Undeformed Chip Thickness Model Research Articles

Introducing abrasive wear into undeformed chip thickness modeling with improved grain kinematics in belt grinding

The undeformed chip thickness (UCT) is an essential indicator in understanding the belt grinding mechanism, especially in relation to surface roughness. However, abrasive wear has not been involved in the above modeling studies, even though it always influences the grinding process. In this paper, the evolving grain height distribution, which is governed by the accumulative active grain group, is first quantified using a gamma distribution. Then, based on the geometric analysis of the compliant contact area, improved grain kinematics considering non-uniform grain height is proposed. Finally, based on the above findings, an improved undeformed chip thickness model is established and experimentally validated. The calculated results based on the model show that undeformed chip thickness value approximately obeys a normal distribution at various wear stages unlike a Rayleigh distribution in rigid wheel grinding. The mean and variance of the distribution generally decrease with increasing grinding time, which is supported by the transformation from spiral chips to fragmented chips. Surface prediction is performed to help experimentally verify the reliability of the proposed model, where results illustrate that the predicted and measured roughness exhibits a similar decreasing trend with increasing active grain percentage and grinding time.

Undeformed chip thickness with composite ultrasonic vibration-assisted face grinding of silicon carbide: Modeling, computation and analysis

In order to achieve high efficiency and low damage processing of hard and brittle materials, composite ultrasonic vibration-assisted face grinding (CUVAFG) has been proposed by comprehensively combining the high efficiency of axial ultrasonic vibration grinding (UVAG) and the low damage of elliptic ultrasonic vibration grinding (EVAG). However, the three-dimensional ultrasonic vibration brings about a more complicated machining mechanism than the previous ultrasonic vibration-assisted grinding methodology. Hence, in order to explore the grinding mechanism in deep, this paper first developed a new model of undeformed chip thickness for CUVAFG from the perspectives of the kinematic mechanism and elastic-plastic deformation mechanism. Then the influences of different processing parameters on interference rate and undeformed chip thickness were further confirmed. Finally, CUVAFG experiments of silicon carbide (SiC) ceramics were conducted to study the relationship between the undeformed chip thickness and the resultant grinding forces, specific grinding energy, ground surface morphology and roughness, and subsurface damage. It is found from the experimental results that the critical chip thickness of brittle-ductile transition in CUVAFG is between 0.31 and 0.35 μm. As the undeformed chip thickness is less than the critical value, the grinding forces and the specific grinding energy increases with the undeformed chip thickness, but the ground surface roughness decreases with improved surface morphology and shallow subsurface damage. After exceeding the critical value, the grinding force remains unchanged, the specific grinding energy decreases, and ground surface roughness increases with deteriorated surface morphology and deepened subsurface damage. For the purpose of good machining surface integrity, it is essential to guarantee that the undeformed chip thickness is less than the critical value. The computational and experimental results have demonstrated the contribution of the developed undeformed chip thickness model to understanding the grinding performance of hard and brittle material by CUVAFG.

Investigation on tearing damage of CFRP circular cell honeycomb in end-face grinding

CFRP circular cell honeycomb has promising applications in the aerospace field due to its excellent mechanical properties. However, a large number of periodically distributed tearing damages severely restrict the high-quality machining of CFRP circular cell honeycomb. This paper investigates the formation mechanism of tearing damages during end-face grinding of CFRP circular cell honeycomb and proposes suppression strategies. In this paper, a maximum undeformed chip thickness model considering tearing damage distribution is developed, and the evolution behavior of tearing damage is studied by combining the material removal process and grinding force. The grinding force and maximum tearing damage depth in different grinding conditions are analyzed. The results show that the formation of tearing damage in the cut-in stage is related to the weak stiffness of thin walls and the radial grinding force. The radial grinding force and maximum tearing depth can be altered by changing the maximum undeformed chip thickness which can be adjusted for different grinding speeds, feed rates, and offset ratios. The low-damage machining of CFRP circular cell honeycomb can be achieved by using a large offset ratio and variable feed rate.

