Biological Bone and Replacement Materials in Grinding: Force Model and Processing Capability

Abstract

Grinding is widely used in orthopedic surgery to remove bone tissue material, but due to the complex and brittle structure of bone, it is prone to mechanical stresses that cause cracks and damage to the bone tissue. Furthermore, bone replacement materials typically have high hardness, strength, and brittleness, which lead to increased tool wear and damage, such as cracks and deformation during grinding. Therefore, ensuring the surface quality of bone and replacement materials during the grinding process has become a critical issue. This necessitates the development of grinding force models that consider various processing parameters, such as feed rate and cutting depth, to guide industrial production. However, currently, research on the grinding force prediction models for bone tissue and its replacement materials is relatively scarce, and there is a lack of corresponding grinding force model reviews for unified guidance. Based on this, this article focuses on bone grinding technology and, conducts a critical comparative analysis of the grinding force models for bone tissue and its replacement materials, and then summarizes the grinding force prediction models in the grinding process of bone tissue and bone replacement materials. First, according to the material types and material removal mechanisms, the materials are categorized into bone tissue, bio-inert ceramics, and bio-alloys, and the material removal process during grinding is analyzed. Subsequently, the grinding force prediction models for each material and the accuracy errors of each model are summarized. The paper also reviews the application of these grinding force prediction models, explaining how processing parameters such as feed rate and cutting depth influence grinding forces and their interrelationship. Finally, in light of the current issues in the grinding of bone tissue and replacement materials, potential future research directions are proposed, aiming to provide theoretical guidance and technical support for improving the grinding quality of bone tissue and its replacement materials.

Keywords

Grinding / Bone / Bio-inert ceramics / Bio-alloys / Grinding force

Author Contributions

Conceptualization, X.K. and M.Y.; Methodology, X.K.; Software, Z.L.; Validation, M.Y., C.L. (Chuankun Li), X.C. and Y.Z.; Investigation, X.K.; Data Curation, C.L. (Changhe Li); Writing—Original Draft Preparation, X.K.; Writing—Review & Editing, M.Y.; Supervision, M.L., X.M. and B.L.; Funding Acquisition, M.Y.

Ethics Statement

Not applicable.

Informed Consent Statement

Not applicable.

Data Availability Statement

The data that support the findings of this study are available from the corresponding author, upon reasonable request.

Funding

This study was financially supported by the National Natural Science Foundation of China (Grant Nos. 52205481, 52305477), Support plan for Outstanding Youth Innovation Team in Universities of Shandong Province (2023KJ114), Young Talent of Lifting engineering for Science and Technology in Shandong, China (SDAST2024QTA043), Key Lab of Industrial Fluid Energy Conservation and Pollution Control (Ministry of Education) (CK-2024-0033), General Program of Shandong Provincial Natural Science Foundation (ZR2024ME205).

Declaration of Competing Interest

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.

References

[1] Zheng QC, Zhu YY, Fan ZH, Wang DH, Zhang CQ, Liu SH, et al. Multi-objective optimization of cortical bone grinding parameters based on particle swarm optimization. Proc. Inst. Mech. Eng. Part H-J. Eng. Med. 2023, 237, 1400-1408. doi:10.1177/09544119231206455.

[2] Theler JM. Bone tissue substitutes and replacements. Curr. Opin. Otolaryngol. Head Neck Surg. 2011, 19, 317-321. doi:10.1097/MOO.0b013e32834883f2.

[3] Bock RM, Mcentire BJ, Bal BS, Rahaman MN, Boffelli M, Pezzotti G. Surface modulation of silicon nitride ceramics for orthopaedic applications. Acta Biomater. 2015, 26, 318-330. doi:10.1016/j.actbio.2015.08.014.

[4] Cai BY, Yuan DL, Li GD, Lei K, Han M, Huang YZ, et al. Promoting Osseointegration of New Innocuous Ti-18Zr-13Mo Implant Through Constructing Hierarchically Structured Bioactive Coating. Met. Mater. Int. 2023, 29, 3402-3417. doi:10.1007/s12540-023-01455-1.

[5] Huang R, Lu SM, Han Y. Role of grain size in the regulation of osteoblast response to Ti-25Nb-3Mo-3Zr-2Sn alloy. Colloids Surf. B-Biointerfaces 2013, 111, 232-241. doi:10.1016/j.colsurfb.2013.06.007.

[6] Wathanyu K, Tuchinda K, Daopiset S, Sirivisoot S. Corrosion resistance and biocompatibility of cold-sprayed titanium on 316L stainless steel. Surf. Coat. Technol. 2022, 445, 128721. doi:10.1016/j.surfcoat.2022.128721.

[7] Rodrigues AC, De Souza RNF, Galisa OF, França TV, Bianchi EC, Foschini CR. Effect of Grinding Parameters on Surface Finishing of Advanced Ceramics. Mater. -Rio De Jan. 2016, 21, 1012-1020. doi:10.1590/s1517-707620160004.0093.

