Chip Thickness Model Research Articles

Research on specific cutting energy and parameter optimization in micro-milling of heat-resistant stainless steel

In present research, micro-milling of heat-resistant stainless steel (12Cr18Ni9) is conducted with the purpose of revealing influence mechanism of cutting tool edge radius and cutting parameters on specific cutting energy. In order to clarify the relationship between specific cutting energy and the geometrical characteristics of the cutting tools as well as cutting parameters, a newly designed experimental method is put forward, thereafter, the evolution rules of specific cutting energy along with cutting parameters is researched in detail. Furthermore, a prediction model of the minimum chip thickness is built by using fuzzy logic method based on experimental data, objective to optimize cutting parameters during micro-milling of 12Cr18Ni9, good agreements are achieved between predicted results and experimental results in verification tests, which means the specific cutting energy can be well controlled with the parameter recommended by the constructed model. The above research has great significance in improving tool life and machining quality.

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.

Prediction of grinding force for brittle materials considering co-existing of ductility and brittleness

Grinding of brittle materials is characterized by a complex removal mechanism of both ductile and brittle removal. Therefore, the traditional force models, which are mainly targeted to metallic materials, cannot be fully applied to the force prediction of brittle materials. This paper will propose a new grinding force model for brittle materials considering co-existing of ductile removal force and brittle removal force. The ductile removal force is mainly composed of rubbing force, ploughing force, and chipping force. However, the brittle removal force is more related to rubbing force and fracture chipping force. The proportional coefficient of ductile removal and crack size will be modeled through a series of experiments under different wheel speed and undeformed chip thickness. The working status for a single grit was separated based on the Hertz Theory and chip thickness modeling of Rayleigh probability density function. Grinding experiments have been undertaken by using a high speed diamond grinder on Silicon Carbide, and the results was compared to the force model predictions for validation. The predictive force model shows a reasonable agreement quantitatively with the experimental force data.

An evaluation of micro milling chip thickness models for the process mechanics

An accuracy of the chip thickness models used in the micro milling mechanics models directly affects the accuracy of the cutting force predictions. There are different chip thickness models derived from various kinematic analyses for the micro milling in the literature. This article presents an evaluation of chip thickness models for micro milling by examining their direct effects on predictions of cutting forces. Performances of four chip thickness models for micro milling existing in the literature are tested and compared with the experimental force measurements. Micro end milling experiments were conducted on an aerospace-grade aluminum alloy Al7050 for different feed rate values. The root mean square deviation and the coefficient of determination values between the estimated and measured micro milling forces are presented for the comparative evaluation of the major chip thickness models at various feed per tooth to tool diameter ratios.

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.

A New Uncut Chip Thickness Model for Tilted Helical End Mills through Direct Correspondence with Local Oblique Cutting Geometry

Machining optimization algorithms in end-milling with helical cutters require an efficient and accurate model of the uncut chip thickness (UCT) at every location along the cutting flutes. Past work has either ignored the effects of tool tilt and orientation or treated them with simple assumptions about their coupling with tool shape. The current paper treats the problem with considerably greater generality using an arc-length parameterization of the axis-symmetric tool profile. Each discrete tool move was considered a 3-axis motion. Ignoring tool run-out, UCT was calculated in the direction of direct correspondence to local oblique cutting geometry, i.e., perpendicular to the local cutting edge and cutting velocity. The flute curves were intersected with the engagement contour corresponding to the instantaneous tool-work contact and the UCT inspected within. For a candidate taper ball end mill, the UCT results of the new model were compared with the standard Martellotti model. The new model agrees closely with the Martellotti model in the flank region and predicts a more realistic variation in the ball region.

A new method for cutting force prediction in peripheral milling of complex curved surface

The instantaneous uncut chip thickness and entry/exit angle of tool/workpiece engagement vary with tool path, workpiece geometry and cutting parameters in peripheral milling of complex curved surface, leading to the strong time-varying characteristic for instantaneous cutting forces. A new method for cutting force prediction in peripheral milling of complex curved surface is proposed in this paper. Considering the tool path, cutter runout, tool type(constant/nonconstant pitch cutter) and tool actual motion, a representation model of instantaneous uncut chip thickness and entry/exit angle of tool/ workpiece engagement is established firstly, which can reach better accuracy than the traditional models. Then, an approach for identifying of cutter runout parameters and calibrating of specific cutting force coefficients is presented. Finally, peripheral milling experiments are carried out with two types of tool, and the results indicate that the predicted cutting forces are highly consistent with the experimental values in the aspect of variation tendency and amplitude.

