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

 

[mfgenggear]

3DDave
that is a great find. star for you my friend

excerpt from the white paper

Figure 1.4 Schematic of Cylindrical and Globoidal Worm Gear Pairs
ZA: straight sided axial profile
Convolute heiicoid ZN: straight sided normal profile (straight line generator) (slightly concave axial proflie)
ZI : Involute helicoid
ZK: milled helicoid
Single-enveloping (no straight lines anywhere. conical cutter with
(cylindrical) straight generators)
wormgear drives
ZC1: circular arc profile on
worm grinding wheel
ZC ZC2: circular arc profile in
(circular arc generator) worm normal section
ZC3: circular arc profile In
worm axial section
Typel: worm profile has straight generators(straight line blade)
Double-enveloping Typet: worm profile has straight generators(piane grinding wheel) [gioboidan
wormgear drives
Type3: worm Is generated with conical cutterigrinding wheel

 

[mfgenggear]

RichardWattMatrix (Computer)(OP)11 May 21 07:16
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_form...),

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

Hi Richard
is this in fact a ZK worm.
I have software that can create a DXF of the geometry.
Its old software created by a old barber coleman engineer,(software engineering service) he use to design the tool hobs & cutters.
I use to rely on these guys to design and build my custom hobs and cutters.
barber coleman was purchased by Gleason I believe.

yup that is correct
Pi/(DP*#Thds)= L correction oops
or
Pi/Cp = DP
I am forgetting critical data.

So Spigor thanks for that correction on the ZK worm I getting my wires crossed I was quoting ZA
which is straight sided. I gave you a star my friend.

edit so to add to that when I started when there were no computers, so we had to rely on contact pattern, between a master worm, and the worm wheel at a set center distance.
now with software it's easy, same with spiral and zerol bevels. little history but off topic. with the dxf file geometry
should be able to cad/cam post the XY machine code. or take actual XY measurements in cad.

 

[RichardWattMatrix]

Hi mfgenggear,

Yes, it's definitely a ZK worm according to the drawing that we have (it was provided by a customer asking if our machines can grind ZK worms), so I'm not sure if I can share it for confidentiality reasons.

Richard

 

[mfgenggear]

Richard
do you have center distance?

 

[RichardWattMatrix]

mfgenggear - yes, the value I have for center distance is 105.65 mm.

 

[mfgenggear]

Richard
ok let's start over my computations on my software are not calculating correct, some thing is wrong
give me all the data for both the worm and worm gear
My software are inputs are in normal, need # of teeth for both worm and gear
normal pressure angle , double check the gear wire and measurement over wires.
normal pressure angle

or give me the transverse data and I will pull my notes to calculate normal.
it should say on the drawing if it is normal or transverse data.
since my inputs are in inches I have to convert from mm to inch.

 

[RichardWattMatrix]

mfgenggear,

The data I have from the drawing we were given is as follows (I only have a drawing for the worm gear itself and not the worm wheel):
[ul]
[li]Worm Type: ZK[/li]
[li]Number of teeth (Z): 2[/li]
[li]Normal module (m[sub]x[/sub]): 2.3565[/li]
[li]Normal pressure angle (α[sub]n[/sub]: 15 degrees[/li]
[li]Modification coefficient (x): --[/li]
[li]Hand: left[/li]
[li]Lead angle (γ): 14.9770 degrees[/li]
[li]Reference diameter (d): 18.2367 mm[/li]
[li]Tip diameter (d[sub]a[/sub]): 23 mm[/li]
[li]Root diameter (d[sub]f[/sub]): 11.3 mm[/li]
[li]Tip radius (ρ[sub]a[/sub]): 0.25 - 0.45 mm[/li]
[li]Root radius (ρ[sub]f[/sub]): 0.5 - 0.9 mm[/li]
[li]Dimension over pins (Mdk): 23/683 +- 0.015 mm[/li]
[li]Best pin (DM): 5.0 mm[/li]
[/ul]
The only other information on the drawing are the accuracy and technical requirements, but I don't think they're relevant here.

I'm also going to try using MITCalc on my computer at home to see if I can come up with anything.

Many thanks,
Richard

 

[spigor]

I have checked the worm data you have provided in the messages above and made some calculations of the macrogeometry, so let's let the numbers speak.

The data in your last message is consistent except for:
-The lead angle should be 14.9772 degrees - just for the record as this has no real life meaning.
-The dimension over Ø5 pins was specified as 23.000 and 23/683. In such case the tips would get pointed way before the Ø23. I suspect that Ø5 is incorrect, as it should be approx. Ø3.85. Please check it and let know what the pin diameter should really be, and what the dimension over pins is - 23.000 or 23.683?