[8] Gao LM, Lu XJ, Zhang XG, Meng QG, Jin ZM. Lubrication Modelling of Artificial Joint Replacements: Current Status and Future Challenges. Lubricants 2022, 10, 238. doi:10.3390/lubricants10100238.

[9] Feng JB, Chen R, Li B, Jiang BH, Li B. The Current Trend of Antibacterial Prostheses and Prosthetic Surface Coating Technologies to Prevent Prosthetic Joint Infection for Artificial Joint Replacement. J. Biomater. Tissue Eng. 2023, 13, 1046-1060. doi:10.1166/jbt.2023.3342.

[10] Kuncická L, Kocich R, Lowe TC. Advances in metals and alloys for joint replacement. Prog. Mater. Sci. 2017, 88, 232-280. doi:10.1016/j.pmatsci.2017.04.002.

[11] Ostrowski N, Lee B, Enick N, Carlson B, Kunjukunju S, Roy A, et al. Corrosion protection and improved cytocompatibility of biodegradable polymeric layer-by-layer coatings on AZ 31 magnesium alloys. Acta Biomater. 2013, 9, 8704-8713. doi:10.1016/j.actbio.2013.05.010.

[12] Han JJ, Wan P, Ge Y, Fan XM, Tan LL, Li JJ, et al. Tailoring the degradation and biological response of a magnesium-strontium alloy for potential bone substitute application. Mater. Sci. Eng. C-Mater. Biol. Appl. 2016, 58, 799-811. doi:10.1016/j.msec.2015.09.057.

[13] Liu C, Tong SK, Yue YF, Wang HX, Song JP, Li YB, et al. Laser-based fabrication of superwetting titanium alloy with enhanced corrosion and erosion-corrosion resistance. Colloids Surf. a-Physicochem. Eng. Asp. 2024, 688, 133648. doi:10.1016/j.colsurfa.2024.133648.

[14] Xu W, Lu X, Wang LN, Shi ZM, Lv SM, Qian M, et al. Mechanical properties, in vitro corrosion resistance and biocompatibility of metal injection molded Ti-12Mo alloy for dental applications. J. Mech. Behav. Biomed. Mater. 2018, 88, 534-547. doi:10.1016/j.jmbbm.2018.08.038.

[15] Saji VS, Choe HC, Ko YM, Ahn H. Nanotube Morphology and Corrosion Resistance of a Low Rigidity Quaternary Titanium Alloy for Biomedical Applications. J. Nanosci. Nanotechnol. 2010, 10, 4635-4639. doi:10.1166/jnn.2010.1715.

[16] Zhi PX, Liu LX, Chang JK, Liu CZ, Zhang QL, Zhou J, et al. Advances in the Study of Magnesium Alloys and Their Use in Bone Implant Material. Metals 2022, 12, 1500. doi:10.3390/met12091500.

[17] Yang M, Ma H, Li ZH, Hao JC, Liu MZ, Cui X, et al. Force model in electrostatic atomization minimum quantity lubrication milling GH4169 and performance evaluation. Front. Mech. Eng. 2024, 19, 28. doi:10.1007/s11465-024-0800-8.

[18] Wang WH, Wang F, Zhao HF, Yan K, Huang CL, Yin Y, et al. Injectable Magnesium-Zinc Alloy Containing Hydrogel Complex for Bone Regeneration. Front. Bioeng. Biotechnol. 2020, 8, 617585. doi:10.3389/fbioe.2020.617585.

[19] Mohammadi H, Beddu S, Petra M, Sepantafar M, Ebadi M, Yap BK, et al. Advances in silicon nitride ceramic biomaterials for dental applications—A review. J. Mater. Res. Technol. -JmrT 2024, 28, 2778-2791. doi:10.1016/j.jmrt.2023.12.186.

[20] Tang ZR, Li XF, Tan YF, Fan HS, Zhang XD. The material and biological characteristics of osteoinductive calcium phosphate ceramics. Regen. Biomater. 2018, 5, 43-59. doi:10.1093/rb/rbx024.

[21] Wang JL, Zhang LL, Wang K. Bioactive ceramic-based materials: beneficial properties and potential applications in dental repair and regeneration. Regen. Med. 2024, 19, 257-278. doi:10.1080/17460751.2024.2343555.

[22] Lemos CAA, Verri FR, Gomes JMD, Batista VED, Cruz RS, Oliveira H, et al. Ceramic versus metal-ceramic implant-supported prostheses: A systematic review and meta-analysis. J. Prosthet. Dent. 2019, 121, 879-886. doi:10.1016/j.prosdent.2018.09.016.

[23] Chanda A, Singharoy R, Xue WC, Bose S, Bandyopadhyay A. Bone cell-materials interaction on alumina ceramics with different grain sizes. Mater. Sci. Eng. C-Biomim. Supramol. Syst. 2009, 29, 1201-1206. doi:10.1016/j.msec.2008.09.023.

