Normal Rake Angle Research Articles

Digital dynamic modeling and topology optimized design of shell face mills

This paper presents digital modeling of shell face mills in milling cylinder heads. The cutter's structural dynamics and its mode shapes are predicted using a Finite Element system. The geometries of the cutter body and inserts are imported from their Computer Aided Design (CAD) models. The insert edge is discretized into small segments to model its varying normal rake and inclination angles, which affect the cutting mechanics. The cutter is dynamically assembled with the target machine tool spindle using the receptance coupling method. A general dynamic cutting force model, which considers the varying edge geometry and inserts’ run-outs, is developed and used to predict cutting forces and chatter stability diagrams. The proposed model is experimentally verified to demonstrate the feasibility of the systematic application of physics-based digital design and analysis of tools for the mass machining of specific parts. The cutter body shape is optimized to increase the stiffness of the bending mode shape that caused chatter via topology optimization, which led to five-fold increase in the absolute stable depth of cut.

Modeling and verification of cortical bone drilling forces based on tissue structure heterogeneity

Bone drilling mechanism study is the basis for the optimization of cortical bone drilling process and drill geometry. In this paper, a drilling force model for modified drills with thinned chisel edge is established considering the heterogeneous structure of cortical bone. The bone mineral density is embedded into the established model, the model can predict the axial thrust force change along the drilling depth direction, and the model is verified through cortical bone drilling experiments. The thrust force and torque predicted by the model are in good agreement with the drilling experimental results of cortical bone drilling. Then, the drilling performance of the modified drill and the common drill is compared through cortical bone drilling experiments. Compared with common drill bits, the maximum reduction in average thrust force of the modified drill bit during stable drilling is 21.21 % (n = 2500 rpm, Vf=60 mm/min). The maximum reduction in average roughness of the hole wall is 21.87 % (n = 500 rpm, Vf=10 mm/min). The drill chisel edge thinning design reduces the negative impact of the negative normal rake angle on the cutting lip of common drill on drilling force and stability. Therefore, the drill bit chisel edge thinning design can effectively improve the drilling performance.

Geometric Modeling of Serrated Cutters for Endmilling Forces using Local Oblique Cutting and Rake Normal Correspondence

For nonstandard endmills with sinusoidal and circular serrations on nominally helical cutting edges, the edge space curve was subdivided into straight edge elements for constant increments of arc length. To calculate the local normal rake angle at the serrated edge point, Local Rake Normal Correspondence used the normal vector on the rake face of the corresponding unserrated helical edge point at the same axial cross section. Uncut chip thickness h was computed under Local Oblique Cutting Correspondence published earlier. Stabler’s rule specified chip flow direction and Lazoglu mechanistic normal and friction force coefficients completed the straight edge cutting element forces. Local force contribution vectors summed over the tool engagement resulted in global tool forces. Number of straight edge element computations were minimized with the hypotheses (a) cutting predominantly occurs at the vicinity of serration tips and (b) only the stock surfaces swept by flutes immediately prior and following the current flute need be considered for h. Interaction of axial cross sections at a significant fraction of the serration wavelength was noted. Thus, treating tool axial subdivisions in relative isolation for h is untenable. However, local normal rake angle on the serrated edges followed earlier published trends. For a square endmill, sinusoidally serrated, cutting with low axial depth of cut ADOC, modeled forces showed idle periods and unbalance fluctuations during a full rotation, but not the data; modeled forces for an identical unserrated helical cutter were lower than the serrated. For the same endmill with circular serrations cutting at high ADOC, no idle periods or unbalance were predicted and the agreement with published data was better.

Accurate Modeling of Working Normal Rake Angles and Working Inclination Angles of Active Cutting Edges and Application in Cutting Force Prediction.

The normal rake angle is an important geometric parameter of a turning tool, and it directly affects the accuracy of the cutting force prediction. In this study, an accurate model of the working normal rake angle (WNRA) and working inclination angle (WIA) is presented, including variation in the cutting velocity direction. The active cutting edge of the turning tool is discretized into differential elements. Based on the geometric size of the workpiece and the position of the differential elements, the cutting velocity direction of each differential element is calculated, and analytical expressions for the WNRA, WIA, and working side cutting edge angle are obtained for each differential element. The size of the workpiece is found to exert an effect on the WNRA and WIA of the turning tool. The WNRA and WIA are used to predict the cutting force. A good agreement between the predicted and experimental results from a series of turning experiments on GH4169 with different cutting parameters (cutting depth and feed rate) demonstrates that the proposed model is accurate and effective. This research provides theoretical guidelines for high-performance machining.

