improved prediction of spindle-holder-tool - CiteSeerX
IMPROVED PREDICTION OF SPINDLE-HOLDER-TOOL FREQUENCY RESPONSE FUNCTIONS
By CHI HUNG CHENG
A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 2007
1
© 2007 Chi Hung Cheng
2
To my family, my grandfather, and Lord Jesus Christ
3
ACKNOWLEDGMENTS The author would like to thank his advisor Dr. Tony L. Schmitz, for his understanding, patience, and unconditional support. Thanks also go to Dr. John Schueller, Dr. Nagaraj Arakere, Dr. Gloria Wiens, and Dr. Jacob Hammer for serving as committee members. The author also appreciates Dr. John C. Ziegert for always bringing in new ideas when there is a bottle neck and Dr. Nam Ho Kim for helping with micro tool finite element simulation. The thank list extends to the members in Machine Tool Research Center from 2003 to 2007, for all the team works and memorable moments together. With special thanks to Mr. Scott Payne and Mr. Vadim Tymianski for always being “partners of crimes” when there is the need. Finally the author would like to thank his family for the support in every aspect, and the saints in the Church in Gainesville for their loving tender care. Praise the Lord. This work wouldn’t have been done without the sovereign arrangements.
4
TABLE OF CONTENTS page ACKNOWLEDGMENTS ...............................................................................................................4 LIST OF TABLES...........................................................................................................................7 LIST OF FIGURES .........................................................................................................................9 ABSTRACT...................................................................................................................................14 CHAPTER 1
INTRODUCTION ..................................................................................................................16 High Speed Machining ...........................................................................................................16 Chatter And Stability Lobe Diagram......................................................................................16 Objective.................................................................................................................................18
2
LITERATURE REVIEW .......................................................................................................22 Milling Stability Prediction ....................................................................................................22 Experimental Method .............................................................................................................22 Predictive (Non-Experimental) Methods................................................................................23 System Dynamics Acquisition ........................................................................................23 Stability Analysis.............................................................................................................25
3
RECEPTANCE COUPLING SUBSTRUCTURE ANALYSIS ............................................31 Two-Component Receptance Coupling Substructure Analysis .............................................31 Rigid Connection.............................................................................................................31 Non-Rigid Connection with a Linear Spring...................................................................32 Non-Rigid Connection with a Linear Spring and a Damper ...........................................33 Non-Rigid Connection with Linear and Rotational Springs and Dampers .....................34 Three-Component Receptance Coupling Substructure Analysis ...........................................37 Inverse Receptance Coupling Substructure Analysis .............................................................38 Substructure Beam Modeling .................................................................................................41 Euler-Bernoulli Beam......................................................................................................41 Timoshenko Beam...........................................................................................................43 Fluted Tool Modeling .............................................................................................................45
4
ROTATING FREQUENCY RESPONSE FUNCTION PREDICTION................................54 Runout Signal Filtering...........................................................................................................54 Runout Signal ..................................................................................................................55 Runout Filtering...............................................................................................................55 The FRF Prediction from Rotating Standard Holder Measurements .....................................57
5
Stability Boundary Validation ................................................................................................58 5
MICRO SCALE TOOL FREQUENCY RESPONSE FUNCTION PREDICTION..............73 Micro Scale Tools on Macro Machine Systems .....................................................................73 Sensor Options for Micro Tools ......................................................................................73 Modeling Description......................................................................................................74 Experimental Setup .........................................................................................................76 Micro Scale Tools on Micro Spindles ....................................................................................78 The S Value Consideration..............................................................................................78 Sensitivity of Standard Artifact Length...........................................................................79 Micro Tool Frequency Response Function Prediction....................................................80
6
MACRO SCALE TOOL FREQUENCY RESPONSE FUNCTION PREDICTION ............95 Variation in Spindle-Base Receptances with Standard Holder Geometry .............................95 Experimental Results ..............................................................................................................95 The HSK-63A Interface ..................................................................................................96 The CAT-40 Interface .....................................................................................................97 The HSK-100A Interface ................................................................................................98
7
CONCLUSIONS AND FUTURE WORK...........................................................................115 Conclusions...........................................................................................................................115 Future Work..........................................................................................................................116
LIST OF REFERENCES.............................................................................................................118 BIOGRAPHICAL SKETCH .......................................................................................................121
6
LIST OF TABLES Table
page
3-1
Fixed-free steel rod first mode frequency comparison between different beam modeling methods..............................................................................................................52
3-2
Average of area section properties for fluted endmills......................................................53
3-3
Average of area section properties for fluted endmills......................................................53
4-1
HSK-63A short hollow standard holder substructure dimensions.....................................71
4-2
Solid holder substructure dimensions. ...............................................................................71
4-3
Material properties used in RCSA modeling. ....................................................................71
4-4
Substructure dimensions of Regofix collet holder with 12.7 mm diameter, 127 mm overhang carbide tool blank...............................................................................................72
