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Research Papers

Transient Vibration Analysis Method for Predicting the Transient Behavior of Milling With Variable Spindle Speeds

[+] Author and Article Information
Xinzhi Wang

State Key Laboratory of Mechanical,
System and Vibration,
School of Mechanical Engineering,
Shanghai Jiao Tong University,
Shanghai 200240, China
e-mail: 1130209030@sjtu.edu.cn

QingZhen Bi

State Key Laboratory of Mechanical,
System and Vibration,
School of Mechanical Engineering,
Shanghai Jiao Tong University,
Shanghai 200240, China
e-mail: biqz@sjtu.edu.cn

Tao Chen

State Key Laboratory of Mechanical,
System and Vibration,
School of Mechanical Engineering,
Shanghai Jiao Tong University,
Shanghai 200240, China
e-mail: sjtu-chent@sjtu.edu.cn

Limin Zhu

State Key Laboratory of Mechanical,
System and Vibration,
School of Mechanical Engineering,
Shanghai Jiao Tong University,
Shanghai 200240, China
e-mail: zhulm@sjtu.edu.cn

Han Ding

State Key Laboratory of Mechanical,
System and Vibration,
School of Mechanical Engineering,
Shanghai Jiao Tong University
Shanghai 200240, China
e-mail: hding@sjtu.edu.cn

1Corresponding author.

Manuscript received November 8, 2018; final manuscript received March 19, 2019; published online April 2, 2019. Assoc. Editor: Tony Schmitz.

J. Manuf. Sci. Eng 141(5), 051009 (Apr 02, 2019) (10 pages) Paper No: MANU-18-1781; doi: 10.1115/1.4043265 History: Received November 08, 2018; Accepted March 19, 2019

Variable spindle speed (VSS) technique is widely adopted for its effective suppression of chatter. However, heavy transient vibrations occur in practical machining operations although the stable machining parameters are selected according to the asymptotic stability analysis methods. In this paper, this problem is addressed through establishing a transient vibration analysis method to predict the transient behavior of VSS milling. Firstly, the discrete dynamical map of VSS milling is constructed, and the response to initial conditions (RTICs) and the response to external forcing (RTEF) can fully describe the general milling dynamics. On this basis, two transient vibration growth phenomena are found and proved that strong transient vibrations are induced by the transient growth of RTIC or RTEF. To fully predict the transient vibration growth phenomenon, the proposed method adopts the transient stability and receptivity analyses to evaluate RTIC and RTEF, respectively. Other than the existing methods, it gives a stability criterion based on both eigenvalues and nonnormal eigenvectors and considers the transient behavior to external excitation. Besides simulations, a real milling test in an existing work and VSS milling experiments are adopted for verification. The results show good agreement with the prediction of the proposed method.

