Chip Thickness Distribution Research Articles

Surface topography prediction of slider races using formed grinding wheel shape and material removal mechanism

Compared with the roughness, the three-dimensional (3D) topography parameters, surface microstructure geometric characteristics and other information can more fully evaluate the grinding quality of the slider raceway surface. In this paper, based on the 3D topography model of the abrasive particle distribution on the surface of the formed grinding wheel, the material removal mechanism between the abrasive particle and the raceway surface is analyzed. With the undeformed chip thickness distribution model as the intermediate variable, the 3D topography model of the slider raceway surface is established, and the model verification is carried out from the roughness and the geometric characteristics of the surface microstructure, respectively. At the same time, the surface microstructure is extracted from the topography model, and the effects of different grinding process parameters on the geometric characteristics such as the height to width ratio, depth to width ratio and distribution density of groove, convex peak and peak valley structures are studied. Results are shown that AS,TH increase from [0.05 0.6 μm] to [0.25 0.8 μm] and FGH grows from [0.11 1.05 μm] to [0.5 1.61 μm] when the grinding depth rises from 1 μm to 4 μm. AS, TH are firstly decreased from [0.17 0.61 μm] to [0.08 0.52 μm] and then increased to [0.26 0.78 μm], and the FGH declines from [0.34 1.01 μm] to [0.16 0.86 μm] and then increases to [0.51 1.38 μm] with the feeding speed is in [25, 28 m/min]. In addition, in the range of grinding wheel linear velocity [28, 34 m/s], the AS,TH decreases from [0.19 0.81 μm] to [0.1 0.55 μm] and the FGH decreases from [0.55 1.6 μm] to [0.2 1.1 μm]. This can prepare for the subsequent research on the impact of the topography characteristics on the friction coefficient and wear amount of the slider raceway surface.

Prediction of undeformed chip thickness distribution and surface roughness in ultrasonic vibration grinding of inner hole of bearings

Prediction of undeformed chip thickness distribution and surface roughness in ultrasonic vibration grinding of inner hole of bearings

A parametric modeling for fast radial infeed planning process in gear skiving

In gear skiving, the infeed planning process for the multiple radial infeed strategy affects cutting efficiency, local cutting features, and cutter life. The maximum uncut chip thickness nonlinearly changes with infeed combinations, making the infeed planning process challenging. Here, we propose a parametric model to achieve fast infeed planning based on the uncut chip thickness in parametric space. First, the relation between the infeed and chip boundary evolution is elucidated; then, the concept of initial uncut chip geometry (iUCG) is established to perform fast infeed planning according to the chip boundary and uncut chip thickness distribution. An industrial case study is presented to validate the method and demonstrate the implementation. As a result, a decision-making principle that includes infeed planning starting from the finishing to the rough stages enables fast planning owning to the invariance of iUCG and lower simulation capacity requirement on the chip boundary. In such case, the infeed of the “previous” skiving pass can be efficiently determined according to the maximum uncut chip thickness criterion with a constraint condition. The proposed parametric model advances the infeed planning process, further contributing to the multivariable optimization of gear skiving.

Rapid stability analysis of serrated end mills using graphical-frequency domain methods

Serrated tools result in an irregular distribution of chip thickness and varying time delays along their flutes that disturb the regenerative chatter mechanism and maximize productivity in rough machining operations. The chatter stability simulation with such tools is complex due to the delay differential equations with multiple and distributed delays. Although the time domain numerical integration methods and the semi-discretization method are accurate, they are computationally expensive and hence inhibit the optimal design of serrated cutters. Despite the advantages that serrated tools offer, there has been little attention paid to rapidly predict stability lobes diagram for these tools to help instruct their optimal designs. To address this need, new graphical-frequency methods are presented to solve for stability of serrated tools with arbitrary geometry. The graphical method averages the number of teeth in cut to make the system time-invariant and results in a closed-form analytical solution. It reduces the simulation time by up to ∼99% compared to the semi-discretization method. Generalized solutions to the classical zero-order approximation and the multi-frequency methods are also presented by using the Nyquist stability criterion. The use of the zero-order approximation method and the multi-frequency method reduces simulation times by up to ∼97% and ∼79% respectively compared to the semi-discretization method. These are significant improvements over reports in the previous literature. Stability predictions are validated experimentally and benchmarked with high-fidelity time domain methods. The presented methods are general and can be applied to any end mill with non-uniform pitch and helix angles as well.

