Normal Rake Angle Research Articles

Influence of Three-Dimensional Stability Lobes on the Cutter Design

According to the model of three-dimensional stability and the relationship between the parameters of oblique cutting and milling coefficients, this paper analyzes the influence of the cutter geometry parameters (helix angle, normal rake angle) on the three-dimensional stability of the spindle speed, axial and radial depths. On the same cutting condition, it should choose the cutter of having the bigger helix angle and normal rake angle to cut the thin-walled plate, which can increase the stability of cutting process and improving efficiency and quality.

A New Approach to Five-Axis CNC Flute Grinding of Solid End-Mills

The traditional cutting tools grinding reveals inexact tool flutes that altered the tool strength and affect the chip evacuation capabilities. Moreover, the normal rake angles are neither exact nor varying smoothly on the rake face along the cutting edge. Adopting the rake face grinding process, the wheel shape and path are optimized using GODLIKE scheme in order to grind the tool flutes with exact helical and normal rake angles while keeping close matching to the designed flutes. A tapered ball-end mill is considered in this study due to its extensive role in five-axis sculpture surfaces machining. With this approach proposed, a simple grinding wheel replaces the complex wheels commonly used, and the deviation between the designed and the generated flutes reveals less than 4 % of the tool minor radius. Beside all, a relationship between the radial and the normal rake angles are established.

Analytical modeling and experimental investigation of ultrasonic-vibration assisted oblique turning, part II: Dynamics analysis

In the present study, a theoretical model has been developed for the analysis of the dynamics of ultrasonic-vibration assisted oblique turning. Various parameters including inclination angle, normal rake angle, tool cutting edge angle, cutting velocity, feed rate, vibration frequency and amplitude were taken into consideration in addition to other dynamics parameters such as inertial effect. The thin shear plane theory was used for the analysis. The time dependent and average cutting forces could be estimated and compared with the cutting forces in conventional turning.

Effect of side edge angle and effective rake angle on top burrs in micro-milling

Abstract Experimental investigations on the effect of side wall edge strengthening, to reduce top burr formation, in micro-milling slots in Al-6061 alloy using a carbide tool are reported here. The side edge is strengthened by increasing the edge angle to a value higher than the usual 90°. Side edge angle is varied in two ways: one, by changing the work geometry and two, by introducing a taper into the milling tool. The burrs formed are examined qualitatively in a scanning electron microscope and quantitatively using a surface profiler. The analysis of the results shows that top burrs are reduced both by strengthening the side edge and also by the effect of the taper angle in the micro-milling tool. The effect of the side edge angle in the tool can be attributed to the edge strengthening. On the other hand, an analysis of the tapered tool geometry indicates that the velocity rake, normal rake and effective rake angles increase with the taper angle and can hence explain the observed burr reductions.

Comparison of central composite and orthogonal array designs for cutting force and surface roughness prediction modelling in turning

Development of empirical models in turning operation has been a major activity in metal cutting research. This paper presents an application of central composite face centred (CCF) and L18(21 × 37) orthogonal array designs for developing cutting force and surface roughness models in case of turning AISI 1015 steel with HSS tool. Three process parameters namely cutting speed, feed, depth of cut and three tool parameters namely side cutting edge angle, inclination angle, normal rake angle were considered in developing the cutting force and surface roughness models. Each parameter was set at three levels. Based on the experimental data, mathematical models in terms of process and tool parameters were developed using multiple linear regression. Finally, central composite and orthogonal array designs are compared with respect to effect analysis and empirical model building. Confirmation tests were performed to verify the predictability of the developed models.

A Hybrid Approach to Predict Residual Stresses Induced by Ball-End Tool Finishing Milling of a Bainitic Steel

The objective of this study is to predict the residual stresses induced by ball-end milling using an hybrid approach based on a numerical simulation where thermo-mechanical loads equivalent to the cutting process are applied directly on to the final surface of the workpiece without modelling the material removal. The applied loading is derived from the measurement of the maximum cutting forces and the measurement by IR camera of the temperature in the tertiary shear zone. The 2D simplified model proposed herein is derived from the analysis of oblique cutting with elementary cutting tools and makes it possible to take account of the normal rake and local helix angles as well as the lead angle of the tool. The feasibility of the approach is assessed by comparing experimental measurements and numerical predictions of the residual stresses induced by ball-end tool finishing milling of flat specimens made of a bainitic steel.

