying unnecessarily.

It obviously doesn't matter, but I'm confused about the axial forces. For a 45-degree spiral (at least while there is an oil film), I expect the axial forces due to driving the gears should be approximately equal in magnitude to the circumferential force applied to the slave gear. Intuition (admittedly never a reliable guide to this sort of problem) suggests that this should be at least of the same magnitude as the net forces generated by the pressure of the pumped gas. (For what it is worth, that is based on the assumption that the axial force due to pumped gas should be nil in the sections of spirals that are effectively blind, and to approach the useful driving forces where there is flow along the channels).

As you are keeping the thread angle constant, I don't believe that increasing the addenda/dedenda will significantly increase the distance the oil will need to flow to escape the contact area.

Presumably an increased contact area for the drive region corresponds to an increased gap somewhere else in the rotation - or are you able to make sufficient modifications to the remainder of the shape for that to be untrue.

I believe that the equation I posted earlier should be valid for the peak sliding velocity in these regions.

Regards

Fyz

I confess. 'Tis I who distorted the definitions.

You are correct, the driving region will become asymmetric.

Regarding the axial forces, you are correct regarding the mechanical driving forces on the contact zone. The high axial loads of the bearings stem primarily from the pressure forces acting on the end planes of the rotors. I have a marked up picture to illustrate. Assume P1 is atmospheric pressure and P2 is 300 psig. The projected area on each end of the rotor upon which the pressure acts is the sum of all the areas of the rotor body, rotor end and bearing journal shoulder and is reduced to simply the cross section of the rotor taken at the transverse plane. That surface area for these rotors is about 10 square inches and is the same at each end. The resulting axial force on the bearing set is about 3000 lbf. The mechanically induced axial force is about 1/10 of that or less.

I believe I can make the necessary modifications to increase the contact area without significantly affecting the gaps ( and resulting leakage paths). Contact would begin about 10 degrees earlier in the rotation of the main rotor (in this picture, it is the one the arrows are pointing to). By increasing the addendum on the main rotor from 1 mm to 5 mm increases the length of the line of action from about 9 mm to about 30 mm and the length of the contact line on each tooth increases from about 13 mm to about 43 mm. I believe it is reasonable to assume that the contact area increases by about the same amount, allowing for some deformation due to Hertzian contact stresses.

By the way, I finally got "fyz". good one.

That was a most generous confession - I should never have found out. Thanks also for the illustration with annotation - I see that I had still misunderstood, as I had in mind an alternative arrangement that is more akin to a simple gear compressor, with the air flowing radially, and just uses the screw gears to remove the driving and sealing discontinuities. Here I think the air is driven along the axis. Apart from any sections that are 'blinded' at the ends by the housings, the differential pressure will presumably be over the whole areas, and not just the sections that are flat. The drive force will simply transfer a proportion of the pressure on the slave so that it appears on the driving gear - given the fill ratio, I guess that would be about half.

I agree your comments about contact area. What I was trying to indicate is that the increase in contact length should somewhat help to help keep the oil within the contact region, but the improvement in that regard (over and above what you will automatically get due to the reduced pressure) will probably be slight, because the flow along the radial curvature will not be that much reduced.

So far as I can see, given the constraints you are already doing everything practical to improve the situation - except perhaps for finding an oil supplier with a more helpful technical department (an activity for when the mods are in progress, I guess).

Regards

Fyz (yup - half the time I don't know what the Boz I am doing or talking about)

Fyz

With the longer contact line, I am hoping that the boundary layer of oil attached to each rotor will stay attached and that the viscous properties of the oil will keep the oil film thick enough to prevent metal to metal contact and the resulting excessive wear. I think by properly shaping the convergent area, we should be able to drag enough oil into the contact zone.

Thanks for being such a good sounding board. I think I can work out the mechanical part. Fluid film boundary layer theory mght be a different thing.

If anything I am trying to do doesn't make sense or you think of something else, let me know.

Thanks for posing the problem - and being willing to put up with my ignorance. It's been good for me and very instructive - I need something unfamiliar to think about from time to time.

I agree that the longer contact length should reduce any lateral slip of the oil (relative to the closing direction). The concern remains that backwards longitudinal slip may not be helped as as much one would like. With luck, the increased contact dimension will mean that the contact area should not get quite as hot; hopefully, that really is the root of the problem...

"Fluid film boundary layer theory might be a different thing."
You'd need accurate properties for the specific oil at the operating temperature...

Using search terms such as "sliding contact velocity in helical gears" will turn up the following and many other such references. Most require login and fee for the full papers.

Elastohydrodynamics of a Worm Gear Contact

Journal of Tribology -- April 2001 -- Volume 123, Issue 2, pp. 268-275

S. Kong, K. Sharif, H. P. Evans, and R. W. Snidle, Professor

School of Engineering, Cardiff University, CF2 3TA, United Kingdom

(Received February 8, 2000; revised June 16, 2000)

The paper is concerned with prediction of elastic contact and elastohydrodynamic film thickness in worm gears. Using the undeformed geometry of the gap between gear teeth in contact a three-dimensional elastic contact simulation technique has been developed for calculation of the true area of elastic contact under load relative to the wheel and worm surfaces. A parallel investigation of elastohydrodynamic lubrication effects has been carried out using a special non-Newtonian, thermal solver which takes account of the nonsymmetrical and spin aspects of worm contacts. An interesting feature of the results obtained is the discovery of regions of poor film forming due to entrainment failure at the edges of the contact.

Stan

Thanks for the reference

John

John, Stan

Unless I am hopelessly adrift here, this paper applies to a worm driving a cog, which is a completely different configuration. (N.B. there is little difficulty in calculating the sliding velocities in that case. Without actually reading the paper I can't be absolutely certain, but I think the paper is mainly about the behaviour of the oil and shaping the surfaces to assist in its retention. The basic physics of that is of course relevant, but the detail may not carry over too well to configurations where the sliding is a relatively small component, and pressure gradients relatively large.)

Having said that, Professor Snidle is almost certainly worth talking to if you can manage it.

Regards

Fyz

I wonder if they can do something with parallel axis helical screw rotors?