Screw Thread Measurement

While I was cutting threads for the Floor Lamp poles, I tried measuring my progress over wires:

Floor Lamp - tube fitting - thread measurement
Floor Lamp – tube fitting – thread measurement

Those are three lengths of music wire, slightly bent from their storage roll, held in place with a precision clamp metric micrometer. Given the crudity of the setup, the uncalibrated wire diameter, and my lack of thread-fu, the results came out both close and unconvincing.

A set of real thread measuring wires being cheap & readily available, I’m prepared for the next time around this block:

Thread Measuring Wires - eBay set
Thread Measuring Wires – eBay set

The 185 mil “wires” (they’re all allegedly ground rod) will let me cut threads matching things like a Jesus nut; they’re suited for 3 TPI / 8 mm pitch screws. Mostly, wires from the front row will be all I ever need.

Which look like this in action:

Thread Measuring Wires - eBay setThread Measuring Wires - detail
Thread Measuring Wires – eBay setThread Measuring Wires – detail

The black doodad (the set includes half a dozen for all the wire sizes) fits over the micrometer anvil and holds two wires betwixt anvil and screw, leaving me to manipulate the screw, the third wire, and the micrometer with my remaining hands. Hence the vise holding the micrometer, which is known to be Very Bad Practice.

From the side:

Thread Measuring Wires - overview
Thread Measuring Wires – overview

All of the smaller wires measure 0.5 mil too thin, which is likely due to my lack of calibrated measurement equipment:

Thread Measuring Wires - scant 24 mil
Thread Measuring Wires – scant 24 mil

The few thread pitch diameters I measured also came out slightly too small, again likely due to calibration and screw tolerances.

The LittleMachineShop description of measuring threads over wires seems entirely adequate.

To forestall link rot, a slightly rearranged version of their tables of wire constants:

Thread Wire Measurement Constants
Thread Wire Measurement Constants

The lower table has metric thread pitches with the wire sizes in inches.

You measure the distance over the recommended wire (in inches or millimeters, as appropriate), subtract the constant, and get the pitch diameter in the same units. Conversely, add the constant to the desired pitch diameter to get the target over-wire distance, carefully cut the thread until it measures a bit less than that, back up sixty seconds, and cut it spot on.

Verily, it is written: there is no UnDo key (⎌) in machine shop work.

Floor Lamp: Threaded Fittings

The reshaped copper elbow on the floor lamp now has the right angle, but lacks threaded connections to the tubes. The OEM tube threads are close to M15×1, thus prompting the change gear exercise persuading Tiny Lathe™ to cut metric threads.

Chuck up a length of 5/8 inch aluminum tube, clean up the end, and poke a thread runout slot into it:

Floor Lamp - tube fitting - thread runout
Floor Lamp – tube fitting – thread runout

Turn the soon-to-be-thread OD to 14.7 mm, well under the minimum 14.794 mm major thread diameter. I figure it’s better to match the existing not-quite-standard tube threads than to get all fussy about tolerances:

Floor Lamp - tube fitting - thread OD
Floor Lamp – tube fitting – thread OD

Drill out the tube to 27/64 inch = 0.422 inch = 10.7 mm, a bit larger than the OEM fittings, to easily pass the JST-SM connector I added so I could take the lamp apart:

Floor Lamp - tube fitting - drilling bore
Floor Lamp – tube fitting – drilling bore

Yeah, you’re not supposed to let the swarf build up like that, but it’s hard to stop when you’re getting good chip.

Break the sharp edges:

Floor Lamp - tube fitting - ready for threading
Floor Lamp – tube fitting – ready for threading

Set up for threading:

Floor Lamp - tube fitting - external threading setup
Floor Lamp – tube fitting – external threading setup

That’s a really nice Warner laydown threader I won as a Cabin Fever door prize quite some years ago.

A comprehensive discussion of threading may be handy.

The compound is at 90° to the cross slide, because the DRO housing doesn’t let the compound swivel to the proper angle for thread cutting. I’m just ramming the threader straight into the tube, taking sissy cuts, and hoping for the best.