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References

Quintana, G., and Ciurana, J., 2011, “Chatter in Machining Processes: A Review,” Int. J. Mach. Tools Manuf., 51(5), pp. 363–376. [CrossRef]
Bi, Q. Z., Huang, J., Lu, Y. A., Zhu, L. M., and Ding, H., 2019, “A General, Fast and Robust B-Spline Fitting Scheme for Micro-Line Tool Path Under Chord Error Constraint,” Sci. China Technol. Sci. 62(2), pp. 321–332. [CrossRef]
Altintas, Y., and Weck, M., 2004, “Chatter Stability of Metal Cutting and Grinding,” CIRP Annals Manuf. Technol., 53(2), pp. 619–642. [CrossRef]
Yan, R., Li, H., Peng, F., Tang, X., Xu, J., and Zeng, H., 2017, “Stability Prediction and Step Optimization of Trochoidal Milling,” ASME J. Manuf. Sci. Eng., 139(9), pp. 091006. [CrossRef]
Tang, X., Zhu, Z., Yan, R., Chen, C., Peng, F., Zhang, M., and Li, Y., 2018, “Stability Prediction Based Effect Analysis of Tool Orientation on Machining Efficiency for Five-Axis Bull-Nose End Milling,” ASME J. Manuf. Sci. Eng., 140(12), p. 121015. [CrossRef]
Lu, Y., Ding, Y., and Zhu, L., 2017, “Dynamics and Stability Prediction of Five-Axis Flat-End Milling,” ASME J. Manuf. Sci. Eng., 139(6), p. 061015. [CrossRef]
Tuysuz, O., and Altintas, Y., 2017, “Frequency Domain Updating of Thin-Walled Workpiece Dynamics Using Reduced Order Substructuring Method in Machining,” ASME J. Manuf. Sci. Eng., 139(7), p. 071013. [CrossRef]
Comak, A., and Altintas, Y., 2018, “Dynamics and Stability of Turn-Milling Operations With Varying Time Delay in Discrete Time Domain,” ASME J. Manuf. Sci. Eng., 140(10), p. 101013. [CrossRef]
Niu, J., Ding, Y., Geng, Z., Zhu, L., and Ding, H., 2018, “Patterns of Regenerative Milling Chatter Under Joint Influences of Cutting Parameters, Tool Geometries, and Runout,” ASME J. Manuf. Sci. Eng., 140(12), p. 121004. [CrossRef]
Honeycutt, A., and Schmitz, T., 2017, “A Numerical and Experimental Investigation of Period-N Bifurcations in Milling,” ASME J. Manuf. Sci. Eng., 139(1), p. 011003. [CrossRef]
Tao, H., Zhu, L., Du, S., Chen, Z., and Han, D., 2018, “Robust Active Chatter Control in Milling Processes With Variable Pitch Cutters,” ASME J. Manuf. Sci. Eng., 140(10), p. 101005. [CrossRef]
Sexton, J., Milne, R., and Stone, B., 1977, “A Stability Analysis of Single-Point Machining With Varying Spindle Speed,” Appl. Math. Model. 1(6), pp. 310–318. [CrossRef]
Altintas, Y., and Chan, P. K., 1992, “In-Process Detection and Suppression of Chatter in Milling,” Int. J. Mach. Tools Manuf., 32(3), pp. 329–347. [CrossRef]
Soliman, E., and Ismail, F., 1997, “Chatter Suppression by Adaptive Speed Modulation,” Int. J. Mach. Tools Manuf., 37(3), pp. 355–369. [CrossRef]
Al-Regib, E., Ni, J., and Lee, S. H., 2003, “Programming Spindle Speed Variation for Machine Tool Chatter Suppression,” Int. J. Mach. Tools Manuf., 43(12), pp. 1229–1240. [CrossRef]
Ding, L., Sun, Y., and Xiong, Z., 2018, “Online Chatter Suppression in Turning by Adaptive Amplitude Modulation of Spindle Speed Variation,” ASME J. Manuf. Sci. Eng., 140(12), p. 121003. [CrossRef]
Tsao, T. C., Mccarthy, M. W., and Kapoor, S. G., 1993, “A New Approach to Stability Analysis of Variable Speed Machining Systems,” Int. J. Mach. Tools Manuf., 33(6), pp. 791–808. [CrossRef]
Jayaram, S., Kapoor, S. G., and Devor, R. E., 2000, “Analytical Stability Analysis of Variable Spindle Speed Machining,” ASME J. Manuf. Sci. Eng., 122(3), pp. 391–397. [CrossRef]
Sastry, S., Kapoor, S. G., Devor, R. E., and Dullerud, G. E., 2001, “Chatter Stability Analysis of The Variable Speed Face-Milling Process,” ASME J. Manuf. Sci. Eng., 123(4), pp. 753–756. [CrossRef]
Sastry, S., Kapoor, S. G., and Devor, R. E., 2015, “Floquet Theory Based Approach for Stability Analysis of the Variable Speed Face-Milling Process,” ASME J. Manuf. Sci. Eng., 124(1), pp. 10–17. [CrossRef]
Tamas, I., and Gabor, S., 2004, “Stability Analysis of Turning With Periodic Spindle Speed Modulation via Semidiscretization,” J. Vib. Control, 10(12), pp. 1835–1855.
Long, X., and Balachandran, B., 2010, “Stability of Up-Milling and Down-Milling Operations With Variable Spindle Speed,” J. Vib. Control, 16(16), pp. 1151–1168. [CrossRef]
Seguy, S., Insperger, T., Arnaud, L., Dessein, G., and Peign, G., 2010, “On the Stability of High-Speed Milling With Spindle Speed Variation,” Int. J. Adv. Manuf. Technol., 48(9–12), pp. 883–895. [CrossRef]
Totis, G., 2009, “Rcpma New Method for Robust Chatter Prediction in Milling,” Int. J. Mach. Tools Manuf., 49(3), pp. 273–284. [CrossRef]
Ding, Y., Niu, J., Zhu, L. M., and Ding, H., 2016, “Numerical Integration Method for Stability Analysis of Milling With Variable Spindle Speeds,” ASME J. Vib. Acoust., 138(1), p. 011010. [CrossRef]
Niu, J., Ding, Y., Zhu, L. M., and Ding, H., 2016, “Stability Analysis of Milling Processes With Periodic Spindle Speed Variation via the Variable-Step Numerical Integration Method,” ASME J. Manuf. Sci. Eng., 138(11), p. 114501. [CrossRef]
Sexton, J. S., and Stone, B. J., 1980, “An Investigation of the Transient Effects During Variable Speed Cutting,” ARCHIVE J. Mech. Eng. Sci. 1959–1982 (vols 1–23), 22(3), pp. 107–118.
Smith, S., and Tlusty, J., 1993, “Efficient Simulation Programs for Chatter in Milling,” Annals Cirp, 42(1), pp. 463–466. [CrossRef]
Campomanes, M. L., and Altintas, Y., 2003, “An Improved Time Domain Simulation for Dynamic Milling at Small Radial Immersions,” ASME J. Manuf. Sci. Eng., 125(3), pp. 416–422. [CrossRef]
Otto, A., and Radons, G., 2013, “Application of Spindle Speed Variation for Chatter Suppression in Turning,” CIRP J. Manuf. Sci. Technol., 6(2), pp. 102–109. [CrossRef]
Bi, Q., Wang, X. Z., Chen, H., Zhu, L. M., and Ding, H., 2018, “Non-Normal Dynamic Analysis for Predicting Transient Milling Stability,” J. Dyn. Syst. Meas. Control, 140(8), p. 084501. [CrossRef]
Farkas, M., 2013, Periodic Motions, Vol. 104, Springer Science & Business Media, New York.
Schmid, P. J., and Henningson, D. S., 2012, Stability and Transition in Shear Flows, Vol. 142, Springer Science & Business Media, New York.
Wan, M., Zhang, W. H., Dang, J. W., and Yang, Y., 2009, “New Procedures for Calibration of Instantaneous Cutting Force Coefficients and Cutter Runout Parameters in Peripheral Milling,” Int. J. Mach. Tools Manuf., 49(14), pp. 1144–1151. [CrossRef]

