Skip to main content
SpringerLink
Log in

Research on design and cutting performance of revolving lemniscate milling cutter

  • ORIGINAL ARTICLE
  • Published:
The International Journal of Advanced Manufacturing Technology Aims and scope Submit manuscript

Abstract

An increasing number of cutting tools with different geometric shapes are needed owing to the increasing complexity of the workpiece surfaces in aerospace and automotive molding. A new kind of milling cutter is designed, which is named as revolving lemniscate milling cutter (RLMC for short). The parametric mathematical models of RLMC are proposed. Mathematical models of cutting edge curves are proposed to provide the theoretical basis for RLMC precision manufacturing. Equivalent helix angle, curvature radius of tool rotation surface, effective cutting linear velocity, and scallop height are studied. Corresponding numerical simulation results are also provided as graphical representations. Three RLMC with different tool parameters are manufactured, and contrast experiments are conducted to prove that using RLMC in end milling can achieve better machining quality. The parametric design and application research provide a new method and theoretical basis for other new types of milling cutters.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19
Fig. 20
Fig. 21
Fig. 22

Similar content being viewed by others

Data availability

All data generated or analyzed during this study are included in this article.

Code availability

Not applicable.

Abbreviations

r :

Tool radius

θ, a :

Curvilinear parameters of lemniscate of Gerono

D :

Axial length of the end part of RLMC

φ e,φ c,φ o :

Surface parameters

S(θ,φ e):

Rotation surface of the revolving lemniscate end part of RLMC

C(φ c,z):

Rotation surface of the cylindrical shank part of RLMC

l :

Axial length of the cylindrical shank part of RLMC

O c :

Cutter location point

S o :

Right helicoid

r z :

Radius of a point on the right helicoid

β 0 :

The helix angle of the cutting edge on the cylindrical shank part of RLMC

C e :

Cutting edges in the revolving lemniscate end part of RLMC

C c :

Cutting edges in the cylindrical shank part of RLMC

N f :

Number of cutter teeth

β :

Helix angle

α :

Inclination angle of inclined plane

β RLMC :

Equivalent helix angle of the revolving lemniscate end part of RLMC

β BEM :

Equivalent helix angle of ball end mill

S θ(θ,φ e), S φ(θ,φ e):

Partial derivative formulas

E, F, G :

Coefficients of the first fundamental form of the rotation surface

L, M, N :

Coefficients of the second fundamental form of the rotation surface

n t :

Unit normal vector of the rotation surface

k 1, k 2 :

The two principal curvatures of the rotation surface

k n :

Normal curvature

R 1, R 2 :

Principle curvature radius

R min :

The minimum curvature radius of the workpiece surface

k max :

The maximum curvature of the workpiece surface

V RLMC :

Effective cutting linear velocity of RLMC

V BEM :

Effective cutting linear velocity of ball end mill

n :

Spindle speed

t :

Motion parameter

a e :

Cutting width

h RLMC :

Scallop height of RLMC

h BEM :

Scallop height of ball end mill

References

  1. Zhao PY, Song YF, Jiang B, Fan LL, Wang B (2023) Effect of contact stiffness on cutter flank frictionand wear in milling process considering cutting vibration. Int J Adv Manuf Technol 127(11-12):5577–5598. https://doi.org/10.1007/S00170-023-11895-Z

    Article  Google Scholar 

  2. Masatoshi I, Takehiro H, Eiji S (2020) High-efficiency smooth-surface high-chatter-stability machining ofthin plates with novel face-milling cutter geometry. Precis Eng 64:165–176. https://doi.org/10.1016/j.precisioneng.2020.03.024

    Article  Google Scholar 

  3. Khamza K, Urinov U, Lyudmila D, Sukhrob S, Samandar S (2020) Improving the efficiency of milling with using of the milling cutter with cover (high speed milling (HSM)). IJITEE 9(4):3310–3316. https://doi.org/10.35940/ijitee.d1853.029420

    Article  Google Scholar 

  4. Chen T, Li R, Xiang JP, Gao WJ, Wang YS (2020) Study on the design and cutting performance of stepped bi-directional milling cutters for hole making of CFRP. Int J Adv Manuf Technol 108(3):3021–3030. https://doi.org/10.1007/s00170-020-05429-0

    Article  Google Scholar 

  5. Liu XL, Fan MC, Ji W, Wang GY, Chen T (2016) Research on models of design and NC manufacturing for ellipsoid end mill. Int J Adv Manuf Technol 8(9-12):2729–2744. https://doi.org/10.1007/s00170-015-8097-8