[24] Gao T, Xu PM, Wang W, Zhang YB, Xu WH, Wang YQ, et al. Force model of ultrasonic empowered minimum quantity lubrication grinding CFRP. Int. J. Mech. Sci. 2024, 280, 109522. doi:10.1016/j.ijmecsci.2024.109522.

[25] Tanner KE. Bioactive ceramic-reinforced composites for bone augmentation. J. R. Soc. Interface 2010, 7, S541-S557. doi:10.1098/rsif.2010.0229.focus.

[26] Yang M, Kong M, Li CH, Long YZ, Zhang YB, Sharma S, et al. Temperature field model in surface grinding: A comparative assessment. Int. J. Extrem. Manuf. 2023, 5, 042011. doi:10.1088/2631-7990/acf4d4.

[27] Yang YY, Yang M, Li CH, Li RZ, Said Z, Ali HM, et al. Machinability of ultrasonic vibration-assisted micro-grinding in biological bone using nanolubricant. Front. Mech. Eng. 2023, 18, 1. doi:10.1007/s11465-022-0717-z.

[28] Babbar A, Jain V, Gupta D, Agrawal D, Prakash C, Singh S, et al. Experimental analysis of wear and multi-shape burr loading during neurosurgical bone grinding. J. Mater. Res. Technol. -JmrT 2021, 12, 15-28. doi:10.1016/j.jmrt.2021.02.060.

[29] Liu MZ, Li CH, Yang M, Gao T, Wang XM, Cui X, et al. Mechanism and enhanced grindability of cryogenic air combined with biolubricant grinding titanium alloy. Tribol. Int. 2023, 187, 108704. doi:10.1016/j.triboint.2023.108704.

[30] An QL, Fu YC, Xu JH. A new technology on enhancing heat transfer during grinding of titanium alloy. Ind. Lubr. Tribol. 2010, 62, 168-173. doi:10.1108/00368791011034557.

[31] Yang M, Hao JC, Wu WT, Li ZH, Ma YQ, Zhou ZM, et al. Critical cutting thickness model considering subsurface damage of zirconia grinding and friction—Wear performance evaluation applied in simulated oral environment. Tribol. Int. 2024, 198, 109881. doi:10.1016/j.triboint.2024.109881.

[32] Zhao ML, Xue BX, Li BH, Zhu JM, Song WB, Nie LX. Modeling of grinding force in longitudinal ultrasonic vibration-assisted grinding alumina ceramics and experimental evaluation. Int. J. Adv. Manuf. Technol. 2024, 131, 2325-2339. doi:10.1007/s00170-023-11590-z.

[33] Li C, Duan J, Zhang XH, Shi ZY, Yuchi GZ, Zhang SH, et al. Grinding performance integrated experimental evaluation on alumina ceramics with leaf-vein bionic grinding wheel. Int. J. Adv. Manuf. Technol. 2022, 121, 2525-2537. doi:10.1007/s00170-022-09502-8.

[34] Zhang GF, Wang ZG, Chen WX, Li JT, Sun H, Zhang K. Single-Point Grinding of Alumina and Zirconia Ceramics Under Two-Dimensional Compressive Prestress. Int. J. Precis. Eng. Manuf. 2020, 21, 1-9. doi:10.1007/s12541-019-00232-8.

[35] Zhang XH, Kang ZX, Li S, Shi ZY, Wen DD, Jiang J, et al. Grinding force modelling for ductile-brittle transition in laser macro-micro-structured grinding of zirconia ceramics. Ceram. Int. 2019, 45, 18487-18500. doi:10.1016/j.ceramint.2019.06.067.

[36] Dambatta YS, Sarhan AAD, Sayuti MB, Bin Abd Shukor MH. Fuzzy logic method to investigate grinding of alumina ceramic using minimum quantity lubrication. Int. J. Appl. Ceram. Technol. 2019, 16, 1668-1683. doi:10.1111/ijac.13219.

[37] Liu DW, Li CH, Xu PM, Wang W, Zhang YB, Yang M, et al. SiCp/Al composites from conventional to empowered machining: Mechanisms and processability. Compos. Struct. 2024, 346, 118433. doi:10.1016/j.compstruct.2024.118433.

[38] Li CH, Zhang YB, Said Z. Enhanced manufacture technology based on emission reduction and carbon reduction in cutting and grinding. Int. J. Adv. Manuf. Technol. 2024, 131, 1963-1974. doi:10.1007/s00170-024-13216-4.

[39] Li BK, Ding WF, Zhu YJ, Li CH, Zhang YB, Yang M, et al. Design and grindability assessment with cup shaped electroplated CBN wheel grinding turbine disc slots of powder metallurgy superalloy FGH96. Chin. J. Aeronaut. 2024, 37, 521-534. doi:10.1016/j.cja.2023.12.030.