Modeling and estimation of cutting forces in ball helical milling process

Milling forces play an important role in the milling process and are generally calculated by the mechanistic or numerical methods; reliable model of cutting forces is very important for the simulation of milling process, which has big scientific significance to further improve machining quality. Ball helical milling technology is used to make holes based on the cutting principle of helical milling using ball end cutter, and due to the influence of spherical surface machining characteristic, the modeling of cutting force in ball helical milling is difficult. Therefore, the main purpose of this paper is to establish an analytical cutting force model in the ball helical milling process. Considering cutting characteristics in the axial feed, the kinematics of ball helical milling is first presented, then the chip thickness distribution in different directions along the cutting edges is predicted. Furthermore, based on the characteristics of helical milling technology and geometry shape of ball end cutter and the classical mechanical cutting force model, through the study on the ball-end milling mechanics, a new relatively accurate theoretical cutting force model is established. At the same time, cutting force coefficients are identified through instantaneous force method according to the Ti-alloy experimental research result. Finally, higher simulation precision of cutting force model in ball helical milling process is received.

Geometric models of non-standard serrated end mills

Serrated end mills reduce process forces and improve chatter-free material removal rates. Improvements in cutting performance are governed mainly by the serration profile on these cutters. The geometric models of serration profiles are necessary to guide the design of improved cutters. Since these geometric models are usually not available a priori, this paper presents two methods to reconstruct geometric models from scanned measurements of eight different serrated cutter types available commercially. One representation is parametric-based, and another is NURBS-based. Reconstructed serration profiles are classified as the standard sinusoidal, circular, and trapezoidal profile types; and the non-standard semi-circular, circular-elliptical, semi-elliptical, inclined semi-circular; and the inclined circular types. For all eight profiles, the variation in local radius and irregular chip thickness distribution that are a characteristic of serrated cutters are captured by both approaches to approximate the geometry. Force models with the proposed geometric models as inputs are used to predict forces and those forces were experimentally validated. Validated forces confirm that the proposed geometric models are indeed correct. Comparing the cutting performance of all eight serrated cutters suggests that the circular and non-standard serrated end mills can preferentially reduce cutting forces as compared to the standard sinusoidal and/or trapezoidal profiles. However, in terms of the ratios of maximum to minimum peak resultant cutting force, we find that the standard sinusoidal profiled cutter outperforms the other four-fluted cutters, whereas the non-standard inclined circular profiled cutter retains its advantages over other three-fluted cutters.

Modeling of the Distribution of Undeformed Chip Thickness Based on the Real Interference Depth of the Active Abrasive Grain

Distribution of the maximum undeformed chip thickness can be approximated as the reproduction of grooves and protrusions of the grinding surface. It plays a very important role in grinding process as it has a close influence on the prediction and modeling of grinding forces, tool life, and surface quality, as well as process stability. In this study, it is investigated from the perspective of the real interference depth of the active abrasive grain to cater to the performance evaluation of the grinding surface. Firstly, image processing techniques combined with three dimensional topography tests are utilized to extract grains' essential characteristics such as the protrusion height, shape, distribution and density. Then, grains' wear is quantified by the probability assignment function and Dempster-Shafer evidence theory. Based on this, the actual interference depth of a single grain is determined. Through grain's kinematics analysis and considering the effect of contact deformation on the actual contact arc length and affective cutting edge density, the distribution of chip thickness in the current grinding area is defined and its distribution model is established. Model's correctness and rationality are verified by grinding experiments of the slider raceway. Results demonstrate the grain's interference depth highly depends on its protrusion height, wear amount and grinding depth which is a primary contributor to the size of undeformed chip thickness, and grains' density, contact deformations mainly affect its distribution. The quantified distribution model of the maximum undeformed chip thickness lays a foundation for the topography modeling and integrity research of grinding surfaces.

