Progress in grinding mechanical modeling of fiber reinforced SiC ceramic matrix composites
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摘要: 纤维增强碳化硅陶瓷基复合材料(FRCMC)因其高比强度和比模量、以及优异的耐高温、耐腐蚀等性能已成为航空航天、轨道交通以及核能工业等领域的优选材料。尽管FRCMC是由成型技术制备,但一些加工工艺,例如磨削对于提升尺寸精度和表面完整性是必要的,在FRCMC结构件的高性能制造中不可或缺。然而,高硬度和脆性的材料属性及其结构上的不均质性和力学性能上的各向异性等特点是高效低损伤磨削加工的技术难点。磨削力作为反馈和控制生产过程质量和精度的关键信号,受磨削过程砂轮与工件几何学与运动学等多参数协同作用的影响,解析磨粒与工件的微观力学行为并建立磨削力预测模型,对深度理解材料去除机制、指导高性能制造至关重要。基于此,首先分析了磨削过程中材料特性及磨削参数对磨粒与FRCMC相互作用的影响规律,揭示了FRCMC磨削过程的材料去除机制。其次,系统回顾了FRCMC磨削力预测模型的研究现状,从单颗磨粒磨削力、磨粒几何学、纤维随机分布几何特性以及材料去除阶段判定准则分析推导了磨削力的建模过程。进一步的,从磨屑的成形机制、未变形切屑厚度、磨粒运动学等角度,分析了超声振动辅助磨削FRCMC的材料去除机制及磨削力力学行为的特殊性。最后,针对FRCMC材料去除机制和磨削力模型,分析了当前研究的潜在问题与研究热点。目标是为FRCMC制定可行的低损伤磨削准则,并建立溯源递进的理论框架以推动FRCMC磨削力模型的发展。Abstract: Fiber reinforced SiC ceramic matrix composites (FRCMC) have emerged as preferred materials in aerospace, nuclear energy, and other cutting-edge scientific and technological fields owing to their exceptional specific strength and modulus, as well as superior resistance to high temperatures and chemicals. Although FRCMC are prepared by molding techniques, some machining processes, such as grinding, are necessary to enhance dimensional accuracy and surface integrity, and are indispensable in the high-performance fabrication of FRCMC structural components. However, the innate material properties of high hardness and brittleness, coupled with structural characteristics such as anisotropy and non-homogeneity, pose challenges for efficient and low-damage grinding. The grinding force, serving as a crucial indicator for feedback and control in the production process, is influenced by synergistic effect of multiple parameters of the grinding process, such as wheel and workpiece geometry and kinematics. Therefore, elucidating the mechanical behavior of abrasive grains and work-pieces, and modeling the grinding force, are imperative for comprehending the processing mechanism and guiding efficient production practices. Based on this, the paper firstly analyzed the influence of material properties and grinding parameters on the interaction mechanism between abrasive grains and FRCMC during the grinding process. Secondly, the current research status of FRCMC grinding force prediction modeling was systematically reviewed. The modeling process of grinding force was analytically deduced from the grinding force of a single grain, the geometry of the grain, the geometric properties of the random distribution of fibers, and the criteria for determining the stage of material removal. Furthermore, it discussed the unique aspects of material removal mechanisms and grinding force modeling for ultrasonic vibration-assisted grinding of FRCMC from the viewpoints of the chips shaping mechanism, the thickness of the undeformed chips, and the kinematics of the abrasive grains. Finally, the paper discussed current research gap, and identifies potential research hotspots. The objective is to formulate practical guidelines for low-damage grinding of FRCMC and establish a robust theoretical framework to advance grinding force modeling not only for FRCMC but also for other materials.
