Modeling and analysis of the material removal profile for free abrasive polishing with sub-aperture pad

This paper addresses the problem of material removal in free abrasive polishing (FAP) with the sub-aperture pad both theoretically and experimentally. The effects of some polishing conditions upon the material removal are analyzed, including not only the process parameters, which refer to the normal force, angular spindle velocity and angular feed rate, but also the abrasive grain size, polishing slurry properties, topographical parameters of the sub-aperture pad, as well as tool path curvature. Based on the analysis, a model of material removal profile is proposed to facilitate more accurate polishing. First, by analyzing the contact among polishing pad, abrasive grain and workpiece surface in the micro level, the removal depth per unit length of the polishing path is derived, which is defined as the material removal index. Then, the distribution of this removal index can be obtained via modeling the pressure and relative sliding velocity in the contact region of polishing pad and workpiece. After that, the material removal profile can be calculated by integrating the material removal index along the tool path in the tool-workpiece contact region. To verify the effectiveness of the proposed model, a series of polishing experiments have been conducted. Experimental results well demonstrate that our model can accurately predict the material removal depth during the FAP.     

磨粒刻划单晶SiC的SPH与FEM耦合仿真分析

目的 进一步理解金刚石线锯加工硬脆晶体材料的去除特性.方法 采用SPH与FEM耦合算法,分析磨粒刻划单晶碳化硅工件过程中的材料去除动态响应,研究不同磨粒压入深度与几何形状条件对磨粒接触力、工件刻划表面形貌与应力分布的影响规律,分析磨粒恒定深度刻划与变深度刻划两种方式下磨粒刻划工件材料的动态响应.结果 磨粒接触力的各方向分量均随刻划时间发生波动,其中x与z轴方向的磨粒接触力随时间的变化趋势相近,平稳刻划时段的磨粒接触力均值拟合方程分别为fx=3.0956h2.7264,fz=11.3813h2.6214.磨粒压入深度是影响刻划过程中工件刻划截面形貌及应力分布的主要因素.相较于圆锥体磨粒,球体磨粒刻划后的工件材料截面形貌更粗糙,但工件材料的变形及损伤层深度更小.在磨粒变深度刻划方式下,随着磨粒压入深度的增加,刻划过程中的工件材料发生了脆塑转变.结论 在保证材料去除率的条件下,需降低磨粒压入深度,以降低磨粒接触力,获得更平整的工件表面刻划形貌与更低的等效应力.     

抛光垫表面微细结构对抛光性能的影响试验

抛光垫是影响抛光加工效率和表面质量的关键因素之一,但影响规律和作用机理尚不清晰。为研究抛光垫表面微细结构对抛光性能的影响规律,制作有、无固结磨料的表面六边形微细结构抛光垫,分别对YG15硬质合金、单晶Si和单晶4H-SiC三种硬度差异较大的工件进行抛光试验。结果表明：各抛光垫对不同硬度工件抛光效果的影响规律一致,随着抛光工件的硬度增大,各抛光垫的材料去除率（MRR）减小,表面粗糙度Ra增大。抛光垫内的固结磨料能将MRR提高5～10倍,但也会导致Ra增大5～20倍。抛光垫表面微细结构会使得抛光过程中有效接触面积Ap和有效磨粒数Ns减小而导致MRR下降,而抛光垫硬度的增加能够部分弥补抛光垫表面微细结构造成的影响,抛光工件硬度越大,弥补效果越好。增加游离磨料能够有效降低抛光后Ra并提高硬度较大工件的MRR（上升约8%）,但对硬度较小工件的MRR有抑制作用（下降约27%）。根据抛光试验结果,建立工件-磨料-抛光垫接触模型,深入分析抛光垫表面微细结构、表面硬度对不同硬度工件抛光MRR和表面质量的作用机理,为不同工件抛光时抛光垫的选择提供了理论基础。     

硬质合金刀具材料化学机械抛光机理研究

目的研究硬质合金刀具材料化学机械抛光(CMP)机理,为改善硬质合金刀具表面质量提供理论支持。方法分析硬质合金刀具材料在酸性抛光液中的化学反应,研究硬质合金刀具材料CMP的化学反应机理。基于接触力学理论计算抛光垫与工件的实际接触面积和单个磨粒的实际切削面积,在运动学分析的基础上,建立硬质合金刀具材料CMP的材料去除率模型,通过实验验证材料去除率模型的有效性。结果在酸性抛光液中,硬质合金被氧化成Co_3O_4。当工件、抛光垫、磨粒类型、工件安装位置确定时,材料去除率与抛光载荷、磨粒浓度和抛光盘转速有关。常用硬质合金抛光条件下,抛光YG8刀具的修正系数Kcm为8.53,抛光后刀具的最低表面粗糙度能达到48nm,材料去除率为62.381nm/min,材料去除率的理论值和实验值的最大相对误差为13.25%,消除了表面缺陷,获得了较好的镜面效果。结论建立的材料去除率模型具有一定的有效性,对硬质合金刀具材料进行化学机械抛光能消除刀具的表面缺陷,改善表面质量。     