Modeling of grinding chip thickness distribution based on material removel mode in grinding of SiC ceramics

Modeling of grinding chip thickness distribution based on material removel mode in grinding of SiC ceramics

Influence of surface topography evolution of grinding wheel on the optimal material removal rate in grinding process of cemented carbide

Most of the reported studies on the optimization of grinding parameters do not consider the evolution of the surface topography of grinding wheels, and the established empirical models will no longer apply when the surface conditions of the grinding wheel changes. In this paper, an integrated model based on the surface topography of grinding wheel is established. The grinding process of cemented carbide is simulated using the established model, and the simulation results are analyzed to obtain the surface roughness model and the specific grinding energy model based on the undeformed chip thickness distribution. Subsequently, the grinding constraint models are defined according to the two grinding constraints—surface roughness and specific grinding energy. Through inversion analysis, the maximum material removal rate of the given grinding wheel surface conditions satisfying the defined grinding constraints are obtained, and the influence rules of the grinding wheel surface conditions on the maximum material removal rate are analyzed. Then the grinding wheel surface conditions are adjusted by changing the radial dressed height of the grinding wheel and the arrangement distance of the grains in wheel circumferential direction to improve the maximum material removal rate of the grinding wheel. Finally, the optimization results are verified through grinding tests of cemented carbide.

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.

Mechanics of turn-milling operations

Turn-milling machines, which are capable of carrying out turning and milling operations, are widely used in machining complex parts in one set-up. However, due to the complex kinematics and tool-workpiece interaction, turn milling operations are mainly carried out by relying on costly machining trials and experience. This paper presents the mechanics of turn-milling operations to predict cutting forces, torque and power requirements. Typical turn milling process involves three linear (x,y.z) and two rotary drives of the machine tool. The resulting feed vector is modeled as a function of linear velocities of the drives, and angular speeds of workpiece and tool spindles. The generalized chip thickness distribution is modeled as a function of linear feed drive motions, tool and workpiece spindle rotations. The cutting force predictions are experimentally verified for sample cylindrical and ball end mills. The identification of productive tool and workpiece spindle speeds is demonstrated using chip load limit of the tools and torque-power constraints of the turn milling machine tools.

Effects of log position in the stem and commercial thinning on jack pine chip dimensions produced by a chipper-canter

Fifteen stems of jack pine (Pinus banksiana Lamb.) coming from three commercial thinned (CT) plots (control, moderate, and intensive thinning) in the Abitibi-Temiscamingue region, Canada, were cross-cut into three 2.4 m length sections: bottom, middle, and top logs. Logs were processed with a chipper-canter at three cutting widths (CW 12.7, 19.1, and 25.4 mm), producing chips and a three faced cant. Chips were assessed by thickness, width, and length. Knot characteristics [total knot number (TKN) and area (TKA)] were assessed in the three cant faces. Growth ring attributes [earlywood density, latewood density (LWD), ring density (RD), earlywood proportion (EWP), ring width, and rings per mm], mechanical properties (shear, splitting, modulus of elasticity and modulus of rupture in bending), and basic density were evaluated on samples obtained within each CW area. The weighted mean chip thickness (WCT) was significantly affected by the log position in the stem (LPS) and CW. WCT increased as CW increased. Jack pine produce thicker chips than black spruce, when processed under the same cutting parameters. Thickness of chips coming from bottom and middle logs was similar due to a greater taper of the bottom log, which slightly increased this dimension. Thickest chips were produced in the top log due to a higher TKA and TKN towards the top of the stem. Multiple linear regressions showed that TKA, CW, and RD were significant predictors of WCT. Chip size distributions were significantly affected by the CT, LPS, and CW. Thinned stands logs appeared to produce smaller chips than natural stand logs. Moreover, chip thickness distribution was affected primarily by TKA and EWP, while the width and length distribution was mainly affected by EWP, LWD, and TKN. Chip size in jack pine is to some degree determined by knot attributes, growth ring characteristics, and wood density of the raw material. These results suggest the potential advantage of sorting logs prior to chipping, either by species, LPS and/or provenance (thinned or natural stands).

