In-situ density measurement for plastic injection molding via ultrasonic technology

Abstract

Density variation during the injection molding process directly reflects the state of plastic melt and contains valuable information for process monitoring and optimization. Therefore, in-situ density measurement is of great interest and has significant application value. The existing methods, such as pressure−volume−temperature (PVT) method, have the shortages of time-delay and high cost of sensors. This study is the first to propose an in-situ density measurement method using ultrasonic technology. The analyses of the time-domain and frequency-domain signals are combined in the proposed method. The ultrasonic velocity is obtained from the time-domain signals, and the acoustic impedance is computed through a full-spectral analysis of the frequency-domain signals. Experiments with different process conditions are conducted, including different melt temperature, injection speed, material, and mold structure. Results show that the proposed method has good agreement with the PVT method. The proposed method has the advantages of in-situ measurement, non-destructive, high accuracy, low cost, and is of great application value for the injection molding industry.

Graphical abstract

Keywords

ultrasonic measurement / melt density / in-situ measurement / injection molding

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Nomenclature

2s + 1	Filter window size
b	Intercept of the linear fitting
c	Ultrasonic velocity
f	Frequency
fc	Central frequency of the transducer
h	Thickness of plastic melt
H(f)	Transfer function of the echo signals
j	Imaginary unit
k	Slope of the linear fitting
K	Proportionality propagation coefficient
m	Coefficient that convert the unit of damping coefficient from Np/cm to dB/cm
P	Melt pressure
R_{u_1{u}_2}	Correlation function of u1 and u2
R0, R1	Reflection coefficients of the Material 1/Material 2 surface and Material 2/Material 3 surface, respectively
\mathrm{\Delta }t	Time delay between u_1\left(t\right) and u_2\left(t\right)
T_0, T_0^{\prime }	Transmission coefficients of the ultrasonic waves passing forward and backward through the Material 1/Material 2 surface, respectively
T	Melt temperature
u\left(t\right):	Time-domain signals
U_0	Original ultrasonic signal generated ultrasonic transducer
U_1, U_2	First and second echo signals reflected from the two surfaces of Material 2, respectively
U\left(f\right)	Amplitude spectrum of signals
U_1\left(f\right), U_2\left(f\right)	Amplitude spectrum of U_1 and U_2, respectively
V	Specific volume
Z_0, Z_1, Z_2	Acoustic impedances of Materials 1, 2, and 3, respectively
\alpha	Damping coefficient
\rho	Density

Acknowledgements

This work was supported by the “Pioneer” and “Leading Goose” R&D Program of Zhejiang, China (Grant No. 2022C01069), the National Natural Science Foundation of China (Grant No. 51875519), the Key Project of Science and Technology Innovation 2025 of Ningbo City, China (Grant No. 2021Z044), and the Project of Innovation Enterprises Union of Ningbo City, China (Grant No. 2021H002). The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

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