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Power and Stability Limits in Milling
Power and Stability Limits in Milling S. Smith' (21, W. R. Winfough2, H. J. Borchers3 Department of Mechanical Engineering and Engineering Science, University of North Carolina a t Charlotte, Charlotte, USA 2The lngersoll Milling Machine Company, Rockford, USA 3Thelngersoll Cutting Tool Company, Rockford, USA Received on January 6,2000
Abstract The metal removal rate (MRR) in milling is typically limited by the dynamics of the tool-spindle combination or by the power. If the tool is stiff, the power is limiting, and the spindle stalls before chattering. If the tool is flexible, there is a spindle speed range where chatter is limiting. Many tools have some spindle speeds where chatter is limiting and others where power is limiting. This paper presents a new 'power lobe" diagram which is independent of the workpiece material. Combined with the power curve for the spindle, this "stable power" diagram defines the achievable MRR for the entire machine dynamics. Keywords: Milling, Spindle Power Limit, Stability Limit
1 INTRODUCTION In most milling operations, the stable metal removal rate that can be delivered is limited by either the dynamic characteristics of the tool-holder-spindle combination or by the available power of the spindle. If the tool is rather short and stiff, then the available power limits machining performance, and the spindle stalls before chatter can ocwr. If the tool is long and flexible, then there is a large spindle speed range where chatter limits machining performance. Many tool - spindle combinations have some spindle speeds where the occurrence of chatter is the limiting factor and others where power is the limitation. For example, a particular tool in a particular spindle tool may be prone to chatter in the low spindle speed range, and require the use of the stability lobe effect to improve the metal removal rate. However, at higher spindle speeds, where the stability lobe effect is available, spindle power may limit the ability to fully use a large stable zone. This paper presents a new "power lobe" diagram which shows the power required to perform machining operations at the limit of stability as a function of the spindle speed. When combined with the power curve for the spindle the "stable power" diagram defines achievable stable metal removal rate for a tool-holder-spindle combination. The diagram highlights which limitation is stronger for particular spindle-tool combination across the useful spindle speed range. Machine tool builders can use these diagrams for spindle design and motor selection. Machine tool users who are already familiar with the power curves can use the diagrams for tool selection and cutting parameter selection. 2 CONSTRUCTIONOF THE POWER LOBE DIAGRAM AND STABLE POWER DIAGRAM The stability lobe diagram in milling is well-known (for
Annals of the ClRP Vol. 49/1/2000
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example References [I] [lo]), and methods for its computation or simulation have been presented by many researchers. It is most common to plot the permissible stable axial depth of cut versus the spindle speed. However, the achievable metal removal rate in a milling operation is often limited not only by the stability, but by the available power as well. The intent of this paper is to combine the traditional stability lobe diagram with the spindle power diagram to highlight which limitation is stronger for particular spindletool- workpiece combinations. This "power lobe" diagram can be used by the machine tool builder for spindle and motor design, or by the machine tool user for selection of appropriate tooling. Additionally, the "power lobe" diagram allows the general industrial community a more intuitive way to interpret stability and gives the machine tool builders and end users a method to validate cycle time estimates, which are based on delivering available power with acceptable surface quality. The construction of the stability lobe diagram has been described in the references, and generally, the stability lobe diagram is constructed assuming a fixed radial depth of cut. We will follow the common practice of producing slotting lobes (the most limiting case), because slotting is often encountered in milling operations (such as in internal cornering and feed-out motions in pockets). The stability lobe diagram shows the axial depth of cut at the transition from stable to unstable machining as a function of spindle speed. A typical example of a stability lobe diagram is shown in Figure 1. This diagram was computed for 6 copies of the same 20,000 rpm, 75 kW hydrostatic high-speed milling spindle. The tool is a 25 mm diameter 2-flute solid carbide end mill, with 100 mm overhang from the face of
309
the tool holder. The workpiece material is 7075-T6 aluminum with a specific power of 7 x lo8 Nlm2. The measured frequency response functions (FRFs) which were used to compute Figure 1 are shown in Figure 2. The spindles exhibit good dynamic consistency as described in Reference [ l l ] , although there is some damping variation.