Simulation for optimizing grain pattern on Engineered Grinding Tools

Engineered Grinding Tools (EGT) are characterized by a predetermined and controlled arrangement of the abrasive grains. The distribution of the abrasive grains can be used to enhance the grinding process by improving space for coolant supply and for chip removal. This is especially interesting for grinding operations with high specific material removal rates. A numerical method was developed to optimize the grain pattern on EGT. This method consists of a stochastic tool model, a kinematic process model, a material removal model and a grain wear model. The tool model comprehends the relevant geometric properties of the abrasive layer. The material removal model is based on the assumption of a kinematic-geometrical cutting condition. The wear model is based on a grain load limit and the grains’ load is assumed to be proportional to its cutting area. Once the cutting area of one grain exceeds the limit value, wear takes place. The model validation is presented comparing the wear behavior of EGT and workpiece roughness achieved with numerical and experimental methods.     

Nanometer-scale characteristics of polycrystalline YAG ceramic polishing

Polycrystalline yttrium aluminum garnet (YAG) ceramics used as laser gain media require nanometer-scale surface geometries to minimize light scattering. Generally, uneven material removal between grains and excessive material removal at the grain boundaries retards smoothing of the ceramic surfaces. This paper describes the effects of the mechanical properties and polishing tool structures on the tool contact against the target surface during polishing. This, in addition to the abrasive type and size, influences the polishing characteristics, especially the material removal at the grain boundaries, the grain enhancement, the grain dislodgement, and the resulting nanometer-scale geometries of the polished surfaces.     

基于微元材料去除模型的单摆抛光平面度预测

为探究单摆参数对抛光工件平面度的影响,提出一种基于速度和压强分布耦合的抛光微元材料去除模型,以预测工件表面平面度。从单颗磨粒的材料去除出发,建立工件表面各微元单位时间内材料去除厚度模型,并将工件相对抛光垫速度和工件表面压强分布耦合代入模型;根据工件初始面形提取微元高度值,结合各微元材料去除的厚度,计算抛光后的工件表面平面度;试验验证平面度预测方法。结果表明:仿真与实际抛光后的面形的变化趋势相同,平面度PV₂₀值绝对偏差小于12.0%,平面度预测可靠。      

On the mechanics of the grinding process, Part III—thermal analysis of the abrasive cut-off operation

This is Part III of a 3 part series on the Mechanics of the Grinding Process. Part I deals with the stochastic nature of the grinding process, Part II deals with the thermal analysis of the fine grinding process and this paper (Part III) deals with the thermal analysis of the cut-off operation. Heat generated in the abrasive cut-off operation can affect the life of resin bonded grinding wheels and cause thermal damage to the workpiece. Thermal analysis of the abrasive cut-off operation can, therefore, provide guidelines for proper selection of the grinding conditions and optimization of the process parameters for improved wheel life and minimal thermal damage to the workpiece. In this investigation, a new thermal model of the abrasive cut-off operation is presented based on statistical distribution of the abrasive grains on the surface of the wheel. Both cutting and ploughing/rubbing that take place between the abrasive grains and the work material are considered, depending on the depth of indentation of the abrasives into the work material. In contrast to the previous models, where the apparent contact area between the wheel and the workpiece was taken as the heat source, this model considers the real area of contact, namely, the cumulative area of actual contacting grains present at the interface as the heat source. It may be noted that this is only a small fraction of the total contact area as only a small percentage of the abrasive grains present on the surface of the cut-off wheel are in actual contact with the workpiece at any given time and even a smaller fraction of them are actual cutting grains taking part in the cut-off operation. Since, the Peclet number, N_Pe in the case of cut-off grinding is rather high (a few hundred), the heat flow between the work and the contacting abrasive grains can be considered to be nearly one-dimensional. In this paper, we consider the interaction between an abrasive grain and the workpiece at the contact interface. Consequently, the heat source relative to the grain is stationary and relative to the workpiece is fast moving. The interface heat source on the grain side as well as on the workpiece side is equivalent to an infinitely large plane heat source with the same heat liberation intensity as the circular disc heat source. However, it will be shown in the paper that the contacting times are different. For example, the abrasive grain contacts the heat source, as it moves over the wheel-work interface, for a longer period of time ( milliseconds) whereas the workpiece contacts the heat source for shorter period of time ( a few microseconds). The temperature in the grinding zone is taken as the sum of the background temperature due to the distributed action of the previous active grains operating in the grinding zone (global thermal analysis) and the localized temperature spikes experienced at the current abrasive grain tip-workpiece interfaces (local thermal analysis), similar to the work reported in the literature [Proc Roy Soc (London) A 453 (1997) 1083]. The equivalent thermal model developed in the present investigation is simple and represents the process more realistically, especially the heat partition. The model developed provides a better appreciation of the cut-off operation; a realistic estimation of the heat partition between the wheel, the workpiece, and the chip; thermal gradients in the workpiece due to abrasive cut-off operation, and an insight into the wear of the cut-off wheels.     