4-5
Substructure dimensions of Regofix collet holder with 25.4 mm diameter, 127 mm overhang carbide tool blank...............................................................................................72
4-6
Substructure dimensions of the endmill-shrink fit holder described in Figure 4-15. ........72
5-1
CAT-40 standard holder artifact substructure section dimensions. ...................................93
5-2
CAT-40 ER-25 collet holder and tool substructure section dimensions............................93
5-3
S values for micro standard artifacts..................................................................................94
5-4
Tapered tool (23.5 mm OH) substructure section dimensions. .........................................94
6-1
HSK-63A long hollow standard holder artifact substructure dimensions. ......................111
6-2
Substructure dimensions for HSK-63A long shrink fit holder (section I at free end). ....111
6-3
Substructure dimensions for HSK-63A long shrink fit holder (section I at free end). ....112
6-4
Extended holder lengths of the HSK-63A standard artifacts and shrink fit holders........112
6-5
CAT-40 long hollow standard holder artifact substructure dimensions. .........................112
6-6
CAT-40 short hollow standard holder artifact substructure dimensions. ........................112
6-7
CAT-40 short solid standard holder artifact substructure dimensions.............................112
6-8
CAT-40 shrink fit holder substructure dimensions..........................................................112
7
6-9
CAT-40 long collet holder substructure dimensions. ......................................................112
6-10
CAT-40 short collet holder substructure dimensions. .....................................................113
6-11
Extended holder lengths of the CAT-40 standard artifacts and tested holders................113
6-12
HSK-100A short hollow standard holder artifact substructure dimensions. ...................113
6-13
HSK-100A long soild standard holder artifact substructure dimensions.........................113
6-14
Substructure dimensions of Briney HSK100ASF-075-433 shrink fit holder with Sandvik A393.T-19 10 175 carbide adapter and two square insert cutting head. ...........113
6-15
Substructure dimensions of Briney HSK100AE-125-472 set screw holder with Mitsubishi Carbide MBN 10 1000 TB steel tapered ball end..........................................114
6-16
Extended holder lengths of the HSK-100A standard artifacts and tested holders...........114
8
LIST OF FIGURES Figure
page
1-1
HSM cutting speed ranges for various materials. ..............................................................20
1-2
Scheme of (flexible) cutting edge passing through workpiece surface. ............................20
1-3
Stable cut and unstable cut (chatter) on a workpiece surface. ...........................................21
1-4
Example stability lobe diagram. ........................................................................................21
1-5
Block diagram for cutting process with regenerated wavy surface. ..................................21
2-1
Different approaches to determine stable cutting conditions.............................................28
2-2
Ball bearing contact angles at high speed rotation.............................................................29
2-3
Impact testing performed on standard artifact with modal hammer and laser vibrometer. .........................................................................................................................29
2-4
Example of time-domain simulation of an unstable cutting process. ................................30
2-5
Predicted and measured FRF of a 100 mm diameter inserted endmill. .............................30
3-1
Components joined with a rigid connection. .....................................................................46
3-2
Components connected with a linear spring. .....................................................................47
3-3
Assembly with linear spring and damper...........................................................................48
3-4
Assembly with linear and rotational springs and dampers. ...............................................49
3-5
Generic case of two substructures with rigid connection. .................................................50
3-6
Three-component RCSA model for tool-holder-spindle assembly. ..................................50
3-7
Spindle and decomposed standard holder artifact. ............................................................50
3-8
Ansys Workbench frequency simulation for 19.1 mm diameter fixed-free steel rod with 80 mm length. ............................................................................................................51
3-9
Cutting edge of a four fluted flat endmill cutter. ...............................................................51
3-10
Solid model of two-fluted endmill cross-section. ..............................................................52
4-1
Speed-dependent FRFs of the standard holder at five different spindle speeds: {0, 2500, 7500, and 10000} rpm. ............................................................................................60
9
4-2
Example setup for rotating FRF measurement. .................................................................61
4-3
Example of holder and runout signal resultant response. ..................................................61
4-4
Scheme of tachometer-aided runout filtering setup. ..........................................................62
4-5
Illustration of once-per-revolution signal identification ....................................................62
4-6
Example of shrink fit holder time-domain runout filtering. ..............................................63
4-7
Frequency response function comparison with/without time-domain filtering.................64
4-8
Short hollow standard holder geometry and substructure coordinates. .............................64
4-9
Experimental setup of standard holder (HSK-63A interface) rotating FRF measurement. .....................................................................................................................65
4-10
Solid holder geometry and substructure coordinates. ........................................................65
4-11
Solid holder FRF measurement and prediction at {10000, 12000, and 16000} rpm. .......66
4-12
Geometry of Regofix collet holder with tool.....................................................................66
4-13
Measured and predicted FRFs for Regofix collet holder with 12.7 mm diameter 127 mm overhang carbide tool blank at 10,000 rpm. ...............................................................67
4-14
Measured and predicted FRFs for Regofix collet holder with 25.4 mm diameter 127 mm overhang carbide tool blank at 10,000 rpm. ...............................................................67
4-15
Geometry of 19.1 mm diameter, four flutes, carbide endmill with 76.1 mm overhang length clamped in Command shrink fit holder. .................................................................68
4-16
Stability lobes for FRF measurement at 0 rpm and predictions at {10000 and 16000} rpm for 19.1 mm diameter, four flute, carbide endmill .....................................................68
4-17
Setup for cutting tests. The tool shank deflections were measured using two orthogonal capacitance probes...........................................................................................69
4-18
Example results for 8000 rpm slotting cuts. ......................................................................70
4-19
Comparison of test cut results to predicted stability boundaries determined from 0 rpm (measured) and {10000 and 16000} rpm (predicted) FRFs. ......................................71
5-1
Example setup of high speed machining with micro tools. ...............................................82
5-2
Dimension comparison of a 1mm diameter, two-flute micro endmill to a penny. ............82
5-3
CAT-40 standard holder artifact geometry. .......................................................................82
10
5-4
CAT-40 ER-25 collet holder and tool geometry................................................................83
5-5
Experimental setup for CAT-40 collet holder with 3.18 mm steel tool shank. .................83
5-6
Magnitudes of H 41 FRFs measurements (top) and predictions (bottom). ........................84
5-7