    Article  Google Scholar 

  6. Masahiko J, Isamu G, Takeshi W, Jun-ichi K, Masao M (2007) Development of cbn ball-nosed end millwith newly designed cutting edge. J Mater Process Tech 192-193(5):48–54. https://doi.org/10.1016/j.jmatprotec.2007.04.054

    Article  CAS  Google Scholar 

  7. Mendoza MM, Eman KF, Wu SM (1983) Development of a new milling cutter for aluminium honeycomb[J]. Int J Mach Tool 23(2-3):81–91. https://doi.org/10.1016/0020-7357(83)90009-4

    Article  Google Scholar 

  8. Zhao ZY, Wang SB, Wang SL, Wang ZH, Huang Q (2022) Ball-end milling cutter design method to-wards the maximum material removal rate under surface roughness constraints. J Manuf Process 78:254–264. https://doi.org/10.1016/J.JMAPRO.2022.04.018

    Article  Google Scholar 

  9. Zhang AS, Liu XL, Yang SC (2014) The milling cutter design and simulation for complex cavity machining. Mater Sci Forum 3256(800-801):465–469. https://doi.org/10.4028/www.scientific.net/MSF.800-801.465

    Article  Google Scholar 

  10. Yang Y, Wang Y, Liu Q (2019) Design of a milling cutter with large length–diameter ratio based on embedded passive damper. J Vib Control 25(3):506–516. https://doi.org/10.1177/1077546318786594

    Article  Google Scholar 

  11. Zhang YH, Ji HZ (2020) Wear optimization of titanium alloy cutter milled with microtextured ball-end milling cutter. Adv Mech Eng 12(1):1–10. https://doi.org/10.1177/1687814019892102

    Article  CAS  ADS  Google Scholar 

  12. Kishawy HA, Salem A, Hegab H, Balazinski M (2021) Micro-textured cutting tools: phenomenological analysis and design recommendations. CIRP Annals 70(1):65–68. https://doi.org/10.1016/j.cirp.2021.04.081

    Article  Google Scholar 

  13. Suzuki N, Takahashi W, Igeta H, Nakanomiya T (2020) Flank face texture design to suppress chatter vibration in cutting. CIRP Annals 69(1):93–96. https://doi.org/10.1016/j.cirp.2020.04.037

    Article  Google Scholar 

  14. Tong X, Qu Q (2023) Optimizing the micro-texture and cutting parameters of ball-end milling cutters to achieve milling stability. P I Mech Eng D-J Aut 327(2):326–335. https://doi.org/10.1177/09544089221104073

    Article  CAS  Google Scholar 

  15. Yang SC, Su S, Wang XL, Ren W (2020) Study on mechanical properties of titanium alloy with micro-texture ball-end milling cutter under different cutting edges. Adv Mech Eng 12(7). https://doi.org/10.1177/1687814020908423

  16. Li Y, Wang FJ, Zhang BY, Deng J, Fu R, He QS, Ma X (2023) A novel discrete-edge ball end millingcutter: suitable for milling weakly rigid curved CFRP parts. J Mater Process Tech 317. https://doi.org/10.1016/J.JMATPROTEC.2023.117996

  17. Hu XM, Qiao HY, Yang MY, Zhang YM (2022) Research on milling characteristics of titanium alloy TC4 with variable helical end milling cutter. Machines 10(7):537–537. https://doi.org/10.3390/MACHINES10070537

    Article  Google Scholar 

  18. Jiang SL, Zhan DN, Liu Y, Sun YW, Xu JT (2022) Modeling of variable-pitch/helix milling system considering axially varying dynamics with cutter runout offset and tilt effects. Mech Syst Signal Pr 168. https://doi.org/10.1016/J.YMSSP.2021.108674

  19. Yu HB, Zheng ML, Zhang W, Nie WY, Bian TC (2022) Optimal design of helical flute of irregular tooth end milling cutter based on particle swarm optimization algorithm. P I Mech Eng D-J Aut 236(7):3323–3339. https://doi.org/10.1177/09544062211042052

    Article  Google Scholar 

  20. Xiong B, Wei Y, Gu D, Zhao DF, Wang BQ, Liu SL (2021) Chatter stability analysis of variable speedmilling with helix angled cutters. P I Mech Eng 235(5):850–861. https://doi.org/10.1177/0954405420971079

