Milling feeds and depth of cut?

I think of the depth / diameter of cut in terms of surface area in contact with the tool. You want vise contact to be larger than tool contact. If I have to cut a slot, I don't go as deep per pass. It's a balancing act. With a 3/8" HSS end mill, I generally run about 0.100" depth for roughing. I am on a Bridgeport, so you would probably need to use less, perhaps start with 0.050"? Are you using any cutting oil or other lubricant? If not, try brushing some on.

x/tooth is more of a CNC thing. Most manual operators won't be able to get to the feed rates involved. Feed based on cut feel and sound. Avoid climb cuts, they are more likely to grab the part and move it in the vise. It looks like you're making a T-Nut? Try a longer piece and make a few at the same time. Try to use the whole width of the vise jaws, a larger grip is less likely to slip. If you can't, use the middle of the jaws. If you're off to the side, it's more likely to lose grip. I just made some for my lathe, here's what I did...

Cut a 6" long piece of material, the length of the vise jaws. Use parallels to hold it up so I can access the sides to cut down. Conventional cut the sides, you can cut both ways, just use the back side of the part for the other direction. In my case, I only needed one pass, because I was using a carbide rougher and the machine is rigid enough to handle it. Start slow, make a pass at, say, 0.020" and see how it feels when cutting. Increase slowly so you can more easily detect problems before the part moves. You shouldn't have to use much force to turn the handwheel. Once the T shape is made, use the bandsaw to cut them down, then drill/tap.

The previous post had a good thought, rotate the part 90 degrees and drop it down for a better grip and do one side at a time.
 
The suggestion that my mill is not appropriate for climb cutting may be the key. Even though I understood what a climb cut is, I had not understood that as something to be avoided. (Kind of stupid, as I knew to avoid climb cuts with a wood router). I was feeding in both directions, a no-no. The climb cuts may be the root cause of my issues with part holding and end mill breaking. Presumably I can travel in the "climb cut" directions if I don't feed before I do that. The correct sequence, then, would be to cut in the right direction, reverse the direction of travel, feed the desired amount, and then make a second pass.
I would guess that your machine would handle a climb cut spring pass on the return but not much more. It's all about backlash and machine mass/rigidity.

I did not think about the depth of cut as a percentage of the tool diameter.
Feed/tooth and stepover is not something manual machinists really even think about. I never thought about until I had CNC equipment, even after 40 years of manually turning cranks. It took me a while to adjust my thinking about the way an end mill works. Now I apply what I have learned from CNC setup to manual machining also and have better results.

What do you do when you are forced to cut the full tool diameter, as when machining a slot? Take very light cuts? I have been drilling before cutting a slot, as using the end mill as a drill did not seem to work very well.
End mills don't like to plunge straight into the material. Drilling an undersize starter hole or ramping in is the proper way to cut a full width slot. I think in the case of a mill-drill is is not really practical to try to ramp into the cut, so a drilled starter hole is the best option.
 
If you are cutting a slot that reaches an edge, lots of plunge cut with a stepover of no more than 1/4 to 1/3 of the end mill can be useful, followed by a finish pass to widen and clean up both sided of the slot.

Plunge cutting helps a lot of flexible tool issues!

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I will state something which has been omitted.

Look at your CHIPS.

They should be uniform looking and look they have been cleanly cut from the metal. They shouldn't look tortured and torn.
They should not be too thick, or shavings-thin.
They should not look like they were harvested from the burning gates of hell (not excessively discolored).

I frequently must work with "mystery metal". I make my best guess at what it is, but I can be wrong. The character of the metal you are cutting can change what you want for your RPMs and Feeds. Sometimes the material you want to work is "variable". I have to machine welded parts from time to time, and sometimes the welds can be surprisingly hard. Other times, shockingly soft.

The appearance of the chips tell me a LOT. It is always the first evaluation you do, when things are "not quite right".
 
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