[40] Ji CH, Sheng R, Wu H, Zhou ZM, Yan X, Dong L, et al. Bibliometric analysis and research trends in minimum quantity lubrication for reducing cutting forces. Int. J. Adv. Manuf. Technol. 2024, 135, 4995-5033. doi:10.1007/s00170-024-14793-0.

[41] Gu GQ, Wu SJ, Wang DZ, Zhang BX, Li CH, Liang ZQ. Machining mechanism of metal glass cutting based on ultrasonic vibration tool path. Int. J. Adv. Manuf. Technol. 2024, 130, 2343-2368. doi:10.1007/s00170-023-12818-8.

[42] Gong P, Zhang YB, Wang CJ, Cui X, Li RZ, Sharma S, et al. Residual stress generation in grinding: Mechanism and modeling. J. Mater. Process. Technol. 2024, 324, 118262. doi:10.1016/j.jmatprotec.2023.118262.

[43] Irazu E, Alonso U, Izquierdo B, Godino L. Grinding of C/SiC ceramic matrix composites: Influence of grinding parameters on tool wear. Wear 2024, 558, 205582. doi:10.1016/j.wear.2024.205582.

[44] Liu MY, Wang J, Li Y, Cheng KY, Huan Y, Li N. Development of mechanical equivalent porous structures for 3D-printed artificial femoral heads. Acta Mech. Sin. 2025, 41, 624089. doi:10.1007/s10409-024-24089-x.

[45] Ganjiani M, Ghobadi S, Faraji G. Evaluating the ductile failure characteristics of CuZn30 brass under different stress conditions. Eng. Fail. Anal. 2025, 167, 108932. doi:10.1016/j.engfailanal.2024.108932.

[46] Zhang SY, Qu DJ, Luo BW, Wang LC, Li H, Wang HJ. Regulation of Osteogenic Differentiation of hBMSCs by the Overlay Angles of Bone Lamellae-like Matrices. Acs Appl. Mater. Interfaces 2024, 16, 56801-56814. doi:10.1021/acsami.4c12847.

[47] Cojocaru E, Oprea M, Vlasceanu GM, Nicolae MC, Popescu RC, Mereuta PE, et al. Dual nanofiber and graphene reinforcement of 3D printed biomimetic supports for bone tissue repair. Rsc Adv. 2024, 14, 32517-32532. doi:10.1039/d4ra06167e.

[48] Anetai Y,Doi K, Takegawa H, Koike Y, Yui M, Yoshida A, et al. Diffusion equation quantification: Selective enhancement algorithm for bone metastasis lesions in CT images. Phys. Med. Biol. 2024, 69, 245007. doi:10.1088/1361-6560/ad965c.

[49] Liu F, Wang HY, Zhao B, Zhang W, Wang Q, Niu YS, et al. Study on deposition of biomedical Ta coating on Ti6Al4V alloy substrate by CVD and its properties. Surf. Coat. Technol. 2025, 495, 131593. doi:10.1016/j.surfcoat.2024.131593.

[50] Kasman S, Ozan S, Wen CE. Influence of pulse duration and frequency of laser surface texturing on the surface roughness and microstructure of CoCr28Mo alloy for biomedical applications. Mater. Test. 2024, 67, 36-48. doi:10.1515/mt-2024-0139.

[51] Kaneta H, Shoji T, Kato Y, Shozen H, Ueki S, Morita H, et al. Relationship Between the Subchondral Trabecular Bone Microstructure in the Hip Joint and Pain in Patients with Hip Osteoarthritis. Cartilage 2024, 131, 2254-4459. doi:10.1177/19476035241302978.

[52] Guo W, Li P, Wei YT, Zhao L, Pang YH, Huang YJ, et al. Ionic substitution through bredigite doping for microstructure and performance adjustment in DLP 3D-printed TPMS porous HA bone scaffolds. Virtual Phys. Prototyp. 2024, 19, e2423840. doi:10.1080/17452759.2024.2423840.

[53] Al-Goraee A, Al-Shami A, Alshami AS, Dhasarathy A, Ismail N, Guidinger J, et al. A hierarchically porous and SLIT3-releasing scaffold for bone tissue engineering applications. J. Mater. Sci. 2024, 60, 414-431. doi:10.1007/s10853-024-10379-z.

[54] Wang ZH, Chen HW, Song QH, Reng YH, Sui JB, Shu LM. A Review on Cutting Mechanism for Bone Material. J. Mech. Eng. 2021, 57, 2-32.

[55] Yang Y, Ling C, Li Y, Peng S, Xie D, Shen L, et al. Microstructure development and biodegradation behavior of additively manufactured Mg-Zn-Gd alloy with LPSO structure. J. Mater. Sci. Technol. 2023, 144, 1-14. doi:10.1016/j.jmst.2022.09.059.

[56] Yang M, Li CH, Zhang YB, Wang YG, Li BK, Li RZ. Theoretical Analysis and Experimental Research on Temperature Field of Microscale Bone Grinding under Nanoparticle Jet Mist Cooling. J. Mech. Eng. 2018, 54, 194-203.