偏置量对固结磨料小工具头抛光面形收敛效率的影响

目的 解决自由曲面磨抛面形收敛困难的问题,提高抛光小工具头的抛光效率.方法 提出一种偏置式固结磨料小工具头,基于固结磨料小工具头的结构特征参数,建立抛光小工具头的去除函数理论模型,并进行仿真分析,应用定点抛光法建立抛光小工具头去除函数实验模型,并验证抛光小工具头理论去除函数合理性,基于CCOS技术原理建立工件表面定量去除模型,通过虚拟加工实验探索偏置量对固结磨料小工具头抛光钛合金后的面形收敛效率的影响.结果 归一化理论去除函数曲线与实验曲线吻合度较高,定点抛光去除函数仿真模型能够很好地预测定点抛光斑的去除轮廓形状.抛光小工具头抛光钛合金的面形误差随偏置量增加,呈现先减小、后增大的趋势,无偏置的抛光小工具头抛光后,面形数据均方根(RMS)收敛效率为54.56％,波峰值与谷峰值之差(PV)的收敛效率为60.21％,当抛光小工具头偏置量为1.5 mm时,抛光后的RMS收敛效率达到最高,为73.83％,PV收敛效率为69.68％.结论 固结磨料小工具头去除函数理论模型可指导确定性材料去除,偏置量为1.5 mm时的抛光小工具头具有最强的修正误差能力,可以显著提高固结磨料小工具头抛光工艺的面形收敛效率.     

Modeling surface roughness in the stone polishing process

In this paper, a new method for modeling and predicting the surface roughness of the workpiece in the stone polishing process is developed. This method is based on the random distribution of the stone grain protrusion heights and the force balance by contact grains. To do so, first, the topography of a polishing stone is generated based on a Gaussian distribution with the mean value and standard deviation determined from a given stone grit number. Second, the plasticity theory is applied to determine the micro depth of cut of a single grain for a given workpiece hardness (Brinell number). Third, a search method is developed to determine the number of the contact grains and the micro depth of cut, based on the force balance principle between the force applied on the stone and the forces transmitted to the grains that are in contact with the workpiece. Fourth, a method is presented for predicting the surface roughness based on the micro depth of cut and contact grains. A good agreement of the prediction results with the experimental data proves the effectiveness of the proposed method.     

双磨粒抛光单晶Si的分子动力学模拟

目的 通过分子动力学(MD)模拟,获得双金刚石磨粒抛光单晶Si的去除机理.方法 采用一种新的单晶硅三体磨粒抛光方法,测试双磨粒的抛光深度和横向/纵向间距对三体磨粒抛光的影响,从而获得相变、表面/亚表面损伤等情况,并获得抛光过程中温度及势能的变化情况.结果 对比抛光深度为1、3 nm时配位数的情况,发现抛光深度为1 nm时,抛光完成时相变的原子数是4319,而抛光深度为3 nm时,相变原子数为12516.随着磨粒在Si工件表面抛光深度的加深,抛光和磨蚀引起的相变原子和损伤原子的数目增加.仿真结果还表明,单晶Si相变原子的种类和数目随磨粒横向间距的增加而增加,随着纵向间距的增加反而减少.系统的初始温度设为298 K,抛光深度为1 nm时,抛光完成时的温度是456 K,而抛光深度为3 nm时,温度是733 K.抛光完成时,纵向组和横向组的温度仅相差30～40 K.在抛光深度、横向间距和纵向间距3个对照组中,抛光深度对亚表面损伤的影响最大.抛光深度为3 nm时,亚表面的损伤深度最大,从而导致更多的材料从单晶Si工件表面去除.结论 双磨粒的抛光深度和间距不仅对硅的表面微观结构产生影响,还对相变产生影响.模拟参数相同时,较大的抛光深度和横向间距下会产生更多的相变原子,因此相变受抛光深度的影响最大,受纵向间距的影响最小.     