Solid Ceramic Toroidal End Mill

The possibility of designing solid ceramic end mills with different geometry is considered. A mathematical model is developed for the cutting section of the mill on the basis of functional relations between the main geometric parameters of a ceramic end mill with a toroidal cutting section. Possible correlations are analyzed among parameters determining tool performance: the shape and size of its helical rake surface, the normal rake angle in its toroidal section, and the strength of the mill. The stress is assessed by finite-element modeling in ANSYS software. The results of finite-element modeling and geometric analysis of the cutting section confirm the need to create a special recess in the toroidal cutting section.

Optimization of simplified grinding wheel geometry for the accurate generation of end-mill cutters using the five-axis CNC grinding process

A simple geometric and optimal method is adopted for the five-axis CNC grinding of the end-mill cutters. In this research, initially a simplified parametric profile of the grinding wheel is constructed using line segments and circular arcs. The equation of the wheel swept-surface in five-axis grinding is derived. Then subjected to the flute profile design, the profile parameters of the grinding wheel, its relative location, and orientation with respect to the end-mill cutter are optimized, ensuring a specified normal rake angle. Finally, validation of the newly developed method has been performed using the CAD simulation; two virtually ground flutes are measured and compared with the given specifications. The normal rake angle is related with the radial rake angle by a relationship established in this work. This innovative approach can determine the non-standard grinding wheel that can be economically produced or dressed to accurately grind the end-mill cutters using the five-axis CNC grinding process.

A Practical Method of Modelling and Simulation for Ball End Mill CNC Grinding

The spherical cutting edge on the ball end mill directly affects its cutting performance. This paper presents a practical method for end mill rake/clearance face modelling. The rake face is a developed ruled surface to fulfill the desired normal rake angle. Revolution surface of the bottom curve on the rake face avoids the interference between the wheel with the designed rake face while grinding. An equidistance curve of the cutting edge on the sphere is deduced by the geodesic curve in order to adjust the position of the cutting edge. With this new modelling method as a platform, it is very helpful for model modification and contour error compensation. The measurement results show that the average value of contour error on spherical cutting edge of the machined sample is 0.01mm inspected by the tool measuring instrument. Its validity is verified by good agreement between the results computed and the data measured.

Finite element analysis of revolving tip-based cutting process

In revolving tip-based machining, a micro-tip is actuated by a piezoelectric stage to perform trajectory movements. As the tip goes through a translational motion, cutting angles change with every tip revolution. In the present paper, the revolving tip-based cutting process for different cutting angles was simulated by finite element method (FEM), and the shear zones were detected. Based on the maximum shear stress principle, the meshed elements in the shear zones were analyzed statistically. The results reveal that with a certain compressive stress state of primary deformation zone, the directions of the maximum shear stress of the inside elements manifested better consistency, thus indicating a more stable cutting process. The variation in yield stresses with respect to normal rake angle was analyzed, and consequently, the optimal cutting angles for revolving tip-based machining were obtained. With the optimized machining parameters, a cross-channel microstructure with smooth sides and sharp inner corners are machined successfully, and finally, a microfluidic chip was prepared by the machined microchannel. Therefore, it can be concluded that the existing tip-based nanomanufacturing technique has a promising potential for the machining of microchannels.

A Novel Approach to Profile-Milling for End-Mill Flutes in 4-Axis CNC Turn-Milling Machines, Part I: Mathematical Modeling

In industry, two main operations are used to produce end-mills; grinding and milling. While grinding is more suited for hard end-mills, milling is more attracting in less-hard end-mills since it is more efficient and productive. However, milling the end-mills is currently conducted based on the technical experience, and to the best knowledge of the authors, no mathematical foundation has yet been established. Thus, a profile-milling approach to machine end-mill flutes in 4-axis CNC turn-milling machines is developed and introduced in this work for the first time. The approach employs the cutting edge tangents, and the rake face normals in determining a cutter’s path that ensures an accurate normal rake angle along the rake face. Knowing the cutter’s path, the approach generates a swept surface which is very essential in the profile-milling simulation and in controlling the flutes shapes. However, the profile-milling simulation is conducted in the extended part of this article over several case studies where the developed approach is validated. Overall, this approach is significantly enhancing the CNC programming techniques for multi-axis profile-milling of the end-mill flutes as well as laying a good foundation for the CAD /CAM/CAE of end-mills.