Hollow needle tissue insertion force model

In this study, a mechanistic approach using elementary cutting tool (ECT) edges of varying inclination and normal rake angles is demonstrated to be capable to predict hollow needle insertion force. A needle force model is developed and validated for the specific case of 11 gauge two-plane symmetric needles. Blades of varying inclination and rake angles are inserted into bovine liver to determine the specific force of initial tissue cutting for the given edge geometry; this information is applied to the ECT force model which is validated against experimental force results of hollow needles inserted into bovine liver.

A practical method to determine rake angles of twist drill by measuring the cutting edge

Rake angle and its distribution on the cutting edge of a twist drill are of vital importance to its performance. This paper presents a practical method to determine the cutting edge and rake angles. Firstly, 3D coordinates of the points on the cutting edge are inspected by using 2D measurement apparatus. Secondly, the flute profile is deduced from the data measured, and the rake angles are evaluated by numerical computation. Conventionally, rake angle calculation is based on a series of plane definitions and laborious work in plane projection is inevitable. To facilitate the process, a vector based procedure is presented. As an example, cutting edge of a standard drill is measured by using tool microscope and image-based instrument. In each case, the normal rake angle distribution is determined. Numerical results exhibit that average error and mean square error of the latter deviated from the former are 0.95 o and 0.33 o, respectively. It verifies the validity of the proposed procedure and the measurement device.

Geometry, specification, and drilling performance of a plane rake faced drill point design

A study of a modified drill point design with plane rake faces is presented. The critical geometries that uniquely define the drill point design are analysed based on the international standard. The study shows that the modified drill design yields positive normal rake angle on the entire lips and point relieving in the chisel edge region. An experimental study of drilling a high tensile steel using 7–13 mm high-speed steel (HSS) drills with titanium nitride (TiN) coatings has been carried out to assess the new drill point design. It shows that the modified plane rake faced (PRF) drills can reduce the thrust force by as much as 46.9 per cent with an average of 23.8 per cent, as compared to the conventional twist drills under the corresponding cutting conditions, while the reduction in torque is also significant with the maximum of 24.9 per cent. These drilling performance improvements are comparable to those from using the multi-facet drills that were claimed as one of the most heartening drill developments in several decades for drilling force reduction, while the PRF drills can be easily sharpened using the conventional twist drill grinders. The drill-life tests amply demonstrate the superiority of the PRF drills over the conventional twist drills.

Mathematical Modeling of a Complex Helical Drill Point

Helical drill points provide a superior cutting performance, particularly when drilling microholes. Complex helical drill points retain the advantages of conventional helical drills while providing a further strengthening of the cutting edge. However, no methods currently exist for systematically modeling drills of this type. The proposed method has three distinct features. First, the mathematical model of the complex helicoid grinding surface enables the normal and tangential vectors of the abrasive wheel to be explicitly derived. Second, the mathematical models of the flute and flank surfaces are integrated, and thus the cutting edges and chisel edges can be obtained using a simple numerical calculation procedure. Finally, the derivation of the model is straightforward and expresses the drill’s characteristics (e.g., the chisel edge, the lip clearance angle, the heel clearance, the normal rake angle, and the normal clearance angle) in accordance with International Organization for Standardization standards. When integrated with appropriate computer numerical control (CNC) software, the modeling approach presented in this study provides a powerful tool for the design and manufacturing of complex helical drill points with a variety of geometrical designs.

Effect of Helix Angle and Normal Rake Angle on Stability in End Milling

Chatter phenomenon often occurs during end milling of metal-cutting and becomes a common limitation to achieve high productivity and part quality. This paper studies the relationship expression between the parameters of oblique cutting and milling coefficients by analyzing the geometrical relationship of oblique cutting, and derives the mathematic expressions in theory between the cutter parameters and chatter. For the purpose of chatter avoidance, this paper studies the effect of helix angle and normal rake angle on milling stability under the condition of the same milling parameters, and plots the three-dimensional stability lobes of the spindle speed, axial and radial depths. It can be found that the milling stability is increased with the increment of helix angle and normal rake angle. Through the three-dimensional lobe, it is possible to choose the appropriate cutter parameters to reduce and avoid the chatter.

