ZK worm parameters 5

[RichardWattMatrix]

Hello,

I am working with an existing software application that generates dressing programs for different types of threads and worms and I have been asked to look into its support for ZK type worms.

I have been reading up the documentation we have on this (sadly some of it appears to have been lost when the company has moved offices over the years) and I've found some research papers on the internet which have given me some assistance so far, for example, "ZK-Type Dual-Lead Worm and Worm Gear Drives: Geometry" by B-W Bair and Professor C-B Tsay from the Transactions of the ASME journal in September 1998, along with a copy of the DIN 3975 standard that has helped and a few of the internal design notes.

The application I'm working with does ask for some standard values such as tip (OD) diameter, reference (pitch) circle diameter, root diameter, helix angle, whether it's a single- or dual-lead worm, whether it's right- or left-hand worm and the lead.

It does ask for some data about the generating tool: pressure angles, helix angle, tip & root fillet radii, tip width and tip diameter.

I was wondering if anyone would be able to guide me on what data would be provided on a schematic for a ZK worm please?

Many thanks,

Richard Watt

 

[RichardWattMatrix]

I'd just like to add to my initial post since I've found some more information since then: we've received a sample drawing from a customer of a ZK worm part which now gives me an idea of one possible set of data that could be provided (I've put the DIN 3975 symbol after each item):

[ul]
[li]Number of teeth (z[sub]1[/sub])[/li]
[li]Normal module (m[sup]n[/sup])[/li]
[li]Normal pressure angle (α[sub]n[/sub])[/li]
[li]Hand (left/right)[/li]
[li]Lead angle (γ)[/li]
[li]Reference diameter (d[sub]m1[/sub])[/li]
[li]Tip diameter (d[sub]a1[/sub])[/li]
[li]Root diameter (d[sub]f1[/sub])[/li]
[li]Tip radius (ρ[sup]a1[/sup])[/li]
[li]Root radius (ρ[sub]f1[/sub])[/li]
[/ul]

I can then calculate the following from the above:

[ul]
[li]Axial pressure angle (α[sub]x[/sub])[/li]
[li]Axial pitch (p[sub]x[/sub])[/li]
[li]Axial module (m[sub]x[/sub])[/li]
[li]Lead (p[sub]z1[/sub])[/li]
[/ul]

From my reading of the DIN 3975 standard, the minimum data required to "define the worm flank form beyond all doubt" are:

[ul]
[li]Milling/grinding cutter diameter (d[sub]0[/sub])[/li]
[li]Worm parameters:
[ul]
[li]Number of teeth (z[sub]1[/sub])[/li]
[li]Module (m)[/li]
[li]Reference lead angle (γ[sub]m[/sub])[/li]
[/ul]
[/li]
[li]Or:
[ul]
[li]Reference diameter (d[sub]m1[/sub])[/li]
[li]Angle of generation (α[sub]0[/sub])[/li][/li]
[/ul]
[/ul]

This standard also mentions that as the cutter diameter (d[sub]0[/sub]) increases, then the ZK worm approximates more and more to the ZI form, which we already have working in our application, and as the value of d[sub]0[/sub] decreases, then the ZK worm approximates more and more to the ZN form, which we also have in our application: if I knew what the value of d[sub]0[/sub] where this changeover occurs was, I could then have our application use the ZI or ZN code according to the value of d[sub]0[/sub].

I would like to now calculate the (X,Y) coordinates for the set of points that define the ZK tool and worm profiles and was wondering if anyone knows how this would be done please?

 

[spigor]

All that you have written above seems to be right to me.

I would like to now calculate the (X,Y) coordinates...

apps.dtic.mil/dtic/tr/fulltext/u2/a239134.pdf
Page 324.
Might be reasonable to get a newer edition of this book.
I could calculate the profile coordinates based on your example numbers, so we could see if the results match.

 

[mfgenggear]

Richard
typically worm gears have to be cut with a hob that has the same attributes of the worm. an a master worm is used to inspect pattern and center distance. the hob will be slightly larger than the worm.
typically a worm if single thread will be machined like a thread, if dual lead can then be machined as a helical gear. there are many ways to machine the worm, single point on a lathe, thread grind or hobbed.
if it is dual lead it can be inspected with 2 wires, a single lead requires three wires. important to under stand the mfg method used. a worm and worm gear must be machined as a set to control pattern and
center distance. here a short paper from gear technology.

https://www.geartechnology.com/issues/1013x/worm_gears.pdf

 

[RichardWattMatrix]

Hi everyone,

Apologies for being away from the thread for a while: we've managed to find a ZK worm drawing submitted to us by a customer so I've been using that to help me.

spigor: what data would you need in order to calculate the profile coordinates please?

mfgenggear: I do have a number of papers and a copy of the book suggested by spigor, and I did save a copy of that article. Unfortunately, I am flying a little bit blind on this as my predecessor did include ZK worms but the documentation he left seems to be incomplete (and there have been at least 2 office moves since he was here), and we're trying to verify it.

