Vibration characteristics and machining performance of a novel perforated ultrasonic vibration platform in the grinding of particulate-reinforced titanium matrix composites

doi:10.1007/s11465-022-0730-2

Front. Mech. Eng.

2023, Vol. 18

Issue (1) : 14 https://doi.org/10.1007/s11465-022-0730-2

RESEARCH ARTICLE

Vibration characteristics and machining performance of a novel perforated ultrasonic vibration platform in the grinding of particulate-reinforced titanium matrix composites

Yang CAO, Biao ZHAO(

), Wenfeng DING, Qiang HUANG

National Key Laboratory of Science and Technology on Helicopter Transmission, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China

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Abstract

Ultrasonic vibration-assisted grinding (UVAG) is an advanced hybrid process for the precision machining of difficult-to-cut materials. The resonator is a critical part of the UVAG system. Its performance considerably influences the vibration amplitude and resonant frequency. In this work, a novel perforated ultrasonic vibration platform resonator was developed for UVAG. The holes were evenly arranged at the top and side surfaces of the vibration platform to improve the vibration characteristics. A modified apparent elasticity method (AEM) was proposed to reveal the influence of holes on the vibration mode. The performance of the vibration platform was evaluated by the vibration tests and UVAG experiments of particulate-reinforced titanium matrix composites. Results indicate that the reasonable distribution of holes helps improve the resonant frequency and vibration mode. The modified AEM, the finite element method, and the vibration tests show a high degree of consistency for developing the perforated ultrasonic vibration platform with a maximum frequency error of 3%. The employment of ultrasonic vibration reduces the grinding force by 36% at most, thereby decreasing the machined surface defects, such as voids, cracks, and burnout.

Keywords ultrasonic vibration-assisted grinding perforated ultrasonic vibration platform vibration characteristics apparent elasticity method grinding force surface integrity

Corresponding Author(s): Biao ZHAO

Just Accepted Date: 07 September 2022 Issue Date: 17 March 2023

Cite this article:

Yang CAO,Biao ZHAO,Wenfeng DING, et al. Vibration characteristics and machining performance of a novel perforated ultrasonic vibration platform in the grinding of particulate-reinforced titanium matrix composites[J]. Front. Mech. Eng., 2023, 18(1): 14.

URL:

https://academic.hep.com.cn/fme/EN/10.1007/s11465-022-0730-2
https://academic.hep.com.cn/fme/EN/Y2023/V18/I1/14

Fig.1 Illustrations of the ultrasonic vibration-assisted grinding system: (a) basic composition, (b) geometry model of the perforated ultrasonic vibration platform, and (c) vibration mode of the ultrasonic vibration platform.

Fig.2 Development approach of the perforated ultrasonic vibration platform.

Fig.3 Illustration of the perforated ultrasonic vibration platform: (a) geometry of the perforated platform, (b) vibration unit with a top surface hole, and (c) vibration unit with a side surface hole.

Tab.1 Material parameters under the L2T1 vibration mode [24,27]

Fig.4 Illustration of the vibration unit with a top surface hole.

Fig.5 Illustration of the vibration unit with a side surface hole.

Fig.6 Relationship between the frequency reduction ratio and the volume reduction ratio in the case of the vibration unit with (a) a top surface hole and (b) a side surface hole. AEM: apparent elasticity method, FEM: finite element method. Adj. R²: adjusted determination coefficient which indicates the similarity between the fitted curve and the results of FEM. The range of Adj. R² is 0?1. A higher value of Adj. R² indicates that the fitted curve of FEM is more accurate. The unit of h is mm.

Fig.7 Influence of (a) top surface holes and (b) side surface holes on the resonant frequency. AEM: apparent elasticity method, FEM: finite element method.

Fig.8 Displacement distribution along the x direction of the platform resonator under the condition of (a) platform without holes, (b) platform with holes, (c) platform with small holes, (d) platform with minimal holes, (e) small-sized platform without holes, and (f) small-sized platform with holes.

Fig.9 Effects of circular holes on the size and vibration characteristics of the vibration platform: size and displacement distribution of the vibration platform (a) without and (b) with circular holes; (c) comparison of the displacement distributions between the vibration platforms with and without circular holes when the same value of maximum force drives the platforms.