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In order to create the power lobe diagram, we recognize that the average power consumed in a milling operation depends on the workpiece material and is approximately proportional to the metal removal rate:
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n
f / (nm) = N + E / (24
where f is the chatter frequency, n is the spindle speed, m is the number of teeth on the tool, N is the integer number of cycles of the vibration between the passage of subsequent teeth, and E / (24 is the phase shift between the vibration and the wave left on the surface by previous cutting.
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where Ks is the specific power of the workpiece material, Re[G] is the negative real part of the oriented FRF, and maVg is the average number of teeth in the cut. The equation used for the spindle speeds in Figure 1 is
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Spindle Speed (rprn) Figure I: Stability lobe diagram for a 25 mm diameter, 2flute solid carbide end mill, with a 100 mm tool extension. The figure has lobes for 6 copies of the same spindle.
where MRR is the metal removal rate. The metal removal rate is given by: MRR=abcmn
(4)
Where a is the radial depth of cut, b is the axial depth of cut, c is the chip load, and n is the spindle speed. The parameters cmn combine to give the feed.
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In addition to the information required for the stability lobe diagram, we select a chip load, and then use the axial depth of cut at the limit of stability from Equation (1) in Equation (4), and compute the power using Equation (3).The result shows power at the limit of stability versus spindle speed and is a "power lobe" diagram. When the spindle power cuwe is superimposed on the power lobe diagram, it is a 'stable power" diagram as shown in Figure 3. In this case, the spindle has constant torque up to 10,000 rpm where the power is 75 kW. Between 10,000 rpm and the top speed of the spindle (20,000 rprn), there is constant power of 75 kW.
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Spindle Speed (rpm) Figure 2: Real (top) and Imaginary (bottom) parts of the FRF's for a 25 mm diameter, 2-flute solid carbide end mill, with a 100 mm tool extension in 6 spindles. These FRF's were used to generate the stability lobes in Figure 1.
Figure 3: Stable power diagram for the same 25 mm diameter, 2-flute solid carbide end mill, with a 100 mm tool extension in the same 6 spindles as in Figures 1 and 2, 0.2 mm chip load, aluminum 7075 -T6.
The equation for axial depth of cut (blim ) in Figure 1 is blim = -1/(2 Ks Re[G]
310
(1)
3
INTERPRETATIONAND APPLICATION
Figure 3 shows the stable power diagram corresponding
to the same spindles and tool as Figure 1, and using a chip load of 0.2 mm. In this figure, it can be seen that the tool dynamics are more limiting than the available power in the useful spindle speed range from 2500 rpm up to a little over 15,000 rpm. At those speeds, chatter is encountered substantially before the spindle stalls. However, between about 16,000 rpm and 20,000 rpm, a stable zone from the stability lobe diagram allows for machining at full power, if the spindle speed is carefully controlled and properly selected (see Reference [12]).
removal rate in aluminum would be higher than in cast iron. Examination of the stable power diagram, however shows that this is not the case. Figure 6 shows the stable power diagram corresponding to Figure 4, and using a chip load of 0.2 mm. In Figure 6, it can be seen that over the entire speed range of the spindle (0 20,000 rpm) this tool is so stiff that in all cases the spindle will stall before the chatter limit is reached. In this case, the spindle is substantially under-powered for this tool-spindle combination.
In this case, the spindle is over-powered in comparison to the tool over most of the spindle speed range. Only if the tool-spindle combination was specifically designed for machining aluminum in the 16,000 to 20,000 rpm range is this motor selection appropriate as shown in this case.
Figure 7 shows the stable power diagram corresponding to Figure 5, and using a chip load of 0.45 mm. Again, the spindle is substantially under-powered. In this case, the dynamic flexibility is over designed by about a factor of 10. However, if a more powerful spindle motor were available, it can be seen that in the cast iron machining, the maximum stable deliverable power could be about 4.5 times greater than in the aluminum machining. The power is greater in the cast iron case partly because the chip load was increased from 0.2 mm to 0.45 mm. However, a stronger effect is that the increase in the number of teeth has moved a higher stable zone down to the top speed of the spindle (20,000 rpm). This is related to the tool tuning idea which was described in References [5] and [9] and which has been achieved in the spindle design and manufacture shown here.
