Research Papers

Multigrain Smoothed Particle Hydrodynamics and Hertzian Contact Modeling of the Grinding Force in Atherectomy

[+] Author and Article Information
Yihao Zheng

Mechanical Engineering,
University of Michigan,
2380 G.G. Brown, 2350 Hayward Street,
Ann Arbor, MI 48109
e-mail: yhzheng@umich.edu

Yao Liu

Mechanical Engineering,
University of Michigan,
2380 G.G. Brown, 2350 Hayward Street,
Ann Arbor, MI 48109
e-mail: yaoliuz@umich.edu

Yang Liu

Mechanical Engineering,
University of Michigan,
2380 G.G. Brown, 2350 Hayward Street,
Ann Arbor, MI 48109
e-mail: yliume@umich.edu

Albert J. Shih

Mechanical Engineering, Biomedical Engineering,
University of Michigan,
2380 G.G. Brown, 2350 Hayward Street,
Ann Arbor, MI 48109
e-mail: shiha@umich.edu

1Corresponding author.

Manuscript received September 19, 2018; final manuscript received December 19, 2018; published online March 1, 2019. Assoc. Editor: Radu Pavel.

J. Manuf. Sci. Eng 141(4), 041015 (Mar 01, 2019) (8 pages) Paper No: MANU-18-1669; doi: 10.1115/1.4042603 History: Received September 19, 2018; Accepted December 19, 2018

This study investigated the grinding force in rotational atherectomy, a clinical procedure that uses a high-speed grinding wheel to remove hardened, calcified plaque inside the human arteries. The grinding force, wheel motion, and ground surface were measured based on a ring-shape bovine bone surrogate for the calcified plaque. At 135,000, 155,000, and 175,000 rpm wheel rotational speed, the grinding forces were 1.84, 1.92, and 2.22 N and the wheel orbital speeds were 6060, 6840, and 7800 rpm, respectively. The grinding wheel was observed to bounce on the wall of the bone surrogate, leaving discrete grinding marks. Based on this observation, we modeled the grinding force in two components: impact and cutting forces. The impact force between the grinding wheel and the bone surrogate was calculated by the Hertz contact model. A multigrain smoothed particle hydrodynamics (SPH) model was established to simulate the cutting force. The grinding wheel model was built according to the wheel surface topography scanned by a laser confocal microscope. The workpiece was modeled by kinematic-geometrical cutting. The simulation predicted a cutting force of 41, 51, and 99 mN at the three investigated wheel rotational speeds. The resultant grinding forces, combining the impact and cutting forces modeled by the Hertz contact and SPH simulation, matched with the experimental measurements with relative errors less than 10%.