A new approach to the modeling of oblique cutting processes

A new upper-bound model that incorporates force equilibrium parallel to the cutting edge is proposed for oblique cutting operations. The energy approach is framed in terms of the normal shear angle and two new fundamental variables that characterize the energy requirements of the oblique cutting process. SLIP is a kinematic variable and is defined as the ratio of the shear velocity imparted to the chip on the shear plane parallel to the cutting edge, to the incoming velocity in the same direction. RATIO is a force-based variable and is defined as the ratio of the friction force on the rake face to the resultant shear force in the shear plane. Calibration of the model for either real time identification purposes or for process planning/optimization requires experimental force data but no shear angle data, making it very suitable for the analysis of cutting operations with non-straight cutting edges. The relationships between SLIP, chip flow angle, and RATIO are shown to be remarkably consistent over a very wide range of inclination and normal rake angles. Finally, the authors demonstrate the success of the model using existing experimental data.

A new methodology for designing a curve-edged twist drill with an arbitrarily given distribution of the cutting angles along the tool cutting edge

The present study aims at the development of a new methodology for designing a curve-edged twist drill with an arbitrarily given distribution of the cutting angles along the tool cutting edge. The new methodology consists of 81 major mathematical equations and is developed using a method of mapping relevant planes and straight lines of a cutting tool (such as the cutting plane and the cutting edge) as corresponding image points and image lines on a projection plane. The developed methodology is used to intuitively and graphically analyze and determine the relationship between the orientation of the cutting edge and the cutting angles at each point on the cutting edge. A set of image points and image lines is established to calculate the cutting angles on the cutting edge of a twist drill, including the working tool rake angle, the working tool inclination angle, the working cutting edge angle, and the working normal rake angle. Three computer case studies are provided to show curved cutting edges that correspond, respectively, to a linear distribution of the working tool rake angle, a combined linear and uniform distribution of the working tool rake angle, and a linear distribution of the working tool inclination angle along the tool cutting edge. Finally, a set of metal drilling experiments is performed to compare the drilling torque and the thrust force between a conventional straight-edged twist drill and a new curve-edged twist drill that has a combined linear and uniform distribution of the working tool rake angle along the tool cutting edge. The experimental results show that the new curve-edged drill reduces the drilling torque by 28.5% and the thrust force by 24.6% on average.

Modeling and Computer Simulation of Grinding for Ball-End Milling Cutter with Equal Normal Rake Angle

In this paper, a new mathematical model and grinding method of ball-end milling cutter are proposed, based on the orthogonal spiral cutting edge curve. The movements of grinding wheel and ball-end milling cutter are presented while grinding rake face. In order to grind conveniently and avoid interference, a conical wheel is also designed and employed to grind the rake face of ball-end milling cutter on a grinder. In order to improve the machining characteristics of ball-end milling cutter, the model of rake face with equal rake angle is established. The software of ball-end milling cutter is developed to design and optimize different shapes of rake face. Furthermore, the simulation analysis on rake face with equal rake angle is carried out to confirm the validation of the mathematical models.

A novel CNC grinding method for the rake face of a taper ball-end mill with a CBN spherical grinding wheel

A novel method using a CBN spherical grinding wheel to grind the rake face of a taper ball-end mill and the configuration of corresponding CNC tool grinder are presented. This method utilizes the self-adaptation characteristics of a sphere to decrease the number of simultaneous cooperative axes of a CNC tool grinder and to smooth the rake face on the transition area between the taper and the ball-end of the mill. In order to obtain an accurate normal rake angle, which is one of the key factors affecting tool cutting performance, a moving coordinate system based on the required normal rake angle and the cutting edge was established. Then, by the proposed moving coordinate system, an algorithm to determine the position and orientation of a spherical grinding wheel, the basis of CNC code generation, is proposed and the relevant formulations are deduced. The 3D simulation of rake face grinding for a taper ball-end mill with constant helical angle indicates that the number of simultaneous cooperative axes of the CNC tool grinder is decreased from five to four and the smooth transition of the rake face is realized by the proposed method herein.

A study of high-performance plane rake faced twist drills.: Part I: Geometrical analysis and experimental investigation

A study of a modified drill point design with plane rake faces for drilling high-tensile steels is presented. A geometrical analysis has shown that the modified drill point design yields positive normal rake angle on the entire lips and point relieving in the vicinity of the chisel edge. This drill geometry can be expected to reduce the cutting forces and torque, and hence reduce the possible drill breakages when drilling high-tensile steels. An experimental study of drilling an ASSAB 4340 high-tensile steel with 7–13 mm titanium nitride (TiN) coated high-speed steel (HSS) drills has shown that the modified drills can reduce the thrust force by as much as 46.9%, as compared to the conventional twist drills under the corresponding cutting conditions, while the average reduction of torque is 13.2%. Drill-life tests have also been carried out and confirmed the superiority of the modified drills over the conventional twist drills. In some cases, the conventional drills were broken inside the workpiece, while the modified drills performed very well under the same cutting conditions. To mathematically predict the drilling performance and optimise the drilling process using the plane rake faced drills, predictive models for the cutting forces, torque and power will be developed in the second part of this investigation.

