For a given radial DOC when milling, the stability lobe diagram shows the combinations of axial DOC and spindle speed that will result in either chatter or stable milling. Slot milling is the least stable case, and NC programming based on stability for slotting automatically means that other radial DOC operations are also stable.
However, besides the stability issue when slotting, there are other constraints that have an impact on the choice of toolpath. For example, the geometry of the finished part is affected by the surface location error (SLE). Typical NC programming software only accounts for the kinematic motion of the tool, assuming the tool is a rigid cylinder and the workpiece is a rigid prism. However, the tool is a collection of cutting edges bound together, and the tool and the workpiece deflect in response to the cutting force. It is the combination of the deflections and the position of the cutting edges that imparts the finished surface (see the Machine Technology column in the August 2010 issue).
The finished surface is often mislocated, and the SLE is not intuitive. The surface location depends on the frequency of the teeth passing, dynamic characteristics of the system, helix angle, workpiece material and chip load.
To describe the effect of milling dynamics on the finished workpiece, Dr. Tony Schmitz at UNC Charlotte has produced a modified stability lobe diagram, including restrictions on SLE. He calls it the “super diagram” (Figures 1, 2 and 3).
All images courtesy of R. Zapata and T. Schmitz
Figure 1. Milling super diagram with the maximum SLE specified to be no more than 30µm and a chip load of 0.15mm per tooth.
The SLE in Figure 1 is specified to be no more than 30µm, and the chip load is set at 0.15mm per tooth. Black regions indicate the conditions where chatter would occur. White regions indicate where the machining would be stable and the SLE specification would be met. Gray regions indicate where the machining would be stable but the SLE specification would not be met. Figure 1 shows the SLE specification is not met in a large portion of the stable machining zone. The feasible machining conditions to satisfy stability and SLE criterea are mostly located around 40,000 rpm and less than a 2mm axial DOC or around 25,000 rpm and less than a 1mm axial DOC.
Interestingly, there are some regions where a larger axial DOC results in a better SLE than in regions with a smaller axial DOC. The super diagram only considers the maximum absolute SLE and does not, for instance, indicate surface roughness.
Relaxing the specification by allowing the SLE to be as large as 70µm results in the super diagram shown in Figure 2. In that case, a substantially larger feasible machining zone is available.
Figure 2. Milling super diagram with the maximum SLE specified to be no more than 70µm and a chip load of 0.15mm per tooth.
In a similar way, reducing the chip load opens up more feasible machining zones until, with a chip load of 0.075mm per tooth and a permissible SLE of 70µm, all stable cuts satisfy the SLE condition (Figure 3).
Figure 3. Milling super diagram with the maximum SLE specified to be no more than 70µm and a chip load of 0.075mm per tooth.
The milling super diagram can be created for any radial DOC. It is particularly useful in the process planning stage, where it serves as a guide to the NC programmer for selecting appropriate cutting conditions. CTE
Parameters used in the super diagram examplesParameterValue
Stiffness
5×106
Damping percentage
5
Natural frequency
2,400 Hz
Tool diameter
6.35mm
Helix angle
45°
Number of teeth
4
Tangential cutting
coefficient
700 N/mm2
Normal cutting coefficient
210 N/mm2
Feed per tooth
0.15 mm/tooth (Figures 1, 2)
0.075 mm/tooth (Figure 3)
Radial DOC
3.175mm
About the Author: Dr. Scott Smith is a professor and chair of the Department of Mechanical Engineering at the William States Lee College of Engineering, University of North Carolina at Charlotte, specializing in machine tool structural dynamics. Contact him via e-mail at kssmith@uncc.edu. For more information about the milling super diagram, see R. Zapata and T. Schmitz, 2009, “A New ‘Super Diagram’ for Describing Milling Dynamics,” Transactions of NAMRI/SME, 36: 245-252.
Related Glossary Terms
- chatter
chatter
Condition of vibration involving the machine, workpiece and cutting tool. Once this condition arises, it is often self-sustaining until the problem is corrected. Chatter can be identified when lines or grooves appear at regular intervals in the workpiece. These lines or grooves are caused by the teeth of the cutter as they vibrate in and out of the workpiece and their spacing depends on the frequency of vibration.
- cutting force
cutting force
Engagement of a tool’s cutting edge with a workpiece generates a cutting force. Such a cutting force combines tangential, feed and radial forces, which can be measured by a dynamometer. Of the three cutting force components, tangential force is the greatest. Tangential force generates torque and accounts for more than 95 percent of the machining power. See dynamometer.
- feed
feed
Rate of change of position of the tool as a whole, relative to the workpiece while cutting.
- gang cutting ( milling)
gang cutting ( milling)
Machining with several cutters mounted on a single arbor, generally for simultaneous cutting.
- helix angle
helix angle
Angle that the tool’s leading edge makes with the plane of its centerline.
- milling
milling
Machining operation in which metal or other material is removed by applying power to a rotating cutter. In vertical milling, the cutting tool is mounted vertically on the spindle. In horizontal milling, the cutting tool is mounted horizontally, either directly on the spindle or on an arbor. Horizontal milling is further broken down into conventional milling, where the cutter rotates opposite the direction of feed, or “up” into the workpiece; and climb milling, where the cutter rotates in the direction of feed, or “down” into the workpiece. Milling operations include plane or surface milling, endmilling, facemilling, angle milling, form milling and profiling.
- numerical control ( NC)
numerical control ( NC)
Any controlled equipment that allows an operator to program its movement by entering a series of coded numbers and symbols. See CNC, computer numerical control; DNC, direct numerical control.
- slotting
slotting
Machining, normally milling, that creates slots, grooves and similar recesses in workpieces, including T-slots and dovetails.
- stiffness
stiffness
1. Ability of a material or part to resist elastic deflection. 2. The rate of stress with respect to strain; the greater the stress required to produce a given strain, the stiffer the material is said to be. See dynamic stiffness; static stiffness.
- toolpath( cutter path)
toolpath( cutter path)
2-D or 3-D path generated by program code or a CAM system and followed by tool when machining a part.
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