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Shih, A. J., Liu, Y., and Zheng, Y., 2016, “Grinding Wheel Motion, Force, Temperature, and Material Removal in Rotational Atherectomy of Calcified Plaque,” CIRP Ann. – Manuf. Technol., 65(1), pp. 345–348. [CrossRef]
Barbato, E., Carrié, D., Dardas, P., Fajadet, J., Gaul, G., Haude, M., Khashaba, A., Koch, K., Meyer-Gessner, M., Palazuelos, J., Reczuch, K., Ribichini, F. L., Sharma, S., Sipötz, J., Sjögren, I., Suetsch, G., Szabó, G., Valdés-Chávarri, M., Vaquerizo, B., Wijns, W., Windecker, S., de Belder, A., Valgimigli, M., Byrne, R. A., Colombo, A., Di Mario, C., Latib, A., Hamm, C., European Association of Percutaneous Cardiovascular Interventions, 2015, “European Expert Consensus on Rotational Atherectomy,” EuroIntervention, 11(1), pp. 30–36. [CrossRef] [PubMed]
Kim, M. H., Kim, H. J., Kim, N. N., Yoon, H. S., and Ahn, S. H., 2011, “A Rotational Ablation Tool for Calcified Atherosclerotic Plaque Removal,” Biomed. Microdevices, 13(6), pp. 963–971. [CrossRef] [PubMed]
Nakao, M., Tsuchiya, K., Maeda, W., and Iijima, D., 2005, “A Rotating Cutting Tool to Remove Hard Cemented Deposits in Heart Blood Vessels Without Damaging Soft Vessel Walls,” CIRP Ann. Manuf. Technol., 54(1), pp. 37–40. [CrossRef]
Liu, Y., Li, B., Zheng, Y., and Shih, A., 2017, “Experiment and Smooth Particle Hydrodynamics Simulation of Debris Size in Grinding of Calcified Plaque in Atherectomy,” CIRP Ann. Manuf. Technol., 66(1), pp. 325–238. [CrossRef]
Reisman, M., Shuman, B. J., Dillar, D., Fei, R., Misser, K. H., Gordon, L. S., and Harms, V., 1998, “Analysis of Low-Speed Rotational Atherectomy for the Reduction of Platelet Aggregation,” Catheter. Cardiovas. Diagn., 45(2), pp. 208–214. [CrossRef]
Liu, Y., Li, B., Kong, L., Liu, Y., and Zheng, Y., 2018, “Experimental and Modeling Study of Temperature in Calcified Plaque Grinding,” Int. J. Adv. Manuf. Technol., 99, pp. 1013–1021.
Rüttimann, N., Roethlin, M., Buhl, S., and Wegener, K., 2013, “Simulation of Hexa-Octahedral Diamond Grain Cutting Tests Using the SPH Method,” Procedia CIRP, 8, pp. 322–327. [CrossRef]
Liu, Y., Li, B., Wu, C., and Zheng, Y., 2016, “Simulation-Based Evaluation of Surface Micro-Cracks and Fracture Toughness in High-Speed Grinding of Silicon Carbide Ceramics,” Int. J. Adv. Manuf. Technol., 86(1), pp. 799–708. [CrossRef]
Liu, Y., Li, B., Wu, C., Kong, L., and Zheng, Y., 2018, “Smoothed Particle Hydrodynamics Simulation and Experimental Analysis of SiC Ceramic Grinding Mechanism,” Ceram. Int., 44(11), pp. 12194–12203. [CrossRef]
Cao, J., Wu, Y., Li, J., and Zhang, Q., 2016, “Study on the Material Removal Process in Ultrasonic-Assisted Grinding of SiC Ceramics Using Smooth Particle Hydrodynamic (SPH) Method,” Int. J. Adv. Manuf. Technol., 83(5), pp. 985–994. [CrossRef]
Shen, R. D., Wang, X. M., and Yang, C. H., 2014, “Numerical Simulation of High Speed Single-Grain Cutting Using a Coupled FE-SPH Approach,” Appl. Mech. Mater., 483, pp. 3–8. [CrossRef]
Su, C., Ding, J. M., and Zhu, L. D., 2011, “Simulation Research on Cutting Process of Single Abrasive Grain Based on FEM and SPH Method,” Adv. Mater. Res., 186, pp. 353–357. [CrossRef]
Rüttimann, N., Buhl, S., and Wegener, K., 2010, “Simulation of Single Grain Cutting Using SPH Method,” J. Mach. Eng., 10(3), pp. 17–29.
Shen, R. D., Wang, X. M., and Yang, C. H., 2014, “Coupled FE-SPH Simulation of a High-Speed Grinding Process Using a Multiple-Grain Model,” Adv. Mater. Res., 989, pp. 3248–3251. [CrossRef]
Eder, S. J., Cihak-Bayr, U., and Pauschitz, A., 2015, “Nanotribological Simulations of Multi-Grit Polishing and Grinding,” Wear, 340, pp. 25–30. [CrossRef]
Flores, P., and Lankarani, H. M., 2016, Contact Force Models for Multibody Dynamics, Springer, Dordrecht, Netherlands.
Brinksmeier, E., Aurich, J. C., Govekar, E., Heinzel, C., Hoffmeister, H.-W., Klocke, F., Peters, J., Rentsch, R., Stephenson, D. J., Uhlmann, E., Weinert, K., and Wittmann, M., 2006, “Advances in Modeling and Simulation of Grinding Processes,” CIRP Ann. Manuf. Technol., 55(2), pp. 667–696. [CrossRef]
Dodge, J. T., Brown, B. G., Bolson, E. L., and Dodge, H. T., 1992, “Lumen Diameter of Normal Human Coronary Arteries. Influence of Age, Sex, Anatomic Variation, and Left Ventricular Hypertrophy or Dilation,” Circulation, 86(1), pp. 232–246. [CrossRef] [PubMed]
Zheng, Y., Liu, Y., Pitre, J. J., Bull, J. L., Gurm, H. S., and Shih, A. J., 2018, “Computational Fluid Dynamics Modeling of the Burr Orbital Motion in Rotational Atherectomy With Particle Image Velocimetry Validation,” Ann. Biomed. Eng., 46(4), pp. 567–578. [CrossRef] [PubMed]
Szabó, M. E., Taylor, M., and Thurner, P. J., 2011, “Mechanical Properties of Single Bovine Trabeculae Are Unaffected by Strain Rate,” J. Biomech., 44(5), pp. 962–967. [CrossRef] [PubMed]
Crowninshield, R. D., and Pope, M. H., 1974, “The Response of Compact Bone in Tension at Various Strain Rates,” Ann. Biomed. Eng., 2(2), pp. 217–225. [CrossRef]


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Fig. 1

Grinding of plaque in rotational atherectomy

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Fig. 2

Experimental setup

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Fig. 3

FG,Y measurement and the averaged grinding force FG

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Fig. 4

Ground surface: (a) ESEM images at three rotational speeds, (b) discrete grinding in RA, and (c) confocal microscopy measurement of the depth of penetration, width, and length of a grinding mark

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Fig. 5

Dynamics of the grinding wheel in RA discrete grinding: (a) kinematics configuration, (b) impact, hydraulic, and cutting forces, and (c) the change of velocity of the grinding wheel during impact

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Fig. 6

SPH simulation: (a) geometrical configuration and (b) close-up view of the grinding wheel model with abrasive grains and depth of penetration f (unit: mm)

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Fig. 7

Multigrain grinding wheel modeling: (a) wheel abrasive surface topography, (b) flat- and point-tip grains, (c) flat-tip and (d) point-tip grain models and dimensions, (e) height distribution of all measured grains, and (f) multigrain wheel model

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Fig. 8

Workpiece modeling with SPH particles and LFE and dimensions (unit: µm)

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Fig. 9

Kinematic-geometrical cutting of the workpiece: (a) starting and (b) ending configurations and (c) surface after K-G cutting

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Fig. 10

SPH simulation results of (a) grinding force magnitude on each grain and their summation Fg, (b) grain engagement with the workpiece, and (c) the von-Mises stress at five positions



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