Measured and predicted H 41 with 46.0 mm tool overhang (marked as 9 in Fig. 5-6)......84
5-8
Measured and predicted H 41 with 50.8 mm tool overhang (marked as 12 in Fig. 5-6)....85
5-9
Multiplication factor (MF) determined from visual fit in relation to the tool overhang with a linear approximation superimposed. .......................................................................85
5-10
FRFs of H 44 , magnitude measurements (top) and predictions (bottom). ..........................86
5-11
Measured and predicted H 44 with 46.0 mm tool overhang (marked as 9 in Fig. 5-10)....86
5-12
Measured and predicted H 44 with 50.8 mm tool overhang (marked as 12 in Fig. 510). .....................................................................................................................................87
5-13
NSK HES 500 electric micro spindle. ...............................................................................87
5-14
Experimental setup for determination of micro spindle-base receptances. .......................88
5-15
Prediction of tool point FRF for 3.18 mm diameter, 21 mm overhang steel rod by a 17 mm overhang standard artifact with three different S values. ......................................89
5-16
FRF prediction of a 3.18 mm diameter, 21 mm overhang steel rod by 20 mm (solid) and 17 mm (dotted) overhang standard tool artifacts ........................................................90
5-17
Example 3.18 mm shank diameter tapered tool (no flutes) with 1.5 mm diameter tool tip. ......................................................................................................................................90
5-18
Geometry of NSK HES 500 micro spindle with tapered tool............................................91
5-19
Tool tip measurement of tapered tool with an overhang of 23.5 mm compared to predictions based on different standard artifact overhang lengths.....................................91
5-20
Measurement of tapered tool (with overhang length of 25.5 mm) FRF compared with selected standard artifact FRF predictions.........................................................................92
5-21
FRFs for free-free tapered tool and standard artifact responses coupled to rigid spindle receptances. ...........................................................................................................93
6-1
HSK-63A spindle-base receptances calculated by long and short hollow standard holders................................................................................................................................99
6-2
Geometry of HSK-63A long hollow standard hollow holder artifact..............................100 11
6-3
HSK-63A shrink fit holders: long hollow (left) and short hollow (right)........................100
6-4
HSK-63A FRF predictions for long shrink fit holder by short hollow artifact with different S values in comparison with measured FRF (heavy solid line). .......................101
6-5
HSK-63A long shrink fit holder FRF predictions using two different standard holders in comparison with measured FRF (heavy solid line). ....................................................101
6-6
HSK-63A short shrink fit holder FRF predictions using two different standard holders in comparison with measured FRF (heavy solid line). .......................................102
6-7
Geometry of CAT-40 long hollow standard holder artifact.............................................102
6-8
Geometry of CAT-40 short hollow standard holder artifact............................................103
6-9
Geometry of CAT-40 short solid standard holder artifact. ..............................................103
6-10
CAT-40 shrink fit holder FRF predictions in comparison with measured FRF (heavy solid line). ........................................................................................................................104
6-11
CAT-40 long collet holder FRF predictions in comparison with measured FRF (heavy solid line)..............................................................................................................104
6-12
CAT-40 short collet holder FRF predictions in comparison with measured FRF (heavy solid line)..............................................................................................................105
6-13
Geometry of HSK-100A short hollow standard holder artifact.......................................105
6-14
Geometry of HSK-100A long solid standard holder artifact. ..........................................106
6-15
Geometry of Briney HSK100ASF-075-433 shrink fit holder with Sandvik A393.T19 10 175 carbide adapter and two square insert cutting head. .......................................106
6-16
Geometry of Briney HSK100AE-125-472 set screw holder with Mitsubishi Carbide MBN 10 1000 TB steel tapered ball end mill with one round carbide insert. .................107
6-17
HSK100ASF-075-433 shrink fit holder with Sandvik A393.T-19 10 175 carbide adapter and two square insert cutting head measurement and prediction........................107
6-18
HSK100ASF-075-433 shrink fit holder with Sandvik A393.T-19 10 175 carbide adapter and two square insert cutting head measurement and prediction........................108
6-19
HSK100ASF-075-433 shrink fit holder with Sandvik A393.T-19 10 175 carbide adapter and two square insert cutting head measurement and prediction........................108
6-20
HSK100ASF-075-433 shrink fit holder with Sandvik A393.T-19 10 175 carbide adapter and two square insert cutting head measurement and prediction........................109
12
6-21
HSK100AE-125-472 set screw holder with Mitsubishi Carbide MBN 10 1000 TB steel tapered ball end mill with one round carbide insert measurement and prediction .109
6-22
HSK100AE-125-472 set screw holder with Mitsubishi Carbide MBN 10 1000 TB steel tapered ball end mill with one round carbide insert measurement and prediction ..110
6-23
HSK100AE-125-472 set screw holder with Mitsubishi Carbide MBN 10 1000 TB steel tapered ball end mill with one round carbide insert measurement and prediction .110
6-24
HSK100AE-125-472 set screw holder with Mitsubishi Carbide MBN 10 1000 TB steel tapered ball end mill with one round carbide insert measurement and prediction ..111
13
Abstract of Dissertation Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy IMPROVED PREDICTION OF SPINDLE-HOLDER-TOOL FREQUENCY RESPONSE FUNCTIONS By Chi Hung Cheng August 2007 Chair: Tony L. Schmitz Major: Mechanical Engineering High speed machining (HSM) offers tremendous capabilities for discrete part manufacturing because it can provide high material removal rates (MRR) in metals, plastics, and composites with good surface finish. To realize these benefits, stability lobe diagrams, which define regions of stable cutting as a function of spindle speed and axial depth of cut, can be used to select appropriate cutting conditions. Computation of these diagrams requires that the dynamics of the cutting system (the machine, spindle, holder, and tool assembly) be known. Typically, impact testing (i.e., exciting the structure with an instrumented hammer and recording the response with a linear transducer) is used to record the required tool point frequency response. However, due to the diversity of tool holders and tools available to end users, it can be prohibitively time-consuming to perform impact testing for each possible combination. Further, it is difficult to measure the responses of 1) small tools using traditional methods; and 2) spindles during high speed rotation. The former is necessary for new micro-milling applications, while the latter is required because the at-speed response for some spindles can differ from the nonrotating response. This study provides a method to address these situations. The tool tip response for a given machine-spindle-holder-tool assembly is predicted by coupling a spindle measurement with
14
finite element models of the holder and tool using the method of receptance coupling substructure analysis (RCSA). RCSA enables a user to analytically couple arbitrary tool-holder combinations to an archived spindle response. Therefore, the user must perform only a single test on the spindle in question. Given this information, the tool point response for any tool-holder can be performed via a ‘virtual impact test’. Comparisons of predictions and experimental results are provided for 1) micro-tools; and 2) macro-scale tools coupled to a spindle that exhibits changing dynamics with spindle speed.