Modelling and optimisation of surface roughness from microgrinding of nickel-based single crystal superalloy using the response surface methodology and genetic algorithm

Microgrinding is an important method for machining microparts and structures and has received intense focus in the micro-manufacturing field. First, this paper establishes a mathematical model of the maximum undeformed chip thickness and analyses the removal mechanism of nickel-based single crystal superalloy in the microgrinding process. Second, microgrinding experiments perpendicular to the nickel-based single crystal superalloy DD98 (100) crystal plane are designed and carried out using a microgrinding tool; using the response surface methodology, which is based on central composite design, the influence of the spindle speed, feed rate, and grinding depth on the grinding surface roughness is analysed. First-order and second-order prediction models of the surface roughness are established. Then, according to the residual analysis and ANOVA, an accurate model is obtained. The model’s accuracy and scientificity is verified by experiments. Finally, optimum grinding parameters of the second-order model for minimising the surface roughness are acquired using a genetic algorithm. The result shows that the spindle speed has the largest influence on the surface roughness, followed by the feed rate, and the grinding depth has the smallest influence. When the spindle speed is 56.8 kr/min, feed rate is 36 μm/s, and grinding depth is 14 μm; the grinding surface roughness is the minimum (Ra = 563 nm). These provide a significant theoretical and practical reference for the microgrinding process of nickel-based single crystal superalloy.

Parametric chip thickness model based cutting forces estimation considering cutter runout of five-axis general end milling

In the process of sculpture surfaces machining, due to the changes of the cutter orientation and the inevitable eccentricity between tool and spindle, machining parameters optimization based on five-axis cutting force is quite a challenge. To solve this problem, this study proposes a new method, cutting edge element moving(CEEM) method, to calculate instantaneous undeformed chip thickness(IUCT), to distinguish cutter/workpiece engagement(CWE) area and to simulate five-axis machining cutting force considering runout for general end mills. On the basis of upper work, the parameter representation of IUCT is deduced by the parametric expression of coordinate transformation matrix and feed vector, and resolved to three sub models about tool orientation, tool orientation change and cutter runout. At last, cutting force coefficients and cutter runout parameters are calibrated by cutting test and dial gauge testing. And inclined axis cutting test for bull nose mill, cylinder face-milling test for ball end mill and conical surface flank milling test for flat end mill are carried out to verify the effectiveness of the proposed model and related decomposition model. Combined with the specific test, some analysis about peak values, mean values and peak to peak difference values of cutting forces in various tool orientations are conducted, and the effect to cutting force from the changes of lead and tilt angles are evaluated. Some conclusions obtained and the methods utilized can be used to optimize tool orientation and feed rate etc.

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.

The influence of tangential and torsional vibrations on the stability lobes in metal cutting

Chatter vibrations in machining are studied. Special attention is paid to the effect of structural vibrations in the cutting speed direction. These so-called tangential vibrations may dominate the dynamics in drilling, sawing or grinding, where the torsional dynamic stiffness is much lower than the lateral, axial or radial dynamic stiffness. The inclusion of tangential vibrations in the chip thickness model leads to a delay differential equation (DDE) with state-dependent delay in the time domain. It is shown that the system is equivalent to a DDE with constant delay if it is described in terms of the spindle rotation angle. The analysis of metal cutting vibrations in the angular domain is very useful because in this case the delay is a constant parameter. Numerical examples for turning and drilling processes are presented. An extension of the universal oriented transfer function method for the stability analysis in the frequency domain is presented, which includes the tangential regenerative effect. An additional term appears in the oriented transfer function, which can stabilize or destabilize critical eigenmodes and may also lead to new instabilities in comparison with the conventional analysis.

Off-line feedrate optimization with multiple constraints for corner milling of a cavity

High quality and high efficiency are very important factors in the mold industry and must be considered in machining technology development. Corners are one of the typical features in a cavity mold that can cause low accuracy, tool wear, cutter defection, and vibration. Therefore, off-line feedrate optimization in a corner-milling process has been proposed as a means for avoiding these drawbacks. The corner-milling process could be divided into five stages according to the contact conditions between the cutter and workpiece. An improved chip thickness model based on the actual trajectory of the cutter was presented to predict the movement of the cutter along a curved path. Various feedrate optimizations were presented with varying control parameters. In this paper, three feedrate optimizations were implemented using three control parameters, relative volume, milling force, and cutter deflection, based on the differential element method (DEM). A corner-milling force experiment indicated that the simulation results using a modified milling force model agreed well with actual experimental milling results. Following this, a feedrate optimization with multiple constraints was built, according to a combination of three feedrate optimizations and then consider the acceleration and deceleration limitation. The simulation by using the method in this paper demonstrated that the machining time of rough milling, semi-finish milling, and finish milling could be reduced. In addition, it was found that the resulting milling force varies within a narrow range.

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.