Kiss the OD with the cutter, set the cross slide DRO to zero, position the cutter just off the end of the tube, close the split nuts around the leadscrew, engage the threading dial at a conspicuous mark:

Mini-Lathe Threading Dial - aligned
Mini-Lathe Threading Dial – aligned

The first real pass looked good:

Floor Lamp - tube fitting - first thread pass
Floor Lamp – tube fitting – first thread pass

The runout slot is 1/16 inch = 1.6 mm wide and I’m running the lathe dead slow, so there’s plenty of time to punch the STOP button as the cutter enters the slot and let the spindle coast down. Flip the switch to REVERSE, crank the cross slide out a turn (1 mm with 0.3 mm of crank backlash), run the cutter back to the starting point, crank the cross slide in, and iterate until the fitting screws into one of the OEM lamp tubes:

Floor Lamp - tube fitting - final thread
Floor Lamp – tube fitting – final thread

The 5/8 inch tube is just a smidge too small for the copper fitting, so knurl the fitting to enlarge the OD slightly more than a smidge:

Floor Lamp - tube fitting - knurled
Floor Lamp – tube fitting – knurled

Break the knurl edges, part off the fitting, clean up the new end, and do it all over again:

Floor Lamp - tube fitting - threaded adapters
Floor Lamp – tube fitting – threaded adapters

The knurls got filed down to an exact slip fit in the copper elbow and will eventually be epoxied in place.

The cut-off tube on the lamp head also needs internal threads, so bore out the interior to flatten the weld seam:

Floor Lamp - tube fitting - cleaning tube bore
Floor Lamp – tube fitting – cleaning tube bore

No pix of the threading, but you have the general idea; the tube wall is a scant 0.6 mm thick, so this isn’t the place for full-spec threads. I stopped when the OEM tube screwed in place.

Apart from the hideous solder job, it came together pretty well:

Floor Lamp - tube fitting - unpainted
Floor Lamp – tube fitting – unpainted

It’s much more stable than Kapton-wrapped tubes jammed into a bare copper fitting, although that’s not saying much.

A rattle-can finish seems appropriate …

Mini-Lathe: Threading Dial Alignment

As received, the mini-lathe’s threading dial was misaligned by about 1/4 division, which is nearly halfway to the next engagement point midway between the divisions:

Mini-Lathe Threading Dial - as received - colorized
Mini-Lathe Threading Dial – as received – colorized

I added the red lacquer crayon while contemplating what to do, because I thought the dial was swaged onto the shaft. It turns out to be threaded, so I marked where the dial should be, grabbed the shaft in the (soft-jawed) bench vise, and twisted the dial with a Vise-Grip until it lined up:

Mini-Lathe Threading Dial - aligned
Mini-Lathe Threading Dial – aligned

Well, it’s closer than it was, OK?

There’s about that much slop on either side of the index line coming from the loose gear engaging the leadscrew, so that’s as good as it gets.

Mini-Lathe: Metric Change Gear Tables

Running my assortment of custom 3D printed change gears through the LittleMachineShop calculator and copying the results into a spreadsheet for E-Z formatting produces a useful table:

The same table in text-ish format, minus the colored highlights marking the custom gears:

PitchABCDActualErrorIn 10 pitches
0.10
208020800.0990.786%0.008
207920800.1000.468%0.005
208020790.1000.468%0.005
0.20
207940800.2010.473%0.009
208040790.2010.473%0.009
407920800.2010.473%0.009
408020790.2010.473%0.009
0.25
205535810.2490.225%0.006
208135550.2490.225%0.006
355520810.2490.225%0.006
0.30
205735650.3000.023%0.001
206535570.3000.023%0.001
0.40
205545650.4000.088%0.004
206545550.4000.088%0.004
0.50
215045600.5000.012%0.001
216045500.5000.012%0.001
218060500.5000.012%0.001
423521800.5000.012%0.001
605021800.5000.012%0.001
0.60
355740650.6000.022%0.001
356540570.6000.022%0.001
405735650.6000.022%0.001
406535570.6000.022%0.001
0.70
355545650.6990.087%0.006
356545550.6990.087%0.006
455535650.6990.087%0.006
456535550.6990.087%0.006
507755810.7000.006%0.000
508155770.7000.006%0.000
557750810.7000.006%0.000
0.75
425045800.7500.012%0.001
428045500.7500.012%0.001
455042800.7500.012%0.001
458042500.7500.012%0.001
0.80
405545650.7990.088%0.007
406545550.7990.088%0.007
455540650.7990.088%0.007
456540550.7990.088%0.007
205579570.8000.010%0.001
205779550.8000.010%0.001
1.00
215060401.0000.012%0.001
425045601.0000.012%0.001
426045501.0000.012%0.001
428060501.0000.012%0.001
455042601.0000.012%0.001
456042501.0000.012%0.001
605042801.0000.012%0.001
1.25
215060321.2500.013%0.002
354045501.2500.013%0.002
424045601.2500.013%0.002
428060401.2500.013%0.002
454042601.2500.013%0.002
602021801.2500.013%0.002
604042801.2500.013%0.002
1.50
424045501.5000.013%0.002
454042501.5000.013%0.002
1.75
654257801.7510.029%0.005
2.00
424060502.0000.012%0.003
425060402.0000.012%0.003
604042502.0000.012%0.003
2.50
423260502.5000.012%0.003
424060402.5000.012%0.003
425060322.5000.012%0.003
602042802.5000.012%0.003
603242502.5000.012%0.003
3.00
655080553.0020.061%0.018
655580503.0020.061%0.018
805065553.0020.061%0.018
3.50
574065423.5010.029%0.010
574265403.5010.029%0.010
652157803.5010.029%0.010
654057423.5010.029%0.010
654257403.5010.029%0.010
4.00
602042504.0000.012%0.005
5.00
552160504.9890.215%0.107
553580404.9890.215%0.107
554080354.9890.215%0.107
602155504.9890.215%0.107
803555404.9890.215%0.107
804055354.9890.215%0.107
354581205.0010.012%0.006
455577205.0010.012%0.006
772045555.0010.012%0.006
Mini-Lathe Metric Change Gear Trains

The basic formulas:

TPI = 16 / ((A/B) x (C/D))
Pitch = 25.4 / TPI = 1.5875 x ((A/B) x (C/D))

So, for example, a 4-50-42-60 train will produce a 1 mm thread pitch with 120 ppm error adding up to a mere 1 micron in 10 pitches:

Mini-Lathe change gears - stacked 50-42 - installed
Mini-Lathe change gears – stacked 50-42 – installed

Overall, the errors are so low as to not matter, even without using the custom gears, but it’s the principle of the thing …

Mini-lathe Metric Threading: Stackable Change Gear Generator

Although OpenSCAD’s MCAD library includes a gear generator, I don’t profess to understand the relations between reality and its myriad parameters, plus I vaguely recall it has a peculiar definition for Diametral Pitch (or some such). Rather than fiddle with all that, I start with an SVG outline from Inkscape’s Gears extension and go all 3D on it.

So, the “gear blank” looks like this after extruding the SVG:

Mini-lathe change gear - 42 tooth - SVG import
Mini-lathe change gear – 42 tooth – SVG import

Producing this is a lot easier in OpenSCAD than in real life:

Mini-lathe change gear - 42 tooth - solid model
Mini-lathe change gear – 42 tooth – solid model

OpenSCAD centers the blank’s bounding box at XY=0, which won’t be exactly on the bore centerline for gears with an odd number of teeth. One tooth sits at 0° and two teeth bracket 180°, so the bounding box will be a little short on one side

A reference for gear nomenclature & calculations will come in handy.

For a 21 tooth module 1 gear, which should be pretty close to the worst case in terms of offset:

  • Pitch dia = d = 21 × 1 = 21 mm
  • Tip dia = da = d + 2m = 23 mm
  • Tip radius = da/2 = 11.5 mm
  • Tooth-to-tooth angle = 360/21 = 17.143°
  • Radius to tangent across adjacent teeth = 11.5 × cos 17.143°/2 = 11.372 mm

An actual metal 21 tooth gear measures 22.87 mm across a diameter, dead on what those numbers predict: 11.5 + 11.372 = 22.872 mm.

