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 …

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