Ultrasonic measurement of tie-bar stress for die-casting machine
Received date: 23 Jul 2021
Accepted date: 24 Oct 2021
Published date: 15 Mar 2022
Copyright
In die casting, the real-time measurement of the stress of the tie-bar helps ensure product quality and protect the machine itself. However, the traditional magnetic-attached strain gauge is installed in the mold and product operating area, which hinders the loading and unloading of the mold and the collection of die castings. In this paper, a method for real-time measurement of stress using ultrasonic technology is proposed. The stress variation of the tie-bar is analyzed, and a mathematical model between ultrasonic signal and stress based on acoustoelastic theory is established. Verification experiments show that the proposed method agrees with the strain gauge, and the maximum of the difference square is only 1.5678 (MPa)2. Furthermore, single-factor experiments are conducted. A higher ultrasonic frequency produces a better measurement accuracy, and the mean of difference squares at 2.5 and 5 MHz are 2.3234 and 0.6733 (MPa)2, respectively. Measurement accuracy is insensitive to probe location and tonnage of the die-casting machine. Moreover, the ultrasonic measurement method can be used to monitor clamping health status and inspect the dynamic pulling force of the tie-bar. This approach has the advantages of high precision, high repeatability, easy installation, and noninterference, which helps guide the production in die casting.
Chaojie ZHUO , Peng ZHAO , Kaipeng JI , Jun XIE , Sheng YE , Peng CHENG , Jianzhong FU . Ultrasonic measurement of tie-bar stress for die-casting machine[J]. Frontiers of Mechanical Engineering, 2022 , 17(1) : 7 . DOI: 10.1007/s11465-021-0663-1
D | Ultrasonic probe diameter |
E | Elastic modulus |
f | Ultrasonic probe frequency |
K | Acoustoelastic coefficient |
K1 | Material coefficient |
l, m | The third-order elasticity coefficients |
n | Number of experiments |
Δt | Ultrasonic time difference |
r | Standard deviation |
rs | Standard deviation of strain gauge |
ru | Standard deviation of ultrasonic |
s0 | Natural length of the tie-bar with no stress |
s1 | Length of the tie-bar with σ stress |
t0 | Ultrasonic propagation time with no stress |
t1 | Ultrasonic propagation time with σ stress |
v | Ultrasonic wave speed |
v0 | Velocity with no stress |
vσ | Velocity with σ stress |
w | Ultrasonic wavelength |
σ | Stress of the tie-bar |
σi | Stress measured by the strain gauge |
σj | Stress measured by the ultrasonic method |
ε | Strain |
ρ0 | Density of the tie-bar |
λ, μ | The second-order elastic coefficients |
θ0 | Half divergence angle of the ultrasound |
Difference square | |
Mean of the difference squares | |
Maximum of the difference square |
Table A1 Ultrasonic measurement results of verification experiments
Pulling force/kN | /MPa | /MPa | /(MPa)2 | /(MPa)2 | /MPa | /MPa |
---|---|---|---|---|---|---|
100 | 6.23628 | 6.8461 | 1.5678 | 1.5678 | 0.0486 | 0 |
6.30124 | 6.8461 | |||||
6.30124 | 6.8461 | |||||
6.23628 | 6.8461 | |||||
6.36620 | 6.8461 | |||||
300 | 18.3840 | 19.1067 | 1.3876 | 0.0118 | 0 | |
18.6439 | 19.1067 | |||||
18.7088 | 19.1067 | |||||
18.6439 | 19.1067 | |||||
18.5789 | 19.1067 | |||||