15
CHAPTER 1 INTRODUCTION High Speed Machining High speed machining (HSM) is an important capability in modern, discrete part manufacturing. Using the higher cutting speeds made possible by improved cutting tool materials and coatings, the machine operation time is reduced significantly (Fig. 1-1 [1]). The use of HSM makes it possible to efficiently produce complex parts and, therefore, reduce assembly time and costs relative to the traditional approach where simpler shapes are machined and then mechanically joined. High speed machines typically use direct drive spindles, i.e., a spindle shaft with permanent magnets is driven by a coil located within the surrounding housing. Modern spindle designs can reach top speeds of 40,000 rpm and higher with powers at the many tens of kW level. At these higher speeds, micro-milling (or milling with very small diameter cutters) is now realizable because reasonable cutting speeds, or peripheral velocities of the cutting edge, can still be maintained even though the cutting edge radius may only be fractions of a millimeter. The advantage of high speed micro-machining is that it provides a process capable of producing complex, free form, three-dimensional (3-D) structures from virtually any material. This provides an alternative to typical MEMS (micro electro mechanical systems) fabrications techniques, such as silicon etching, that are generally limited to 2-D geometries and specialized materials. Therefore, it can be expected that the demand of HSM will continue to increase. Chatter And Stability Lobe Diagram Surface location error (SLE) and chatter, or unstable machining conditions, impose limitations on machining efficiency. For any machining operation, the cutting force acting on the
16
tool causes it to vibrate. This vibration can lead to chatter and corresponding large forces and potential damage. Even if the operation is stable, however, the vibration state of the tool as it leaves the newly created surface defines the location of that surface. Variations in the process parameters can yield either undercut (less material removed than commanded) or overcut (more material removed) situations; this phenomenon is referred to as surface location error. For either limitation, it is important to note that the tool-holder-spindle-machine assembly response as reflected at the tool point (free end of the tool) strongly influences the final behavior. Chatter occurs due to the inherent feedback mechanism in machining. In turning and milling operations, the tool cutting edge makes multiple passes through the workpiece surface to achieve the desired dimension. For each pass, the tool vibrations are imprinted on the surface. Therefore, the workpiece surface is not uniform and the current chip thickness depends both on the current tool vibrations and those during the previous pass (Fig. 1-2), which Arnold [2] refers to as the regeneration of waviness. As the cutting edge removes the wavy surface, the force is modulated by the varying chip thickness, which leads to further vibration. Depending on the machining parameters, the feedback system can become unstable and chatter occurs (Fig. 1-3). The large force and significant tool deflections associated with chatter can be identified audibly. It not only creates an unacceptable machined surface finish, but can also damage the machine tool, spindle bearings, tool, and workpiece. To avoid chatter, stability lobe diagrams can be applied. These diagrams (as shown in Fig. 1-4) enable the machine operator to choose a proper spindle speed-chip width (axial depth for peripheral end milling) for stable cutting conditions. The concept of the stability lobe diagram was first developed in 1956 [3]. However, large industrial benefits were not realized until the high speed machines became commercially available. As can be seen in Fig. 1-4, the width of the
17
stable regions (beneath the lobes) tends to widen as the spindle speed becomes higher. Therefore, operating in these higher speed regions increases the material removal rate both by the increased cutting speed and higher axial depth of cut. Methods used to compute the stability limit are described in Chapter 2. The feedback mechanism in machining can also be represented using a block diagram approach as shown in Fig. 1-5 [4]. The system dynamics are represented by a second order plant in the forward path. The force is determined by multiplying the difference between the current and time-delayed chip thickness valued by the gain, represented by the product of the specific cutting energy and chip width. Based on this block diagram, the limiting chip width can be expressed for turning operations as shown in Eq. 1.1 where FRF is the system frequency response function. This equation emphasizes the importance of the system dynamics in milling performance.