    Article  Google Scholar 

  21. Korovin G, Petrushin S, Gubaidulina R (2018) Machining of titanium alloys with wave milling cutters. Mater Sci Forum 4748:79–85. https://doi.org/10.4028/www.scientific.net/MSF.927.79

    Article  Google Scholar 

  22. Sultan AA, Okafor AC (2016) Effects of geometric parameters of wavy-edge bull-nose helical end-millon cutting force prediction in end-milling of Inconel 718 under MQL cooling strategy. J Manuf Process 23:102–114. https://doi.org/10.1016/j.jmapro.2016.05.015

    Article  Google Scholar 

  23. Ren KM, Wang GY (2022) Simulation and experimental study on reverse helical milling with the gradual-removal reverse edge milling cutter under ultrasonic-assisted condition. Materials 15(3):1117–1117. https://doi.org/10.3390/ma15031117

    Article  CAS  PubMed  PubMed Central  ADS  Google Scholar 

  24. Pelayo GU (2019) Modelling of static and dynamic milling forces in inclined operations with circle-segment end mills. Precision Eng 56:123–135. https://doi.org/10.1016/j.precisioneng.2018.11.007

    Article  Google Scholar 

  25. Sheng DP, Lu FX, Wan HS (2021) Experimental study of milling cutter with high damping alloy sleeve. JPCS 2002(1). https://doi.org/10.1088/1742-6596/2002/1/012021

  26. Dragoi MV, Rosca DM, Folea MF, Oancea G (2021) A fully symmetrical high performance modular milling cutter. Symmetry 13(3):496–496. https://doi.org/10.3390/SYM13030496

    Article  ADS  Google Scholar 

  27. Fan MC, Bi CX, Yue CX, Liu XL (2023) Research on double-arc cutting tool design and cutting performance. Appl Sci 13(6):3689–3689. https://doi.org/10.3390/APP13063689

    Article  CAS  Google Scholar 

  28. Li Y, Fan JW, Wang XF, Liu YJ (2019) Design of formed milling cutter for double-helix screw based on noninstantaneous envelope method. Adv Mech Eng 5:260–280. https://doi.org/10.1155/2013/431919

    Article  CAS  Google Scholar 

  29. Cheng XF, Ding GF, Li R, Ma XJ, Qin SF, Song XL (2014) A new design and grinding algorithm forball-end milling cutter with tooth offset center. P I Mech Eng A-J Aut 228(7):687–697. https://doi.org/10.1177/0954405413503318

    Article  Google Scholar 

  30. Wu WG, Yu QX, Chang X, Pang SQ (2004) Design theory and experiment of the step face milling cutter based on free cutting. Key Eng Mater 259-260:132–136. https://doi.org/10.4028/www.scientific.net/KEM.259-260.132

    Article  Google Scholar 

Download references

Funding

This research was funded by National Nature Science Foundation of China, U22A20128 and Natural Science Foundation of Heilongjiang Province of China, TD2022E003.

Author information

Authors and Affiliations

  1. Key Laboratory of Advanced Manufacturing and Intelligent Technology, Ministry of Education, Harbin University of Science and Technology, Harbin, 150080, China

    Mengchao Fan, Chunxu Bi, Xianli Liu & Mingna Ding

  2. Beijing Engineering Research Center of Precision Measurement Technology and Instruments, Beijing University of Technology (BJUT), Beijing, 100124, China

    Huixu Song

Authors
  1. Mengchao Fan
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Chunxu Bi
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Xianli Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Mingna Ding
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Huixu Song
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

MF: conceptualization, methodology, formal analysis, investigation, experiments, writing—original draft, writing—review and editing, visualization; CB: project administration, conceptualization, supervision, writing—review and editing; XL: supervision, writing—review and editing; MD: methodology, formal analysis; HS: investigation, validation.

Corresponding author

Correspondence to Huixu Song.

Ethics declarations

Ethics approval

The content studied in this article belongs to the field of metal processing and does not involve humans and animals. This article strictly follows the accepted principles of ethical and professional conduct.

Consent to participate

My co-authors and I would like to opt in to In Review.

Consent for publication

I agree with the Copyright Transfer Statement.

Conflict of interest

The authors declare no competing interests.

Additional information

Publisher’s Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Fan, M., Bi, C., Liu, X. et al. Research on design and cutting performance of revolving lemniscate milling cutter. Int J Adv Manuf Technol 130, 5895–5911 (2024). https://doi.org/10.1007/s00170-024-13020-0

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00170-024-13020-0

Keywords

Search

Navigation