500 | 31.5711 | 31.9511 | 0.3181 | 0.0862 | 0 | |
31.8310 | 31.9511 | |||||
31.7011 | 31.9511 | |||||
31.7660 | 31.9511 | |||||
31.7011 | 31.9511 | |||||
700 | 44.1736 | 44.2117 | 0.0234 | 0.0636 | 0 | |
44.1736 | 44.2117 | |||||
44.1087 | 44.2117 | |||||
44.1736 | 44.2117 | |||||
44.3035 | 44.2117 | |||||
900 | 57.7505 | 57.6399 | 0.0696 | 0.0411 | 0 | |
57.7505 | 57.6399 | |||||
57.8155 | 57.6399 | |||||
57.7505 | 57.6399 | |||||
57.6855 | 57.6399 |
Table A2 Measurement results of ultrasonic and strain gauge of #3 tie-bar with different ultrasonic probe frequencies
Probe frequency/MHz | Pulling force/kN | /MPa | /ns | /MPa | /(MPa)2 | /(MPa)2 |
---|---|---|---|---|---|---|
2.5 | 100 | 6.04139 | 104.948 | 6.2621 | 0.3094 | 2.3234 |
5.97643 | 104.948 | 6.2621 | ||||
6.04139 | 104.948 | 6.2621 | ||||
6.04139 | 104.948 | 6.2621 | ||||
5.97643 | 104.948 | 6.2621 | ||||
300 | 19.5533 | 335.832 | 19.1062 | 1.1865 | ||
19.6183 | 335.832 | 19.1062 | ||||
19.5533 | 335.832 | 19.1062 | ||||
19.6183 | 335.832 | 19.1062 | ||||
19.6183 | 335.832 | 19.1062 | ||||
2.5 | 500 | 31.7011 | 566.717 | 31.9503 | 0.1754 | 2.3234 |
31.7660 | 566.717 | 31.9503 | ||||
31.7011 | 566.717 | 31.9503 | ||||
31.8959 | 566.717 | 31.9503 | ||||
31.8310 | 566.717 | 31.9503 | ||||
700 | 45.4728 | 797.601 | 44.7945 | 2.0490 | ||
45.4079 | 797.601 | 44.7945 | ||||
45.4079 | 797.601 | 44.7945 | ||||
45.4728 | 797.601 | 44.7945 | ||||
45.4079 | 797.601 | 44.7945 | ||||
900 | 57.5556 | 1007.496 | 56.4709 | 7.8967 | ||
57.8155 | 1007.496 | 56.4709 | ||||
57.7505 | 1007.496 | 56.4709 | ||||
57.7505 | 1007.496 | 56.4709 | ||||
57.7505 | 1007.496 | 56.4709 | ||||
5 | 100 | 6.23628 | 115.445 | 6.8461 | 1.5678 | 0.6733 |
6.30124 | 115.445 | 6.8461 | ||||
6.30124 | 115.445 | 6.8461 | ||||
6.23628 | 115.445 | 6.8461 | ||||
6.36620 | 115.445 | 6.8461 | ||||
300 | 18.3840 | 335.840 | 19.1067 | 1.3876 | ||
18.6439 | 335.840 | 19.1067 | ||||
18.7088 | 335.840 | 19.1067 | ||||
18.6439 | 335.840 | 19.1067 | ||||
18.5789 | 335.840 | 19.1067 | ||||
500 | 31.5711 | 566.730 | 31.9511 | 0.3181 | ||
31.8310 | 566.730 | 31.9511 | ||||
31.7011 | 566.730 | 31.9511 | ||||
31.7660 | 566.730 | 31.9511 | ||||
31.7011 | 566.730 | 31.9511 | ||||
700 | 44.1736 | 787.125 | 44.2117 | 0.0234 | ||
44.1736 | 787.125 | 44.2117 | ||||
44.1087 | 787.125 | 44.2117 | ||||
44.1736 | 787.125 | 44.2117 | ||||
44.3035 | 787.125 | 44.2117 | ||||
900 | 57.7505 | 1028.510 | 57.6399 | 0.0696 | ||
57.7505 | 1028.510 | 57.6399 | ||||
57.8155 | 1028.510 | 57.6399 | ||||
57.7505 | 1028.510 | 57.6399 | ||||
57.6855 | 1028.510 | 57.6399 |
Table A3 Measurement results of ultrasonic and strain gauge of #3 tie-bar of different ultrasonic probe locations
Probe location | Pulling force/kN | /MPa | /ns | /MPa | /(MPa)2 | /(MPa)2 |
---|---|---|---|---|---|---|
Near positioning hole | 100 | 6.23628 | 115.445 | 6.8461 | 1.5678 | 0.6733 |
6.30124 | 115.445 | 6.8461 | ||||
6.30124 | 115.445 | 6.8461 | ||||
6.23628 | 115.445 | 6.8461 | ||||
6.36620 | 115.445 | 6.8461 | ||||
300 | 18.3840 | 335.840 | 19.1067 | 1.3876 | ||
18.6439 | 335.840 | 19.1067 | ||||
18.7088 | 335.840 | 19.1067 | ||||
18.6439 | 335.840 | 19.1067 | ||||
18.5789 | 335.840 | 19.1067 | ||||
500 | 31.5711 | 566.730 | 31.9511 | 0.3181 | ||