Interestingly, the power lobe diagram is independent of the workpiece material. If we look at a slotting operation, then the average number of teeth in the cut in Equation (1) is the half of the number of teeth on the tool. If we substitute this expression for the axial depth of cut in Equation (4) we are left with Pavs = acn/Re[G] The stable power diagram is dependent on the number of teeth on the tool, even though that the number of teeth does not explicitly appear in Equation (5). The reason is that the number of teeth changes the spindle speed scale on the stability lobe diagram as shown in Equation (2), and the power computation includes the product of axial depth of cut and spindle speed. 4 TOOLSPINDLE DESIGN AND TOOL SELECTION INTEGRATION
Stable power diagrams provide insight, which is useful in several ways to machine tool builders and users. For machine tool builders, the recognition that the achievable metal removal rate, the spindle-tool dynamics, and the spindle motor characteristics are very tightly bound is important. Machine tool builders should have a target tool or tools in mind in addition to the workpiece material when designing the spindle. The stable power diagram is a useful aid in selecting an appropriate spindle motor, or in tuning the tool and spindle dynamics (for example by changing bearing placement) to optimize the metal removal rate for the selected tool(s). Spindles designed without consideration of the tooling that will be most often used in the spindle will almost certainly miss the optimum performance with that tooling package. As an example, Figure 4 shows the stability lobe diagram for the same spindles as in Figure 3,but with an 4-insert face mill, machining aluminum. This tool has an optimum speed of about 15,000 rpm, where the depth of cut can be about 0.18 m. Figure 5 shows the stability lobe diagram for the same spindles, but with a &insert face mill machining cast iron. Here at 20,000 rpm, the axial depth of cut can be almost 0.08 m. The permissible axial depth of cut is different from Figure 4 because of the change in specific power and the number of teeth, while the stable zones have moved horizontally because of the change in the number of teeth. From these figures, it might appear that the metal
The stable zone at about 15,000 rpm in Figure 6 corresponds to the stable zone at about 10,000 rpm in Figure 7, because it moved down in the ratio of the number of teeth (15,000 4 / 6 = 10,000). At the peak of those corresponding stable zones, the stable metal removal rate is higher for cast iron because of the chip load ratio, and because of the spindle speed ratio (2000 (0.45 / 0.2) (1OOOO I 15000) = 3000).
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Spindle Speed (rpm) Figure 4: Stability lobe diagram 75 mm diameter, 4toothed inserted face mill, aluminum 7075-T6. If the tooling package is not completely dictated by the process, machine tool users can use the stable power diagram to select tools which more optimally utilize existing spindles. If the machining process largely dictates the tooling package, they can use the stable power diagrams to make a more rational comparison between competing machines. The issue is not how much power can spindle motor provide, but rather how much power is available for stable milling with the tool(s) which are most prevalent in the process.
311
workpiece material. These diagrams can be used in the integration process both by machine tool builders during the design process and by machine tool users seeking to optimize the use of existing machines. Additionally, these diagrams can allow the end users a method to compare and to rationally justify equipment in the specification stage.
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ACKNOWLEDGEMENTS The authors gratefully acknowledge the assistance of the lngersoll Milling Machine Company and Jerry Halley at the Boeing Company in the completion of this work. 6
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Spindle Speed (rpm) Figure 5: Stability lobe diagram 75 mm diameter, 6toothed inserted face mill, cast iron.
7
REFERENCES Y. Altintas , E. Budak, 1995,Analytical Prediction of Stability Lobes in Milling, Annals of the CIRP,
44111951357-362. T. Sata, T. Inamura, 1974,Stability Analysis of the Cutting Process at Varying Spindle Rotation, Annals of the ClRP ,2311:119- 123. J. Tlusty (l), W. Zaton, F. Ismail, 1983, Stability Lobes in Milling, Annals of the ClRP, 32/1:309-
31 3.
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Spindle Speed (rpm) Figure 6:Stable power diagram for a 75 mm diameter, 4toothed face mill, 0.2 mm chip load, aluminum 7075-T6.