Practical implementation of cutting force model for step drill using 3D CAD data

As an extension of the cutting force model, which was developed by analyzing the forces on rake and relief face, a practical method of cutting force model is suggested. By a calibration test, cutting coefficients are determined, including the information on tool geometry, work material and cutting conditions such as cutting speed and feed rate. As inputs for the force model, normal rake angle and normal relief angle were obtained by a new method from the measured angles using a 3D CAD machine. This practical force model can be applied for machining CFRP successfully, which was proved from the experiments.

Research on Grinding of Micro Ball End Mill with Equal Normal Rake Angle and Equal Radial Relief Angle

Research on Grinding of Micro Ball End Mill with Equal Normal Rake Angle and Equal Radial Relief Angle

Model for the prediction of low-frequency lateral vibrations in drilling process with pilot hole

A model that predicts the appearance of low-frequency lateral vibrations in drilling with pilot hole is proposed in this work. These vibrations, called whirling in the literature, are responsible for the generation of lobe-shaped holes during drilling. The present model considers both the influence of the regenerative effect of vibrations on the cutting forces and the influence of the process damping phenomenon that appears along the main cutting edges. In order to model cutting forces, cutting edges are divided into discrete elements and for each of them oblique cutting model is employed. Specific cutting forces at each cutting edge element are calculated as function of cutting speed and normal rake angle value. A new methodology is developed to analyze the motion equation of the drill in the frequency domain in order to predict the appearance of whirling vibrations during drilling with pilot hole. Regarding the depth of cut and the spindle rotational speed, drilling stability limits against low-frequency lateral vibrations are obtained. Moreover, in the presence of vibrations, the model can predict the whirling frequencies that are excited depending on the established cutting conditions. In addition, the stability model is experimentally validated via drilling tests over pilot holes of different diameters for a wide range of cutting conditions. In order to study the appearance of low-frequency vibrations and to avoid the appearance of other vibrations such as regenerative chatter, the analysis is focused on low spindle speed values. A comparison between predicted vibration frequencies and actual frequencies in measured cutting forces during drilling tests is carried out and a good correlation between them is observed.

A new method for evaluating the normal rake angle and inclination angle on medical needles.

Hollow needles are the most frequently used medical equipment. The design of a hollow needle that best enables medical procedures requires a better understanding of needle tip geometry. Calculating the cutting angles of a needle for a complex surface topology is difficult. This article proposes a new method based on non-Euclidean geometry for the analysis of biopsy needle tip. The method can be used to calculate the cutting angles on any pipe needle. To verify the validity of this method, the normal rake angle and inclination angle on four types of needles (bias bevel needle, cylinder surface needle, curved surface needle and Cournand-type needle) were investigated. It was found that calculation of the cutting angles was simple and convenient using this method, especially for the curved surface needles. Images of the cutting angles from the Cournand-type needles revealed that the smaller bevel angle [Formula: see text] resulted in a higher normal rake angle [Formula: see text] and inclination angle [Formula: see text]. As [Formula: see text] increased, the range of the normal rake angle [Formula: see text] became larger at first and then became smaller.

Analysis of local cutting edge geometry on temperature distribution and surface integrity when dry drilling of aeronautical alloys

A suitable choice of tool geometry and tool material and the optimization of cutting conditions is the way towards dry machining, especially for difficult to machine materials. The current paper proposes an experimental work about dry drilling of AA 7075 aluminium and more particularly Ti-6Al-4V titanium alloys. Effects of complex drill geometry on thrust force and cutting temperature variations are explored. This study includes drill normal rake angle definition using a mathematical formulation based on tool CAD definition. Temperature distribution along the drill cutting edge is estimated with a specific device. Cutting forces are measured using a dynamometer table. Hole surface integrity is studied by observation of microstructures, on surface and sub-surface. Micro-hardness tests complete the measurements. Results show that temperature is much higher when drilling titanium Ti-6Al-4V than when drilling aluminium AA7075, with variations from 450 to 540 °C along the main cutting edge. Temperature variation along the cutting edge depends on cutting speed, work material and local geometry. Microstructural observations reveal that surface and subsurface are affected with grains elongation in cutting direction. Temperature and microstructural deformation increase with drilling depth.

Time-averaged and Instantaneous Mechanistic Models using Artificial Force Synthesis in Helical End Milling

This paper aims to develop field-deployable mechanistic milling models with the aid of the Virtual Machining Simulation Environment (VMSE). Stabler's rule and sharp tool hypotheses were adopted. VMSE force components for artificial materials with unit normal (Kn) and friction (Kf) force coefficients were least-squares-fit to experimental values to obtain actual Kn and Kf and then functionally fit to chip thickness h, speed v and normal rake angle α. The new approach was tested with a simple ball end mill tool. Both time-averaged (MMa model) and location-averaged instantaneous (MMi model) force components from a subset of experimental data were used. Physical force components reported by the VMSE with both MMa and MMi for the complete test matrix agreed with their experimental counterparts. MMi significantly expanded the range of h and was identical to MMa in the common range.