31.8310 | 566.730 | 31.9511 | ||||
31.7011 | 566.730 | 31.9511 | ||||
31.7660 | 566.730 | 31.9511 | ||||
31.7011 | 566.730 | 31.9511 | ||||
700 | 44.1736 | 787.125 | 44.2117 | 0.0234 | ||
44.1736 | 787.125 | 44.2117 | ||||
44.1087 | 787.125 | 44.2117 | ||||
44.1736 | 787.125 | 44.2117 | ||||
44.3035 | 787.125 | 44.2117 | ||||
900 | 57.7505 | 1028.510 | 57.6399 | 0.0696 | ||
57.7505 | 1028.510 | 57.6399 | ||||
57.8155 | 1028.510 | 57.6399 | ||||
57.7505 | 1028.510 | 57.6399 | ||||
57.6855 | 1028.510 | 57.6399 | ||||
Near radius | 100 | 6.3662 | 115.445 | 6.3272 | 0.0220 | 0.0105 |
6.4312 | 115.445 | 6.3272 | ||||
6.3012 | 115.445 | 6.3272 | ||||
6.3012 | 115.445 | 6.3272 | ||||
6.2363 | 115.445 | 6.3272 | ||||
300 | 19.5533 | 346.335 | 19.5533 | 0.0085 | ||
19.6183 | 346.335 | 19.5533 | ||||
19.5533 | 346.335 | 19.5533 | ||||
19.5533 | 346.335 | 19.5533 | ||||
19.4883 | 346.335 | 19.5533 | ||||
500 | 31.7011 | 556.235 | 31.7141 | 0.0118 | ||
31.7660 | 556.235 | 31.7141 | ||||
31.7660 | 556.235 | 31.7141 | ||||
31.7011 | 556.235 | 31.7141 | ||||
31.6361 | 556.235 | 31.7141 | ||||
700 | 45.4728 | 808.115 | 45.4469 | 0.0051 | ||
45.4079 | 808.115 | 45.4469 | ||||
45.4079 | 808.115 | 45.4469 | ||||
45.4728 | 808.115 | 45.4469 | ||||
45.4728 | 808.115 | 45.4469 | ||||
900 | 58.4651 | 1039.005 | 58.4911 | 0.0051 | ||
58.5300 | 1039.005 | 58.4911 | ||||
58.4651 | 1039.005 | 58.4911 | ||||
58.5300 | 1039.005 | 58.4911 | ||||
58.4651 | 1039.005 | 58.4911 |
Table A4 Measurement results of ultrasonic and strain gauge of #3 tie-bar with different tonnages of die-casting machine
Mechanical tonnage/t | Pulling force/kN | /MPa | /ns | /MPa | /(MPa)2 | /(MPa)2 |
---|---|---|---|---|---|---|
400 | 100 | 6.3662 | 115.445 | 6.3272 | 0.0220 | 0.0105 |
6.4312 | 115.445 | 6.3272 | ||||
6.3012 | 115.445 | 6.3272 | ||||
6.3012 | 115.445 | 6.3272 | ||||
6.2363 | 115.445 | 6.3272 | ||||
300 | 19.5533 | 346.335 | 19.5533 | 0.0085 | ||
19.6183 | 346.335 | 19.5533 | ||||
19.5533 | 346.335 | 19.5533 | ||||
19.5533 | 346.335 | 19.5533 | ||||
19.4883 | 346.335 | 19.5533 | ||||
500 | 31.7011 | 556.235 | 31.7141 | 0.0118 | ||
31.7660 | 556.235 | 31.7141 | ||||
31.7660 | 556.235 | 31.7141 | ||||
31.7011 | 556.235 | 31.7141 | ||||
31.6361 | 556.235 | 31.7141 | ||||
700 | 45.4728 | 808.115 | 45.4469 | 0.0051 | ||
45.4079 | 808.115 | 45.4469 | ||||
45.4079 | 808.115 | 45.4469 | ||||
45.4728 | 808.115 | 45.4469 | ||||
45.4728 | 808.115 | 45.4469 | ||||
900 | 58.4651 | 1039.005 | 58.4911 | 0.0051 | ||
58.5300 | 1039.005 | 58.4911 | ||||
58.4651 | 1039.005 | 58.4911 | ||||
58.5300 | 1039.005 | 58.4911 | ||||
58.4651 | 1039.005 | 58.4911 | ||||
800 | 200 | 6.1017 | 298.8505 | 6.0664 | 0.0034 | 0.0332 |
6.1369 | 298.8505 | 6.0664 | ||||
6.0311 | 298.8505 | 6.0664 | ||||
5.9606 | 298.8505 | 6.0664 | ||||
6.1017 | 298.8505 | 6.0664 | ||||
600 | 21.4793 | 1065.4670 | 21.7050 | 0.0326 | ||
21.7262 | 1065.4670 | 21.7050 | ||||
21.8320 | 1065.4670 | 21.7050 | ||||
21.7262 | 1065.4670 | 21.7050 | ||||
21.7615 | 1065.4670 | 21.7050 | ||||
1000 | 34.6702 | 1721.6388 | 34.9453 | 0.0512 | ||
35.0934 | 1721.6388 | 34.9453 | ||||
35.0229 | 1721.6388 | 34.9453 | ||||
34.9524 | 1721.6388 | 34.9453 | ||||
34.9876 | 1721.6388 | 34.9453 | ||||