Generalized mechanics and dynamics of metal cutting operations for unified simulations

This paper presents the unified modeling of mechanics and dynamics of metal cutting operations such as turning, boring, drilling and milling. The distribution of chip thickness along the cutting edges of tools are evaluated using the generalized geometric and kinematic model of the operations [1]. The effect of relative vibrations between the cutting edge and workpiece segments are considered. The force contributed by each oblique cutting edge segment is evaluated from shear stress, shear angle and friction coefficient defined in orthogonal cutting data base. The tool cutting loads are evaluated by summing the differential cutting forces along all engaged cutting edges using the generalized geometric transformations presented in [1]. The chatter stability is solved in modal coordinate system, and the forced vibration marks left on the finish surface are predicted in discrete time domain. The process damping, multiple-regenerative phase delays which depend on the tool geometry and operations are considered. The application of the proposed unified mechanics and dynamics model is demonstrated experimentally in drilling, milling with indexable cutters and various end mills, and in opening large holes with multi-functional drilling/boring heads.

Physics-based analysis of minimum quantity lubrication grinding

Minimum quantity lubrication (MQL), which is to apply a minimum amount of lubricant directly into the contact zone, is a promising alternative to substantially reduce the lubricant cost caused by conventional flood cooling. In order to advance the MQL technique into grinding situations, understanding of the process and evaluation of the performance is necessary. Most documented studies thus far concerning MQL grinding are built upon experimental observations with individual and separate treatment of grinding performance measures such as grinding force, temperature, wheel wear, and surface roughness. This paper develops the analytical understanding of mechanical and thermal effects of MQL in grinding and profiles the MQL performance as functions of process and fluid application parameters. Physics-based predictive models are formulated to quantitatively describe the grinding force considering the lubrication effect of MQL. The friction coefficient under MQL condition is first predicted based on boundary lubrication theory, followed by the single grit force and grit distribution analysis. Further, surface roughness is calculated from the results of undeformed chip thickness distribution through probabilistic analysis. Additionally, energy partition and temperature distribution in the workpiece have been developed based on the moving heat source model. Material constitutive model are utilized to capture the influence of temperature and strain rate on the material flow stress. Experimental measurements of force, temperature, and surface roughness have also been pursued to calibrate and validate the predictive models.

Prediction of cutting forces in three and five-axis ball-end milling with tool indentation effect

Simulation of multi-axis ball-end milling of dies, molds and aerospace parts with free-form surfaces is highly desirable in order to optimize the machining processes in virtual environment ahead of costly trials. This paper presents a mechanics model that predicts the cutting forces in feed (x), normal (y) and axial (z) directions by modeling the chip thickness distribution, and cutting and indentation mechanics. The shearing forces are based on commonly known cutting mechanics models. The indentation of the cutting edge into the work material is modeled analytically by considering elasto-plastic deformation of the work material pressed by a rigid cutting tool edge with a positive or negative rake angle. The distribution of chip thickness and geometry of indentation zone are evaluated by considering five-axis motion of the tool along the toolpath. The proposed model has been experimentally validated in plunge indentation, as well as in three and five-axis ball-end milling of free-form surfaces. The prediction of axial (z) cutting forces is shown to be improved significantly when the proposed indentation model is integrated into the mechanics of ball-end milling.

Time domain simulation of torsional–axial vibrations in drilling

A time domain model of the torsional–axial chatter vibrations in drilling is presented. The model considers the exact kinematics of rigid body, and coupled torsional and axial vibrations of the drill. The tool is modeled as a pretwisted beam that exhibits axial and torsional deflections due to torque and thrust loading. A mechanistic cutting force model is used to accurately predict the cutting torque and thrust as a function of feedrate, radial depth of cut, and drill geometry. The drill rotates and feeds axially into the workpiece while the structural vibrations are excited by the cutting torque and thrust. The location of the drill edge is predicted using the kinematics model, and the generated surface is digitized at discrete time intervals. The distribution of chip thickness, which is affected by both rigid body motion and structural vibrations, is evaluated by subtracting the presently generated surface from the previous one. The model considers nonlinearities in cutting coefficients, tool jumping out of cut and overlapping of multiple regeneration waves. Force, torque, power and dimensional form errors left on the surface are predicted using the dynamic chip thickness obtained from the exact kinematics model. The stability of the drilling process is also evaluated using the time domain simulation model, and compared with extensive experiments. This paper provides details of the mathematical model, experimental verification and simulation capabilities. Although the surface finish from unstable cutting can be predicted realistically, the actual drilling stability cannot be determined without including process damping.

