Abstract
One of the major limitations of micro-milling applications in industries is its fast tool wear, which leads to low machining precision and efficiency. An accurate force model is fundamental for optimization micro-milling processes and minimize the tool wear. However, a generic model with tool runout and wear effect has not yet been established, which limits its practical application under varied working conditions. In this paper, a new idea is introduced by applying the spatial analytic geometry (SAG) method, under this framework the micro-milling force model is established based on the analysis of the geometrical relationship among the cutting edge positions, pre-processed workpiece morphology, and cutting force directions considering tool runout and wear effect. In this model, the tool runout is identified exclusively by only one parameter, namely the distance away from the center that perpendicular to the feed direction, so that it could be calibrated conveniently by calculating the ratio of resultant forces corresponding to different cutting edges. The tool wear–induced force is then modeled as increment of force coefficients to the original model. Therefore, the new force model with considering tool wear has the same form as the fresh tool. Finally, the accuracy and efficiency of the model are validated by experiments under varied working conditions.
Similar content being viewed by others
Abbreviations
- SA:
-
Spatial analytic geometry
- UCT:
-
Uncut chip thickness
- XwYwZw-Ow :
-
Workpiece coordinates
- XTYTZT-OT :
-
Tool coordinates
- XSYSZS-OS :
-
Spindle coordinates
- dFr, Fr :
-
Radial force
- dFt, Ft :
-
Tangential force
- φ :
-
Rotation angle of the tool
- Ktc, Krc :
-
Coefficients of tangential and radial force
- dh j :
-
UCT of the discrete element
- db :
-
Length of the discrete element along the tool edge
- Nj :
-
Amount of the discrete element
- r1, r2 :
-
Rotating radius around the ZS-axis for the two edges
- r out :
-
Tool runout
- xout, yout :
-
Tool axis position parameters
- θ out :
-
Angle between YS-axis and linkage of tool edge and center
- r t :
-
Tool radius
- f t :
-
Feed per tooth
- rts1, rts2 :
-
Rotation radiuses of the two edges
- \( {K}_{\mathbf{tc}}^{\mathbf{wear}} \), \( {K}_{\mathbf{rc}}^{\mathbf{wear}} \) :
-
Coefficients of tangential and radial force considering tool wear
- P :
-
Tool lead
- N :
-
Number of edges
References
Zhang X, Yu T, Wang W, Zhao J (2019) Improved analytical prediction of burr formation in micro end milling. Int J Mech Sci 151:461–470. https://doi.org/10.1016/j.ijmecsci.2018.12.005
Davim JP (2014) Modern mechanical engineering. Materials Forming, Machining and Tribology. https://doi.org/10.1007/978-3-642-45176-8
Mian AJ, Driver N, Mativenga PT (2011) Estimation of minimum chip thickness in micro-milling using acoustic emission. 225 (9):1535-1551. https://doi.org/10.1177/0954405411404801
Kang IS, Kim JS, Kim JH, Kang MC, Seo YW (2007) A mechanistic model of cutting force in the micro end milling process. J Mater Process Technol 187-188:250–255. https://doi.org/10.1016/j.jmatprotec.2006.11.155
Afazov SM, Ratchev SM, Segal J (2010) Modelling and simulation of micro-milling cutting forces. J Mater Process Technol 210(15):2154–2162. https://doi.org/10.1016/j.jmatprotec.2010.07.033
Afazov SM, Zdebski D, Ratchev SM, Segal J, Liu S (2013) Effects of micro-milling conditions on the cutting forces and process stability. J Mater Process Technol 213(5):671–684. https://doi.org/10.1016/j.jmatprotec.2012.12.001