Fig.10 Vibration characteristics of the testing setups.

Fig.11 Vibration characteristics of the perforated platform: (a) modal analysis, (b) harmonic response analysis, (c) transient dynamic analysis, and (d) impedance test results.

Fig.12 Vibration mode verification: (a) comparison of amplitude distributions obtained through simulation and vibration tests, (b) ultrasonic misting in position I, (c) ultrasonic misting in position II, (d) ultrasonic misting in position III, and (e) ultrasonic misting on the workpiece surface.

Tab.2 Ultrasonic vibration-assisted grinding condition

Fig.13 Ultrasonic vibration-assisted grinding experimental setup.

Fig.14 Effects of vibration amplitude on grinding force.

Fig.15 Effects of vibration amplitude on grinding force ratio.

Fig.16 Influence of ultrasonic amplitude on the machined surface roughness.

Fig.17 Effect of ultrasonic vibration on the machined surface quality: the conventional grinding-machined surface topographies observed through (a) optical microscope and (b) scanning electron microscope, (c) illustration of reinforcement particle fracture and pullout in conventional grinding, the ultrasonic vibration-assisted grinding-machined surface topographies observed through (d) optical microscope and (e) scanning electron microscope, (f) illustration of ductility removal behavior in ultrasonic vibration-assisted grinding.

Abbreviations
AEM	Apparent elasticity method
CG	Conventional grinding
FEM	Finite element method
L2T1	Longitudinal full-wave and transverse halfwave
PTMC	Particulate-reinforced titanium matrix composite
UVAG	Ultrasonic vibration-assisted grinding
Variables
a_p	Depth of cut
A	Ultrasonic amplitude
A_x, A_y	Displacements along the x and y directions, respectively
b_w	Width of the workpiece
E	Elasticity modulus
E_1x	Apparent elastic modulus along the x₁-axis
E_ax, E_ay	Apparent elastic modulus along the x and y directions, respectively
f	Ultrasonic frequency
f₀	Resonant frequency of the platform without holes
f_AEM-1, f_FEM-1	Resonant frequency of the platform only with top surface holes obtained through the modified AEM and FEM, respectively
f_AEM-2, f_FEM-2	Resonant frequency of the platform only with side surface holes obtained through the modified AEM and FEM, respectively
F	Uniformly distributed force exerted on the side surface of the vibration unit
F_n	Normal grinding force
F_t	Tangential grinding force
h	Thickness of the 1/4 vibration unit
k_f	Frequency reduction ratio
k_v	Volume reduction ratio
k_v1, k_v2	Reduction values of the platform volume when the top and side surface holes are generated, respectively
k_x, k_y	Half-wave numbers along the x and y directions, respectively
K_1x, K_1y	Influence of top surface holes on the apparent elastic modulus along the x and y directions, respectively
K_2x, K_2y	Influence of side surface holes on the apparent elastic modulus along the x and y directions, respectively
l₁	Distance to the edge of the vibration unit
l_m, l_n	Length and width of the 1/4 vibration unit with a surface hole, respectively
l_p	Length of the vibration unit with a side surface hole
l_x, l_y	Length and width of the vibration platform, respectively
?l_1x	Elongation of the vibration unit along the force direction
?l_1y, ?l_2y	Elongation of the vibration unit along the y₁- and y₂-axis, respectively
m	Quantity of the top surface holes along the x direction
n	Quantity of the top surface holes along the y direction
n_x, n_y	Coupling coefficients along the x and y directions, respectively
p	Quantity of side surface holes
r₁, r₂	Radii of the top and side surface holes, respectively
Ra	Surface roughness
S	Side area of the 1/4 vibration unit without holes
v_s	Grinding speed
v_w	Worktable infeed speed
V	Volume of holes
V₀	Volume of a vibration platform without holes
ε(x₁)	Strain along the x₁ direction
$ε ˉ$	Average strain
η	Correction factor
η₁, η₂	Correction factors of top and side surface holes, respectively
ν	Poisson’s ratio
ρ	Material density
σ	Stress
σ(x₁)	Stress along the x₁ direction
$σ ˉ$	Average stress
χ	Correction factor of the vibration mode

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