[57] Zou L, Wen DH, Zhang LH, Chen ZZ, Xiao YT, Liang J. Computational Model and Experimental Study for Bone Tissue Grinding Forces. China Mech. Eng. 2020, 31, 3016-3023.

[58] Danda A, Kuttolamadom MA, Tai BL.A mechanistic force model for simulating haptics of hand-held bone burring operations. Med. Eng. Phys. 2017, 49, 7-13. doi:10.1016/j.medengphy.2017.06.041.

[59] Gaziano P, Monaldo E, Falcinelli C, Vairo G. Elasto-damage mechanics of osteons: A bottom-up multiscale approach. J. Mech. Phys. Solids 2022, 167, 104962. doi:10.1016/j.jmps.2022.104962.

[60] Sun JG, Li CH, Zhou ZM, Liu B, Zhang YB, Yang M, et al. Material Removal Mechanism and Force Modeling in Ultrasonic Vibration-Assisted Micro-Grinding Biological Bone. Chin. J. Mech. Eng. 2023, 36, 129. doi:10.1186/s10033-023-00957-8.

[61] Zhu YY, Zheng QC, Zhang SQ, Wang GL, Hu YH.Simulation and research on ultrasonic vibration-assisted grinding of cortical bone. J. Tianjin Univ. Technol. 2024, 26, 1-6.

[62] Hu YH, Hu XC, Fan ZH, Liu Z, Zhang CQ, Fu WH. Cortical bone grinding mechanism modeling and experimental study for damage minimization in craniotomy. Proc. Inst. Mech. Eng. 2021, 236, 320-328. doi:10.1177/09544119211060135.

[63] Zhu Z, Hu ZW, Zhang ZB, Xu XP. Study on grinding force of bovine cortical bone by different grinding wheels. Diam. Abras. Eng. 2014, 34, 13-16.

[64] Liao ZR, Axinte DA. On chip formation mechanism in orthogonal cutting of bone. Int. J. Mach. Tools Manuf. 2016, 102, 41-45. doi:10.1016/j.ijmachtools.2015.12.004.

[65] Liao ZR, Axinte DA, Gao T. On modelling of cutting force and temperature in bone milling. J. Mater. Process. Technol. 2019, 266, 627-638. doi:10.1016/j.jmatprotec.2018.11.039.

[66] Choudhary A, Paul S. Surface generation in high-speed grinding of brittle and tough ceramics. Ceram. Int. 2021, 47, 30546-30562. doi:10.1016/j.ceramint.2021.07.233.

[67] Choudhary A, Chakladar ND, Paul S. Identification and estimation of defects in high-speed ground C/SiC ceramic matrix composites. Compos. Struct. 2021, 261, 24-29. doi:10.1016/j.compstruct.2020.113274.

[68] Kuzin VV, Grigoriev SN, Volosova MA. Computer Engineering of the Surface Layer of Ground Al2O3-TiC Ceramics. Thermal Analysis. Refract. Ind. Ceram. 2020, 61, 418-423. doi:10.1007/s11148-020-00496-y.

[69] Chen SG, Lin B, Han XS, Liang XH. Automated inspection of engineering ceramic grinding surface damage based on image recognition. Int. J. Adv. Manuf. Technol. 2013, 66, 431-443. doi:10.1007/s00170-012-4338-2.

[70] Zhao DL, Yu KD, Sun TF, Jing XR, Wan YZ, Chen KF, et al. Material-Structure-Function Integrated Additive Manufacturing of Degradable Metallic Bone Implants for Load-Bearing Applications. Adv. Funct. Mater. 2023, 33, 76-80. doi:10.1002/adfm.202213128.

[71] Xu ZR.Research trends and progress in the field of metal materials and bone repair: Comprehensive bibliometric and visual analysis ( 2012-2021). Front. Mater. 2022, 9, 135-142. doi:10.3389/fmats.2022.954525.

[72] Lv YT, Wang BH, Liu GH, Tang YJ, Lu EY, Xie KG, et al. Metal Material, Properties and Design Methods of Porous Biomedical Scaffolds for Additive Manufacturing: A Review. Front. Bioeng. Biotechnol. 2021, 9, 267-274. doi:10.3389/fbioe.2021.641130.

[73] Liang WQ, Dong YQ, Shen HL, Shao RY, Wu XD, Huang XG, et al. Materials science and design principles of therapeutic materials in orthopedic and bone tissue engineering. Polym. Adv. Technol. 2021, 32, 4573-4586. doi:10.1002/pat.5445.

[74] Liu Y, Lv SC, Sun XW, Yang HR, Dong ZX, Mu SB, et al. Comparative study of tool wear mechanisms in drilling ZrO 2 ceramics using various tool types. J. Braz. Soc. Mech. Sci. Eng. 2024, 46, 635. doi:10.1007/s40430-024-05220-2.

