If the feed per tooth is set as one of cutting conditions, undeformed chip thickness is not equal to the feed per tooth.
Because these following things have an effect on undeformed chip thickness.
- Cutting edge angle (or Approach angle)
- Tool diameter
- Insert shape (polygonal and round inserts)
- Engage angle and disengage angle
Tool diameter is determined by machining area. For example, ae is larger than 80 mm, tool diameter must be larger than 80mm.
Engage angle and disengage angle are determined by machining conditions and tool path.
Thus, if these conditions are already determined, degree of freedom of changing undeformed chip thickness is low.
\( f_{zreal} = f_{z} \cos \left( \theta_{approach} \right) \cos \left( \theta_{engage} \right) \)
\( f_{zreal} \):undeformed chip thickness (nominal thickness of cut)
\( f_{z} \):Feed per tooth
\( \theta_{approach} \):Approach angle
\( \theta_{engage} \):Engage angle or disengage angle(you have to select the angle which can maximize the undeformed chip thickness)
\( \theta_{engage} \) is 0 degree on a center cut.
However, if the machining process is changed to shoulder milling, \( \theta_{engage} \) becomes smaller.
Larger cutter diameter and smaller radial depth of cut on shoulder milling are able to reduce an engage angle.
However, in this situation, a real cutting distance become longer, and a tool wear occurs faster.
Engage angle and disengage angle have an effect on tool failures and burr, too.
Engage angle determins which position of the cutting edge starts to engage the workpiece.
The position has three patterns; edge, one point of rake face, all points of rake face.
Especially, all points of rake face is the worst. Because of impulse force.
The situation occurs when R.R. is equel to the engage angle.
Engaging with the edge is the best. And then, engaging with one point of the rake face is better.
Disengage angle determins the undeformed chip thickness at disengage point of the workpiece.
If the undeformed chip thickness at disengage point is large, large cutting force suddenly goes to zero.
Thus, the tensile force is appled to the cutting edge.
The tensile force causes the breakage.
On the other hand, if the undeformed chip thickness at disengage point is small, workpiece near the disengege point is easy to be plastically deformed.
This plastic deformation leads to the burr.
This is a trade-off problem.
When you increase number of teeth to increase Material Removal Rate, the density of teeth is increased.
High density of teeth has the possibility to increase the number of engaged cutting teeth.
The number of engaged cutting teeth increases the change of cutting area during one tool rotation.
The situtation increases the cutting force, the workpiece displacement and the tool displacement.
The most inportant thing is that the increasing effect to the cutting force by the number of engaged cutting teeth is not equal to the increment of the main spindle power.
The following equation shows that the main splindle power is proportional to material removal rate, not to the number of engaged cutting teeth.
\(\displaystyle P_{c} = \cfrac{a_{p} a_{e} V_{f} K_{c}}{60 \times 10^6 \times \eta} = \cfrac{M_{RR} \times K_{c}}{60 \times 10^6 \times \eta} \)
\( P_{c} \):Main spindle power
\( a_{p} \):Axial depth of cut
\( a_{e} \):Radial depth of cut
\( V_{f} \):Feed speed
\( K_{c} \):Specific cutting force
\( \eta \):Machine efficiency
\( M_{RR} \):Material Removal Rate(Metal Removal Rate)
In this application, the real cutting distance shows the distance which the cutting edge actually machines the workpiece during one tool rotation.
The real cutting distance can be calculated with the tool diameter, the engage angle and the disengage angle.
In fact, feed per tooth affects real cutting distance, too.
"Cutting distance" shows the cutting tool moving distance.
"Real cutting distance" shows the scratching distance of the cutting tool and the workpiece.
Thus, this value is propotional to the tool wear.
For example, the real cutting distance of fz=0.1mm/t under the cutting distance=100mm is 2.5 longer than the real cutting distance of fz=0.25mm/t.
When the feed per tooth is increased largely, the creater wear tends to occur easily.
This is also the trade-off problem.