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Weck, W., Verhaag, E., Gather, M., 1975,Adaptive Control for Face Milling Operations with Strategies for Avoiding Chatter Vibrations and for Automatic Cut Distribution, Annals of the ClRP, Vol. 2411:
405-409. Davies, M., Dutterer, B., Pratt, J., Schaut , A., Bryan, J., 1998, On the Dynamics of High-speed Milling with Long, Slender Endmills, Annals of the ClRP, 47115 5 59. Tlusty, J., Smith, S., Winfough, W.R., 1996, Techniques for the Use of Long Slender End Mills in High-speed milling, Annals of the ClRP, 4511:393
-
- 397. F
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Smith, S., Tlusty, J., 1993, Efficient Simulation Programs for Chatter in Milling, Annals of the CIRP, 42/1:433 436. Tlusty, J. 1986, Dynamics of High Speed Milling, ASME Journal of Engineering for Industry, 108:59-
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Spindle Speed (rpm) Figure 7:Stable power diagram for a 75 mm diameter, 6toothed face mill, 0.45 mm chip load, cast iron. CONCLUSIONS The metal removal rate which can be achieved with a given tool-spindle combination depends on the dynamic characteristics of the system and on the available power from the spindle motor. In order to maximize the utilizationof the machine, the design and selection of the tool, spindle and motor should be tightly integrated. Ideally, the spindle motor should deliver full power in the target operating range for the tool and cutting should be power-limited in this range, but just barely. The paper presented the power lobe diagram and the stable power diagram which are independent of the 5
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Smith, S., Winfough, W.R., Halley, J., 1998,The Effect of Tool Length on Stable Metal Removal Rate in High Speed Milling, Annals of the ClRP, VOl. 4711: 307-310. [lOISmith, S., Tlusty, J., 1997,Current Trends in High Speed Machining", ASME Journal of Manufacturing Science and Engineering, 1 19:664 - 666. IllJSmith, S., Winfough, W.R., Young, K., Halley, J., 2000, The Effect of Dynamic Consistency in Spindles on Cutting Performance, submitted to the Transactions of the NAMRI, 2000. [12]Smith, S.,Tlusty, J., 1992,Stabilizing Chatter by Automatic Spindle Speed Regulation, Annals of the CIRP, Vol. 4111 :433-436.
Abstract The metal removal rate (MRR) in milling is typically limited by the dynamics of the tool-spindle combination or by the power. If the tool is stiff, the power is limiting, and the spindle stalls before chattering. If the tool is flexible, there is a spindle speed range where chatter is limiting. Many tools have some spindle speeds where chatter is limiting and others where power is limiting. This paper presents a new 'power lobe" diagram which is independent of the workpiece material. Combined with the power curve for the spindle, this "stable power" diagram defines the achievable MRR for the entire machine dynamics. Keywords: Milling, Spindle Power Limit, Stability Limit
1 INTRODUCTION In most milling operations, the stable metal removal rate that can be delivered is limited by either the dynamic characteristics of the tool-holder-spindle combination or by the available power of the spindle. If the tool is rather short and stiff, then the available power limits machining performance, and the spindle stalls before chatter can ocwr. If the tool is long and flexible, then there is a large spindle speed range where chatter limits machining performance. Many tool - spindle combinations have some spindle speeds where the occurrence of chatter is the limiting factor and others where power is the limitation. For example, a particular tool in a particular spindle tool may be prone to chatter in the low spindle speed range, and require the use of the stability lobe effect to improve the metal removal rate. However, at higher spindle speeds, where the stability lobe effect is available, spindle power may limit the ability to fully use a large stable zone. This paper presents a new "power lobe" diagram which shows the power required to perform machining operations at the limit of stability as a function of the spindle speed. When combined with the power curve for the spindle the "stable power" diagram defines achievable stable metal removal rate for a tool-holder-spindle combination. The diagram highlights which limitation is stronger for particular spindle-tool combination across the useful spindle speed range. Machine tool builders can use these diagrams for spindle design and motor selection. Machine tool users who are already familiar with the power curves can use the diagrams for tool selection and cutting parameter selection. 2 CONSTRUCTIONOF THE POWER LOBE DIAGRAM AND STABLE POWER DIAGRAM The stability lobe diagram in milling is well-known (for