1400 | 48.0022 | 2390.8040 | 48.1362 | 0.0434 | ||
47.9317 | 2390.8040 | 48.1362 | ||||
48.0375 | 2390.8040 | 48.1362 | ||||
48.3802 | 2390.8040 | 48.1362 | ||||
48.3196 | 2390.8040 | 48.1362 | ||||
1800 | 64.4026 | 3196.4010 | 64.4802 | 0.0343 | ||
64.6143 | 3196.4010 | 64.4802 | ||||
64.4379 | 3196.4010 | 64.4802 | ||||
64.5790 | 3196.4010 | 64.4802 | ||||
64.3674 | 3196.4010 | 64.4802 |
1 |
ShahaneS, AluruN, FerreiraP, KapoorS G, VankaS P. Optimization of solidification in die casting using numerical simulations and machine learning. Journal of Manufacturing Processes, 2020, 51 : 130– 141
|
2 |
LiuW P, PengT, TangR Z, UmedaY, HuL K. An internet of things-enabled model-based approach to improving the energy efficiency of aluminum die casting processes. Energy, 2020, 202 : 117716
|
3 |
GreßT, MittlerT, ChenH, StahlJ, SchmidS, KhalifaN B, VolkW. Production of aluminum AA7075/6060 compounds by die casting and hot extrusion. Journal of Materials Processing Technology, 2020, 280 : 116594
|
4 |
LeeJ, LeeY C, KimJ T. Migration from the traditional to the smart factory in the die-casting industry: novel process data acquisition and fault detection based on artificial neural network. Journal of Materials Processing Technology, 2021, 290 : 116972
|
5 |
WeilerJ P. A review of magnesium die-castings for closure applications. Journal of Magnesium and Alloys, 2019, 7( 2): 297– 304
|
6 |
YooM, SongJ, OhJ, KangS, KimK, YangS, MoonM. Development of a bus armrest fabrication process with a high-vacuum, high-pressure die-casting process using the AM60 alloy. Robotics and Computer-Integrated Manufacturing, 2019, 55 : 154– 159
|
7 |
CornacchiaG, DioniD, FaccoliM, GislonC, SolazziL, PanviniA, CecchelS. Experimental and numerical study of an automotive component produced with innovative ceramic core in high pressure die casting (HPDC). Metals, 2019, 9( 2): 217
|
8 |
JeongS I, JinC K, SeoH Y, KimJ D, KangC G. Mold structure design and casting simulation of the high-pressure die casting for aluminum automotive clutch housing manufacturing. The International Journal of Advanced Manufacturing Technology, 2016, 84 : 1561– 1572
|
9 |
PisarekB P, KołakowskiD, PacyniakT. Simulation of stress distribution in a thick-walled bushing produced by die-casting. Archives of Foundry Engineering, 2017, 17( 4): 127– 132
|
10 |
CaoH J, ChenE, YiH, LiH C, ZhuL Q, WenX H. Multi-level energy efficiency evaluation for die casting workshop based on fog-cloud computing. Energy, 2021, 226 : 120397
|
11 |
DongX X, FengL Y, WangS H, NybergE A, JiS X. A new die-cast magnesium alloy for applications at higher elevated temperatures of 200–300 °C. Journal of Magnesium and Alloys, 2021, 9( 1): 90– 101
|
12 |
RaoB Q, ZhouH W, OuyangH B, WanY J, ZhangY H, WuJ Y. Study on the clamping force measurement and partial load regulation technology of injection molding machine. CIRP Journal of Manufacturing Science and Technology, 2017, 19 : 19– 24
|
13 |
ChenJ W, SchlaepherB. New measurement techniques of injection molding machine clamping force. Engineering Plastics Application, 2010, 38(2): 75− 77 (in Chinese)
|
14 |
ChangW T, LeeW I, HsuK L. Analysis and experimental verification of mechanical errors in nine-link type double-toggle mold/die clamping mechanisms. Applied Sciences (Basel, Switzerland), 2021, 11( 2): 832
