工件旋转法磨削硅片的磨粒切削深度模型

半导体器件制造中,工件旋转法磨削是大尺寸硅片正面平坦化加工和背面薄化加工最广泛应用的加工方法。磨粒切削深度是反映磨削条件综合作用的磨削参量,其大小直接影响磨削工件的表面/亚表面质量,研究工件旋转法磨削的磨粒切削深度模型对于实现硅片高效率高质量磨削加工具有重要的指导意义。通过分析工件旋转法磨削过程中砂轮、磨粒和硅片之间的相对运动,建立磨粒切削深度模型,得到磨粒切削深度与砂轮直径和齿宽、加工参数以及工件表面作用位置间的数学关系。根据推导的磨粒切削深度公式,进一步研究工件旋转法磨削硅片时产生的亚表面损伤沿工件半径方向的变化趋势以及加工条件对磨削硅片亚表面损伤的影响规律,并进行试验验证。结果表明,工件旋转法磨削硅片的亚表面损伤深度沿硅片半径方向从边缘到中心逐渐减小,随着砂轮磨粒粒径、砂轮进给速度、工件转速的增大和砂轮转速的减小,加工硅片的亚表面损伤也随之变大,试验结果与模型分析结果一致。     

Modeling and simulation of grinding surface topography considering wheel vibration

Grinding is an important means of realizing precision and ultra-precision machining. Vibration caused by an unbalanced grinding wheel in grinding process has a significant impact on the quality of workpiece surface. However, the effect of wheel surface topography and/or the relative vibration between grinding wheel and workpiece are not considered in most researches. Taking the relative vibration between grinding wheel and workpiece into account, alongside the abrasive grain trajectory equation, a new analysis and simulation model for surface topography of the grinding process is established. The model for the topography of the grinding wheel surface is first studied, and subsequently, a new simulation model for surface topography of the grinding process is proposed. Case studies are performed at the end, and the influence of grinding wheel vibration amplitude, wheel grit number, as well as grinding parameters on the surface waviness and roughness is discussed. The simulation results could be used to optimize the actual grinding process to improve the ground surface quality or predict the surface topography by given grinding parameters.     

硅片低损伤磨削砂轮及其磨削性能

针对传统金刚石砂轮磨削硅片存在的表面/亚表面损伤问题,研制了一种用于硅片化学机械磨削加工的新型常温固化结合剂软磨料砂轮。根据化学机械磨削加工原理和单晶硅的材料特性,设计的软磨料砂轮以氧化铈为磨料,二氧化硅为添加剂,氯氧镁为结合剂。研究了软磨料砂轮的制备工艺,分析了软磨料砂轮的微观组织结构和成分。通过测量加工硅片的表面粗糙度、表面微观形貌和表面/亚表面损伤,进一步研究了软磨料砂轮的磨削性能。最后,与同粒度金刚石砂轮磨削和化学机械抛光(CMP)加工的硅片进行了对比分析。结果表明,采用软磨料砂轮磨削的硅片其表面粗糙度Ra1nm,亚表面损伤仅为深度30nm的非晶层,远好于金刚石砂轮磨削硅片,接近于CMP的加工水平,实现了硅片的低损伤磨削加工。     

磨削参数对超细硬质合金磨削表面粗糙度的影响

在使用金刚石砂轮的平面磨床上对超细硬质合金进行了磨削试验研究。通过扫描电子显微镜观察磨削表面形貌和用表面粗糙度测定仪测量磨削表面粗糙度,分析了磨削参数对超细硬质合金磨削表面粗糙度的影响。研究结果表明,同一切深下,超细硬质合金磨削表面粗糙度随砂轮粒度的增大而增大。采用相同粒度砂轮磨削,切深较小时,超细硬质合金磨削表面粗糙度随切深的增加而增大,当切深增大到一定值后,磨削表面粗糙度值逐渐降低。     

Elastic recovery of monocrystalline silicon during ultra-fine rotational grinding