Modeling the cutting edge geometry of scalpel blades

Scalpel blades are commonly used in surgery to perform invasive medical procedures, yet there has been limited research on the geometry that makes up these cutting instruments. The goal of this article is to define scalpel blade geometry and examine the cutting forces and deflection between commonly used scalpel blades and phantom gel. The following study develops a generalized geometric model that describes the cutting edge geometry in terms of normal rake and inclination angle of any continuously differentiable scalpel cutting edge surface. The parameter of scalpel-tissue contact area is also examined. The geometry of commonly used scalpel blades (10, 11, 12, and 15) is compared to each other and their cutting force through phantom gel measured. It was found that blade 10 displayed the lowest average total steady-state cutting force of 0.52 N followed by blade 15, 11, and 12 with a cutting force of 1.17 N (125% higher than blade 10). Blade 10 also displayed the lowest normalized cutting force of 0.16 N/mm followed by blades 15, 12, and 11 with a force of 0.19 N/mm (17% higher than blade 10).

Effect of Cutting Conditions on Tool Wear in Driven Rotary Cutting of Maraging Steel

In this paper, driven rotary cutting of maraging steel was carried out and the influence on tool wear of difference cutting conditions was investigated. As cutting conditions, different coolant conditions, cutting speeds, circumferential velocity ratios, tool inclination angles, tool rotation directions and normal rake angles were tested. We found that as the coolant quantity decreased and cutting speed increased, the width of flank wear increased. It was also found that the circumferential velocity ratio, tool inclination angle, tool rotation direction and normal rake angle have optimal conditions that decrease wear. Optimal conditions were chosen, and a tool life test was carried out. As a result, driven rotary cutting was achieved with 11 or more times the tool life of conventional turning.

Analyses of a new four-facet drill

In this paper, a new four-facet drill was presented and analyzed. For evaluating the performance of the new and conventional drills, the geometrical analyses of the rake faces and flank surfaces as well as the prediction of cutting forces and torques were conducted. The results showed that the normal rake and clearance angles along the cutting lips of the new drill are always positive and a positive constant, respectively. In contrast, those of the conventional one are negative at certain points on cutting lips close to the drill axis and variable, respectively. Therefore, the cutting forces and torques of the new drill in drilling can be reduced as compared with the conventional one. The prediction of cutting forces and torques in drilling the workpiece made of plain-carbon steel (AISI1045) showed that the reductions of the total thrust force and torque along cutting lips for the new drill over the conventional drill are up to 50.12 and 26.54 %, respectively, and hence, the tool life of the new drill is expected to be longer than the conventional one’s.

Five-axis rake face grinding of end-mills with circular-arc generators

The rake angles and the cores of the end-mill cutting tools are very important for they control the cutting forces during machining, the strength of the cutting edges, the rigidity of the end-mills and the chips removal capability. Thus, grinding end-mill flutes with accurate rake angles and accurate cores is very crucial in cutting tools’ industry. Flutes grinding is normally accomplished using two axis CNC grinding machines; however, this requires grinding-wheels with free-form profiles, expensive and uneasy to make, and the produced cutting edges and the normal rake angles along these edges are inaccurate. Hence, this work extends the five-axis CNC grinding approach developed by the first author to grinding of circular-arc ball end-mills. The generic mathematical equations of the grinding-wheel orientations and locations are first derived. Then, the grinding-wheel path is generated and the produced flute surface is precisely modeled. With standard grinding-wheels, computer simulation for the grinding approach is conducted and proved to produce precise end-mill cores, accurate cutting edges and accurate rake angles along these edges.

Design of a New Micro Single Flute Drill

A new micro single flute drill was presented in this study. For the convenience of developing a solid model, and doing a geometrical analysis, its geometry including the flute and flank surfaces is presented mathematically. According to the geometrical analysis, the normal clearance angles and normal rake angles along the cutting lip of the new micro dill are always invariant, and positive, respectively. Hence its cutting force in drilling is reduced. Furthermore, with only one main flute, the new micro drill gets stronger, and its cutting torque can be also decreased. Therefore it is expected that the tool life of the new micro drill is much longer than that of the conventional drill. Keyword: New micro drill, micro drill, single cutting edge