Mechanics of boring processes—Part I

Mechanics of boring operations are presented in the paper. The distribution of chip thickness along the cutting edge is modeled as a function of tool inclination angle, nose radius, depth of cut and feed rate. The cutting mechanics of the process is modeled using both mechanistic and orthogonal to oblique cutting transformation approaches. The forces are separated into tangential and friction directions. The friction force is further projected into the radial and feed directions. The cutting forces are correlated to chip area using mechanistic cutting force coefficients which are expressed as a function of chip-tool edge contact length, chip area and cutting speed. For tools which have uniform rake face, the cutting coefficients are predicted using shear stress, shear angle and friction coefficient of the material. Both approaches are experimentally verified and the cutting forces in three Cartesian directions are predicted satisfactorily. The mechanics model presented in this paper is used in predicting the cutting forces generated by inserted boring heads with runouts and presented in Part II of the article [1].

Mechanics and dynamics of general milling cutters.: Part II: inserted cutters

Inserted cutters are widely used in roughing and finishing of parts. The insert geometry and distribution of inserts on the cutter body vary significantly in industry depending on the application. This paper presents a generalized mathematical model of inserted cutters for the purpose of predicting cutting forces, vibrations, dimensional surface finish and stability lobes in milling. In this paper, the edge geometry is defined in the local coordinate system of each insert, and placed and oriented on the cutter body using the cutter's global coordinate system. The cutting edge locations are defined mathematically, and used in predicting the chip thickness distribution along the cutting zone. Each insert may have a different geometry, such as rectangular, convex triangular or a mathematically definable edge. Each insert can be placed on the cutter body mathematically by providing the coordinates of the insert center with respect to the cutter body center. The inserts can be oriented by rotating them around the cutter body, thus each insert may be assigned to have different lead and axial rake angles. By solving the mechanics and dynamics of cutting at each edge point, and integrating them over the contact zone, it is shown that the milling process can be predicted for any inserted cutter. A sample of inserted cutter modeling and analysis examples are provided with experimental verifications.

Mechanistic Modeling of the Ball End Milling Process for Multi-Axis Machining of Free-Form Surfaces

A mechanistic modeling approach to predicting cutting forces is developed for multi-axis ball end milling of free-form surfaces. The workpiece surface is represented by discretized point vectors. The modeling approach employs the cutting edge profile in either analytical or measured form. The engaged cut geometry is determined by classification of the elemental cutting point positions with respect to the workpiece surface. The chip load model determines the undeformed chip thickness distribution along the cutting edges with consideration of various process faults. Given a 5-axis tool path in a cutter location file, shape driving profiles are generated and piecewise ruled surfaces are used to construct the tool swept envelope. The tool swept envelope is then used to update the workpiece surface geometry employing the Z-map method. A series of 3-axis and 5-axis surface machining tests on Ti6A14V were conducted to validate the model. The model shows good computational efficiency, and the force predictions are found in good agreement with the measured data.

The prediction of cutting forces in the ball-end milling process—I. Model formulation and model building procedure

This paper presents a model for the prediction of cutting forces in the ball-end milling process. The steps used in developing the force model are based on the mechanistic principles of metal cutting. The cutting forces are calculated on the basis of the engaged cut geometry, the underformed chip thickness distribution along the cutting edges, and the empirical relationships that relate the cutting forces to the undeformed chip geometry. A simplified cutter runout model, which characterizes the effect of cutter axis offset and tilt on the undeformed chip geometry, has been formulated. A model building procedure based on experimentally measured average forces and the associated runout data is developed to identify the numerical values of the empirical model parameters for the particular workpiece/cutter combination.