Any good at mathematics, I need some help.

[moogieParticipant @moogie]

With slow going on my DIY lathe build, I’m trying to plan ahead for when I want to add single point cutting to it. This is where I need your help.  I’m trying to calculate the gearing required for a 1mm pitch thread. So with one turn of the chuck the carriage needs to move 1mm. I know there are electronic lead screw available but my budget doesn’t stretch  that far, so I’ll have to do it mechanically.  If someone could have a look at the images below and see if I’m correct in my calculations I would be very grateful. Thanks.

[duncan webster 1Participant @duncanwebster1]

Screwcutting via a rack and pinion ix unusual to say the least

[JasonBModerator @jasonb]

The majority of screwcutting lathes use a lead screw, your rack or feed shaft are likely to be less accurate and also have a lot of backlash. Cheapest option would be to redo it with a metric lead screw rather than the feed shaft. A groove along the screw will drive the feed and cross feed.

[moogieParticipant @moogie]

Thanks for the advice,  I’ll look into it and have a redesigned.

[JasonBModerator @jasonb]

I’m not sure the maths is right either but happy to be corrected.

Rack pitch x 15T = 94.2497mm per turn of the 15T gear

100/108 = 0.9259

1/26 = 0.0385

28/55 = .5091

24/48 = 0.5

 

So 0.9259 x 0.0385 x 0.5091 x 0.5 = 0.009

0.009 x 94.2497 = 0.8552mm per chuck rev

[JasonBModerator @jasonb]

Changing the 28T to 33T would get you quite close @ 1.007mm

[moogieParticipant @moogie]

Thanks Jason.

if i change the 100/108 to 100/92 that gets me 1.0039mm per chuck rev.

At least my calculation weren’t too far off, just one gear. Closer than i thought i would have gotten.

[DC31kParticipant @dc31k]

As above, the original gives 350/1287 x pi = 0.85mm plus change. The 0.8552 above is only good to two decimal places as fractions are better cancelled and then calculated not individually decimalised and then amalgamated.

The revised one gives 25/78 x pi = 1.01 minus change.

[Nigel Graham 2Participant @nigelgraham2]

Hmm.

It is better to use a leadscrew and change-wheels (or screw-cutting gearbox – which amounts to the same thing though is less fiddly to use).

If you can, use a much coarser pitch than 1mm. Without knowing the overall size of your lathe, I would suggest 3mm pitch as the mimium – this is pretty well the metric equivalent of the 1/8″ pitch on a 3/4″ dia screw, used on many small lathes such as the Myford series designed primarily for inch-based work.

It’s best to use a trapezoidal form of lead-screw thread, and this, together with appropriate nuts, is available as threaded stock rod from the likes of HPC Gears and other transmission-components stockists. These are of ground finish, intnded indeed for making lead-screws.

I don’t know trapezoidal metric screw-thread forms but would think from the ISO-M series of “ordinary” threads, a 3mm-pitch one would have an outside diameter about 20-25mm.

You could use standard studding, which is of right-hand thread (an important point I’ll come to) but it and the nuts will probably wear quite rapidly. If you do, then go for stainless-steel studding. From experience this has a decent surface finish whereas plain old zinc-plated mild-steel studding is often rough old stuff for holding the workshop together, not precision machine components! Use leaded-bronze or cast-iron (or aluminium alloy??) for the half-nuts on this.

 

Note the hand of the thread. It is commonly left-hand but can be a right-hand thread, with due regard to the drive from the spindle. That is normally via a tumbler reverse gear anyway, so you can cut threads of either hand.

You would need fit half-nuts, aka clasp nuts, otherwise you have to wind everything backwards for each iteration of the screw-cutting.

 

A lathe set up like this also needs a “Thread Dial Indicator” to show you when to re-engage the nuts for the next bite, so the tool always engages the thread correctly. It consists of a pinion, normally but perhaps not compulsorily of worm-wheel form, of appropriate pitch engaging the lead-screw, and directly rotating a dial with, usually, 8 divisions (at least on inch-pitch lathes). It is designed to be swung out of engagement when not in use, to save wear on this relatively fragile component. It allows the lathe to continue revolving, and in the same direction, throughout the operation, saving time but more importantly in our context, wear-and-tear on the motor and machinery.

The clasp-nut assembly does need careful fitting to ensure smooth operation, so each turn of its own thread always lines up when you close the nut around the leadscrew just when the TDI tells you.

Get it all right and it makes single-point screw-cutting a pleasure!

.

Jason suggests a groove (properly, a key-way) along the leadscrew to drive the normal turning feeds. This transfers the motion via a pinion bored to a close sliding fit on the leadscrew, with an internal key to engage the groove.

You can do that, I think some small lathes are so fitted; but if possible a separate, parallel, plain shaft with just a keyway for that function, is the better option. The headstock has a [screw-cutting – neutral – feed] selector mechanism on the gears linking the two shafts to the change-wheels so you can’t accidentally engage both at once.

 

Since you are fitting power cross as well as long feeds it’s wise to fit the feed direction selector with a simple locking control to prevent inadvertently moving it straight across its central neutral point and engaging the other direction. This can be interlocked with the feed ON/OFF lever.

(It was horribly easy to make that mistake on my old, IXL-badged Erhlich lathe. I used a bolt in the control’s locking-pin hole as a safety “blind”!)

.