Annals of the ClRP Vol. 49/1/2000
-
example References [I] [lo]), and methods for its computation or simulation have been presented by many researchers. It is most common to plot the permissible stable axial depth of cut versus the spindle speed. However, the achievable metal removal rate in a milling operation is often limited not only by the stability, but by the available power as well. The intent of this paper is to combine the traditional stability lobe diagram with the spindle power diagram to highlight which limitation is stronger for particular spindletool- workpiece combinations. This "power lobe" diagram can be used by the machine tool builder for spindle and motor design, or by the machine tool user for selection of appropriate tooling. Additionally, the "power lobe" diagram allows the general industrial community a more intuitive way to interpret stability and gives the machine tool builders and end users a method to validate cycle time estimates, which are based on delivering available power with acceptable surface quality. The construction of the stability lobe diagram has been described in the references, and generally, the stability lobe diagram is constructed assuming a fixed radial depth of cut. We will follow the common practice of producing slotting lobes (the most limiting case), because slotting is often encountered in milling operations (such as in internal cornering and feed-out motions in pockets). The stability lobe diagram shows the axial depth of cut at the transition from stable to unstable machining as a function of spindle speed. A typical example of a stability lobe diagram is shown in Figure 1. This diagram was computed for 6 copies of the same 20,000 rpm, 75 kW hydrostatic high-speed milling spindle. The tool is a 25 mm diameter 2-flute solid carbide end mill, with 100 mm overhang from the face of
309
the tool holder. The workpiece material is 7075-T6 aluminum with a specific power of 7 x lo8 Nlm2. The measured frequency response functions (FRFs) which were used to compute Figure 1 are shown in Figure 2. The spindles exhibit good dynamic consistency as described in Reference [ l l ] , although there is some damping variation.
E
0.03
Y
c.
3
g
(2)
0.02
5 n
In order to create the power lobe diagram, we recognize that the average power consumed in a milling operation depends on the workpiece material and is approximately proportional to the metal removal rate:
a3
n
f / (nm) = N + E / (24
where f is the chatter frequency, n is the spindle speed, m is the number of teeth on the tool, N is the integer number of cycles of the vibration between the passage of subsequent teeth, and E / (24 is the phase shift between the vibration and the wave left on the surface by previous cutting.
0.04
-
where Ks is the specific power of the workpiece material, Re[G] is the negative real part of the oriented FRF, and maVg is the average number of teeth in the cut. The equation used for the spindle speeds in Figure 1 is
0.01
0 0
5000
10000
15000
20000
25000
Spindle Speed (rprn) Figure I: Stability lobe diagram for a 25 mm diameter, 2flute solid carbide end mill, with a 100 mm tool extension. The figure has lobes for 6 copies of the same spindle.
where MRR is the metal removal rate. The metal removal rate is given by: MRR=abcmn
(4)
Where a is the radial depth of cut, b is the axial depth of cut, c is the chip load, and n is the spindle speed. The parameters cmn combine to give the feed.
F-SF -E
0.5
In addition to the information required for the stability lobe diagram, we select a chip load, and then use the axial depth of cut at the limit of stability from Equation (1) in Equation (4), and compute the power using Equation (3).The result shows power at the limit of stability versus spindle speed and is a "power lobe" diagram. When the spindle power cuwe is superimposed on the power lobe diagram, it is a 'stable power" diagram as shown in Figure 3. In this case, the spindle has constant torque up to 10,000 rpm where the power is 75 kW. Between 10,000 rpm and the top speed of the spindle (20,000 rprn), there is constant power of 75 kW.
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Spindle Speed (rpm) Figure 2: Real (top) and Imaginary (bottom) parts of the FRF's for a 25 mm diameter, 2-flute solid carbide end mill, with a 100 mm tool extension in 6 spindles. These FRF's were used to generate the stability lobes in Figure 1.
Figure 3: Stable power diagram for the same 25 mm diameter, 2-flute solid carbide end mill, with a 100 mm tool extension in the same 6 spindles as in Figures 1 and 2, 0.2 mm chip load, aluminum 7075 -T6.
