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

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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.

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2s + 1:

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b :

Intercept of the linear fitting

c :

Ultrasonic velocity

f :


f c :

Central frequency of the transducer

h :

Thickness of plastic melt


Transfer function of the echo signals


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 0, R 1 :

Correlation function of u1 and u2

R 0, R 1 :

Reflection coefficients of the Material 1/Material 2 surface and Material 2/Material 3 surface, respectively

Δt :

Time delay between u1(t) and u2(t)

T o, T0 :

Transmission coefficients of the ultrasonic waves passing forward and backward through the Material 1/Material 2 surface, respectively

T :

Melt temperature


Time-domain signals

U o :

Original ultrasonic signal generated ultrasonic transducer

U 1, U 2 :

First and second echo signals reflected from the two surfaces of Material 2, respectively


Amplitude spectrum of signals

U 1(f), U 2(f):

Amplitude spectrum of U1 and U2, respectively

V :

Specific volume

Z 0, Z1, Z 2 :

Acoustic impedances of Materials 1, 2, and 3, respectively

α :

Damping coefficient

ρ :



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This work was supported by the “Pionerr” 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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Correspondence to Peng Zhao.

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Dong, Z., Zhao, P., Ji, K. et al. In-situ density measurement for plastic injection molding via ultrasonic technology. Front. Mech. Eng. 17, 58 (2022).

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