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

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.

Key words： ultrasonic vibration-assisted grinding; perforated ultrasonic vibration platform; vibration characteristics; apparent elasticity method; grinding force; surface integrity

Nomenclature

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
ap	Depth of cut
A	Ultrasonic amplitude
Ax, Ay	Displacements along the x and y directions, respectively
bw	Width of the workpiece
E	Elasticity modulus
E1x	Apparent elastic modulus along the x1-axis
Eax, Eay	Apparent elastic modulus along the x and y directions, respectively
f	Ultrasonic frequency
f0	Resonant frequency of the platform without holes
fAEM-1, fFEM-1	Resonant frequency of the platform only with top surface holes obtained through the modified AEM and FEM, respectively
fAEM-2, fFEM-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
Fn	Normal grinding force
Ft	Tangential grinding force
h	Thickness of the 1/4 vibration unit
kf	Frequency reduction ratio
kv	Volume reduction ratio
kv1, kv2	Reduction values of the platform volume when the top and side surface holes are generated, respectively
kx, ky	Half-wave numbers along the x and y directions, respectively
K1x, K1y	Influence of top surface holes on the apparent elastic modulus along the x and y directions, respectively
K2x, K2y	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
lm, ln	Length and width of the 1/4 vibration unit with a surface hole, respectively
lp	Length of the vibration unit with a side surface hole
lx, ly	Length and width of the vibration platform, respectively
∆l1x	Elongation of the vibration unit along the force direction
∆l1y, ∆l2y	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
nx, ny	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
vs	Grinding speed
vw	Worktable infeed speed
V	Volume of holes
V0	Volume of a vibration platform without holes
ε(x1)	Strain along the x1 direction
\overline{\epsilon }	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
\overline{\sigma }	Average stress
χ	Correction factor of the vibration mode

Acknowledgements

This work was financially supported by the National Natural Science Foundation of China (Grant Nos. 51921003, 92160301, 52175415 and 52205475), the Science Center for Gas Turbine Project, China (Grant No. P2022-A-IV-002-001), the Natural Science Foundation of Jiangsu Province, China (Grant No. BK20210295), and the Postgraduate Research & Practice Innovation Program of Jiangsu Province, China (Grant No. KYCX20_0179).

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