Micromachining of brittle materials like monocrystalline silicon to obtain deterministic surface topography is a 21st Century challenge. As the scale of machining has shrunk down to sub-micrometre dimensions, the undulations in the machined topography start to overlap with the extent of elastic recovery (spring back) of the workpiece, posing challenges in the accurate estimation of the material's elastic recovery effect. The quantification of elastic recovery is rather complex in the grinding operation due to (i) randomness in the engagement of various grit sizes with the workpiece as well as (ii) the high strain rate employed during grinding as opposed to single grit scratch tests employed in the past at low strain rates. Here in this work, a method employing inclination of workpiece surface was proposed to quantify elastic recovery of silicon in ultra-fine rotational grinding. The method uniquely enables experimental extraction of the elastic recovery and tip radius of the grits actively engaged with the workpiece at the end of the ultra-fine grinding operation. The proposed experimental method paves the way to enable a number of experimental and simulation endeavours to develop more accurate material constitutive models and grinding models targeted towards precision processing of materials. It can also be shown that using this method if the tip radius distribution of active grits is measured at different time instances, then this data can be used to assess the state of the grinding wheel to monitor its wear rate which will be a useful testbed to create a digital twin in the general framework of digital manufacturing processes.     

The effect of dynamic behavior on surface roughness of ball screw under the grinding force

The dynamic behavior of a ball screw under a moving grinding force and the resulting ball screw surface roughness are investigated. The system includes a ball screw, a headstock, a tailstock, a steady rest, a grinding wheel, and a wheel head. Equations of motion of the system are derived through Lagrangian approach combined with global assumed mode method in this study. The transient responses of the system due to a moving force are evaluated using Runge?CKutta method. Results show that the steady rest can reduce 90% vibration in a grinding process. An equation is proposed to predict the maximum response by the cutting depth. Then we simulate the grain height distribution on the grinding wheel, considering transient response on the ball screw and the grinding wheel. Lastly, the ball screw surface roughness could be simulated via calculating the depth of all working grains. The purpose of using grinding process is that the ball screw needs fine surface roughness. The ball screw surface roughness is influenced by the grain size more than the structure numbers can be.     

Analytical modeling of grinding wheel loading phenomena

Wheel surface condition plays an important role in the grinding operation. Grinding wheel loading, meaning chip accumulation in the space between grains, leads to deteriorating wheel cutting ability and causes excessive force and temperature. This paper presents an analytical model of wheel loading phenomena as a function of cutting parameters, wheel structure, and material properties. The model is based on the adhesion of workpiece material to abrasive grain surface. It is validated by experimental results from grinding nickel-based superalloy with cubic boron nitride vitrified wheel. This model considers wheel specifications including abrasive grains size and the number of cutting edges. Cutting parameters and process temperature are the other determinant factors. On the basis of this model and empirical results, the effects of the various process parameters are presented.     

Modeling of grinding wheel topography based on a joint method of 3D microscopic observation and embedded grindable thermocouple technique

The grinding wheel generally has a complicated topography for the irregularity of abrasive grits, which always has an important influence on the final quality of the grinding workpiece. In this paper, a joint method of microscopic observation and grindable thermocouple technique was adopted to model the wheel topography. The grinding wheel topography was first modeled through microscopic observation by an in-position 3D microscope KH-7700 installed on the grinding machine. Based on the measurement of grit sizes, shapes, and distributions through the 3D microscope, a wheel surface model was established and a static grit number model based on Rayleigh distribution was proposed. Moreover, a numerical model was given to validate the proposed Rayleigh distribution model of an active grit number. In order to investigate the real abrasive grit number in a grinding process, an embedded grindable thermocouple was used to detect the dynamic variation of temperature signals, which will reflect the variation of in-process wheel topography under different process parameters, machine status, and even the grit-workpiece interaction status. Through the experimental analysis, it can be concluded that the increase of depth of cut a_p could help to greatly increase the active grit number to the grinding process, while the increase of workpiece speed V_w and decrease of wheel speed V_s could lead to a subtle increase of the grit number. Moreover, the active grit number is about one fourth to one third of the static grits. The contact arc length between the wheel (CBN) and the workpiece (Ti-6Al-4V) was calculated by the contact time from the workpiece surface temperature data, and it was found that the actual contact arc length was about 1.5~2 times of the geometric size.     