b=
−1 (1.1) 2 K s Re(FRF (ω )) Objective
Currently, the tool point FRF is measured by impact testing, where an instrumented hammer (or modal hammer) is used to excite the tool-holder-spindle-machine assembly and the resulting vibration is measured by an appropriate linear transducer, typically a low mass accelerometer. Because the assembly dynamics depend on the individual components as well as their interactions, a new test must be performed for each combination or change in setup (e.g., if the tool overhang length is changed). In many industrial situations, it is not practical to measure each combination due to time restrictions. An additional complication is that these tool point dynamic measurements are necessarily completed with no spindle rotation (zero spindle speed), but in some situations the system dynamics can vary with spindle speed [5]. For micro-milling,
18
the situation is even more problematic because, even for zero spindle speed, it can be difficult or impossible to carry out impact tests on very small diameter endmills (
By CHI HUNG CHENG
A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 2007
1
© 2007 Chi Hung Cheng
2
To my family, my grandfather, and Lord Jesus Christ
3
ACKNOWLEDGMENTS The author would like to thank his advisor Dr. Tony L. Schmitz, for his understanding, patience, and unconditional support. Thanks also go to Dr. John Schueller, Dr. Nagaraj Arakere, Dr. Gloria Wiens, and Dr. Jacob Hammer for serving as committee members. The author also appreciates Dr. John C. Ziegert for always bringing in new ideas when there is a bottle neck and Dr. Nam Ho Kim for helping with micro tool finite element simulation. The thank list extends to the members in Machine Tool Research Center from 2003 to 2007, for all the team works and memorable moments together. With special thanks to Mr. Scott Payne and Mr. Vadim Tymianski for always being “partners of crimes” when there is the need. Finally the author would like to thank his family for the support in every aspect, and the saints in the Church in Gainesville for their loving tender care. Praise the Lord. This work wouldn’t have been done without the sovereign arrangements.
4
TABLE OF CONTENTS page ACKNOWLEDGMENTS ...............................................................................................................4 LIST OF TABLES...........................................................................................................................7 LIST OF FIGURES .........................................................................................................................9 ABSTRACT...................................................................................................................................14 CHAPTER 1
INTRODUCTION ..................................................................................................................16 High Speed Machining ...........................................................................................................16 Chatter And Stability Lobe Diagram......................................................................................16 Objective.................................................................................................................................18
2
LITERATURE REVIEW .......................................................................................................22 Milling Stability Prediction ....................................................................................................22 Experimental Method .............................................................................................................22 Predictive (Non-Experimental) Methods................................................................................23 System Dynamics Acquisition ........................................................................................23 Stability Analysis.............................................................................................................25
3
RECEPTANCE COUPLING SUBSTRUCTURE ANALYSIS ............................................31 Two-Component Receptance Coupling Substructure Analysis .............................................31 Rigid Connection.............................................................................................................31 Non-Rigid Connection with a Linear Spring...................................................................32 Non-Rigid Connection with a Linear Spring and a Damper ...........................................33 Non-Rigid Connection with Linear and Rotational Springs and Dampers .....................34 Three-Component Receptance Coupling Substructure Analysis ...........................................37 Inverse Receptance Coupling Substructure Analysis .............................................................38 Substructure Beam Modeling .................................................................................................41 Euler-Bernoulli Beam......................................................................................................41 Timoshenko Beam...........................................................................................................43 Fluted Tool Modeling .............................................................................................................45
4
ROTATING FREQUENCY RESPONSE FUNCTION PREDICTION................................54 Runout Signal Filtering...........................................................................................................54 Runout Signal ..................................................................................................................55 Runout Filtering...............................................................................................................55 The FRF Prediction from Rotating Standard Holder Measurements .....................................57
5
Stability Boundary Validation ................................................................................................58 5
MICRO SCALE TOOL FREQUENCY RESPONSE FUNCTION PREDICTION..............73 Micro Scale Tools on Macro Machine Systems .....................................................................73 Sensor Options for Micro Tools ......................................................................................73 Modeling Description......................................................................................................74 Experimental Setup .........................................................................................................76 Micro Scale Tools on Micro Spindles ....................................................................................78 The S Value Consideration..............................................................................................78 Sensitivity of Standard Artifact Length...........................................................................79 Micro Tool Frequency Response Function Prediction....................................................80
6
MACRO SCALE TOOL FREQUENCY RESPONSE FUNCTION PREDICTION ............95 Variation in Spindle-Base Receptances with Standard Holder Geometry .............................95 Experimental Results ..............................................................................................................95 The HSK-63A Interface ..................................................................................................96 The CAT-40 Interface .....................................................................................................97 The HSK-100A Interface ................................................................................................98
7
CONCLUSIONS AND FUTURE WORK...........................................................................115 Conclusions...........................................................................................................................115 Future Work..........................................................................................................................116
LIST OF REFERENCES.............................................................................................................118 BIOGRAPHICAL SKETCH .......................................................................................................121
6
LIST OF TABLES Table
page
3-1
Fixed-free steel rod first mode frequency comparison between different beam modeling methods..............................................................................................................52
3-2
Average of area section properties for fluted endmills......................................................53
3-3