|
15 |
FuK X, ZhengZ X, ZhangH W. Design of double-toggle clamping mechanism for die-casting machine based on the multi-body dynamics and finite element method. Applied Mechanics and Materials, 2013, 427–429: 179– 186
|
16 |
PhaniK K, NiyogiS K, MaitraA K, RoychaudhuryM. Strength and elastic modulus of a porous brittle solid: an acousto-ultrasonic study. Journal of Materials Science, 1986, 21( 12): 4335– 4341
|
17 |
PrasathR, DanylukS, ZagarolaS. Non-contact stress measurement in PET preforms. Polymer-Plastics Technology and Materials, 2019, 58( 16): 1802– 1809
|
18 |
BrayD E, TangW. Subsurface stress evaluation in steel plates and bars using the LCR ultrasonic wave. Nuclear Engineering and Design, 2001, 207( 2): 231– 240
|
19 |
KimJ, ParkJ H, JhangK Y. Decoupled longitudinal and lateral vehicle control based autonomous lane change system adaptable to driving surroundings. IEEE Access: Practical Innovations, Open Solutions, 2021, 9 : 4315– 4334
|
20 |
AyadiA, CulioliJ, AbouelkaramS. Sonoelasticity to monitor mechanical changes during rigor and ageing. Meat Science, 2007, 76( 2): 321– 326
|
21 |
ZhaoP, ZhaoY, ZhangJ F, HuangJ Y, XiaN, FuJ Z. Ultrasonic measurement of clamping force for injection molding machine. Journal of Polymer Engineering, 2019, 39( 4): 388– 396
|
22 |
ZhaoY, ZhaoP, ZhangJ F, HuangJ Y, XiaN, FuJ Z. On-line measurement of clamping force for injection molding machine using ultrasonic technology. Ultrasonics, 2019, 91 : 170– 179
|
23 |
CecchelS, CornacchiaG, PanviniA. Cradle-to-gate impact assessment of a high-pressure die-casting safety-relevant automotive component. JOM, 2016, 68( 9): 2443– 2448
|
24 |
TokuokaT, IwashimizuY. Acoustical birefringence of ultrasonic waves in deformed isotropic elastic materials. International Journal of Solids and Structures, 1968, 4( 3): 383– 389
|
25 |
ZengL, CaoX W, HuangL P, LuoZ. The measurement of lamb wave phase velocity using analytic cross-correlation method. Mechanical Systems and Signal Processing, 2021, 151 : 107387
|
26 |
XiaoW F, YuL Y, JosephR, GiurgiutiuV. Fatigue-crack detection and monitoring through the scattered-wave two-dimensional cross-correlation imaging method using piezoelectric transducers. Sensors (Basel), 2020, 20( 11): 3035
|
27 |
FanZ Q, QiuQ, SuJ, ZhangT H, LinY. Phase noise measurement of an optoelectronic oscillator based on the photonic-delay line cross-correlation method. Optics Letters, 2019, 44( 8): 1992– 1995
|
28 |
LiY, YuS S, DaiL, LuoT F, LiM. Acoustic emission signal source localization on plywood surface with cross-correlation method. Journal of Wood Science, 2018, 64( 2): 78– 84
|
29 |
KomuraI, NagaiS, KashiwayaH, MoriT, AriiM. Improved ultrasonic testing by phased array technique and its application. Nuclear Engineering and Design, 1985, 87 : 185– 191
|
30 |
WangJ G, DengZ F, YangB H, MaS W, FeiM R, LiuL L, YaoY, Chen T, WuY P. Simultaneous identification of parameter and time-delay based on subspace method and cross-correlation function. In: Proceedings of the 36th Chinese Control Conference (CCC). 2017, 2287– 2292
|
31 |
YamamotoN. New method of determining ultrasonic wavelength in liquid. Review of Scientific Instruments, 1954, 25( 10): 949– 950
|
/
〈 | 〉 |