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DRAFT!!!!!!   Understanding Chip Thinning

Chip Thinning effects are really important when using Ball End Mills.
There are two types: Radial Chip Thinning and Axial Chip Thinning
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On a ballnose tool, any cut that meets the tool at less than the full radius of curvature will behave differently than a more standard milling cut. The chip thickness and the advance per tooth will not be the same—the chip thickness will be less. The diagram shows geometrically why this is. As a result of the thinner chip, the advance per tooth can be increased to achieve a higher linear feed rate, resulting in a higher metal removal rate for an application that was already employing a relatively light depth of cut. Again, the effect is most commonly associated with ballnose tools in high speed machining

The diagram also shows the direction of force. The force on the tool shown here is not directed laterally, but instead is directed along the diagonal dashed line from the material up to the centerpoint of the tool’s curve. In other words, instead of being directed all along X and Y, some of the cutting force is directed up into Z, a more rigid axis of the machine, resulting in a more stable cut.
It is common knowledge that a chip produced through a milling process is not of uniform thickness. Assuming climb milling, the chip is thicker towards its beginning than its end. Every chip has a maximum thickness at a single point and gets gradually thinner from there. Given a constant spindle speed and feedrate, the thickness of a chip is a function of its length; the longer the chip, the thicker the chip. And the length  of a chip is a function of the radial depth of cut, or cut width, established in most CAM systems with the stepover parameter. 
Chip load is often confused with chip thickness. In reality, however, chip load, in the prevalent use of the term, is nothing more than a federate expressed in inches per tooth (IPT). IPT × RPM × #flutes = IPM. The IPT value is equal to the thickness of the chip if and only if the width of cut is greater than or equal to 50% of the tool diameter. When the cut width is less than 50% of tool diameter, the maximum chip thickness is less than the IPT value. Again see Figure 1. The feed per tooth values that cutting tool manufacturers recommend are valuable in calculating a feedrate,but they are not the thickness of the chips that will be produced. 

The limiting factor in the application of the radial chip thinning phenomenon is, as per usual, one of practicality rather than one of theory. The calculation is straightforward, but there are serious limitations: The chip thinning calculation is only applicable when the width of cut remains close to constant, and when the cut width is quite small to begin with. In other words, it’s really only useful when finish milling vertical walls, where the cut width is small and minimally variable, for reasons put forth below. This means, of course, that this popular concept can only be used for removing about 1% of the material that gets milled on a daily basis. It is not applicable to rough milling, which is where about 99% of all material gets removed.

If radial chip thinning could be applied to rough milling, huge productivity gains could be had. Though discussions of radial chip thinning are nothing new, the ability to predictably control the maximum thick- ness of a chip during roughing operations very much is. The key is to forget about chip thinning, and focus on active chip thickness control. 
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Varying Cut Widths
Cut widths regularly vary in rough milling. Although it is physically impossible to have no variance in cut width when rough milling, the toolpath that drives the tool can have a huge impact in minimizing that varia- tion.

All machinists know through experience that tradi- tional toolpaths cause uneven tool loads. Any time there is a directional change, a connection from the end of one cut to the beginning of the next, or mo- tion through the center of an area, examples of each of which are depicted in red in Figure 2, the load increases. These increases in load are the direct result of an increase in cut width. As the cut width increases, the chip gets longer, and its thickness increases ac- cordingly. If you have increased the feedrate so that  the chip thickness is at its rated maximum, the results can be catastrophic when these load increases occur, and they will occur. So applying chip thinning calcula- tions to traditional rough milling processes is simply a non-starter.

There are high-speed milling toolpaths on the market that address these changes in cut width to varying degrees, but most of these fail to produce a constant cut width. The fact that the load spikes depicted in Figure 2 (previous page) are predominantly avoided enables the use of more aggressive milling param- eters. But, with one exception, these toolpath technolo- gies actually reduce the percentage of toolpath length that cuts with a constant width. Traditional toolpaths are at least perfectly constant in cut width between their numerous instances of terribleness. Most of these new high speed technologies, in contrast, have virtu- ally no constant cut widths. Don’t be misled; these new toolpaths are superior to traditional methods, at least in specific geometric configurations, in that they avoid many of the load spikes. But they actually move further away from the ideal machining conditions of a constant-width cut, rather than closer to them.
Importantly, there is another common, though not well known, circumstance where the chip thickness, and therefore load on the tool, increases, one that hap- pens with all existing toolpath technologies. And since it is an artifact of simple geometric axioms, it cannot   be avoided. Whenever a cutting tool transitions from cutting along a straight line onto a path of convex curvature (generally a G3 move, assuming climb milling), the engagement angle between the tool and the material increases. This happens even when the radial depth of cut, the cut width, remains perfectly constant. See Figure 3. This happens with any type of toolpath, even those designed to actively manage the   tool engagement angle. It is a simple function of cut- ting material with a round cutting tool, and therefore cannot be circumvented in the world of milling.
The fact that this increase in engagement angle is unavoidable is clear. But the most detrimental aspect of this dynamic is that it happens so quickly. As shown in Figure 4 (see next page), the increase occurs in the span of distance/time from when the periphery of the tool intersects the point of tangency between the linear and circular portions of the current in-process material   boundary, as established by the previous cut, to when the center of the cutter is normal to the same point on the current cut, a short span indeed. This dynamic is in play because of the concentric-natured construction of toolpaths: Whenever arcs are offset from one another in successive cuts within a toolpath, they are concen- tric with each other. It is this geometric configuration that ensures that this spike in tool load is ever present. 

To produce chips of consistent thickness, it is impera- tive to drive cutting tools along a path that maintains a constant width of cut, and that spreads the unavoid   able increase in tool load inherent with entering CCW arcs across a larger distance, and therefore longer time span. Fortunately this is now possible with the latest version of some new toolpath technology. The ideal cutting conditions that these constant-cut-width toolpaths provide has been proven in thousands of cases over the past few years. Combining those well established machining benefits with non-concentric spacing of arcs of adjacent cuts makes chip thickness control possible. Instead of just observing chips getting thinner as they taper to their ends, it is now possible to actively control the maximum thickness of the chips, enabling machine tools and cutting tools to perform even better, and reducing cycle times even further.
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