Average of area section properties for fluted endmills......................................................53
4-1
HSK-63A short hollow standard holder substructure dimensions.....................................71
4-2
Solid holder substructure dimensions. ...............................................................................71
4-3
Material properties used in RCSA modeling. ....................................................................71
4-4
Substructure dimensions of Regofix collet holder with 12.7 mm diameter, 127 mm overhang carbide tool blank...............................................................................................72
4-5
Substructure dimensions of Regofix collet holder with 25.4 mm diameter, 127 mm overhang carbide tool blank...............................................................................................72
4-6
Substructure dimensions of the endmill-shrink fit holder described in Figure 4-15. ........72
5-1
CAT-40 standard holder artifact substructure section dimensions. ...................................93
5-2
CAT-40 ER-25 collet holder and tool substructure section dimensions............................93
5-3
S values for micro standard artifacts..................................................................................94
5-4
Tapered tool (23.5 mm OH) substructure section dimensions. .........................................94
6-1
HSK-63A long hollow standard holder artifact substructure dimensions. ......................111
6-2
Substructure dimensions for HSK-63A long shrink fit holder (section I at free end). ....111
6-3
Substructure dimensions for HSK-63A long shrink fit holder (section I at free end). ....112
6-4
Extended holder lengths of the HSK-63A standard artifacts and shrink fit holders........112
6-5
CAT-40 long hollow standard holder artifact substructure dimensions. .........................112
6-6
CAT-40 short hollow standard holder artifact substructure dimensions. ........................112
6-7
CAT-40 short solid standard holder artifact substructure dimensions.............................112
6-8
CAT-40 shrink fit holder substructure dimensions..........................................................112
7
6-9
CAT-40 long collet holder substructure dimensions. ......................................................112
6-10
CAT-40 short collet holder substructure dimensions. .....................................................113
6-11
Extended holder lengths of the CAT-40 standard artifacts and tested holders................113
6-12
HSK-100A short hollow standard holder artifact substructure dimensions. ...................113
6-13
HSK-100A long soild standard holder artifact substructure dimensions.........................113
6-14
Substructure dimensions of Briney HSK100ASF-075-433 shrink fit holder with Sandvik A393.T-19 10 175 carbide adapter and two square insert cutting head. ...........113
6-15
Substructure dimensions of Briney HSK100AE-125-472 set screw holder with Mitsubishi Carbide MBN 10 1000 TB steel tapered ball end..........................................114
6-16
Extended holder lengths of the HSK-100A standard artifacts and tested holders...........114
8
LIST OF FIGURES Figure
page
1-1
HSM cutting speed ranges for various materials. ..............................................................20
1-2
Scheme of (flexible) cutting edge passing through workpiece surface. ............................20
1-3
Stable cut and unstable cut (chatter) on a workpiece surface. ...........................................21
1-4
Example stability lobe diagram. ........................................................................................21
1-5
Block diagram for cutting process with regenerated wavy surface. ..................................21
2-1
Different approaches to determine stable cutting conditions.............................................28
2-2
Ball bearing contact angles at high speed rotation.............................................................29
2-3
Impact testing performed on standard artifact with modal hammer and laser vibrometer. .........................................................................................................................29
2-4
Example of time-domain simulation of an unstable cutting process. ................................30
2-5
Predicted and measured FRF of a 100 mm diameter inserted endmill. .............................30
3-1
Components joined with a rigid connection. .....................................................................46
3-2
Components connected with a linear spring. .....................................................................47
3-3
Assembly with linear spring and damper...........................................................................48
3-4
Assembly with linear and rotational springs and dampers. ...............................................49
3-5
Generic case of two substructures with rigid connection. .................................................50
3-6
Three-component RCSA model for tool-holder-spindle assembly. ..................................50
3-7
Spindle and decomposed standard holder artifact. ............................................................50
3-8
Ansys Workbench frequency simulation for 19.1 mm diameter fixed-free steel rod with 80 mm length. ............................................................................................................51
3-9
Cutting edge of a four fluted flat endmill cutter. ...............................................................51
3-10
Solid model of two-fluted endmill cross-section. ..............................................................52
4-1
Speed-dependent FRFs of the standard holder at five different spindle speeds: {0, 2500, 7500, and 10000} rpm. ............................................................................................60
9
4-2
Example setup for rotating FRF measurement. .................................................................61
4-3
Example of holder and runout signal resultant response. ..................................................61
4-4
Scheme of tachometer-aided runout filtering setup. ..........................................................62
4-5
Illustration of once-per-revolution signal identification ....................................................62
4-6
Example of shrink fit holder time-domain runout filtering. ..............................................63
4-7
Frequency response function comparison with/without time-domain filtering.................64
4-8
Short hollow standard holder geometry and substructure coordinates. .............................64
4-9
Experimental setup of standard holder (HSK-63A interface) rotating FRF measurement. .....................................................................................................................65
4-10
Solid holder geometry and substructure coordinates. ........................................................65
4-11
Solid holder FRF measurement and prediction at {10000, 12000, and 16000} rpm. .......66
4-12
Geometry of Regofix collet holder with tool.....................................................................66
4-13
Measured and predicted FRFs for Regofix collet holder with 12.7 mm diameter 127 mm overhang carbide tool blank at 10,000 rpm. ...............................................................67
4-14
Measured and predicted FRFs for Regofix collet holder with 25.4 mm diameter 127 mm overhang carbide tool blank at 10,000 rpm. ...............................................................67
4-15
Geometry of 19.1 mm diameter, four flutes, carbide endmill with 76.1 mm overhang length clamped in Command shrink fit holder. .................................................................68
4-16
Stability lobes for FRF measurement at 0 rpm and predictions at {10000 and 16000} rpm for 19.1 mm diameter, four flute, carbide endmill .....................................................68
4-17
Setup for cutting tests. The tool shank deflections were measured using two orthogonal capacitance probes...........................................................................................69
4-18
Example results for 8000 rpm slotting cuts. ......................................................................70
4-19
Comparison of test cut results to predicted stability boundaries determined from 0 rpm (measured) and {10000 and 16000} rpm (predicted) FRFs. ......................................71
5-1
Example setup of high speed machining with micro tools. ...............................................82
5-2
Dimension comparison of a 1mm diameter, two-flute micro endmill to a penny. ............82
5-3
CAT-40 standard holder artifact geometry. .......................................................................82
10
5-4