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图 7 磨削参数对未变形切屑厚度及残余轮廓高度的影响
Figure 7. Effect of grinding parameters on thickness of undeformed chips and scallop height
Sg—Scallop height of workpiece; ap—Grinding depth; vw—Feed speed of workpiece; vs—Linear velocity of grinding wheel; hm—Maximum undeformed chip thickness; The numerical subscripts only represent different working conditions and have no special meaning
图 12 磨削弧区磨粒-FRCMC接触行为
Figure 12. Abrasive grain-FRCMC contact behavior in the grinding arc region
ψ, ψ1, ψ2—Grinding angle of the abrasive grains at different moments; ag—Penetration depth of abrasive grains; agmax—Maximum undeformed chip thickness; z1—Previous grit grinding trajectory; z2—Trajectory of the next grit
图 14 磨粒-纤维螺旋制孔接触力学行为
Figure 14. Contact mechanical behavior of abrasive grain-fiber in helical grinding
FMft—Axial component of fiber removal force; σf—Stress along the axis; P(r)—Normal pressure distribution on the contact surface; lf—Length of fractured fiber under contact area; af—Half of the contact length of the abrasive grain; rf—Radius of abrasive grain
图 15 SiCf/SiC复合材料在不同方向上代表性体积单元(RVE)的荷载[77]
Figure 15. Load schematic of representative volume element (RVE) of SiCf/SiC composite in different directions[77]
σ11—Stress in direction 1; σ33—Stress in direction 3; Δx—Differential unit; E11—Equivalent elastic modulus of the composite in direction 1; $ E_{11}^{\mathrm{f }}$ and $ E_{11}^{\mathrm{m}} $—Elastic modulus of the fiber and matrix in direction 1, respectively; E22 and E33—Equivalent elastic modulus of the composite in directions 2 and 3, respectively; $ E_{33}^{\mathrm{m}} $—Equivalent elastic modulus of the matrix in direction 3; $ E_{33}^2 $—Equivalent elastic modulus of part 2 in direction 3; a—Edge length of the RVE; r—Radius of the fibers; Vf—Volume of fiber fraction; v—Equivalent Poisson's ratio in each direction
图 16 磨粒与不同取向纤维接触产生的裂纹系统[77]
Figure 16. Cracking systems produced by contact of abrasive grains with different fiber orientations[77]
$ C_{\mathrm{H}}^{\mathrm{T}},C_{\mathrm{L}}^{\mathrm{T}} $—Width and depth of the lateral crack when grinding along transverse fiber; $ C_{\mathrm{H}}^{\mathrm{L}},C_{\mathrm{L}}^{\mathrm{L}} $—Width and depth of the lateral crack when grinding along longitudinal fiber; $ C_{\mathrm{H}}^{\mathrm{P}},C_{\mathrm{L}}^{\mathrm{P}} $—Width and depth of the lateral crack when grinding along perpendicular fiber
图 20 旋转超声振动划擦表面损伤评价[112]
Figure 20. Evaluation of surface damage by rotational ultrasonic vibration scratching[112]
wn(i) is the width of surface edge chipping damage (SECD) at place i perpendicular to the direction of scratch, and w is actual width of the scratch in the sampled view; CS—Conventional conventional scratching; UVAS—Ultrasonic vibration-assisted scratching
图 24 磨粒-工件周期性的接触行为
Figure 24. Cyclic abrasive-workpiece contact behaviour
A1—Amplitude of ultrasonic vibration; dp—Distance between the workpiece and the center of vibration of the abrasive grain; zst—The initial contact height between the abrasive grain and the workpiece; zmin—Minimum contact height between the abrasive and the workpiece; hmax—Maximum undeformed cutting chip thickness; t—The moments at different stages of contact; Δt—One contact time of the abrasive grain with the workpiece
表 1 FRCMC传统磨削的磨削力预测模型
Table 1. Grinding force prediction model of FRCMC in conventional grinding
Working condition Grinding force model Key findings and numbers Ref. Grinding Cf/SiC