Figures

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Fig. 1

Vibration displacement during VSS milling [18]

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Fig. 2

Schematic diagram of milling process

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Fig. 3

Triangular spindle speed modulation

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Fig. 4

Geometric interpretation of transient vibration growth: (a) decaying iteration of the vector g superposition of two nonorthogonal eigenvectors S1 and S2 and (b) evaluation of the length of the vector g

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Fig. 5

Maximum energy amplification G(k) curve (red curve) and 2000 growth curves generated under randomly selected initial conditions (black curve) along with their upper and lower envelope curves and mean curve (green curves)

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Fig. 6

A time domain simulation performed at axial cutting depth of 1.8 mm and spindle speed of 9100 rpm: (a) spindle speed variation plot and (b) the RTIC plot

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Fig. 7

A time domain simulation performed at axial cutting depth of 1.3 mm and spindle speed of 9100 rpm: (a) spindle speed variation plot, (b) the RTIC plot, and (c) vibration displacement plot considering both RTIC and RTEF

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Fig. 8

Analysis of the time domain simulation at axial cutting depth of 1.8 mm and spindle speed of 9100 rpm: (a) the RTIC plot and (b) maximum energy amplification G(t) plot

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Fig. 9

Analysis of the time domain simulation at axial cutting depth of 1.3 mm and spindle speed of 9100 rpm: (a) the RTIC plot, (b) maximum energy amplification G(t) plot, (c) vibration displacement plot considering both RTIC and RTEF, and (d) maximum moduli of all the eigenvalues of the transition relation matrix over one sample period

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Fig. 10

Analysis of the cutting test at axial cutting depth of 2 mm and spindle speed of 9100 rpm: (a) vibration displacement plot in a real milling test, (b) maximum energy amplification G(t) plot, and (c) maximum moduli of all the eigenvalues of the transition relation matrix over one sample period

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Fig. 11

Experimental setup: (1) DYRAN impact hammer 5800B4, (2) PCB accelerometer 352A21, (3) flexible workpiece for experiment validation, (4) fixture, (5) workpiece for identifying cutting force coefficients, (6) Kistler dynamometer 9255C, (7) LMS test Lab instrument, (8) the polytec laser vibrometer controller, (9) polytec laser sensor, and (10) Siemens 840D NC system

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Fig. 12

Flexible workpiece geometry

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Fig. 13

Frequency response functions of Workpiece 1 and Workpiece 2: (a) comparison of direct FRFs of flexible workpiece, cutting tool in the X-direction and cutting tool in the Y-direction and (b) comparison of direct FRFs of flexible workpiece before and after machining

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Fig. 14

Flexible workpiece clamping and schematic of vibration tracking set up

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Fig. 15

Analysis of condition A and condition B in milling of workpiece 1: (a) spindle speed variation plot in condition A, (b) vibration displacement plot in condition A, (c) maximum energy amplification G(t) plot in condition A, (d) maximum moduli of all the eigenvalues of the transition relation matrix over one sample period in condition A, (e) spindle speed variation plot in condition B, (f) vibration displacement plot in condition B, (g) maximum energy amplification G(t) plot in condition B, and (h) maximum moduli of all the eigenvalues of the transition relation matrix over one sample period in condition B

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Fig. 16

Analysis of condition C and condition D in milling of workpiece 2: (a) spindle speed variation plot in condition C, (b) vibration displacement plot in condition C, (c) maximum energy amplification G(t) plot in condition C, (d) maximum moduli of all the eigenvalues of the transition relation matrix over one sample period in condition C, (e) spindle speed variation plot in condition D, (f) vibration displacement plot in condition D, (g) maximum energy amplification G(t) plot in condition D, and (h) maximum moduli of all the eigenvalues of the transition relation matrix over one sample period in condition D

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