CAT-40 ER-25 collet holder and tool geometry................................................................83
5-5
Experimental setup for CAT-40 collet holder with 3.18 mm steel tool shank. .................83
5-6
Magnitudes of H 41 FRFs measurements (top) and predictions (bottom). ........................84
5-7
Measured and predicted H 41 with 46.0 mm tool overhang (marked as 9 in Fig. 5-6)......84
5-8
Measured and predicted H 41 with 50.8 mm tool overhang (marked as 12 in Fig. 5-6)....85
5-9
Multiplication factor (MF) determined from visual fit in relation to the tool overhang with a linear approximation superimposed. .......................................................................85
5-10
FRFs of H 44 , magnitude measurements (top) and predictions (bottom). ..........................86
5-11
Measured and predicted H 44 with 46.0 mm tool overhang (marked as 9 in Fig. 5-10)....86
5-12
Measured and predicted H 44 with 50.8 mm tool overhang (marked as 12 in Fig. 510). .....................................................................................................................................87
5-13
NSK HES 500 electric micro spindle. ...............................................................................87
5-14
Experimental setup for determination of micro spindle-base receptances. .......................88
5-15
Prediction of tool point FRF for 3.18 mm diameter, 21 mm overhang steel rod by a 17 mm overhang standard artifact with three different S values. ......................................89
5-16
FRF prediction of a 3.18 mm diameter, 21 mm overhang steel rod by 20 mm (solid) and 17 mm (dotted) overhang standard tool artifacts ........................................................90
5-17
Example 3.18 mm shank diameter tapered tool (no flutes) with 1.5 mm diameter tool tip. ......................................................................................................................................90
5-18
Geometry of NSK HES 500 micro spindle with tapered tool............................................91
5-19
Tool tip measurement of tapered tool with an overhang of 23.5 mm compared to predictions based on different standard artifact overhang lengths.....................................91
5-20
Measurement of tapered tool (with overhang length of 25.5 mm) FRF compared with selected standard artifact FRF predictions.........................................................................92
5-21
FRFs for free-free tapered tool and standard artifact responses coupled to rigid spindle receptances. ...........................................................................................................93
6-1
HSK-63A spindle-base receptances calculated by long and short hollow standard holders................................................................................................................................99
6-2
Geometry of HSK-63A long hollow standard hollow holder artifact..............................100 11
6-3
HSK-63A shrink fit holders: long hollow (left) and short hollow (right)........................100
6-4
HSK-63A FRF predictions for long shrink fit holder by short hollow artifact with different S values in comparison with measured FRF (heavy solid line). .......................101
6-5
HSK-63A long shrink fit holder FRF predictions using two different standard holders in comparison with measured FRF (heavy solid line). ....................................................101
6-6
HSK-63A short shrink fit holder FRF predictions using two different standard holders in comparison with measured FRF (heavy solid line). .......................................102
6-7
Geometry of CAT-40 long hollow standard holder artifact.............................................102
6-8
Geometry of CAT-40 short hollow standard holder artifact............................................103
6-9
Geometry of CAT-40 short solid standard holder artifact. ..............................................103
6-10
CAT-40 shrink fit holder FRF predictions in comparison with measured FRF (heavy solid line). ........................................................................................................................104
6-11
CAT-40 long collet holder FRF predictions in comparison with measured FRF (heavy solid line)..............................................................................................................104
6-12
CAT-40 short collet holder FRF predictions in comparison with measured FRF (heavy solid line)..............................................................................................................105
6-13
Geometry of HSK-100A short hollow standard holder artifact.......................................105
6-14
Geometry of HSK-100A long solid standard holder artifact. ..........................................106
6-15
Geometry of Briney HSK100ASF-075-433 shrink fit holder with Sandvik A393.T19 10 175 carbide adapter and two square insert cutting head. .......................................106
6-16
Geometry of Briney HSK100AE-125-472 set screw holder with Mitsubishi Carbide MBN 10 1000 TB steel tapered ball end mill with one round carbide insert. .................107
6-17
HSK100ASF-075-433 shrink fit holder with Sandvik A393.T-19 10 175 carbide adapter and two square insert cutting head measurement and prediction........................107
6-18
HSK100ASF-075-433 shrink fit holder with Sandvik A393.T-19 10 175 carbide adapter and two square insert cutting head measurement and prediction........................108
6-19
HSK100ASF-075-433 shrink fit holder with Sandvik A393.T-19 10 175 carbide adapter and two square insert cutting head measurement and prediction........................108
6-20
HSK100ASF-075-433 shrink fit holder with Sandvik A393.T-19 10 175 carbide adapter and two square insert cutting head measurement and prediction........................109
12
6-21
HSK100AE-125-472 set screw holder with Mitsubishi Carbide MBN 10 1000 TB steel tapered ball end mill with one round carbide insert measurement and prediction .109
6-22
HSK100AE-125-472 set screw holder with Mitsubishi Carbide MBN 10 1000 TB steel tapered ball end mill with one round carbide insert measurement and prediction ..110
6-23
HSK100AE-125-472 set screw holder with Mitsubishi Carbide MBN 10 1000 TB steel tapered ball end mill with one round carbide insert measurement and prediction .110
6-24
HSK100AE-125-472 set screw holder with Mitsubishi Carbide MBN 10 1000 TB steel tapered ball end mill with one round carbide insert measurement and prediction ..111
13
Abstract of Dissertation Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy IMPROVED PREDICTION OF SPINDLE-HOLDER-TOOL FREQUENCY RESPONSE FUNCTIONS By Chi Hung Cheng August 2007 Chair: Tony L. Schmitz Major: Mechanical Engineering High speed machining (HSM) offers tremendous capabilities for discrete part manufacturing because it can provide high material removal rates (MRR) in metals, plastics, and composites with good surface finish. To realize these benefits, stability lobe diagrams, which define regions of stable cutting as a function of spindle speed and axial depth of cut, can be used to select appropriate cutting conditions. Computation of these diagrams requires that the dynamics of the cutting system (the machine, spindle, holder, and tool assembly) be known. Typically, impact testing (i.e., exciting the structure with an instrumented hammer and recording the response with a linear transducer) is used to record the required tool point frequency response. However, due to the diversity of tool holders and tools available to end users, it can be prohibitively time-consuming to perform impact testing for each possible combination. Further, it is difficult to measure the responses of 1) small tools using traditional methods; and 2) spindles during high speed rotation. The former is necessary for new micro-milling applications, while the latter is required because the at-speed response for some spindles can differ from the nonrotating response. This study provides a method to address these situations. The tool tip response for a given machine-spindle-holder-tool assembly is predicted by coupling a spindle measurement with
14
finite element models of the holder and tool using the method of receptance coupling substructure analysis (RCSA). RCSA enables a user to analytically couple arbitrary tool-holder combinations to an archived spindle response. Therefore, the user must perform only a single test on the spindle in question. Given this information, the tool point response for any tool-holder can be performed via a ‘virtual impact test’. Comparisons of predictions and experimental results are provided for 1) micro-tools; and 2) macro-scale tools coupled to a spindle that exhibits changing dynamics with spindle speed.