(along fiber normal)$ \begin{gathered}F_{\mathrm{t\mathit{x}}}=\delta l_{\mathrm{c}}C\beta'\left(\frac{K_{1\mathrm{C}}^{1/2}H^{9/10}}{E_{\mathrm{w}}^{2/5}}\right)\left(\frac{v_{\mathrm{w}}}{v_{\mathrm{s}}}\right)^{3/4}d_{\mathrm{s}}^{1/12}a_{\mathrm{p}}^{11/12}+ \\ 0.38Cl_{\mathrm{c}}Kd_{\mathrm{a}}\frac{1}{d_{\mathrm{f}}}\left(\int_0^{a_{\mathrm{p}}+h}k_{\mathrm{m}}x_1\mathrm{d}\mathrm{\mathit{z}}+\int_{a_{\mathrm{p}}+h}^{\infty}\left(k_{\mathrm{m}}+k_{\mathrm{b}}\right)x_2\mathrm{d}\mathit{z}\right) \\ \end{gathered} $ Significant increase in grinding force with increasing grinding depth. (2-1) [75] Grinding Cf/SiC
(along fiber normal)$ F = \displaystyle\sum\limits_i^n {\left( {{F_{{\mathrm{est}}}} + {F_{{\mathrm{bst}}}} + {F_{{\mathrm{mst}}}}} \right)} $ The model more accurately predicts the fluctuation amplitude and distribution pattern of the grinding force signal, with a prediction error of less than 10%. (2-2) [72] Grinding SiCf/SiC
(along fiber normal and longitudinal)$ \begin{gathered} {F_{\mathrm{p}}} = \lambda {h_{\mathrm{m}}}{h_{{\mathrm{gm}}}}H\frac{{\left[ {0.333 h_{{\mathrm{gc}}}^2{l_1}{C_{\mathrm{h}}} + 0.298 h_{{\mathrm{gc}}}^2{l_2}{C_{\mathrm{h}}}} \right]}}{{{C_{\mathrm{h}}}\left[ {\sqrt 3 h_{{\mathrm{gc}}}^2\left( {{l_1} + {l_2}} \right) + 6{C_{\mathrm{h}}}{C_{\mathrm{l}}}{l_3}} \right]}} + \\ \lambda {h_{\mathrm{m}}}{h_{{\mathrm{gm}}}}H\frac{{0.684\sqrt {C_{\mathrm{h}}^2 + C_{\mathrm{l}}^2} \left[ {h_{{\mathrm{gm}}}^2{l_{\mathrm{c}}} - h_{{\mathrm{gc}}}^2\left( {{l_1} + {l_2}} \right)} \right]}}{{{C_{\mathrm{h}}}\left[ {\sqrt 3 h_{{\mathrm{gc}}}^2\left( {{l_1} + {l_2}} \right) + 6{C_{\mathrm{h}}}{C_l}{l_3}} \right]}} \\ \end{gathered} $ The average error between predicted and experimental values is 7.43%. (2-3) [101] Notes: In Eq. (2-2), Fest is the grinding force at the elastic scratch stage, Fbst is the grinding force at the brittle removal stage, and Fmst is the grinding force at the matrix removal stage. In Eq. (2-3), hm is the thickness of the workpiece, hgm is the maximum undeformed chip thickness, hgc is the critical depth of cut for brittle removal, lc is the grinding tool/workpiece arc length of contact, l1 is the contact length at the stage of ductile removal, l2 is the contact length at the stage of delayed brittle removal, l3 is the contact length at the stage of brittle removal, H is the Vickers hardness of the workpiece in, and λ is the correction coefficient. 表 2 FRCMC超声振动辅助磨削的磨削力预测模型
Table 2. Grinding force prediction model of FRCMC in ultrasonic vibration-assisted grinding
Working condition Grinding force model Key findings and numbers Ref. Rotary ultrasonic vibratory grinding 2D-Cf/SiC $ {F_{{\mathrm{gdn}}}} = \dfrac{8}{3}{s^2}{{\text{π}} ^2}n_{\mathrm{s}}^2 t_1^2\tan \theta \sqrt {{{\tan }^2}\theta + 2} {H_{\mathrm{v}}} $
$ \begin{gathered} {F_{{\mathrm{gbn}}}} = \left[ {\dfrac{{{a_{\mathrm{p}}}{v_{\mathrm{w}}}}}{{C{v_{\mathrm{s}}}}} - \int_0^{{t_1}} {\tan \theta {h^2}\left( t \right)\sqrt {v_x^2\left( t \right) + v_y^2\left( t \right) + v_{\textit{z}}^2\left( t \right)} {\mathrm{d}}t} } \right]/ \\ 2 C_1^2{\left( {\cot \theta } \right)^{\tfrac{3}{4}}}{\left[ {\dfrac{{{E^{7/4}}}}{{H_{\mathrm{v}}^3{K_{{\mathrm{IC}}}}{{\left( {1 - {v^2}} \right)}^{1/2}}}}} \right]^{1/2}}\int_{{t_1}}^{{t_2}} {\sqrt {v_x^2\left( t \right) + v_y^2\left( t \right) + v_{\textit{z}}^2\left( t \right)} {\mathrm{d}}t} \\ \end{gathered} $The relative average errors in the normal and tangential grinding forces were 11.45% and 20.83%, respectively. (3-1) [119] Two-dimensional ultrasonic vibration grinding 2.5D-Cf/SiC $ F_{\mathrm{n}}=\dfrac{2}{3}a_{\mathrm{gc}}^2\tan\theta\sqrt{\tan^2\theta+2}H_{\mathrm{v}}N_{\mathrm{d}}+N_{\mathrm{b}}\left(\dfrac{a_{\mathrm{p}}^{3/2}bv_{\mathrm{w}}R^{1/2}K_{\mathrm{ID}}^{3/4}H_{\mathrm{v}}^{1/2}}{\sqrt{2}Kl_{\mathrm{u}}v_{\mathrm{s}}N_{\mathrm{a}}}\right) $