[75] Li QZ, Wu Z, Ji BF, Zhang S, Tu R. Cutting Performance of TiN/TiSiN Coated Tool during Turning of Ti6Al4V Titanium Alloy. J. Mater. Eng. Perform. 2024, 78, 886-894. doi:10.1007/s11665-024-09815-7.

[76] Ming WY, Jia HJ, Zhang HM, Zhang Z, Liu K, Du JG, et al. A comprehensive review of electric discharge machining of advanced ceramics. Ceram. Int. 2020, 46, 21813-21838. doi:10.1016/j.ceramint.2020.05.207.

[77] Bifano TG, Dow TA, Scattergood RO. Ductile-Regime Grinding: A New Technology for Machining Brittle Materials. J. Eng. Ind. 1991, 113, 184-189. doi:10.1115/1.2899676.

[78] Yang M, Li CH, Zhang YB, Jia DZ, Li RZ, Hou YL, et al. Effect of friction coefficient on chip thickness models in ductile-regime grinding of zirconia ceramics. Int. J. Adv. Manuf. Technol. 2019, 102, 2617-2632. doi:10.1007/s00170-019-03367-0.

[79] Sun YL, Zuo DW, Wang HY, Zhu YW, Li J. Mechanism of brittle-ductile transition of a glass-ceramic rigid substrate. Int. J. Miner. Metall. Mater. 2011, 18, 229-233. doi:10.1007/s12613-201-0427-0.

[80] Li ZP, Zhang FH, Luo XC, Chang WL, Cai YK, Zhong WB, et al. Material removal mechanism of laser-assisted grinding of RB-SiC ceramics and process optimization. J. Eur. Ceram. Soc. 2019, 39, 705-717. doi:10.1016/j.jeurceramsoc.2018.11.002.

[81] Baraheni M, Amini S. Predicting subsurface damage in silicon nitride ceramics subjected to rotary ultrasonic assisted face grinding. Ceram. Int. 2019, 45, 10086-10096. doi:10.1016/j.ceramint.2019.02.055.

[82] Li C, Zhang FH, Meng BB, Liu LF, Rao XS. Material removal mechanism and grinding force modelling of ultrasonic vibration assisted grinding for SiC ceramics. Ceram. Int. 2017, 43, 2981-2993. doi:10.1016/j.ceramint.2016.11.066.

[83] Qiao GC, Yi SC, Zheng W, Zhou M. Material removal behavior and crack-inhibiting effect in ultrasonic vibration-assisted scratching of silicon nitride ceramics. Ceram. Int. 2022, 48, 4341-4351. doi:10.1016/j.ceramint.2021.10.229.

[84] Xie GZ, Shang ZT, Sheng XM, Wu Y, Yu JW. Grinding Force Modeling for High-speed Deep Grinding of Engineering Ceramics. J. Mech. Eng. 2011, 47, 907-917. doi:10.3901/jme.2011.11.169.

[85] Zhang YB, Li CH, Ji HJ, Yang XH, Yang M, Jia DZ, et al. Analysis of grinding mechanics and improved predictive force model based on material-removal and plastic-stacking mechanisms. Int. J. Mach. Tools Manuf. 2017, 122, 81-97. doi:10.1016/j.ijmachtools.2017.06.002.

[86] Yang M, Li CH, Zhang YB, Jia DZ, Zhang XP, Hou YL, et al. Maximum undeformed equivalent chip thickness for ductile-brittle transition of zirconia ceramics under different lubrication conditions. Int. J. Mach. Tools Manuf. 2017, 122, 55-65. doi:10.1016/j.ijmachtools.2017.06.003.

[87] Bharathi V, Anilchandra AR, Sangam SS, Shreyas S, Shankar SB. A review on the challenges in machining of ceramics. Mater. Today Proc. 2021, 46, 1451-1458. doi:10.1016/j.matpr.2021.03.019.

[88] Xiao XZ, Zheng K, Liao WH, Meng H. Study on cutting force model in ultrasonic vibration assisted side grinding of zirconia ceramics. Int. J. Mach. Tools Manuf. 2016, 104, 58-67. doi:10.1016/j.ijmachtools.2016.01.004.

[89] Bie WB, Zhao B, Gao GF, Chen F, Chang YL, Chen HT. Two-dimensional ultrasonic vibration-assisted dry grinding gear: Grinding force and surface characteristics. Int. J. Adv. Manuf. Technol. 2024, 131, 3021-3038. doi:10.1007/s00170-023-12882-0.

[90] Li HT, Chen T, Li HB, Zhang YW. Influence of ultrasonic vibration on machining quality of down/up grinding in ultrasonic vibration assisted grinding of silicon carbide. Mach. Sci. Technol. 2023, 27, 1-19. doi:10.1080/10910344.2023.2194958.