Constrained grinding optimization for time,cost, and surface roughness using NSGA-II

Selection of parameters in machining process significantly affects quality, productivity, and cost of a component. This paper presents an optimization procedure to determine the optimal values of wheel speed, workpiece speed, and depth of cut in a grinding process considering certain grinding conditions. Experimental studies have been carried out to obtain optimum conditions. Mathematical models have also been developed for estimating the surface roughness based on experimental investigations. A non-dominated sorting genetic algorithm (NSGA II) is then used to solve this multi-objective optimization problem. The objectives under investigation in this study are surface finish, total grinding time, and production cost subjected to the constraints of production rate and wheel wear parameters. The Pareto-optimal fronts provide a wide range of trade-off operating conditions which an appropriate operating point can be selected by a decision maker. The results show the proposed algorithm demonstrates applicability of machining optimization considering conflicting objectives.     

Study on the rotary cup dressing of CBN grinding wheel and the grinding performance

A systematic research is conducted to investigate the effect of rotary cup dressing on vitrified cubic boron nitride grinding performance in grinding of nickel-based superalloys. Grinding performance is evaluated mainly in terms of specific grinding energy and radial wheel wear. The number of active grits per unit area and their slope is considered as the two grinding wheel topographical key parameters for studying grinding performance. Cup dressing conditions with various speed ratios and overlap factors were investigated. In each case, the specific grinding energy and the radial wheel wear were experimentally measured, and then the effect of changing dressing parameters on the grinding performance is analyzed. To provide a view on how various parameters influence specific energy and the importance of wheel topography and grit workpiece interaction, a new specific grinding energy model is developed. Inputs to this model are workpiece parameters, grinding process parameters, and, in particular, the grinding wheel topographical parameters. This model is validated by experimental results. The theoretical values considering the complexity of the grinding process reasonably compare with the experimental results. The effect of number of active grits per unit area and their slope on specific grinding energy and then metal removal mechanism is investigated. The results revealed that the number of active grits per unit area has less effect on specific grinding energy than grits slope.     

Modeling surface roughness for polishing process based on abrasive cutting and probability theory

The surface roughness is a variable used to describe the quality of polished surface. This article presents a surface roughness model based on abrasive cutting and probability theory, which considers the effects of abrasive grain shape, grit and distribution feature, pressure on surface roughness. The abrasive grain protrusion heights are thought to close to Gaussian distribution, and then the relationship between the indentation depth and the pressure based on Hertz contact theory is obtained. Surface roughness prediction model is established by calculating indentation depth of the abrasive grains on workpiece surface. The maximum surface profile height (R_y) is approximately equal to the maximum indentation depth of the abrasive grain. The arithmetic average surface roughness (R_a) is equal to the average indentation depth of the abrasive grain. The effects of process parameters such as pressure and grit on R_y and R_a were simulated and analyzed in detail.     

Modeling and simulation of cutting forces generated during vertical micro-grinding

Micro-grinding using micro-tools has become very prevalent due to the miniaturization of products with increased process requirements. Moreover, this process provides an edge over other competitive processes, especially as a final process step. The quality of the part produced by the micro-scale grinding process can be influenced by various factors, particularly by the induced mechanical forces. Therefore, predictive model of cutting force can provide guidance for further development and optimization of the process. Although there has been a lot of a research conducted on conventional grinding, little knowledge has been accumulated on micro-scale grinding due to the fact that it is an emerging field of research. The early grinding models developed are mostly based on parameters such as wheel and workpiece velocity, depth of cut and grit size of the grinding wheel. Those early models narrated that the grits penetrate and cut the material from the workpiece surface with the generated grinding forces proportional to the removed material. However, those models may not be appropriate for micro-scale grinding due to the mode of material removal and the method of contact between surfaces which is different from the macro-scale method. In addition to that, due to the small feed rate used in brittle material machining, ploughing force needs to be considered intensively in addition to the chip formation force. Therefore, a new analytical model has been proposed to evaluate cutting forces of micro-grinding process based on the process configuration, workpiece material properties and micro-grinding tool topography. The size effect of micro-machining has been carefully considered in this proposed model. Therefore, this approach allows the derivation of cutting force comprising of both the chip formation force and ploughing force. Experimental investigation in a micro-grinding configuration has been pursued to validate the proposed predictive model. The estimated cutting force showed a good correlation with the experimental values except for higher depth of cut and lower feed rate. Additionally, paired T test has been performed to quantify the difference between the predicted and experimental results.     