So the bounding box will be 11.5 mm toward the tooth at 0° and 11.372 mm toward the gap at 180°. The offset will be half that, with the tooth at 0° sitting 0.063 mm too close to the origin. Gears with more teeth will have smaller errors.

Given that we’re dealing with a gear “machined” from plastic goo, that’s definitely close enough:

Mini-Lathe change gears - 1 mm - 45-50-45-60
Mini-Lathe change gears – 1 mm – 45-50-45-60

That’s an earlier version with the debossed legend.

The code can also generate stacked gears for the BC shaft in the middle:

Mini-lathe change gear - 42-55 tooth stacked - solid model
Mini-lathe change gear – 42-55 tooth stacked – solid model

In principle, the key locking the gears together isn’t needed and the bore could fit the inner shaft, rather than the keyed bushing, but then you’d (well, I’d) be at risk of losing the bushing + key in one easy operation.

So it’s better to go with the bushing:

Mini-Lathe change gears - stacked 50-42 - installed
Mini-Lathe change gears – stacked 50-42 – installed

Now, to cut some threads!

The OpenSCAD source code as a GitHub Gist:

Monthly Image: Wappinger Dam Gears

A walk around Wappinger Lake brought me to the old penstock controls:

Wappinger Dam - old penstock gearing - E view
Wappinger Dam – old penstock gearing – E view

Still meshed after all these years:

Wappinger Dam - old penstock gearing - SE view
Wappinger Dam – old penstock gearing – SE view

The “new” penstock intake control, a pair of utterly practical and totally non-photogenic screw drives, sits just to the left of these relics.

A night view of the penstock from some years ago:

Wappingers Falls Bridge - Pixel XL HDR - 2017-09-22
Wappingers Falls Bridge – Pixel XL HDR – 2017-09-22

It still carries water to the recently refurbished power plant downstream on the right.

Those gears will remain meshed after everything else rots away …

Mini-Lathe Metric Threading: 42 Tooth Gear

Going from a 21 tooth gear to a 42 tooth gear means you must reduce the remaining train ratio by a factor of two for a given thread pitch. Here’s a 42-50-45-60 train, with the same -125 ppm error as the 21-50-60-40 train and no screw / washer clearance issues between the A screw and the C gear:

Mini-Lathe change gears - 1 mm - 45-50-45-60
Mini-Lathe change gears – 1 mm – 45-50-45-60

The original 60-40 CD pair has a 3:2 ratio, the 45-60 CD pair is 3:4, so that’s where the factor-of-two reduction happens.

The first pass at the solid model included a debossed legend:

Mini-lathe 42 tooth change gear - Slic3r
Mini-lathe 42 tooth change gear – Slic3r

With a printed gear in hand, I realized the legend must be embossed below the surface, so as not to rub against an adjacent gear; better modeling is in order.

The general idea is to set Inkscape’s (known-good) gear generator to the correct gear parameters (module 1 → 3.14 mm circular pitch, 20° pressure angle):

Inkscape Gear Generator dialog
Inkscape Gear Generator dialog

Save the outline as an SVG:

Inkscape Gear Generator result
Inkscape Gear Generator result

If you do like I did and neatly position the gear at the bottom-left origin, all SVG viewers will show only the Quadrant I arc, probably because Inkscape sets the SVG file to display it that way. I’ve made that mistake before and maybe, someday, I’ll remember.

Load the SVG into OpenSCAD, which will find the entire gear, no matter where it falls in the coordinate space, and spike it at the origin:

linear_extrude(8.0,center=false,convexity=5) 
 import(file="/the-source-directory/Mini-Lathe/Change Gear - 42 teeth.svg",center=true);

The linear_extrude( … center=false … ) keeps the bottom of the blank at Z=0. The import( … center=true … ) puts the 2D shape at the XY origin. Because OpenSCAD centers the bounding box, gears with an odd number of teeth will be ever so slightly off-center, which would matter a whole lot more in a fancier machine tool than a mini-lathe.

All of which produces a tidy 3D gear blank:

Mini-lathe change gear - 42 tooth - SVG import
Mini-lathe change gear – 42 tooth – SVG import

OpenSCAD ignores SVG holes, which isn’t a problem for me, because I’d rather punch the bore, keyway, and so forth programatically.

But that’s another story …