Davoudinejad A, Tosello G, Parenti P, Annoni M (2017) 3D finite element simulation of micro end-milling by considering the effect of tool run-out. Micromachines-Basel 8(6). https://doi.org/10.3390/mi8060187
Chen N, Li L, Wu J, Qian J, He N, Reynaerts D (2019) Research on the ploughing force in micro milling of soft-brittle crystals. Int J Mech Sci 155:315–322. https://doi.org/10.1016/j.ijmecsci.2019.03.004
Kang Y-H, Zheng CM (2012) Fourier analysis for micro-end-milling mechanics. Int J Mech Sci 65(1):105–114. https://doi.org/10.1016/j.ijmecsci.2012.09.008
Wojciechowski S, Mrozek K (2017) Mechanical and technological aspects of micro ball end milling with various tool inclinations. Int J Mech Sci 134:424–435. https://doi.org/10.1016/j.ijmecsci.2017.10.032
Sahoo P, Pratap T, Patra K (2019) A hybrid modelling approach towards prediction of cutting forces in micro end milling of Ti-6Al-4V titanium alloy. Int J Mech Sci 150:495–509. https://doi.org/10.1016/j.ijmecsci.2018.10.032
Arrazola PJ, Özel T, Umbrello D, Davies M, Jawahir IS (2013) Recent advances in modelling of metal machining processes. CIRP Ann 62(2):695–718. https://doi.org/10.1016/j.cirp.2013.05.006
Jing X, Tian Y, Yuan Y, Wang F (2017) A runout measuring method using modeling and simulation cutting force in micro end-milling. Int J Adv Manuf Technol 91(9–12):4191–4201. https://doi.org/10.1007/s00170-017-0076-9
Matsumura T, Tamura S (2017) Cutting force model in milling with cutter runout. Procedia CIRP 58:566–571. https://doi.org/10.1016/j.procir.2017.03.268
Dadgari A, Huo D, Swailes D (2018) Investigation on tool wear and tool life prediction in micro-milling of Ti-6Al-4V. Nanotech Precis Eng 1(4):218–225. https://doi.org/10.1016/j.npe.2018.12.005
Alhadeff LL, Marshall MB, Curtis DT, Slatter T (2019) Protocol for tool wear measurement in micro-milling. Wear 420-421:54–67. https://doi.org/10.1016/j.wear.2018.11.018
Li Z-L, Zhu L-M (2014) Envelope surface modeling and tool path optimization for five-axis flank milling considering cutter Runout. J Manuf Sci E-T ASME 136(4):041021–041029. https://doi.org/10.1115/1.4027415
Li Z-L, Niu J-B, Wang X-Z, Zhu L-M (2015) Mechanistic modeling of five-axis machining with a general end mill considering cutter runout. Int J Mach Tool Manu 96:67–79. https://doi.org/10.1016/j.ijmachtools.2015.06.006
Zhu Z, Yan R, Peng F, Duan X, Zhou L, Song K, Guo C (2016) Parametric chip thickness model based cutting forces estimation considering cutter runout of five-axis general end milling. Int J Mach Tool Manu 101:35–51. https://doi.org/10.1016/j.ijmachtools.2015.11.001
Zhang X, Yu T, Wang W (2018) Prediction of cutting forces and instantaneous tool deflection in micro end milling by considering tool run-out. Int J Mech Sci 136:124–133. https://doi.org/10.1016/j.ijmecsci.2017.12.019
Yun W-S, Cho D-W (2000) An improved method for the determination of 3D cutting force coefficients and runout parameters in end milling. Int J Adv Manuf Technol 16(12):851–858. https://doi.org/10.1007/s001700070001
Hoon Ko J, Cho D-W (2005) 3D ball-end milling force model using instantaneous cutting force coefficients. J Manuf Sci E-T ASME 127(1):1–12. https://doi.org/10.1115/1.1826077
Li K, Zhu K, Mei T (2016) A generic instantaneous undeformed chip thickness model for the cutting force modeling in micromilling. Int J Mach Tool Manu 105:23–31. https://doi.org/10.1016/j.ijmachtools.2016.03.002
Wan M, Zhang W-H, Dang J-W, Yang Y (2009) New procedures for calibration of instantaneous cutting force coefficients and cutter runout parameters in peripheral milling. Int J Mach Tool Manu 49(14):1144–1151. https://doi.org/10.1016/j.ijmachtools.2009.08.005