$ F_{\mathrm{n}}=\dfrac{2}{3}a_{\max}^2\tan\theta\sqrt{\tan^2\theta+2}H_{\mathrm{v}}N_{\mathrm{a}} $The mean relative errors for the normal and tangential grinding forces were 8.49% and 13.59%, respectively. (3-2) [120] Rotary ultrasonic vibration grinding
in 1D-SiCf/SiC$ F_{\mathrm{n}}=\left[\dfrac{60(H)^{3/2}\left(K_{\rm{IC}}\right)^{1/2}\left(1-v_1^2\right)^{1/4}a_{\rm{p}}v_{\rm{f}}}{\begin{array}{l}2k_1k_{\rm{h}}\text{π}dN_{\rm{d}}n_{\rm{s}}(\tan\theta)^{-3/4}E^{7/8} \\ \int_0^{t_1}\sqrt{\left[\dfrac{\text{π}n_{\mathrm{s}}}{30}R\cos\left(\dfrac{\text{π}n_{\mathrm{s}}}{30}t\right)+v_{\mathrm{f}}\right]^2+\left[-\dfrac{\text{π}n_{\rm{s}}}{30}R\sin\left(\dfrac{\text{π}n_{\rm{s}}}{30}t\right)\right]^2+(2\text{π}fA\cos2\text{π}ft)^2\rm{d}t}\end{array}}\right]^{8/9} $ The mean relative errors for the normal and tangential grinding forces were 9.29% and 6.16%, respectively. (3-3) [77] Longitudinal-torsional ultrasonic vibration end grinding SiCf/SiC $ F_{\mathrm{n}}=\left[\dfrac{\begin{gathered}\text{π}\left(R_0+R_i\right)a_{\mathrm{p}}v_{\mathrm{w}}-N_{\mathrm{z}}fL_1\left(r_{\mathrm{g}}^2\arccos\left(1-\dfrac{\delta_{\mathrm{da}}}{r_{\mathrm{g}}}\right)-\left(r_{\mathrm{g}}-\delta_{\mathrm{da}}\right)\sqrt{2r_{\mathrm{g}}\delta_{\mathrm{da}}-\delta_{\mathrm{da}}^2}\right)- \\ N_{\mathrm{\mathrm{z}}}fL_2\left(r_{\mathrm{g}}^2\arccos\left(1-\dfrac{\delta_{\mathrm{ba}}}{r_{\mathrm{g}}}\right)-\left(r_{\mathrm{g}}-\delta_{\mathrm{ba}}\right)\sqrt{2r_{\mathrm{g}}\delta_{\mathrm{ba}}-\delta_{\mathrm{ba}}^2}\right) \\ \end{gathered}}{\dfrac{\text{π}}{2}N_{\mathrm{\mathrm{z}}}fC_2^2\left(1/\tan\varphi\right)^{3/4}\dfrac{E_{\mathrm{e}}^{7/8}}{H_{\mathrm{V}}^{3/2}K_{\mathrm{IC}}^{1/2}\left(1-\nu^2\right)^{1/4}}L_3}\right]^{8/9} $ The maximum relative errors for the normal and tangential grinding forces were 8.51% and 10.19%, respectively. The ultrasonically assisted grinding force exhibited a non-linear decrease compared to conventional grinding. (3-4) [118] Rotary ultrasonic vibratory spiral grinding holes SiCf/SiC $ F\mathrm{_t}=\dfrac{n_{\mathrm{M}}}{4}c_4h_{\mathrm{M}}^2\tan^22\theta_{\mathrm{M}}H_{\mathrm{M}}\arccos\left(1-\dfrac{h_{\mathrm{M}}}{A}\right) $ Higher ultrasonic amplitudes reduced the grinding forces.
(3-5)[76] Notes: In Eq. (3-1), Fgdn is the ductile removal grinding force, Fgbn is brittle removal grinding force, s the feed per cutting point in a cutting cycle, ns is the spindle speed, t1 is the start time of brittle removal, t2 is the maximum undeformed chip thickness forming time, vx(t), vy(t), vz(t) are the velocity for the single abrasive grain, KIC is fracture toughness, and θ is conical abrasive grain half top angle. In Eq. (3-2), agc is the critical cutting depth of brittle removal, b is the width of the grinding area, R is the radius of the grinding tool, KID is the dynamic fracture toughness of the workpiece, K is the correction factor, lu is the contact length between the abrasive grain and the workpiece, and amax is the maximum undeformed chip thickness. In Eq. (3-3), vf is feed rate, f is frequency of ultrasonic vibration, A is amplitude of ultrasonic vibration, R is radius of wheel, and kl, kh are dimensionless coefficients. In Eq. (3-4), R0 is Tool's average radius, Nz is numbers of abrasive grains on the tool periphery end face, L1, L2, and L3 are a single abrasive grain's path length in ductile, ductile-to-brittle transition and brittle regions, and rg is abrasive grain radius. In Eq. (3-5), Ft is grinding force with ultrasonic vibration, nM is number of grains on end face, c4 is coefficient of force of ultrasonic vibration, hM is theoretical grinding thickness, and HM is hardness of matrix. -
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