 

[mfgenggear]

Hi Guys
I am getting the same results as spigor, I have the same questions

MOW
lead angle

My programs were calculating closer but I got funky results on the actual worm geometry.

the Major diameter and the MOW are the same size. the mow measurement will have interference from the gear tip diameter.
I believe the worm addendum and dedendum are incorrect? the whole depth ?
I would recommend to check design with MIT with both worm & gear worm.

Richard please advise if this is a new design from the customer? they may possibly have errors
if not get a sample part if possible to review.

here is a good read on mfg of worms wheel hobs, & worm & worm gears

http://www.tokugawa-gears.com/Hobs technology/Worm wheel hobs.pdf

and

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

 

[mfgenggear]

So the results are in Inch
Normal Circular Tooth Thickness = .085185 (based on 23MM ) If posted mow is incorrect, I can input correct mow if necessary.
Ref Diameter (Pitch Diameter) =.7179904
Ref Base Diameter = .4984344
lead = .6034248
root dia. clears the gear wire by .0335
except I did not get pointed teeth I calculated Normal Tooth Thickness at major diameter =.038287 INCH
best wire in english is .178129

 

[mfgenggear]

I have not run numbers on worm in while.
A standard tooth thickness is .157 inch.
.085 is way to thin, when I get chance I will calculate an mow for this worm.
Now make sure the customer is not given
A measurement over one wire.
We need to calculate over two wires for
Two threads. Even thou it would be preferred with one wire measurement for inspection.

 

[RichardWattMatrix]

Hi mfgenggear and spigor,

Thank you so much for running those parameters through for me: I'm off work today and tomorrow due to the flexible furlough scheme my employer's using, so I've just logged on quickly.

This drawing was submitted to us by a customer making an enquiry (I think as part of a tender/quote request) to see if our machines & software could grind the ZK worm part and it's possible that the drawing is incorrect, like you've said (some of my colleagues have mentioned this as well).

Unfortunately, I don't have any more information on the drawing to hand as I'm at home as I type this so will have to look for some more details (if we have them) when I'm back in the office on Monday.

Richard

 

[spigor]

How about assuming a realistic tooth thickness and moving forward?

 

[spigor]

I have taken worm data as follows:
[ul]
[li]Worm Type: ZK[/li]
[li]Number of teeth (Z): 2[/li]
[li]Normal module (mx): 2.3565[/li]
[li]Normal pressure angle (αn: 15 degrees[/li]
[li]Modification coefficient (x): --[/li]
[li]Hand: left[/li]
[li]Lead angle (γ): 14.9772 degrees[/li]
[li]Reference diameter (d): 18.2367 mm[/li]
[li]Tip diameter (da): 23 mm[/li]
[li]Root diameter (df): 11.3 mm[/li]
[li]Axial tooth thickness on reference diameter: 3.83175 mm[/li]
[/ul]
I calculated the worm profiles on the axial plane, as requested - ZN, ZK/D0=200 mm and ZI forms for your reference:

ZN:
x; y; z
0.992899; 5.655016; 0
1.068107; 5.934158; 0
1.143036; 6.213308; 0
1.217723; 6.492466; 0
1.292197; 6.77163; 0
1.366483; 7.0508; 0
1.440604; 7.329976; 0
1.514576; 7.609156; 0
1.588417; 7.88834; 0
1.662139; 8.167528; 0
1.735755; 8.446719; 0
1.809274; 8.725914; 0
1.882705; 9.005111; 0
1.956057; 9.28431; 0
2.029336; 9.563512; 0
2.102548; 9.842716; 0
2.1757; 10.12192; 0
2.248796; 10.40113; 0
2.32184; 10.68034; 0
2.394836; 10.95955; 0
2.467788; 11.23876; 0

ZI
x; y; z
1.362954; 6.566138; 0
1.375764; 6.679398; 0
1.393514; 6.812788; 0
1.416659; 6.965151; 0
1.445503; 7.135273; 0
1.480212; 7.321916; 0
1.520836; 7.523851; 0
1.567323; 7.739881; 0
1.619545; 7.96886; 0
1.677317; 8.209706; 0
1.740409; 8.461405; 0
1.808567; 8.723017; 0
1.881519; 8.993678; 0
1.958988; 9.272596; 0
2.040698; 9.559048; 0
2.126376; 9.852376; 0
2.215762; 10.15199; 0
2.308606; 10.45734; 0
2.40467; 10.76794; 0
2.503733; 11.08335; 0
2.605586; 11.40318; 0

