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A beginner's video for turning a lidded box .... youtube search, first hit.
Adding some more concerning technique and differences ...
Take a block of wood and stand it on the lathe ways with the end grain facing up ... if it were mounted on the spindle, then the sides of the blank would be end grain and long grain (cutting with the grain of the wood as opposed to across it ... there may be another term for this, but I don't recall it at the moment). Hollowing it out would then be face grain cutting, as you are cutting across the grain and with the grain, as you progress through each revolution.
In turning a bowl, you will be turning end grain or face grain or long grain - all three, as a bowl is a 3D object with multiple complex curves ... the major difference between that and turning a small lidded box is that generally, with the box, you'll be turning endgrain almost exclusively while hollowing, and spindle turning or face grain while turning the sides. Long grain turning on a box is generally eliminated, because you generally will have end grain along the axis of the spindle, with the example block from above laying on it's side, with end grain against your spindle and tailstock ends, all the sides facing out, as in spindle turning.
Now ... in bowl turning, the tools used most often are bowl gouges. This is probably a surprise to new wood turners... :tongue:
The Bowl Gouge
You will learn to master the gouge to do multiple types of cuts. The hollow of the gouge, or flute, is there to help present the edge of the tool as you work your way round the work piece as well as channel the cuttings away from the tool tip so that you can see what you are doing.
In cutting end grain with the gouge, a shearing cut is probably one of the best, leaving a very clean and uncompressed (little to no burnishing) surface, but is difficult to master as it does NOT use the bevel to guide the cut. It leaves a finely cut surface that requires little to no sanding before finishing. Present the tool at a 90 degree angle to the work surface, bevel facing directly AWAY from the surface .... roll the tool very slightly out (top away, bottom towards the work) and gently make contact. Keep the tool tight against the tool rest, pivoting on that contact point as you control the tool tip with the BACK of the tool handle. Longer is better ... more leverage and finer control.
In cutting face or long grain with the gouge, using the bevel to guide the cut is the best course for easy work. Keep tool tight against tool rest ... come in at a steep angle to let the bevel make contact with the work, and then raise the handle from the BACK of the tool to put the cutting edge into contact with the wood. Longer handles are better, for leverage and finer control.
Presenting the gouge at a negative rake angle takes the gouge's bevel away from the work in order to achieve a scraping cut. Again, with no bevel, there's little to no burnishing, leaving a surface that may be fine enough to immediately skip to finishing, with little to no sanding required. It is more difficult to keep the tool under control, as the bevel would normally prevent the tool tip from digging into the work too deeply. Scrapers have a much blunter tip in order to prevent this from happening. Start with the tool tip UNDER the center of rotation (tool rest will seem to be too low) and the back of the tool held HIGH (above the tool tip) with the tool tight against the tool rest. Advance the tool slowly to make contact with the work. Long handles can help to keep the tool under control, but advancing the tool will be more problematic, as there is only you to guide it ... the levering action will be negated without the bevel in play.
As you can see, the bowl gouge is made for multiple purposes. You can turn an entire bowl or lidded box or even pens with just one single bowl gouge. The only things a bowl gouge does NOT do well is anything requiring a square sharp corner or parting something off of the lathe.
The Skew
A skew is great for spindle turning, but has little application in bowl turning ... You could use it to shape the outside of the bowl to some degree, but then you're done with it. It's great for getting a box's outsides round and shaped properly. The most used cuts for boxes will generally be the peeling cut, to help you get down to your target exterior size. The slicing cut with the skew can then help you create an even cylinder to reach your starting point, but then you'll generally put the skew away. Skews can also be used for scraping, but scrapers generally do the job just a bit better and can get into tighter quarters.
What a skew excels at, and other tools fall far behind on, is making beads and finely evened (level) surfaces. Also, nothing else in your chisel collection will achieve a peeling cut nearly as well as a skew can. The peel cut is achieved with the tool handle held far down, tool tight against tool rest, make contact with the bevel ... holding the skew at the angle of it's grind, to present the edge of the blade equally against the work. Lift the tool handle (long handles are best, for this), to present the edge to the work and you'll see why it's called the peel cut in one hell of a hurry. Nothing else removes material quite as fast ... it's excellent for making tenons in a hurry.
A skew can give you sharp corners, provided you can get the tool to fit in there, and can also be used to part off from the lathe. You can turn an entire spindle project with just the skew, but hallowing something with the skew is practically impossible. Now ... if you do all your hallowing by just drilling on the lathe, that could be a different story...
The Scraper
Scrapers come in several shapes and sizes, some with a rounded tip and some with a squared tip. They are generally quite blunt, in appearance, and are designed to be presented with a zero angle or negative angle in order to achieve their cutting action. The bevel is not actually designed to be held in contact with the work ... just the tip. The bevel of a scraper is meant only to reinforce the cutting tip to avoid chipping and breakage. The larger the scraper, the better, as larger, heavier scrapers tend to "chatter" or vibrate less. Use it in the same way I described using the bowl gouge as a scraper.
Scrapers, with their blunter tips, can get away with having a SMALLER handle, for close in work. They are excellent for getting into tight spaces and cutting on end grain, though they work OK for face turning. Scrapers are meant to be used for hollowing objects, and with shorter handles you can easily get into the hollow of a bowl or lidded box to do your work, allowing you to hold the tool at various angles you may find unworkable for a long handled bowl gouge. Many detail tools are scrapers, in design.
The Parting Tool
The diamond parting tool has very little use in bowl turning, other than parting something off the lathe or setting your tenon. In fact, I've only used my parting tool TWICE, since I bought it .... it's very wide to be using for pens, so I haven't turned much with it. I generally part items off using a home made THIN parting tool that I made in my shop.
I went to a big box store and grabbed a cheap(ish) demolition blade (Diablo ... 4 bucks for one, it was decent size at around 7 inches long, and nearly 1/16th inch thick). I shaped it on my belt sander to remove all the teeth and profile the tip to my liking, then I drilled holes through the back of the blade and mounted a wooden handle to it for easier handling.
The THIN parting tool I made is excellent and gets the most use with making pens and saving as much as I can of the cutoff material, but it also shines for parting off a lid with as little of the grain pattern lost as possible, in order to have lids and box bodies that match grain patterns when closed. The same principle is applied for penmaking, to match the grain pattern from one section of the pen to the next.
To use it ... hold the tool tight against the tool rest, and present the bevel to the work ... lift the tool handle to achieve a peeling cut that digs into the work. Make certain you are holding the tool vertically! For every half inch or so of depth, you will need to go back and make a relief cut to allow for your blade clearance so that you can cut deeper without "burning" your work.
A last bit of concern with parting things off the lathe .... Even with a thin parting tool, the wood fibers and grain may be weakened if you make the box or bowl's bottom too thin as you are parting it off, and it will tear the center of the hollow completely out. Always ensure that you are giving yourself at least 1/4" for clearance so that the wood has enough strength to survive the parting process. Sometimes, it may also be best to just get it somewhat close on the lathe, and finish the last inch or so on the bandsaw or with a hand saw and clean it up with some very sharp wood chisels. There is no shame in taking the time to do it by hand if your lathe or your work material gives you difficulty!