Zhang X, Zhang J, Pang B, Zhao W (2016) An accurate prediction method of cutting forces in 5-axis flank milling of sculptured surface. Int J Mach Tool Manu 104:26–36. https://doi.org/10.1016/j.ijmachtools.2015.12.003
Guo Q, Sun Y, Guo D, Zhang C (2012) New mathematical method for the determination of cutter runout parameters in flat-end milling. Chin J Mech Eng 25(5):947–952. https://doi.org/10.3901/cjme.2012.05.947
Zhang X, Pan X, Wang G, Zhou D (2018) Tool runout and single-edge cutting in micro-milling. Int J Adv Manuf Technol 96(1):821–832. https://doi.org/10.1007/s00170-018-1620-y
Attanasio A (2017) Tool run-out measurement in micro milling. Micromachines (Basel) 8(7). https://doi.org/10.3390/mi8070221
Tansel IN, Arkan TT, Bao WY, Mahendrakar N, Shisler B, Smith D, McCool M (2000) Tool wear estimation in micro-machining.: part II: neural-network-based periodic inspector for non-metals. Int J Mach Tool Manu 40(4):609–620. https://doi.org/10.1016/S0890-6955(99)00074-7
Robinson GM, Jackson MJ, Whitfield MD (2007) A review of machining theory and tool wear with a view to developing micro and nano machining processes. J Mater Sci 42(6):2002–2015. https://doi.org/10.1007/s10853-006-0171-z
Malekian M, Park SS, Jun MBG (2009) Tool wear monitoring of micro-milling operations. J Mater Process Technol 209(10):4903–4914. https://doi.org/10.1016/j.jmatprotec.2009.01.013
Abdelrahman Elkaseer AM, Dimov SS, Popov KB, Minev RM (2014) Tool wear in micro-endmilling: material microstructure effects, modeling, and experimental validation. J Micro Nano Manuf 2(4):044502–044510. https://doi.org/10.1115/1.4028077
Bao WY, Tansel IN (2000) Modeling micro-end-milling operations. Part III: influence of tool wear. Int J Mach Tool Manu 40(15):2193–2211. https://doi.org/10.1016/S0890-6955(00)00056-0
Oliaei SNB, Karpat Y (2016) Influence of tool wear on machining forces and tool deflections during micro milling. Int J Adv Manuf Technol 84(9):1963–1980. https://doi.org/10.1007/s00170-015-7744-4
Lu X, Wang F, Jia Z, Si L, Zhang C, Liang SY (2017) A modified analytical cutting force prediction model under the tool flank wear effect in micro-milling nickel-based superalloy. Int J Adv Manuf Technol 91(9–12):3709–3716. https://doi.org/10.1007/s00170-017-0001-2
Thepsonthi T, Özel T (2015) 3-D finite element process simulation of micro-end milling Ti-6Al-4V titanium alloy: experimental validations on chip flow and tool wear. J Mater Process Technol 221:128–145. https://doi.org/10.1016/j.jmatprotec.2015.02.019
Jaffery SHI, Khan M, Ali L, Mativenga PT (2016) Statistical analysis of process parameters in micromachining of Ti-6Al-4V alloy 230 (6):1017–1034. https://doi.org/10.1177/0954405414564409
Yoon HS, Ehmann KF (2016) Dynamics and stability of micro-cutting operations. Int J Mech Sci 115-116:81–92. https://doi.org/10.1016/j.ijmecsci.2016.06.009
Germain D, Fromentin G, Poulachon G, Bissey-Breton S (2013) From large-scale to micromachining: a review of force prediction models. J Manuf Process 15(3):389–401. https://doi.org/10.1016/j.jmapro.2013.02.006
Funding
This project is supported by the Natural Science Foundation of Jiangsu Province of China (No. BK20160563) and the National Natural Science Foundation of China (No. 51605207).
Author information
Authors and Affiliations
Corresponding authors
Additional information
Publisher’s note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Li, G., Li, S. & Zhu, K. Micro-milling force modeling with tool wear and runout effect by spatial analytic geometry. Int J Adv Manuf Technol 107, 631–643 (2020). https://doi.org/10.1007/s00170-020-05008-3
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00170-020-05008-3