I have been making some progress using the customer-provided drawing as test data - I'll dig it out and add the parameters it lists later on.

 

[spigor]

Usually:
-number of starts of the worm,
-reference diameter of the worm,
-lead angle on that reference diameter (or/and axial pitch/axial module - with the lead angle redundant but helpful for checking),
-axial tooth thickness on that reference diameter,
-major and minor diameters of the worm,
-profile angle (also called pressure angle),
-tool diameter.

 

[mfgenggear]

Richard

I am a little confused so bare with me, what type of machine are you trying to program? why would you need the profile coordinates?
are you trying to mill these? Like I said in the previous post worms are single pointed cut with a standard tool.
like cutting a thread, based on the pitch held by the machine and the angle & geometry is on the tool, it chases the worm like 7 or more passes. it would help immensely
to know the manufacturing method and inspection method, for instance a CMM vs cnc gear checker. most gears are now done with a cnc gear checker.
is this a one only or low production, or a medium to high production. for a higher AGMA class a worm must be ground as a thread.
the worm profile is held by the tool. similar would be like cutting a rack. example would be 20 deg. pressure angle except straight sided.
a worm can be hobbed, but it's produced by the tool geometry also. so generally a grinding tool would be dressed but now a days it is pre programmed and
the pertinent data is imputed to the cnc controls. # teeth or starts, pressure angle, lead angle and so on. so what are the required inputs for your machine,
and does it have to be cad/cam post to get the machine code to generate the tool?

 

[BrianE22]

The method used to cut the worm, either a single point tool squared to the workpiece, single point tool tilted at the lead angle, milled, hobbed, or with a grinding wheel with the grinding wheel tilted at the lead angle will produce different profiles of the worm tooth. It's the "generating" action of the cut and the fact that the cutting tool has a different lead angle along the profile (tooth root to tooth tip). The grinding wheel diameter will make a difference in the profile of the tooth. The effect is more pronounced for larger lead angles.

You can produce a straight sided worm with a grinding wheel that has a not straight sided profile. I'd guess the OP is designing software to control the profile of the dressing of a grinding wheel or maybe maybe for a gear tooth profile measurement machine.

 

[mfgenggear]

Brian
It is true, with cnc controls the dressing of the wheel is done automatically. And slight adjustments can be by tilting the wheel while dressing. I basically grew up with old style mechanical dressing where as engineering had to produce the data settings for the machinist to set up his or her machine. However the formulas were supplied by the manufacturer. With the new cnc dialog input all the data is easier. All they have to do is input the gear data. Or worm data. Bow a days there is software out there that can generate an exact gear profile. Within .0001 inch. Trying to recall a good book for that. Buckingham had good formulas, as well as vogel

 

[spigor]

In case of the ZK form some geometrical correlations tend to get more complex than for the ZN and ZI forms. I believe that the OP wants to calculate the grinding wheel's profile to grind the ZK form. The grinding wheel's diameter can be much different from the milling cutter's diameter. The profile of the wheel should compensate for that, as well as for the changes of the grinding wheel's diameter after each profiling. On the other hand, I haven't seen a tool diameter specified on a drawing. If no tool's diameter is specified on the drawing, ZI form could be used. Is it really necessary to use the ZK form? Is there the tool's diameter specified on the part drawing?

 

[mfgenggear]

spigor

almost never is a wheel diameter called out on the drawing. sometimes the wheels have to be dress to remove interference. usually done with single point diamonds like an od grinder.
if that is the case OP needs the tooth space width, but correct me if I am incorrect a worm is like a rack straight sided. only pressure angle is required with the correct tooth space thickness.
it should be easily drawn with cad. and like autocad with a lisp command, I am not a solid works guy but I believe it has a rack and spur gear module. I know freecad does but I don't know how accurate it is.
what actually corrects the geometry is the machine when it interpolates the circular or axial pitch.

 

[mfgenggear]

also as long as the worm and worm gear are cut with the same geometry and are made as a match set that is what is important, unless it is cross axis helicals.

 

[spigor]

mfgenggear

The ZI and ZK forms are not straight sided in no plane. In case of ZK the tool is disc shaped, in case of ZI it can also be thought of as a disc cutter with large diameter. That tool is tilted at a specific angle. That lead angle is specified on the reference diameter of the worm, but on every other diameter the angle of a helix is different from the lead angle. So e.g. at the tool tip the angle of the helix is different from the tool tilt angle. The tool will therefore cut outside the normal plane, as governed by the laws of conjugated surfaces. So in case of the ZK form the profile in the axial plane is dependent on the tool diameter. If this diameter is not called out on the drawing, ZI form could be assumed for safety. But in case of higher lead angles the difference between ZI and ZK as cut with a milling cutter could be big enough to cause manufacturing problems - uneven stock, long grinding times etc., and it doesn't look very professional. That might explain why the OP wants to calculate the ZK profile exactly. He could then calculate the profile corrections for the wheel to grind the exact shape no matter the wheel diameter.