ZK D0=200
x; y; z
1.341905; 6.493639; 0
1.357162; 6.619352; 0
1.377517; 6.763952; 0
1.403314; 6.926276; 0
1.434753; 7.105117; 0
1.471912; 7.299268; 0
1.514763; 7.507547; 0
1.563194; 7.728817; 0
1.617032; 7.961999; 0
1.676055; 8.206084; 0
1.74001; 8.46013; 0
1.808629; 8.72327; 0
1.881631; 8.994709; 0
1.958736; 9.273719; 0
2.039669; 9.55964; 0
2.124162; 9.85187; 0
2.211961; 10.14986; 0
2.302822; 10.45313; 0
2.396517; 10.76122; 0
2.492831; 11.07374; 0
2.591565; 11.39031; 0

I also attach a dxf file with the profiles.
Between the lowest point generated by the cutter and the root diameter there will be a transition curve, dependent on the tool tip radius.

 

[RichardWattMatrix]

Hi spigor,

Going back to your question about the MOW, it's definitely 23.683 mm from the drawing (I just realised I'd entered as 23.0000 in our application, so I've changed that, but it's still giving me some errors that I need to look into).

I'd have to ask if we'd be able to get a sample part from the customer - we usually just get a drawing at quote/tender stage and then they supply parts for acceptance testing if they place an order.

Many thanks to everyone so far,
Richard

 

[spigor]

Then the wire diameter must be wrong, is it not Ø4?

 

[RichardWattMatrix]

The wire diameter is given as "Best Pin DM 5.0 diameter" on the drawing, but it could still be wrong and could be 3.85 as was suggested earlier.

The lead that mfgenggear calculated in inches works out as around 15.3270 mm to 4 decimal places, which is what I calculated myself.

 

[mfgenggear]

Richard
Based on the previous attachment provided :
Quote: Flank form K (worm ZK)
This is obtained with a grinding wheel or with a large diameter milling cutter with straight-sided
flanks inclined by an average angle Ym (figure N°4). The flanks that are obtained are slightly
convex and the amount of this convexity is determined according to the helix of the thread and to
the diameter of the tool. The smaller the tool’s diameter is, the closer this type of profile will be to N
type. Unquote

Based on the above, to obtain the correct geometry the wheel will be dressed straight sided. inclined at Ym
an operator will rough feed in with the Hold Depth and back off for roughing, the Measurement Over Wires/Balls (M.O.W.)
will be for roughing. taking an actual measurement the operator will then feed in to the required finish M.O.W.
a setup part (1st Run) The operator should verify the roughing and the Involute should be within .0254 MM or less
this will verify the correct involute.
what is critical is obtaining the correct roughing and finishing M.O.W. for the operator. (old school)
many new CNC controllers have measuring compensation which can do it automatically.
Turn an aluminum blank and run 2 parts to verify the above. Just run with it, Then check it on a CNC Gear checker for the correct Involute.
this is the best way to verify the results, in order to get the correct Involute the Module and Pressure Angle has to be correct.
the M.O.W. to to obtain the correct circular Tooth Thickness. which maintains the correct center distance. Piece of cake.
a sample part will be the master to verify results with M.O.W and Involute Check, that is a plus.
Have the estimator to allow for the extra cost of these setups, I believe you will be fine, with the thread grinder.
I had operators do many of these in the past. I ran this with my program I wrote many years ago, and Purchased software.

let:
2 T
Normal Module 2.3565 (10.77869722 NDP)
Normal Pressure Angle 15 Deg.
Lead Angle 14.9770 Deg.
Pin/Ball Dimeter 5 mm (.19685039 inch)
Dimension over 2 Wires/Balls
23.698/23.668 mm (.932992/931811 Inch)
normal CTT = 2.3515/2.34340 mm (.09258/.09226 Inch)
Transverse CTT =9.1000/9.06805 mm(.35827/.35701 Inch)
The Pin or Ball Clears the Tip Dia by .34798 mm(.0137 Inch)
The Pin or Ball Clears the Root by 1.18364 mm (.0466 Inch)

 

[mfgenggear]

I tried to draw the worm in Inventor, it's an approximation, I gave a bogus # teeth for the worm wheel.
the circular pitch is correct but the helix angle is slightly off.

 

[spigor]

Could you please now make an axial cutout of the worm to get its axial profile and compare it with mine? I would be interested to see the differences.