[91] Peng Y, Wu YB, Liang ZQ, Guo YB, Lin X. An experimental study of ultrasonic vibration-assisted grinding of polysilicon using two-dimensional vertical workpiece vibration. Int. J. Adv. Manuf. Technol. 2011, 54, 941-947. doi:10.1007/s00170-010-2991-x.

[92] Tang XT, Liu YX, Shi SJ, Chen WS, Qi XD. Development of a Novel Ultrasonic Drill Using Longitudinal-Bending Hybrid Mode. IEEE Access 2017, 5, 7362-7370. doi:10.1109/access.2017.2696566.

[93] Geng D, Lu ZH, Yao G, Liu JJ, Li Z, Zhang DY. Cutting temperature and resulting influence on machining performance in rotary ultrasonic elliptical machining of thick CFRP. Int. J. Mach. Tools Manuf. 2017, 123, 160-170. doi:10.1016/j.ijmachtools.2017.08.008.

[94] Gao GF, Xia ZW, Yuan ZJ, Xiang DH, Zhao B. Influence of longitudinal-torsional ultrasonic-assisted vibration on micro-hole drilling Ti-6Al-4V. Chin. J. Aeronaut. 2021, 34, 254-260. doi:10.1016/j.cja.2020.06.012.

[95] Zhao B, Bie WB, Wang XB, Chen F, Chang BQ. Design and experimental investigation on longitudinal-torsional composite horn considering the incident angle of ultrasonic wave. Int. J. Adv. Manuf. Technol. 2019, 105, 337-341. doi:10.1007/s00170-019- 04220-0.

[96] Wang JJ, Feng PF, Zhang JF, Guo P. Reducing cutting force in rotary ultrasonic drilling of ceramic matrix composites with longitudinal-torsional coupled vibration. Manuf. Lett. 2018, 18, 1-5. doi:10.1016/j.mfglet.2018.08.002.

[97] Chen F, Bie WB, Chang YL, Zhao B, Wang XB, Zhang YM. Analytical and experimental investigation on cutting force in longitudinal-torsional coupled rotary ultrasonic machining zirconia ceramics. Int. J. Adv. Manuf. Technol. 2022, 120, 4051-4064. doi:10.1007/s00170-022-09031-4.

[98] Bie WB, Chen F, Zhao B, Xie SX. A mechanical model of cutting force in end surface grinding of zirconia ceramics using rotary ultrasonic machining with longitudinal-torsional coupled vibration. Int. J. Adv. Manuf. Technol. 2023, 127, 651-664. doi:10.1007/s00170-023-11565-0.

[99] Xie GZ, Huang H, Sheng XM, Mi HQ.Investigation on the Grinding Force and the Ground Damages in the High Efficiency Deep Grinding of Advanced Ceramics. J. Hunan Univ. ( Nat. Sci.) 2008, 35, 26-30.

[100] Wu SX, Zhang FL, Ni YQ, Chen F, Yan ZQ. Grinding of alumina ceramic with microtextured brazed diamond end grinding wheels. Ceram. Int. 2020, 46, 19767-19784. doi:10.1016/j.ceramint.2020.05.009.

[101] Fu H, Jiang L, Song Q, Liu Z, Tong J, Cao C. Grinding surface roughness prediction for silicon nitride ceramics: A dynamic grinding force and frequency domain approach. Ceram. Int. 2023, 49, 35239-35253. doi:10.1016/j.ceramint.2023.08.197.

[102] Cao JG, Wu YB, Li JY, Zhang QJ. A grinding force model for ultrasonic assisted internal grinding (UAIG) of SiC ceramics. Int. J. Adv. Manuf. Technol. 2015, 81, 875-885. doi:10.1007/s00170-015-7282-0.

[103] Ye Z, Wen X, Wan W, Liu F, Bai W, Xu C, et al. Precision Grinding Technology of Silicon Carbide (SiC) Ceramics by Longitudinal Torsional Ultrasonic Vibrations. Materials 2023, 16, 2045-2053. doi:10.3390/ma16165572.

[104] Sun LY, Li HS, Qiu Z, Du TH, Ma LJ. Comparative Study on Grinding Force of Two-Dimensional Ultrasonic Vibration Assisted Grinding Alumina Ceramics. Mach. Tool Hydraul. 2023, 51, 84-88.

[105] Cheng J, Yin GQ, Wen Q, Song H, Gong YD. Study on grinding force modelling and ductile regime propelling technology in micro drill-grinding of hard-brittle materials. J. Mater. Process. Technol. 2015, 223, 150-163. doi:10.1016/j.jmatprotec.2015.04.005.

[106] Sun J, Wu YH, Zhou P, Li SH, Zhang LX, Zhang K. Simulation and experimental research on Si3N4 ceramic grinding based on different diamond grains. Adv. Mech. Eng. 2017, 9, 6789-6798. doi:10.1177/1687814017705596.

[107] Li ZP, Zhang FH, Luo XC, Guo XG, Cai YK, Chang WL, et al. A New Grinding Force Model for Micro Grinding RB-SiC Ceramic with Grinding Wheel Topography as an Input. Micromachines 2018, 9, 7748-7756. doi:10.3390/mi9080368.