Effects of feed direction on material removal behavior in belt grinding of titanium alloys

For abrasive belt grinding, although machine processing selection has been well studied to achieve good machinability, there is still a lack of understanding regarding the influence of feed direction and its mechanism, even though it is a common matter. This paper investigates the differences between up- and down-grinding in belt grinding of TC4, where the grinding forces, material removal performance, surface quality, and chip morphology are captured for the grinding process evaluation and mechanistic analysis In up grinding, it was observed that approximately 21.1 % more material removal can be achieved due to the larger penetration depth of scratching grains when maintaining a constant normal grinding force. Furthermore, the higher tangential grinding force resulting from increased cutting behavior and an additional sliding phase leads to more severe abrasive belt wear, as evidenced by a 22.7 % higher grinding ratio. Comparatively, down grinding mode generates a machined surface with lower roughness in the transverse and longitudinal direction, which can be explained by the minimum chip thickness effect and undeformed chip thickness model. The microscopic characteristics of chips and ground surface provide more evidence on the different chip formation mechanisms between two grinding modes.

Accurate modeling and controlling of weak stiffness grinding system dynamics with microstructured tools

The weak stiffness grinding system often produces uncontrollable vibration, which directly reduces the machining quality. In order to accurately predict and control the weak stiffness grinding system dynamics, an accurate dynamics modeling and the controlling method with microstructured tools are presented innovatively. Based on the real random abrasive grain model, an instantaneous undeformed chip thickness model considering the phase deviation, time accuracy and grinding wheel-workpiece separation caused by vibration is established. On this basis, the controlling principle of microstructured grinding wheel on chip formation mechanism and grinding forces is studied. Then, combined with the element division principle and dynamics parameters of grinding system, the dynamics model of weak stiffness grinding system is established. According to the grinding experimental results based on vibration monitoring, the error rate of the established dynamics model is less than 9.8 %. Compared with the non-structured grinding wheel, the microstructured grinding wheel can control the vibration amplitude, the vibration frequencies and the wheel deflection. Based on the workpiece surface machining results, the addition of microstructures suppresses the phenomena of overcutting and the wheel bounce, and the profile protrusion height caused by grinding vibration is decreased by 77 %. The established dynamics model is of great significance for understanding and control the dynamic behavior of weak stiffness grinding systems.

Surface profile and milling force prediction for milling thin-walled workpiece based on equivalent 3D undeformed chip thickness model

With the development of the aviation manufacturing industry, the application range of thin-walled parts is rapidly increasing. Accurate machining process and surface topography prediction are the keys to ensuring machining quality. This article is based on the relative geometric relationship between the real motion trajectory of the milling cutter and the workpiece; the undeformed chip thickness equation and the two-dimensional surface contour feature algorithm are established. By introducing the parameters of milling cutter critical height, milling cutter helix angle, and lag angle parameters, the three-dimensional surface profile prediction model and the equivalent three-dimensional model considering the chip formation process are derived. And the calculation equations of the instantaneous chip cross-sectional area and the blade-workpiece contact length of the three phases of chip formation are established, respectively. The multiple linear regression method was used to fit the orthogonal test results of titanium alloy Ti-6Al-4 V, so as to complete the dynamic milling force identification, and finally establish the milling force prediction model. The accuracy of the prediction model was verified by the single factor method, and the influence of different parameters on the milling process of thin-walled parts was observed. The results show that the established model has high accuracy in predicting the surface profile and milling force of thin-walled parts. This study provides guidance for efficient prediction of the milling process of thin-walled parts.

Surface roughness prediction in robotic belt grinding based on the undeformed chip thickness model and GRNN method

Surface roughness prediction in robotic belt grinding based on the undeformed chip thickness model and GRNN method

The Modelling and Analysis of Micro-Milling Forces for Fabricating Thin-Walled Micro-Parts Considering Machining Dynamics

In the fabrication process of thin-walled micro-parts, both micro-cutting tools and thin-walled micro-parts have the characteristics of small size and low stiffness. Therefore, the regenerative chatter during the machining process cannot be ignored. The influence of the tool runout error and actual trochoidal trajectories of the cutting edge on micro-milling forces should also be considered comprehensively. In this paper, the tool runout error in the micro-milling process is first analysed, and an instantaneous undeformed chip thickness model is established considering the runout error. On this basis, the dynamic deformation of the micro-cutting tool and thin-walled micro-part is studied, and an instantaneous, undeformed, chip-thickness model is proposed with the consideration of both the runout error and dynamic deformation. The dynamic parameters of the machining system are obtained using the receptance coupling method. Finally, thin-walled micro-part machining experiments are carried out, and the obtained results of micro-milling force simulation based on the proposed model are compared with the experimental results. The results indicate that the micro-milling force modelling, by taking the influence of machining dynamics into account, has better prediction accuracy, and the difference between the predicted resultant forces and the experimental results is less than 11%.