 

[RichardWattMatrix]

mfgenggear,

spigor is correct in that I wish to calculate the grinding wheel profile for a ZK worm as the application generates the NC dressing program to do that based on the worm data entered by the user.

Our application runs on a Siemens 840D sl machine's PCU and generates these dressing programs - it can also be run on a laptop or desktop PC.

Richard

 

[RichardWattMatrix]

Hi spigor,

Thank you for getting back to me - I'm sorry I haven't been on the forum for a few days as I'm currently working on this flexible furlough rota and I'm not allowed to do any work on the days I'n off (the UK government is checking and has already taken a few people to court for breaking this law).

The worm parameters we have are as follows:

Number of starts: 2
Ref diameter: 18.2367 mm
Axial pitch: 7.6635 mm
Axial tooth thickness: we don't have the PLT for this worm, but we have the measuring wire diameter as 5.0000 mm and the size over the wires as 23.0000 mm
Major & minor diameters: the tip diameter is 23.0000 mm and the root diameter is 11.3.000 mm
Profile (pressure) angle: 15.0000 degrees
Tool diameter: we have a tool tip diameter of 200.0000 mm

The worm is a dual lead left-handed thread

Please let me know if you need any other details.

Best regards,

Richard

 

[spigor]

Hi Richard
I was under the impression that the idea is that you would calculate the profile coordinates first, what would possibly bring answers to many of your previous questions, and I double-check your results afterwards. But tables have turned, so for now I need to clarify as follows:
1. Should the x,y coordinates be calculated? That implies points on a plane - an axial plane, or a plane perpendicular to the axis?
2. Or maybe it is the tool's profile in its normal plane that should be found? If the tool tip diameter is 200 mm then what is the ZK form tool diameter? If it is also 200 mm, then this profile would simply be a straight sided reference profile with nothing to calculate.

 

[RichardWattMatrix]

Hi spigor,

Sorry, that's my misunderstanding - I'm still working on the ZK profile calculation code we have as I can't get a full set of profile coordinates myself just yet.

[ol 1]
[li]We calculate the X, Y coordinates for the worm profile on the axial plane.[/li]
[li]The application has a "tool tip diameter" parameter - I've been trying to work out if this refers to the actual tip diameter of the tool or the cutter diameter mentioned in the DIN 3975 standard but I've had no luck yet.[/li]
[li][/li]
[/ol]

So I've tried to work out the tool (cutter) diameter as follows:

[ul]
[li]Worm tooth depth = 5.8500 mm[/li]
[li]Worm tip-Worm ref = (23.0000 - 18.2367) = 4.7633 mm[/li]
[li]Worm ref-Worm root = (18.2367 - 11.3000) = 6.9367 mm[/li]
[li]Tool tip diameter = 200.0000 mm[/li]
[li]Tool diameter (cutter diameter) = 193.0633 mm[/li]
[/ul]

I remembered I do have a set of profile coordinates already calculated and saved to a formatted text file: I'm having some issues attaching it from my work computer, so I'll have to attach it when I get home.

The code calculates the tool profile first and then uses coordinate transformations to calculate the worm profile from the tool profile, but the root point on the worm is about 0.5 mm higher on the Y axis (radius = 6.3912 mm) than where I think it should be (radius = 5.8500 mm).

It does add the tip and root fillet radii arcs in later once it's adjusted the profile to meet the 3-wire or caliper measurement criteria.

I was also wondering if anyone has used the MITcalc tool to help design a ZK worm (I do have a trial version at home that I can reinstall and put the parameters into to see what that provides)?

I apologize for drip-feeding information as I don't want to overload the thread with too much information (as sometimes I post stuff that isn't relevant to what I'm asking about).

Many thanks,
Richard

Edit 10/04/2021 18:59 BST: attached the ZK worm profile coordinates file I mentioned earlier for spigor's reference.

 

[mfgenggear]

Guys I had to take dog to the vet,
So I not at home.

please provide the lead, diametral pitch
And helix angle.
Thanks

 

[RichardWattMatrix]

Hi mfgenggear,

The lead is 15.3270 mm for both leads (since it's a dual lead worm) and the helix angle is 14.9770 degrees.

I had a little trouble with the diametral pitch as I googled the formula and I found one on Engineers' Edge (

https://www.engineersedge.com/gears/worm_gear_formula_table_13534.htm),

but the description and formula in their table is a little confusing:

The description says that you use Worm Lead = "3.1416 / Diametral Pitch * Number of Threads on Worm", but the formula is written as "Worm Lead = 3.1416 * Diametral Pitch Number of Threads on Worm".

I tried rearranging this to get the diametral pitch, but I was getting a value of around 0.4, which doesn't seem right to me.


I do, however, have the axial pitch, which is 7.6635 mm, if that helps?

Thanks,

Richard

 

[3DDave]

Here's a fat read which may be of more general interest; no idea if it applies to ZK worms in particular, but it looks like good background info.

https://core.ac.uk/download/pdf/153776393.pdf

191 pages.