考虑耕犁的超声磨削表面微观形貌建模与预测

超声磨削加工在难加工材料领域得到广泛应用,超声辅助磨削过程中,超声振动参数对磨削后的表面微观形貌具有重要影响,因此,为了在加工前对超声加工后的表面微观形貌进行预测,以优化加工参数。提出一种考虑耕犁的超声磨削表面微观形貌建模与预测方法。假设磨粒为球形,磨粒直径与间距服从高斯分布,给出砂轮形貌的数值生成方法;根据超声磨削运动学,建立考虑磨粒实时切削深度与耕犁影响的三维运动轨迹方程;在此基础上,提出超声磨削表面微观形貌生成的区域逼近求解算法,进而给出超声磨削表面微观形貌生成模型,模拟出超声磨削的三维表面微观形貌。通过试验分别从表面微观形貌的轨迹纹理、表面粗糙度数值两个方面对超声磨削表面微观形貌的模型的正确性进行了验证。     

Online monitoring of precision optics grinding using acoustic emission based on support vector machine

This paper aims to accomplish online monitoring of precision optics grinding with processing condition factors based on theoretical analysis and through grinding experiments. The model for monitoring surface quality of optical elements online (OSQMM) which contains identification model (IM) and interpolation·factor-support vector regression (i?f-SVR) is proposed. IM is applied to analyze and determine which kind of processing condition factors and which kind of its feature parameters are the best one to be used for online monitoring. i?f-SVR which contains the effect factor (fe) and interpolation function (I) to overcome the drawbacks of existing SVR models is applied to predict the monitoring thresholds. The grinding experiments were designed and performed. The influences of technological parameters (e.g., grain size of the grinding wheel, grinding depth, speed of the grinding wheel, speed of the worktable, and materials of workpiece) and processing condition factors (e.g., acoustic emission, grinding force, and vibration) on the surface quality were investigated and analyzed by IM. i?f-SVR was trained and established by the data which were gained through the experiments. After that, the other grinding experiments were performed to apply and verify OSQMM. The results were that the accuracy of alarm for roughness was 85.19 % and the accuracy of alarm for surface shape peak–valley value was 75.93 %. The results show that this method can be effectively applied to monitor the precision optics grinding process online.     

硅片自旋转磨削的运动几何学分析

介绍了硅片自旋转磨削的原理,通过引入节点、节圆概念建立了硅片自旋转磨削的运动学模型,通过分析砂轮与硅片之间的相对运动给出了硅片自旋转磨削的运动轨迹参数方程。在运动学的基础上推导了磨纹长度、磨纹数量以及磨削稳定周期公式。分析了磨纹间距、磨纹密度与磨削表面质量的关系。给出了选定磨削条件下的计算实例。研究结果为提高硅片加工质量及合理选择磨削工艺参数提供了理论依据。     

Optimization of the dressing operation using load cells and the Taguchi method in the centerless grinding process

The finishing processes of industrial components use grinding due to the elevated quality generated by this method. Centerless grinding is among the main manufacturing processes due to its high flexibility, accuracy, and great volume of production that is necessary in modern industry. However, the dressing operation has been a pronounced bottleneck in the centerless grinding process due to the time lost to make the corrections in the grinding wheel. This work presents an optimization of the dressing operation in centerless grinding using load cells and the Taguchi method. The experimental tests were carried out on the shop floor of a manufacturer of shock absorbers. The input parameters were the depth of dressing, the feed rate of dressing, the diameter of the grinding wheel, and the speed of the regulating wheel. The responses were the surface roughness, the roundness error, and the dressing force. The results show that the dressing time was reduced, generating an increase in machine productivity, the surface roughness of the work pieces was reduced with an improvement in quality, and the dressing force was proportional to the depth of dressing.     