Cutting force prediction considering force–deflection coupling in five-axis milling with fillet-end cutter

With the increasing demand for higher quality and performance of equipment and assembly in aerospace, shipbuilding, medical and other fields, the machining accuracy of parts is facing higher requirements. It is particularly important to predict the cutting force accurately, which is the main physical quantity in the machining process and basis of process inspection and quality control. In this paper, the cutting force model in five-axis milling with fillet-end cutter is proposed, which reveals the law of force–deflection coupling. Firstly, the initial cutter deflection model induced by the ideal cutting force ignoring the effect of deflection is built based on analysis of the geometric characteristics of fillet-end cutter. Then, the undeformed chip thickness model is educed considering the cutter posture and cutter deflection. Further, the iterative method is utilized to resolve the coupling relationship between cutter deflection and cutting force. Finally, the cutting force model under force–deflection coupling is established for achieving more accurate prediction. To verify the effectiveness of the proposed cutting force model, the milling experiment is carried out on a five-axis milling center. The measured cutting force values are utilized to inspect the accuracy of prediction models considering and not considering force–deflection coupling, respectively. The results show that the proposed method could improve the prediction accuracy of cutting force, which show the effectiveness of taking force–deflection coupling law into consideration clearly. The influence of cutter posture on cutting force is analyzed using the proposed cutting force model. The cutting force decreases with the increase in lead angle or tilt angle, and the influence of tilt angle is greater than that of lead angle under experimental conditions of five-axis milling using the set process parameters.

Damage formation mechanisms of sintered silicon carbide during single-diamond grinding

In this research, a single-diamond grinding test was performed on sintered silicon carbide (SSiC) to explore the damage formation mechanism. A scanning electron microscope and a transmission electron microscope (TEM) were used to examine the surface and subsurface morphologies of the grinding groove, respectively. The characteristics of the ground surface morphologies reveal that the single-diamond grinding process of SSiC can be classified into purely ductile, primarily ductile, primarily brittle, and purely brittle stages. Based on the high-resolution TEM (HRTEM) images and the corresponding Fast Fourier transform images of the near-surface region, results reveal that the high density of dislocations and amorphization of SiC grains are responsible for the plastic deformation of SSiC. Most of the cracks congregate on the top grains of the ground surface due to the distinct obstruction of the grain boundary on the cracks propagation, and the cracks generated at the grain boundaries emit into the top grain interiors and go up toward the exposed surface for the distortedly deformed region with higher strain energy; Furthermore, stress concentration caused by the dislocation pileups at grain boundaries represents the crack initiation mechanisms for SSiC. Finally, based on the dislocations pile-up theory, a critical undeformed chip thickness model for boundary crack system nucleation is established, which considers the cutting-edge radius, grinding wheel speed, material properties, and grain size of ceramics.

Analytical modeling of surface roughness in precision grinding of particle reinforced metal matrix composites considering nanomechanical response of material

Grinding is usually applied for particle reinforced metal matrix composites (PRMMCs) to achieve high ground surface quality. However, the surface quality especially surface roughness is difficult to predict theoretically due to different mechanical properties of two or more phases inside the PRMMCs. In this study, an analytical model of the surface roughness of ground PRMMCs is developed based on an undeformed chip thickness model with Rayleigh probability distribution by considering the different removal mechanism of metal matrix and reinforcement particles in grinding. GT35, a typical kind of steel based metal matrix composite reinforced with TiC particles is investigated as an example. Nanoindentation experiments are employed for the investigation of nanomechanical properties and cracking behavior of GT35 and the nanoindentation results are integrated in the model. Single factor surface grinding experiments of GT35 are also carried out to understand the material removal mechanism of GT35 and validate this novel surface roughness prediction model. The predicted surface roughness from this model shows good agreement with the experimental results.

