I am reluctant to contribute to this thread as I feel it can only be covered if answered in depth, still here are a few pointers. First I like Ady's idea, as a control systems engineer solving a problem by a process of elimination is a good approach.
Michael is quite correct in suggesting that the spindle not being perpendicular to the machines table. However, I question the word “exactly” as a very slight error can work to ones benefit. I think it was Tubal Cain who recommended when setting up the Dore Westbury milling machine that there should be a very slight error.
If we consider a cut being taken to machine a surface, then inevitably one edge of the cutter will be lower than the other. Even the standards laid down for industrial machines allow this to be the case.
If the cut is being taken such that the leading edge is the highest then when the already machined surface reaches the rear edge this will also be attempting to make a cut, known as back cutting. There is though a major difference, the leading edge will be cutting on the outer diameter whilst the trailing edge the end of the end mill. More importantly, it will be at a very shallow angle to the surface resulting in a width of cut being much greater than that taken by the leading edge but extremely thin.
Unless the cutting edges are razor sharp then this will not be possible and the cutter will only bounce off the surface. As I often say, you cannot take a cut of 0.001mm deep if the edge has a radius on it of 0.002mm. As the workpiece is fed further the depth of cut being called for will increase and eventually the cutter will break through the surface causing a ring to appear. This is why keeping the end cutting edges of an end mill sharp is much more important than the outer diameter edges where surface finish is concerned.
If then the workpiece is fed the other way the trailing edge will be higher and back cutting will, in theory, be eliminated and a much better surface finish achieved. Whilst this is largely true another factor kicks in, that is vibration. As Ady states this is a major factor as whilst the trailing edge is in theory higher, the machine head bouncing up and down will allow the cutter to contact the surface occasionally. The finish will still be far superior to that when fed in the other direction.
If, and that is a big IF, the head is set exactly perpendicular, vibration will result in back cutting in either direction, albeit less than my first example but significantly worse than the second. This I think shows that a small error, as permitted by the machine standards, gives you a choice.
Our knowledgeable moderator, David, once told me that he used to put a little tweak in his CNC programming to eliminate back cutting, showing that perpendicular errors are still present in industrial machines. Vibration, whilst not totally eliminated, would be much less a factor I would have thought.
There is of course the situation where rather than the front and trailing edges being at differing heights, it is the two sides of the cutter. This results in a saw tooth surface but I think I have said enough.
If you go to my website, look in the new site index under T and find” Tramming and the effect on finish achieved” there is much more detail on the subject.
Of course, material spec, speed and feed are also important factors.
I wish I had room for a shaper Ady, lucky you.
Harold