[108] Wan Q, Zou L, Liu S, Wang T, Chen S, Huang Y. Investigation on abrasive wear mechanism of single diamond grain in flexible scribing titanium alloy. Diam. Relat. Mater. 2021, 120, 108631. doi:10.1016/j.diamond.2021.108631.

[109] Zhao J, Zou L, Liu Y, Wang W, Zhang Z. Investigation of friction and wear behavior of titanium alloy-diamond based on the morphology evolution of single abrasive clusters. Wear 2024, 546-547, 205357. doi:10.1016/j.wear.2024.205357.

[110] Cao Y, Zhu YJ, Ding WF, Qiu YT, Wang LF, Xu JH. Vibration coupling effects and machining behavior of ultrasonic vibration plate device for creep-feed grinding of Inconel 718 nickel-based superalloy. Chin. J. Aeronaut. 2022, 35, 332-345. doi:10.1016/j.cja.2020.12.039.

[111] Nik MG, Movahhedy MR, Akbari J. Ultrasonic-Assisted Grinding of Ti6Al4V Alloy. Procedia CIRP 2012, 1, 353-358. doi:10.1016/j.procir.2012.04.063.

[112] Gao T, Zhang XP, Li CH, Zhang YB, Yang M, Jia DZ, et al. Surface morphology evaluation of multi-angle 2D ultrasonic vibration integrated with nanofluid minimum quantity lubrication grinding. J. Manuf. Process. 2020, 51, 44-61. doi:10.1016/j.jmapro.2020.01.024.

[113] Ren JX, Hua DA, Huang Q. A mathematical model of grinding force in grinding of titanium alloys. Acta Aeronaut. Et Astronaut. Sin. 1986, 1, 97-103.

[114] Zhu LD, Yang ZC, Li ZB. Investigation of mechanics and machinability of titanium alloy thin-walled parts by CBN grinding head. Int. J. Adv. Manuf. Technol. 2019, 100, 2537-2555. doi:10.1007/s00170-018-2795-y.

[115] Duan JH, Wu ZF, Ren JB, Zhang GC. Research on Grinding Force Prediction of Flexible Abrasive Disc Grinding Process of TC17 Titanium Alloy. Machines 2024, 12, 143. doi:10.3390/machines12020143.

[116] Liu JL, Liu ZP, Yan YY, Wang XX. Study on the CBN Wheel Wear Mechanism of Longitudinal-Torsional Ultrasonic-Assisted Grinding Applied to TC4 Titanium Alloy. Micromachines 2022, 13, 1480. doi:10.3390/mi13091480.

[117] Li ZH, Zhao YG, Liu GX, Cao C, Liu Q, Zhao DD, et al. Parametric Studies on Finishing of AZ31B Magnesium Alloy with Al2O 3 Magnetic Abrasives Prepared by Combining Plasma Molten Metal Powder with Sprayed Abrasive Powder. Micromachines 2022, 13, 1369. doi:10.3390/mi13091369.

[118] Feng R. Study on grinding force in grinding titanium alloy with diamond grinding wheel. Diam. Abras. Eng. 2022, 42, 193-200.

[119] Liu Y, Xu JY, Xiao GJ, Zhou K. Liu G. Thermo-mechanical coupling during belt grinding and corresponding surface integrity of titanium alloy. Int. J. Adv. Manuf. Technol 2022, 121, 6599-6609. doi:10.1007/s00170-022-09783-z.

[120] Zhang JQ, Li MH, Song PZ, Li ZH. Experimental Study on Milling-grinding Force Model of Titanium Alloy by Milling-grinding with Spherical Grinding Heads. Tool Eng. 2022, 56, 31-36.

[121] Wang XS, Hu H, Zhang XM, Liu X. Analysis and validation of grinding force in TC4 titanium alloy surface grinding. Manuf. Technol. Mach. Tool 2022, 6, 74-79.

[122] Huang Z, Min J, Zhou T, Yang J, Xiao LX, Li LZ. Modeling and analysis of grinding force for grinding titanium alloy with abrasive belt assisted by ultrasonic vibration. J. Jilin Univ. (Eng. Technol. Ed.) 2023, 53, 3069-3077.

[123] Qin N, Pei ZJ, Treadwell C, Guo DM. Physics-Based Predictive Cutting Force Model in Ultrasonic-Vibration-Assisted Grinding for Titanium Drilling. J. Manuf. Sci. Eng. 2009, 131, 041011. doi:10.1115/1.3159050.

[124] Lan T, Feng PF, Zhang JF, Zhang XY, Zheng ZP, Wang JJ. Experimental investigation on the combined effects of mechano-chemical and ultrasonic vibration in titanium alloy grinding. J. Manuf. Process. 2024, 121, 382-393. doi:10.1016/j.jmapro.2024.05.049.