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Longitudinal-torsional coupled rotary ultrasonic machining end surface grinding of SiCf/SiC composites: a mechanical model of cutting force

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Abstract

Composites with a silicon carbide fiber-reinforced silicon carbide matrix (SiCf/SiC) are difficult to be machined by the conventional processing due to its hardness and brittleness. The longitudinal-torsional coupled rotary ultrasonic machining (LTC-RUM) is regarded as an effective processing for the material; however, the SiCf/SiC composite’s material removal mechanism in LTC-RUM has not been reported, as well as the cutting force. In order to better understand the material removal mechanism of SiCf/SiC composites, this study proposed a cutting force model of LTC-RUM end surface grinding of SiCf/SiC composites. Firstly, the motion path of a single abrasive grain was analyzed, and the micromechanical analysis was used to convert a heterogeneous material into an equivalent homogeneous material. Then, a single abrasive grain material removal mechanism was explored by considering the three material removal regions, including ductile region, ductile-to-brittle transition region, and brittle region. The corresponding material removal mechanism of single abrasive grain during each region was analyzed in detail, and the normal and tangential cutting forces were obtained. Finally, a number of designed experiments were carried to verify the developed model and found that the predicted values were in good agreement with the experimental ones, and the maximum relative errors of normal and tangential cutting forces were 8.51 and 10.19%, respectively. Compared with conventional grinding, the cutting force shows a nonlinear decline in LTC-RUM end surface grinding. The results of this study provide a valuable reference for the LTC-RUM SiCf/SiC composites.

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Data availability

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

Abbreviations

A L :

Longitudinal ultrasonic vibration amplitude, µm

A T :

Torsional ultrasonic vibration amplitude, µm

a p :

Cutting depth, µm

C 2 :

Dimensionless constant

C L :

Length of the lateral crack

C H :

Depth of the lateral crack

E e :

Comprehensive SiCf/SiC elastic modulus in the transverse direction, GPa

E m, E f :

Elastic modulus of SiC matrix and fiber in SiCf/SiC composites, GPa

F nad, F nat, F nab :

A single abrasive grain normal cutting force in ductile, ductile-to-brittle transition and brittle regions, N

F tad, F tat, F tab :

A single abrasive grain tangential cutting force in ductile, ductile-to-brittle transition and brittle regions, N

F nd, F nt, F nb :

Normal cutting force in ductile, ductile-to-brittle transition and brittle regions of abrasive grains, N

F td, F tt, F tb :

Tangential cutting force in ductile, ductile-to-brittle transition and brittle regions of abrasive grains, N

F n, F t :

Normal and tangential cutting force, N

f :

Ultrasonic frequency, kHz

f ra :

Fraction of diamond grains

H V :

Vickers hardness of SiCf/SiC composites, GPa

h e :

Exposed height of end face abrasive grain

K IC :

Static fracture toughness, MPa·m1/2

K ID :

Dynamic fracture toughness, MPa·m1/2

L :

A single abrasive grain’s motion path length, µm

L 1, L 2, L 3 :

A single abrasive grain's path length in ductile, ductile-to-brittle transition and brittle regions, µm

L 1-ave, L 2-ave, L 3-ave :

A single abrasive grain's equivalent motion length in ductile, ductile-to-brittle transition and brittle regions, µm

MRR d, MRR t, MRR b :

Material removal rate in the ductile, ductile-to-brittle transition, and brittle regions

n :

Spindle speed, r/min

N a :

Number of active diamond grains

N x, N z :

Numbers of abrasive grains on the tool periphery face and end face

P :

Load, N

R o :

Tool's average radius, mm

r g :

Abrasive grain radius, mm

S x, S z :

Effective cutting areas of the tool periphery face and end face

S tad, S nad :

Single abrasive grain's projected areas of tangential and normal direction in the ductile region

S tat :

Single abrasive grain projected area in the tangential direction

t :

Cutting time, s

t 1, t 2, t 3 :

Cutting time in ductile, ductile-to-brittle transition and brittle regions, s

v w :

Feed rate, mm/min

V m, V f :

Volume fraction of SiC matrix and fiber in SiCf/SiC composites

V d, V t, V b :

Material removal volume in ductile, ductile-to-brittle transition and brittle regions

V de, V te :

Equivalent material removal volume in ductile, ductile-to-brittle transition regions

α :

Angle between the torsional vibration component and the circumferential direction, rad

θ :

Phase difference between longitudinal and torsional vibrations, rad

β 1, β 2, β 3 :

Rotation angle of the tool during the corresponding cutting times, rad

φ :

Semi-angle of abrasive grain

φ 1, φ 2, φ 2 :

Semi-angle of abrasive grain in ductile, ductile-to-brittle transition and brittle regions, rad

υ 12 :

Poisson’s ratio in SiC fibers’ longitudinal direction

υ, υ 21 :

Poisson’s ratio in SiC fiber fibers’ transverse direction

υ m,υ f :

Poisson’s ratio of silicon carbide matrix and fiber

δ g :

Underformed chip thickness of a single abrasive grain, µm

δ gmax :

Maximum undeformed chip thickness, µm

δ gp :

Crucial cutting depth, µm

δ gp -ave, δ gc-ave, δ gb-ave :

Average cutting depth in ductile, ductile-to-brittle transition and brittle regions, µm

δ gc :

Critical cutting depth, µm

δ g1, δ g2, δ g3 :

Underformed chip thickness of a single abrasive grain in ductile, ductile-to-brittle transition and brittle regions, µm

τ :

Coefficient of the ductile region

η :

Ratio of chip width to average underformed chip thickness

ξ :

Volume fraction of diamond tool

µ 1, µ 2 :

Friction coefficients in the ductile and brittle regions

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Funding

This work was financially supported by the National Natural Science Foundation of China (no. 52005164), the Key R&D and Promotion Program (Science and Technology) in Henan Province, China (no. 222103810043, 222102220003, 232102221018), and PhD Research Start-up Fund Project of Pingdingshan University of China (no. PXY-BSQD-2022001, PXY-QNJJ-202003).

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Authors and Affiliations

  1. Henan Province Engineering Research Center of Ultrasonic Technology Application, Pingdingshan University, Pingdingshan, China

    Wenbo Bie, Fan Chen, Shaopeng Chen & Zongxia Fu

  2. School of Mechanical and Power Engineering, Henan Polytechnic University, Jiaozuo, China

    Wenbo Bie, Xiaobo Wang & Bo Zhao

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  1. Wenbo Bie
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  2. Fan Chen
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  3. Xiaobo Wang
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Contributions

WB, FC, and ZF conceived the analysis and wrote the manuscript. XW and BZ provided supervisions on experimentation and manuscript preparation. WB, FC, and ZF collected the data and revised the manuscript. WB, FC, SC, and ZF performed the experiment. The authors discussed each reference paper together and contributed useful ideas for this manuscript.

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Correspondence to Wenbo Bie.

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Bie, W., Chen, F., Wang, X. et al. Longitudinal-torsional coupled rotary ultrasonic machining end surface grinding of SiCf/SiC composites: a mechanical model of cutting force. Int J Adv Manuf Technol 129, 1227–1248 (2023). https://doi.org/10.1007/s00170-023-12360-7

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