Force predictive model for five-axis ball end milling of sculptured surface

As a high precision and high efficiency cutting method, CNC milling of five axis is the first choice for manufacturing parts with complex sculptured surface. Milling force is one of the most important physical parameters in machining which affects the cutting vibration, cutting deformation, cutting heat, and surface quality directly. Aiming at the five-axis ball end milling of sculptured surface, a force predictive model with arbitrary cutter axis vector and feed direction is established. The conditions of micro-cutting edge of three-axis ball end mill involved in cutting are determined by space region limitation at the first. Then, after space rotation transformation, an analytic in-cut cutting edge (ICCE) method for five-axis ball end milling of oblique plane is proposed by judging micro-cutting edge one by one. Based on the idea of differential discretization, the machining of general complex surface can be regarded as a combination of a series of tiny oblique planes. Drawing on the idea to sculptured surface and combining micro-element milling force model and undeformed chip thickness model that is suitable for five-axis ball end milling with arbitrary feed direction, a milling force predictive model for five-axis ball end milling of sculptured surface is established. The results of simulations and experiments show that the ICCE determined by the space region limitation is consistent with the traditional Z-map method and the solid modeling method with high efficiency and precision. The measured force and the predictive force of the five-axis milling on sculptured surface are in good agreement in amplitude and trend, which proves the effectiveness of the milling force predictive model of five-axis ball end milling of sculptured surface.

Modeling and simulation of the distribution of undeformed chip thicknesses in surface grinding

Abstract The distribution of undeformed chip thicknesses is the kinematic “copy” of grain space distribution on a workpiece and has an important influence on the grinding results. In this study, a wheel topography model is developed that can be integrated with a workpiece model, a kinematic model and a calculation model of undeformed chip thickness of a single grain to obtain the distribution of undeformed chip thicknesses. In order to verify the integrated model, a single-layer brazed diamond grinding wheel is fabricated, and the topography measurements of the grinding wheel are conducted. The measured data are used in the integrated model to perform a simulation; the simulation results are consistent with the test results. At the same time, the model is verified with grains that are uniformly distributed. Then, simulations utilizing the integrated model are used to thoroughly study the grinding process. The distribution of grain protrusion height can be controlled by radial numerical dressings on the grinding wheel. Thus, the role of the distribution of grain protrusion height on the undeformed chip thickness distribution can be quantified by using radial numerical dressings on the grinding wheel. Additionally, the relationship between the average value of the distribution of undeformed chip thicknesses, hmean, and the surface roughness can be determined by simulation. It is shown that the surface roughness can be controlled quantitatively by radial numerical dressings on the wheel.

Developing a trend prediction model of subsurface damage for fixed-abrasive grinding of optics by cup wheels.

Fixed-abrasive grinding by cup wheels plays an important role in the production of precision optics. During cup wheel grinding, we strive for a large removal rate while maintaining fine integrity on the surface and subsurface layers (academically recognized as surface roughness and subsurface damage, respectively). This study develops a theoretical model used to predict the trend of subsurface damage of optics (with respect to various grinding parameters) in fixed-abrasive grinding by cup wheels. It is derived from the maximum undeformed chip thickness model, and it successfully correlates the pivotal parameters of cup wheel grinding with the subsurface damage depth. The efficiency of this model is then demonstrated by a set of experiments performed on a cup wheel grinding machine. In these experiments, the characteristics of subsurface damage are inspected by a wedge-polishing plus microscopic inspection method, revealing that the subsurface damage induced in cup wheel grinding is composed of craterlike morphologies and slender cracks, with depth ranging from ∼6.2 to ∼13.2 μm under the specified grinding parameters. With the help of the proposed model, an optimized grinding strategy is suggested for realizing fine subsurface integrity as well as high removal rate, which can alleviate the workload of subsequent lapping and polishing.

Model of the instantaneous undeformed chip thickness in micro-milling based on tooth trajectory

Instantaneous undeformed chip thickness is one of the key parameters in modeling of micro-milling process. Most of the existing instantaneous undeformed chip thickness models in meso-scale cutting process are based on the trochoidal trajectory of the cutting edge, which neglect the influences of cutter installation errors, cutter-holder manufacturing errors, radial runout of the spindle and so forth on the instantaneous undeformed chip thickness. This article investigates the tooth trajectory in micro-milling process. A prediction model of radial runout of cutting edge is built, with consideration of the effects of the extended length of micro-milling cutter and the spindle speed. Considering the effects of cutting-edge trochoidal trajectory, radial runout of cutting edge and the minimum cutting thickness, a novel instantaneous undeformed chip thickness model is proposed, and the phenomenon of single-tooth cutting in micro-milling process is analyzed. Comparisons of cutting forces under different chip thickness models and experimental data indicate that this new model can be used to predict cutting forces.