The equation for axial depth of cut (blim ) in Figure 1 is blim = -1/(2 Ks Re[G]
310
(1)
3
INTERPRETATIONAND APPLICATION
Figure 3 shows the stable power diagram corresponding
to the same spindles and tool as Figure 1, and using a chip load of 0.2 mm. In this figure, it can be seen that the tool dynamics are more limiting than the available power in the useful spindle speed range from 2500 rpm up to a little over 15,000 rpm. At those speeds, chatter is encountered substantially before the spindle stalls. However, between about 16,000 rpm and 20,000 rpm, a stable zone from the stability lobe diagram allows for machining at full power, if the spindle speed is carefully controlled and properly selected (see Reference [12]).
removal rate in aluminum would be higher than in cast iron. Examination of the stable power diagram, however shows that this is not the case. Figure 6 shows the stable power diagram corresponding to Figure 4, and using a chip load of 0.2 mm. In Figure 6, it can be seen that over the entire speed range of the spindle (0 20,000 rpm) this tool is so stiff that in all cases the spindle will stall before the chatter limit is reached. In this case, the spindle is substantially under-powered for this tool-spindle combination.
In this case, the spindle is over-powered in comparison to the tool over most of the spindle speed range. Only if the tool-spindle combination was specifically designed for machining aluminum in the 16,000 to 20,000 rpm range is this motor selection appropriate as shown in this case.
Figure 7 shows the stable power diagram corresponding to Figure 5, and using a chip load of 0.45 mm. Again, the spindle is substantially under-powered. In this case, the dynamic flexibility is over designed by about a factor of 10. However, if a more powerful spindle motor were available, it can be seen that in the cast iron machining, the maximum stable deliverable power could be about 4.5 times greater than in the aluminum machining. The power is greater in the cast iron case partly because the chip load was increased from 0.2 mm to 0.45 mm. However, a stronger effect is that the increase in the number of teeth has moved a higher stable zone down to the top speed of the spindle (20,000 rpm). This is related to the tool tuning idea which was described in References [5] and [9] and which has been achieved in the spindle design and manufacture shown here.
Interestingly, the power lobe diagram is independent of the workpiece material. If we look at a slotting operation, then the average number of teeth in the cut in Equation (1) is the half of the number of teeth on the tool. If we substitute this expression for the axial depth of cut in Equation (4) we are left with Pavs = acn/Re[G] The stable power diagram is dependent on the number of teeth on the tool, even though that the number of teeth does not explicitly appear in Equation (5). The reason is that the number of teeth changes the spindle speed scale on the stability lobe diagram as shown in Equation (2), and the power computation includes the product of axial depth of cut and spindle speed. 4 TOOLSPINDLE DESIGN AND TOOL SELECTION INTEGRATION
Stable power diagrams provide insight, which is useful in several ways to machine tool builders and users. For machine tool builders, the recognition that the achievable metal removal rate, the spindle-tool dynamics, and the spindle motor characteristics are very tightly bound is important. Machine tool builders should have a target tool or tools in mind in addition to the workpiece material when designing the spindle. The stable power diagram is a useful aid in selecting an appropriate spindle motor, or in tuning the tool and spindle dynamics (for example by changing bearing placement) to optimize the metal removal rate for the selected tool(s). Spindles designed without consideration of the tooling that will be most often used in the spindle will almost certainly miss the optimum performance with that tooling package. As an example, Figure 4 shows the stability lobe diagram for the same spindles as in Figure 3,but with an 4-insert face mill, machining aluminum. This tool has an optimum speed of about 15,000 rpm, where the depth of cut can be about 0.18 m. Figure 5 shows the stability lobe diagram for the same spindles, but with a &insert face mill machining cast iron. Here at 20,000 rpm, the axial depth of cut can be almost 0.08 m. The permissible axial depth of cut is different from Figure 4 because of the change in specific power and the number of teeth, while the stable zones have moved horizontally because of the change in the number of teeth. From these figures, it might appear that the metal
The stable zone at about 15,000 rpm in Figure 6 corresponds to the stable zone at about 10,000 rpm in Figure 7, because it moved down in the ratio of the number of teeth (15,000 4 / 6 = 10,000). At the peak of those corresponding stable zones, the stable metal removal rate is higher for cast iron because of the chip load ratio, and because of the spindle speed ratio (2000 (0.45 / 0.2) (1OOOO I 15000) = 3000).