Analysis of Cutting Forces and Mechanism of Chip Formation in Ball End Milling of Inclined Surface (2nd Report)

In order to predict cutting forces and chip formation in milling with a ball end mill for various tool paths, inclination of the workpiece surface and of the tool axis, a cutting model proposed in previous paper is extended to the milling process in which both cutting edges of the sphere and cylindrical portions engage with the workpiece. In the cutting model, elemental chip at any point on the cutting edge is described by simple shear plane oblique cutting model, and the condition of side-curl of the chip is considered. In this paper, cutting edge configurations, inclination and normal rake angles at the sphere and cylindrical portions are discussed. Geometric quantities such as contact region between the cutting edge and the workpiece surface, and undeformed chip thickness along the cutting edge in milling for the tool moving upward or downward on the inclined surface are analyzed, and variation of these geometric quantities with tool rotational angle are also discussed. Three components of the cutting force and chip formation such as chip flow angle, radius of side-curl of the chip and chip form are predicted by using developed cutting model and energy method. The preliminary examination shows that there is the large difference in cutting forces and the chip formation for the tool moving upward or downward on the inclined surface.

A manufacturing model of helical groove on rotary burr and a universal post processing method

A systematic machining theory and precision method to determine cutter location in a grinding system is presented for rotary burr. First, the helical cutting edge on various kinds of revolving surfaces is built. Then, based on the geometry model of the helical cutting edge, the smooth spiral rake surface with constant normal rake angle and flank surface can been formed during the one-pass grinding process by this method. No interference between the grinding wheel and workpiece happens by the wheel special rotation. The method has the characteristic of detaching the grinding wheel path solution from specified machining conditions. The grinding wheel path is suitable for different NC machine tools through post processing. Meanwhile, a mechanism kinematic model of the NC machine tool is built, and a generalized algorithm for post-processing of multi-axis NC machine tools is presented. This model is applied to arbitrary configuration of NC machine tool, and the motion value for each axis will be generated by the inputting structure and motion parameters of the machine tool. The model, together with the machining method mentioned in this paper, make the calculation and generation of the grinding wheel path simpler and universal. At last, the validity of the method given in the paper is identified by an example of grinding.

Mathematical model for helical drill point

Helical drill points provide a superior cutting performance in drilling operations, particularly in micro-hole drilling. This paper presents a comprehensive and straightforward method for the design of helical drill points. The proposed method has three particular features. Firstly, a mathematical model of the helicoid grinding surface is developed. This model allows the normal and tangential vectors of the abrasive wheel to be obtained explicitly. Secondly, the mathematical models of the flute and flank surfaces are integrated and therefore the cutting and chisel edges can be obtained by numerical calculation. Finally, the derivation of the model is straightforward and expresses the drill's characteristics (e.g. the semi-point angle, chisel edge, lip clearance angle, heel clearance, angle tool cutting edge inclination, normal rake angle and normal clearance angle) in accordance with all current international standards. The proposed model is capable of describing a wide range of helical drills. The methodology presented in this study facilitates the production of helical drills on a 6-axis CNC grinding machine.

Drill point geometry of multi-flute drills

This paper presents a comprehensive mathematical model for analysis of the geometries of conical, hyperboloidal, and ellipsoidal drills. The proposed method includes three particular features. The first is that a rotational disk-type abrasive wheel is modeled by revolution geometry, thus allowing for the normal and tangent vectors of an abrasive wheel to be obtained explicitly. Consequently, the tangent and normal vectors along the cutting edges and chisel edges of the produced drill can be obtained. The second feature is the ability of the model to determine and express drill geometries and characteristics (semi-point angle, tool cutting edge inclination, chisel angle, normal rake angle and normal clearance angle) according to all current international standards. Thirdly, the drill’s working geometries are investigated by taking the effect of feed motion into consideration. We found that cutting edge geometry can be studied without significant error even though we neglect the effect of feed. The chisel edge working geometry shows greater variation than tool geometry. Consequently, the effect of feed must be taken into consideration when studying chisel edge action during drilling operation.