A generic instantaneous undeformed chip thickness model for the cutting force modeling in micromilling

The precise modeling of the instantaneous undeformed chip thickness is one of the key issues in the mechanics of micromilling. While most current models noticed the influences of the tool tip trochoidal trajectory and tool runout, they took account only the workpiece removed by immediate passing tooth but not more preceded teeth. These lead to inaccuracy when the single edge cutting occurred, which has been identified to be a prevalent phenomenon in micromilling operation. In this paper, the actual cutting area in micromilling is derived, and then a generic instantaneous undeformed chip thickness model is proposed by considering the cutting trajectory of all passing teeth in one cycle. Additionally, this study derives a criterion that could determine the single-edge-cutting phenomenon in multi-tooth micromilling from the geometric relations. The accuracy of the model is verified by the real experimental data and the result are shown superior to known models.

Study on Influence Laws of Surface Roughness of Micro-Groove in Single Crystal Silicon under Diamond Fly-Cutting

Single crystal silicon has both important application value in the fields of micro-optics and MEMS, and it has been considered as one of the most difficult-to-cut materials because of its hardness and brittleness. Removal mechanism of the silicon was discussed, and the model of undeformed chip thickness was established in this article. According to the data of micro-groove surface roughness from the diamond fly-cutting experiment, the nonlinear relationship curve, between the largest undeformed chip thicknesshmaxand microgroove surface roughnessRa,were obtained using Gaussian-fitting principle, and the regression equation of the fitting curve was also got. Thus the prediction mathematical model of microgroove surface roughness was derived. The influence laws of the main working parameters on theRawere obtained based on the result of this experiment and the response surface of the prediction model, and some conclusions were summarized: the surface roughnessRaof microgroove in the single crystal silicon decreases with the decrease of the cutting depthap, the feed f and the increase of the spindle speednunder the diamond fly-cutting; the experimental results also showed that feedfaffects the value ofRavery much, cutting depthapless, and spindle speednthe least.

Metal Turning Mechanical Model of Machined Surface Roughness

Consider the mechanism of the formation of surface roughness, this paper establish the mechanical model of undeformed chip thickness caused by the cutting edge,and the mechanical model of cutting residues caused by the tool feed movement . By means of Brammertz equation, combining the above two mechanical model,a more perfect surface roughness mechanical mode is established.

Experimental Investigation on Material Removal Process for Micro-grinding of Single Crystal Silicon

Theoretical and experimental analysis on micro-grinding process of single crystal silicon has been investigated in this study. The mathematical model of undeformed chip thickness in slot micro-grinding of single crystal silicon has been built. Diamond tools in this experiment have been employed and slot micro-grinding experiments of single silicon are designed and carried out on a precise micro-machine tool. Influences of micro-grinding parameters to crack length are investigated from analysis of experiment results, the relationships between micro-grinding parameters to surface roughness and micro-grinding force during experiment have been revealed. The relationship between undeformed chip thickness and micro-grinding force results is built, it is found from experiment that the grinding force would increase with the decrease of undeformed chip thickness when the undefromed chip thickness is below lattice constant. It would provide research theory and experimental reference of material removal mechanism in micro-grinding of single crystal silicon.

Predictive modeling of force and power based on a new analytical undeformed chip thickness model in ceramic grinding

The grinding force and power play an important role in ceramic grinding process as they not only have the direct influence on the wheel wear, grinding accuracy, grinding temperature and surface integrity but also have strong influence on local contact deflection and the nature of the contact deflection that has an important effect on the mechanism of material removal. In addition, they are also important to many aspects of ceramic grinding process optimization, monitoring, and control. So the prediction of grinding force and power in ceramic grinding is essential. But, the force and power is governed by many factors and its experimental determination is laborious and time consuming. So the establishment of a model for the reliable prediction of grinding force and power is still a key issue for ceramic grinding. In this study, a new grinding force and power model is developed, for the reliable prediction of grinding force and power in ceramic grinding, based on a new analytical undeformed chip thickness model. This new analytical undeformed chip thickness model is developed on the basis of stochastic nature of the grinding process, governed mainly by the random geometry and the random distribution of cutting edges. The model includes the real contact length that results from combined contact length, due to wheel-workpiece contact zone deflection and the local deflection due to the microscopic contact at the grain level and contact length due to geometry of depth of cut. The proposed model is used to predict the total grinding forces and power in surface grinding. The new model has been validated by conducting experiments on a horizontal surface grinding machine by grinding silicon carbide with diamond grinding wheel. Results indicate that the proposed model shows a good agreement with the experimental data obtained from different kinematic conditions. It also results in a significant reduction in the grinding forces, as compared with that obtained by the force model developed based on the existing undeformed chip thickness model, under the same operating conditions, in silicon carbide grinding.