15
CHAPTER 1 INTRODUCTION High Speed Machining High speed machining (HSM) is an important capability in modern, discrete part manufacturing. Using the higher cutting speeds made possible by improved cutting tool materials and coatings, the machine operation time is reduced significantly (Fig. 1-1 [1]). The use of HSM makes it possible to efficiently produce complex parts and, therefore, reduce assembly time and costs relative to the traditional approach where simpler shapes are machined and then mechanically joined. High speed machines typically use direct drive spindles, i.e., a spindle shaft with permanent magnets is driven by a coil located within the surrounding housing. Modern spindle designs can reach top speeds of 40,000 rpm and higher with powers at the many tens of kW level. At these higher speeds, micro-milling (or milling with very small diameter cutters) is now realizable because reasonable cutting speeds, or peripheral velocities of the cutting edge, can still be maintained even though the cutting edge radius may only be fractions of a millimeter. The advantage of high speed micro-machining is that it provides a process capable of producing complex, free form, three-dimensional (3-D) structures from virtually any material. This provides an alternative to typical MEMS (micro electro mechanical systems) fabrications techniques, such as silicon etching, that are generally limited to 2-D geometries and specialized materials. Therefore, it can be expected that the demand of HSM will continue to increase. Chatter And Stability Lobe Diagram Surface location error (SLE) and chatter, or unstable machining conditions, impose limitations on machining efficiency. For any machining operation, the cutting force acting on the
16
tool causes it to vibrate. This vibration can lead to chatter and corresponding large forces and potential damage. Even if the operation is stable, however, the vibration state of the tool as it leaves the newly created surface defines the location of that surface. Variations in the process parameters can yield either undercut (less material removed than commanded) or overcut (more material removed) situations; this phenomenon is referred to as surface location error. For either limitation, it is important to note that the tool-holder-spindle-machine assembly response as reflected at the tool point (free end of the tool) strongly influences the final behavior. Chatter occurs due to the inherent feedback mechanism in machining. In turning and milling operations, the tool cutting edge makes multiple passes through the workpiece surface to achieve the desired dimension. For each pass, the tool vibrations are imprinted on the surface. Therefore, the workpiece surface is not uniform and the current chip thickness depends both on the current tool vibrations and those during the previous pass (Fig. 1-2), which Arnold [2] refers to as the regeneration of waviness. As the cutting edge removes the wavy surface, the force is modulated by the varying chip thickness, which leads to further vibration. Depending on the machining parameters, the feedback system can become unstable and chatter occurs (Fig. 1-3). The large force and significant tool deflections associated with chatter can be identified audibly. It not only creates an unacceptable machined surface finish, but can also damage the machine tool, spindle bearings, tool, and workpiece. To avoid chatter, stability lobe diagrams can be applied. These diagrams (as shown in Fig. 1-4) enable the machine operator to choose a proper spindle speed-chip width (axial depth for peripheral end milling) for stable cutting conditions. The concept of the stability lobe diagram was first developed in 1956 [3]. However, large industrial benefits were not realized until the high speed machines became commercially available. As can be seen in Fig. 1-4, the width of the
17
stable regions (beneath the lobes) tends to widen as the spindle speed becomes higher. Therefore, operating in these higher speed regions increases the material removal rate both by the increased cutting speed and higher axial depth of cut. Methods used to compute the stability limit are described in Chapter 2. The feedback mechanism in machining can also be represented using a block diagram approach as shown in Fig. 1-5 [4]. The system dynamics are represented by a second order plant in the forward path. The force is determined by multiplying the difference between the current and time-delayed chip thickness valued by the gain, represented by the product of the specific cutting energy and chip width. Based on this block diagram, the limiting chip width can be expressed for turning operations as shown in Eq. 1.1 where FRF is the system frequency response function. This equation emphasizes the importance of the system dynamics in milling performance.
b=
−1 (1.1) 2 K s Re(FRF (ω )) Objective
Currently, the tool point FRF is measured by impact testing, where an instrumented hammer (or modal hammer) is used to excite the tool-holder-spindle-machine assembly and the resulting vibration is measured by an appropriate linear transducer, typically a low mass accelerometer. Because the assembly dynamics depend on the individual components as well as their interactions, a new test must be performed for each combination or change in setup (e.g., if the tool overhang length is changed). In many industrial situations, it is not practical to measure each combination due to time restrictions. An additional complication is that these tool point dynamic measurements are necessarily completed with no spindle rotation (zero spindle speed), but in some situations the system dynamics can vary with spindle speed [5]. For micro-milling,
18
the situation is even more problematic because, even for zero spindle speed, it can be difficult or impossible to carry out impact tests on very small diameter endmills (