超声复合磨料振动抛光方法有限元分析与实验

为研究超声复合磨料振动抛光方法对工件表面材料去除量与工件表面粗糙度的影响,分析了超声复合磨料振动抛光方法;并利用ANSYS Workbench软件分别分析了超声振动条件下和超声复合磨料振动条件下工件表面结构与应力变化情况,同时在超声复合磨料振动条件下通过实验验证超声复合磨料振动抛光技术对工件表面材料去除量与工件表面粗糙度的影响程度。结果表明:超声复合磨料振动条件下工件表面位移小于超声振动条件下的工件表面位移,超声复合磨料振动条件下工件表面应力大于超声振动条件下的工件表面应力;在超声复合磨料振动条件下,影响工件表面粗糙度最显著的因素是磨料质量分数,影响工件表面材料去除量最显著的因素是抛光时间,且磨料质量分数为30%、抛光时间为4 h时,抛光效果最佳。     

考虑单磨粒作用的砂带磨削机理模型

针对磨削过程中材料的定量去除问题，从微观单磨粒角度出发，综合运用弹塑性变形、赫兹接触以及概率统计等理论及方法，构建砂带磨削的材料去除机理模型。首先，分析磨削过程中单个磨粒在工件不同变形阶段的材料去除机理，并根据试验计算结果对该磨削过程进行简化，给出单磨粒受力计算方法；在此基础上，基于磨粒数目与出刃高度分布函数，运用概率统计理论建立微观磨粒与宏观磨削压力平衡方程，求解磨粒切入深度分布函数；再结合单磨粒材料去除体积，用积分运算构建总体材料去除模型；最后通过机器人磨削平台进行TC4合金曲面磨削试验得到材料最大去除深度。结果表明:材料最大去除深度随磨削压力和砂带线速度增大而增大，随砂带进给速度增大而减小；且理论模型的理论预测值与试验值比较，其最大相对误差为17.66%，平均相对误差为10.55%，验证了模型的有效性。      

磨粒半径对金刚石研磨加工影响机制的仿真研究

为解析金刚石磨粒尺寸变化对金刚石材料研磨质量的影响机制,利用分子动力学方法建立球形刚性金刚石磨粒研磨金刚石工件的模型,研究不同磨粒半径下的磨削力变化规律和应力、相变分布。结果表明: 磨粒半径从6a增大到20a(a为金刚石晶格常数),磨削平均法向力和平均切向力均线性增加,但平均法向力增量为平均切向力的3倍;磨粒与工件间的剪切作用相对挤压和摩擦的作用越来越小,且磨削力波动幅度变大表明工件的位错形成更剧烈;同时,磨粒前下方形成的强压应力区和磨粒后方由摩擦引起的集中拉应力区增大,非晶相变区域增大,研磨区后方缺陷增多,工件的加工表面质量变差。当半径为10a、15a和20a的磨粒压入深度为2 nm时,磨粒刻划后的工件表面显微硬度比未刻划时的有所降低,分别减少2.8%、9.6%和18.3%,即磨粒半径增大会显著降低工件表面力学性能。      

钛合金材料页轮磨抛材料去除深度模型

针对钛合金材料页轮磨抛表面去除量难控制的问题,从页轮磨抛的运动过程出发,结合Preston方程、Hertz接触理论及线接触变形等理论方法,建立页轮磨抛的材料去除深度模型。首先,分析磨削过程中页轮的运动和材料去除过程,并通过Preston方程简化磨抛过程,得到材料去除深度与页轮的线速度、接触压强、进给速度之间的关系;其次,通过Hertz接触理论及线接触变形得到接触压强和预压量的关系式,再将预压量代入接触压强,构建材料去除深度理论模型;最后,采用正交试验法和单因素试验法验证该理论模型的准确性,并通过极差分析法分析各参数对页轮磨抛去除深度的影响程度。结果表明:材料去除深度与预压量和页轮线速度成正比,与页轮进给速度成反比,且各参数对页轮磨抛去除深度的影响程度基本相当。模型预测的材料去除深度与试验结果的平均相对误差为6.25%,说明理论模型可准确预测磨削去除深度。      