Study on micro-interacting mechanism modeling in grinding process and ground surface roughness prediction

In the research on grinding process modeling, the stochastic nature of grain sizes and locations need to be considered. A new numerical model was developed which will describe the micro-interacting situations between grains and workpiece material in grinding contact zone. The model was established based on a series of reasonable assumptions, the critical conditions of starting points of plowing and cutting stages, and the redefined grinding contact zone. It indicated that there are four types of grain existing in grinding contact zone: uncontact, sliding, plowing, and cutting grains. The number of grains per unit wheel volume (N _v ) and the undeformed chip thickness (h _cu,max), which are key parameters in grinding process modeling, were firstly obtained. The numbers and distributions of different grain types along grinding contact zone were then obtained and analyzed. Calculation results showed that only a small fraction of grains participate in cutting interactions and the changing laws of each grain types along grinding contact length are very different from each other, which gives a deeper insight into grinding process and can be a good foundation for more precise grinding force prediction and thermal analysis. Another important application of this model is for ground surface roughness prediction and a new method on this purpose was developed. At last, two comparisons were made between calculation results and existing experimental data for validating the work on paper. Comparison results showed that the roughness of ground surface can be well predicted and gave the method theoretically to reduce ground surface roughness.     

基于数值仿真技术的单颗磨粒切削机理

磨削过程是磨具表面大量形状各异的磨粒参与的多刃切削过程。单颗磨粒切削研究是认识复杂磨削作用的重要手段,但是单颗磨粒切削试验的实施和物理量的测量存在一定的难度。针对这一问题,分别建立单颗磨粒切削的物理力学模型和数值仿真模型,利用不同载荷下的划痕试验验证这两个模型的准确性。利用数值仿真技术研究不同工艺参数下的单颗磨粒切削过程,仿真单颗磨粒的耕犁和切削过程,得到不同切削速度下耕犁向切削行为转变的临界切削深度;当切削深度增加到某一个切削深度时,仿真得到的径向和切向切削力均有突然增大的趋势,同时发现低速时切削力增大的程度明显高于较高速度时切削力的增大程度;仿真得到的最高切削温度随切削深度的增加,呈现先增大后减小再增大的特点,且第一个最高切削温度峰值出现在临界切削深度附近,但是随着切削速度的降低,这个现象明显减弱,当切削速度小于600 m/min时,这个现象基本不存在;仿真得到的材料去除率随着切削深度的增加而显著增大,而且切削速度越大,材料去除率越大。     

Influence of wheel speed on surface finish and chip geometry in precision contour grinding

A geometric computer model of a precision grinding operation was developed to calculate the surface features generated during contour grinding with a radiused wheel. This simulation includes the influence of the wheel (rotational speed, diameter, and nose radius), the workpiece (radius at cutting point, rotational speed), and the feedrate of the grinding wheel over the part. The model indicates that small changes in the wheel speed relative to the workpiece can have a dramatic effect on the surface finish over a specific area. Analysis of ground surfaces reveals uniform surface profiles and easily distinguished features that could only be produced by a constant wheel speed. This occurs for an air-bearing, air-turbude grinding spindle that has limited torque and is driven under open-loop control. The effects of the relative speeds are analyzed and an energy-based “phase locking” mechanism is proposed that can provide feedback to the grinding spindle from the material removal operation. By monitoring the spindle speeds during the grinding process and evaluating the resulting surface features, the phase effect has been experimentally verified.     

3D metal removal simulation to determine uncut chip thickness, contact length, and surface finish in grinding

The two most important geometric parameters that describe the mechanics of grinding are the uncut chip thickness and the contact length. Currently, analytical approaches are used to estimate these parameters. The accuracy of these approaches, however, is limited because they do not take into account the random shape, size, and protrusion height and placement of the abrasive grains around the circumference of the grinding wheel. In this paper, a simulation technique was used to gain new insight into the effect of the stochastic nature of grinding wheels on the geometric properties of the grinding process. The simulator was used to calculate the number of active grains, uncut chip thickness, and contact length for a stochastic wheel model of Radiac Abrasive’s WRA-60-J5-V1 grinding wheel. These values were then mapped to every grain on the grinding wheel and used to determine the instantaneous material removal rate of the wheel and workpiece surface finish. There was excellent agreement between the predicted and experimentally measured surface topology of the workpiece. The results suggest that only 10–25 % of the grains on the grinding wheel are active and that the average grinding chip may be as much as ten times thicker and ten times shorter than would be produced by a grinding wheel with a regular arrangement of cutting edges as assumed by existing analytical approaches.