A little extra since you have the luxury of designing your lathe from scratch:

If you can fit a trip-gear to the half-nut control, that is a bonus. It is adjusted to stop the travel when the tool reaches the end of the thread, and until you wind the cross-slide back the tool simply produces a groove round the work at that point. This is normally harmless. I usually cut a run-out groove to depth with a thin parting-tool anyway, if the work allows.

(Production-lathes intended for regular screw-cutting have more elaborate arrangements that stop the feed and retract the tool. A clue to that having been used is the thread stopping at a little run-out ramp instead of a radial groove right round the component. )

 

[Julie AnnParticipant @julieann]

An advantage of using a metric leadscrew with a rational pitch is that when cutting a metric thread the ratio between chuck and carriage movement is rational and hence an exact gear train can be calculated.

Using a rack with a rational module implicitly means that the linear pitch is irrational (due to pi) and hence any gear train will be an approximation.

Julie

[moogieParticipant @moogie]

Thanks everyone for the replies,  I think a redesign is required for the thread cutting and powered carriage and cross slide, but sure isn’t it all part of the fun of making something yourself. Your not supposed to get it correct first time as you won’t learn anything !!

Noel.

[moogieParticipant @moogie]

After a bit of a rethink,  this is what I have come up with.

Quick change gearbox will give me 1, 1.25, 1.5, 1.75, 2, 2.5, 3, 3.5 and 4mm pitches. As I don’t work with imperial,  metric will be fine. I can use an electric motor via a hex shaft to power the cross slide.

[JasonBModerator @jasonb]

What will you do for turning feed rates that are likely to be 1/10th or less than your finest screwcutting pitch or do you have enough of a reduction in the apron.

Left hand threads?

[SillyOldDufferModerator @sillyoldduffer]

Like it, but the pitches need attention; they’re too broad  This table lists the common metric pitches:

Note that a 2:1, 1:1, 1:2 gearbox after the main gearbox provides several related pitches.  Eg. 1.5 pitch can be converted to 0.75 and 3.0, and 1.0 gets 0,5 and 2.0 as well.

Dave

[JasonBModerator @jasonb]

But not many people bother to single point below M6 coarse so may well not be a problem for the OP.

There is allread a 2:1 in the gear box as half of those pitches are double the smaller ones.

[moogieParticipant @moogie]

The range of threads this will give me is more than enough for anything I’ll be making.  How often are left hand threads needed ? If I’m stuck I’ll use a tap as I can’t think at the moment how to achieve that.

The feed for the apron will be via an electric motor from an automatic door which has a 10:1 reduction gearbox and a cheep eBay 24v speed controller.

[moogieParticipant @moogie]

Thread reversing.  Is this what this leaver is for ? If so more thinking required. 🤔

[JasonBModerator @jasonb]

The “tumbler reverse” is a common way to reverse the leadscrew either for L/H threads or to return the carriage while keeping the leadscrew nuts engages.

If you are using the motor to move the carriage then no need to worry about feeding away from the head when turning as you can just run the motor the other way. So that aliviates a lot of the need to run the screw/feed shaft in both directions

I’ve not needed a L/H thread but you may want it for things like the ends of trackrods/suspension links for your cycle carts so you can adjust suspension geometry. or simply stop a part unscrewing itself like you find on bike pedals.

[moogie]

On moogie Said:

The range of threads this will give me is more than enough for anything I’ll be making.  How often are left hand threads needed ?…

Don’t jump to conclusions too quickly!   Although my workshop is deliberately metric throughout, I’m occasionally obliged to cut Imperial threads, and having a lathe that does both is convenient!

Only cut two left-hand threads in a decade, but what I do doesn’t call for them.   Left-hand threads are often  found on vehicles and machines.  Your lathe might need one!

Jason makes a good point about small diameter fine pitch threads being cut with taps and dies rather than turned on a lathe, but never say never.  I’ve made small taps on my lathe, and put fine threads on large diameter tubing – not threaded to a standard fastener size.

Taps and dies are hard work in larger sizes.   A lot of force is needed to cut an M42x4.5 bolt!  So, if I can, big diameter threads (for me M12 and above) are single point cut 80% deep in the lathe, and then finished with a die.  Owning a lathe that produces all the common pitches is more than convenient!

Always best to start a design by writing a Requirement, itself based on a list of needs and constraints.  Be clear about what the equipment is for.

moogies requirements might include:

The lathe shall:

1. cut metric threads [list]
2. cut Left AND Right-hand threads
3. traverse cut under power with 3 very fine threads [list]
4. allow the operator to select the thread from a conveniently placed gearbox, NOT by moving change gears on a Banjo.
5. support the following spindle speeds [list] to be provided by belt drive.
6. …

Now, before starting work on the actual lathe, customer and designer can review cost, features and risks on paper, which is dirt cheap.

• There’s a potential contradiction between requirement 4 (fast thread changing gearbox), and requirement 5 (slow changing belt-drive).
• Quite likely Requirement 1 is incomplete, and should be “cut Imperial threads [list] AND metric threads [list]“.
• Maybe Requirement 2 is over the top and should be “cut Right-hand threads only“.
• Maybe the customer jibs at the cost of Requirement 4, and changes it to “allow the operator to select the thread by moving change gears on a Banjo.”
• Are those [list]s complete and correct?
• Or customer reads the requirement and realises he needs a CNC mill instead…

Dave

[Author]

Posts