玻璃材料高速抛光用固着磨料磨具试验研究

目的实现玻璃材料的高效高质量低成本抛光。方法选择不同添加剂作为辅料制作固着磨料抛光磨具,阐明制作工艺流程、添加剂辅料配方及比例、固着磨料磨具对材料硬度、剪切强度等性能的影响。以工件材料去除率、表面质量以及磨耗比等作为评价指标分析不同添加剂辅料对加工效果的影响,并通过等效系数优化方法确定添加剂辅料的最优配方。结果碳化硅与钼酸铵可增加磨具的硬度和剪切强度,磨具中加入适量氧化铝可有效提高工件表面质量。结论固着磨料抛光磨具的添加剂辅料最优配方为:10.6%(质量分数)4000#Al2O3和2%(质量分数)10000#SiC。     

应用弹性砂轮对铝合金镜面磨削工艺研究

目的解决铝合金手机外壳传统抛光工艺中存在的抛光效率低等问题。方法采用聚氨酯弹性砂轮对6061铝合金进行了磨削加工,使用正交试验研究了磨料粒度、进给速度、切削深度、砂轮线速度对加工表面粗糙度及材料去除率的影响。试验中使用折线走刀方式进行加工,可减轻磨料分布不均带来的影响。使用白光干涉仪测量了加工后表面的粗糙度,通过计算单位时间内工件的质量变化得出了去除率,并通过对结果的综合优化得出了最优工艺参数。结果在选取的16组磨削工艺参数中,可获得的最低表面粗糙度为44.87 nm,最大去除率为0.329 g/min。对表面粗糙度影响最大的因素为磨料粒度,影响最小的因素为进给速度;对材料去除率影响最大的因素为切削深度,影响最小的为进给速度。经过综合优化,最佳工艺参数组合为:砂轮600#,转速2000 r/min,切削深度0.04 mm,进给速度20 mm/min。结论弹性聚氨酯砂轮应用于铝合金磨削可提高加工表面质量,可简化工艺流程,节省备料和安装调整时间,从而提高效率。     

随机网格结构固结磨料磨盘平面磨削性能研究

针对超精密磨削加工过程对工件材料去除效率、表面质量、亚表面损伤等指标的复合需求,提出一种基于泰勒多边形设计的随机网格结构固结磨料磨盘（textured-fixed abrasive plate, T-FAP）,并以光固化树脂作为结合剂基体材料混合微米级氧化铝磨料制备磨盘,使用MATLAB图像分析和磨抛轨迹仿真方法研究磨盘磨削过程中表面磨损时变图案特征对其加工性能的影响,并通过铝制工件的平面磨削实验对磨盘磨削过程中的材料去除率及工件表面粗糙度进行分析。实验结果表明:相比传统固结磨料磨盘,采用随机网格结构磨盘加工的工件表面粗糙度为0.84 μm,材料去除率为3.21 μm/min,能够在保证材料去除率的同时获得较高的表面精度。      

磨粒尺寸和基体硬度对固结磨料抛光YAG晶体的影响

钇铝石榴石(YAG)是一种应用广泛的硬脆难加工材料，其抛光过程工艺复杂、效率低。固结磨料抛光技术具有平坦化能力优、对工件形貌选择性高、磨料利用率高等优点。试验采用固结磨料抛光YAG晶体，研究固结磨料垫的基体硬度和金刚石磨粒尺寸对YAG晶体的材料去除率和表面质量的影响。结果表明:当基体硬度适中为Ⅱ、金刚石磨粒尺寸3～5 μm时，固结磨料抛光YAG晶体效果最优，其材料去除率为255 nm/min，表面粗糙度S_a值为1.79 nm。      

Modeling of contact behavior between polishing pad and workpiece surface

The polishing pad is one of the most significant components within a polishing system. It influences both the material removal rate and the surface finish. Furthermore, the wear behavior of the polishing pad is responsible for the shape accuracy. Nevertheless despite extensive research activity in recent years, there are still gaps of knowledge in terms of the working principle of a polishing pad. In this paper, the contact behavior of a polishing pad (polyurethane foam) with the workpiece surface is examined. For this, the polishing pad is modeled using a finite-element modeling (FEM) program and the deformation by pressing it against the rigid workpiece surface is investigated. Consequently, the local tensions are calculated, which are the basis for the penetration depth and therefore also for the material removal rate. The investigations presented in this paper were carried out within the research project SFB TR/4 funded by the German Research Association, Deutsche Forschungsgemeinschaft (DFG).