Prediction of instantaneous milling force taking runout into account in peripheral milling of curved surface

Prediction of milling forces in peripheral milling of curved surface with variable curvature is complex. And the complexity arises due to the effects of cutter runout. This paper presents a method to predict milling force taking runout into account. Based on the concept of linear interpolation, methods are developed to calculate the instantaneous tool position, angular position, feed direction, and corresponding machining time. Then, a new analytical model of instantaneous uncut chip thickness is derived in the presence of cutter runout by coordinate transformation. In addition, the entry/exit angles are described considering the workpiece boundary. Milling tests are carried out to verify the presented method. A good agreement between predicted results and experimental results both in variation tendency and magnitude is achieved, which shows that the presented method is efficient. Meanwhile, comparative study with the existing method from literature is made.

Research on Error Compensation of Corner Milling Process Based on Milling Force Prediction

In cavity die corner-machining, tool flexible deformation caused by the milling force resulting in the surface error, a method of off-line error compensation is put forward. Instantaneous chip thickness model and the corner milling force model is established based on differential and the characteristics of the corner. Combining the theory of cantilever beam and the finite element analysis, cutting tool elastic deformation model is established.

Strategies for grinding of chamfers in cutting inserts

Abstract In order to increase tool life and improve workpiece quality, cutting processes with geometrically defined cutters demand inserts with a prepared cutting edge. Chamfers are widely used in many processes, since they can provide edge strengthening without damaging the chip flow. In order to achieve a stable and reliable cutting process, uniform chamfer geometry along the insert and high edge quality are necessary. For this, proper grinding strategies for chamfer manufacturing must be taken into account. With the objective of getting knowledge about the chamfer manufacturing process, strategies for grinding of chamfers are investigated in this paper. Chamfers were ground on PCBN, mixed ceramic and cemented carbide cutting inserts with a vitrified bond diamond grinding wheel. A single grain chip thickness model is used to characterize the process and different grinding strategies are analyzed in terms of reduction of chamfer geometry deviation. It was found that high insert rotational speeds increase the edge chipping and that the cutting insert material has a considerable influence on the chamfer geometry deviation.

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.

Time Domain Prediction of Side and Plunge Milling Stability Considering Edge Radius Effect

This article introduces a time domain model of side and plunge milling stability by considering cutting edge radius as well as dynamic motion of cutter center. Dynamic uncut chip thickness generated by side, plunge and ultrasonic milling can be simulated by tracking the cutter center positions at the present and previous vibrations with phase difference. Finally, the dynamic uncut chip thickness models as well as the mechanistic cutting force coefficients considering cutting edge radius are integrated into the time domain model. Especially, cross edge radius varies due to tool wear which affects cutting force coefficients and dynamics as well. Finally, the machining stability and vibrations are estimated using an identified transfer function and predicted cutting forces through the time domain solution. Experimental tests are compared against predicted results for validation of the proposed model.

Decoupled chip thickness calculation model for cutting force prediction in five-axis ball-end milling

Cutting force prediction plays very critical roles for machining parameters selection in milling process. Chip thickness calculation supplies the basis for cutting force prediction. However, the chip thickness calculation in five-axis ball-end milling is difficult due to complex geometrical engagements between parts and cutters. In this paper, we present a method to calculate the chip thickness in five-axis ball-end milling. The contributions of lead and tilt angles in five-axis ball-end milling on the chip thickness are studied separately in detail. We prove that the actual chip thickness can be decoupled as the sum of the ones derived from the two individual cutting conditions, i.e., lead and tilt angles. In this model, the calculation of engagement boundaries of tool–workpiece engagement is easy; thus, time consumption is low. In order to verify the proposed chip thickness model, the chip volume predicted based on the proposed chip thickness calculation model is compared with the theoretical results. The comparison results show that the desired accuracy is obtained with the proposed chip thickness calculation model. The validation cutting tests, which are in a constant material removal rate and with only ball part engaged in cutting, are carried out. The optimized lead and tilt angles are analyzed with regard to cutting forces. The geometrical as well as the kinematics meaning of the proposed method is obvious comparing with the existing models.

Prediction of cutting force in ball-end milling of sculptured surface using improved Z-map

This paper presents an approach for prediction of cutting forces in three-axis ball-end milling of a sculptured surface along an arbitrary tool path. The idea of differentiation is adopted to deal with the problems of varying feed direction, varying cutter engagement, and the consequent varying cutting forces in sculptured surface machining. Based on the differential idea, the whole process of sculptured surface milling is discretized at intervals of feed per tooth, and each segmented process is considered as a small steady-state cutting. For the discrete cuttings, mathematical models of feed turning angle and feed inclination angle are proposed according to the position of start/end points. By using an improved Z-map method, the detailed algorithms of determining the cutter–workpiece interface and the instantaneous in-cut edge segment for sculptured surface machining are suggested. A new integrative chip thickness model which involves the effects of feed turning angle, feed inclination angle, and cutter engagement is also presented. In validation experiment, two practical examples of a sculptured surface three-axis ball-end milling with arbitrary tool path are operated. Comparisons of the predicted cutting forces with the measurements show the effectiveness of the proposed approach.