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Spindle Speed (rpm) Figure 4: Stability lobe diagram 75 mm diameter, 4toothed inserted face mill, aluminum 7075-T6. If the tooling package is not completely dictated by the process, machine tool users can use the stable power diagram to select tools which more optimally utilize existing spindles. If the machining process largely dictates the tooling package, they can use the stable power diagrams to make a more rational comparison between competing machines. The issue is not how much power can spindle motor provide, but rather how much power is available for stable milling with the tool(s) which are most prevalent in the process.
311
workpiece material. These diagrams can be used in the integration process both by machine tool builders during the design process and by machine tool users seeking to optimize the use of existing machines. Additionally, these diagrams can allow the end users a method to compare and to rationally justify equipment in the specification stage.
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ACKNOWLEDGEMENTS The authors gratefully acknowledge the assistance of the lngersoll Milling Machine Company and Jerry Halley at the Boeing Company in the completion of this work. 6
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Spindle Speed (rpm) Figure 5: Stability lobe diagram 75 mm diameter, 6toothed inserted face mill, cast iron.
7
REFERENCES Y. Altintas , E. Budak, 1995,Analytical Prediction of Stability Lobes in Milling, Annals of the CIRP,
44111951357-362. T. Sata, T. Inamura, 1974,Stability Analysis of the Cutting Process at Varying Spindle Rotation, Annals of the ClRP ,2311:119- 123. J. Tlusty (l), W. Zaton, F. Ismail, 1983, Stability Lobes in Milling, Annals of the ClRP, 32/1:309-
31 3.
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Spindle Speed (rpm) Figure 6:Stable power diagram for a 75 mm diameter, 4toothed face mill, 0.2 mm chip load, aluminum 7075-T6.
12000
Weck, W., Verhaag, E., Gather, M., 1975,Adaptive Control for Face Milling Operations with Strategies for Avoiding Chatter Vibrations and for Automatic Cut Distribution, Annals of the ClRP, Vol. 2411:
405-409. Davies, M., Dutterer, B., Pratt, J., Schaut , A., Bryan, J., 1998, On the Dynamics of High-speed Milling with Long, Slender Endmills, Annals of the ClRP, 47115 5 59. Tlusty, J., Smith, S., Winfough, W.R., 1996, Techniques for the Use of Long Slender End Mills in High-speed milling, Annals of the ClRP, 4511:393
-
- 397. F
9Ooo
Smith, S., Tlusty, J., 1993, Efficient Simulation Programs for Chatter in Milling, Annals of the CIRP, 42/1:433 436. Tlusty, J. 1986, Dynamics of High Speed Milling, ASME Journal of Engineering for Industry, 108:59-
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Spindle Speed (rpm) Figure 7:Stable power diagram for a 75 mm diameter, 6toothed face mill, 0.45 mm chip load, cast iron. CONCLUSIONS The metal removal rate which can be achieved with a given tool-spindle combination depends on the dynamic characteristics of the system and on the available power from the spindle motor. In order to maximize the utilizationof the machine, the design and selection of the tool, spindle and motor should be tightly integrated. Ideally, the spindle motor should deliver full power in the target operating range for the tool and cutting should be power-limited in this range, but just barely. The paper presented the power lobe diagram and the stable power diagram which are independent of the 5
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Smith, S., Winfough, W.R., Halley, J., 1998,The Effect of Tool Length on Stable Metal Removal Rate in High Speed Milling, Annals of the ClRP, VOl. 4711: 307-310. [lOISmith, S., Tlusty, J., 1997,Current Trends in High Speed Machining", ASME Journal of Manufacturing Science and Engineering, 1 19:664 - 666. IllJSmith, S., Winfough, W.R., Young, K., Halley, J., 2000, The Effect of Dynamic Consistency in Spindles on Cutting Performance, submitted to the Transactions of the NAMRI, 2000. [12]Smith, S.,Tlusty, J., 1992,Stabilizing Chatter by Automatic Spindle Speed Regulation, Annals of the CIRP, Vol. 4111 :433-436.