Cylindrical End Mill Research Articles

Application of Circular Arc Projection Method in Flute Grinding of Cylindrical End-mills

Application of Circular Arc Projection Method in Flute Grinding of Cylindrical End-mills

A New Method of the Positioning and Analysis of the Roughness Deviation in Five-Axis Milling of External Cylindrical Gear

Abstract Five-axis milling is a modern, flexible and constantly developing manufacturing process, which can be used for the machining of external cylindrical gears by means of cylindrical end mills and special disc mills on universal multi-axis machining centres. The article presents a new method of positioning the tip and the axis of the end mill and the disc cutter in order to ensure a constant value of deviation of the theoretical roughness Rth along the entire length of the tooth profile. The first part presents a mathematical model of the five-axis milling process of the cylindrical gear and an algorithm for calculating the Rth deviation values. The next section describes the positioning of the end mill and the disc cutter. Then, a new method for the empirical determination of the distribution of the involute root angle Δui and the data description by means of the interpolation function are presented and described. In the conducted numerical tests, the influence of the geometrical parameters of the cylindrical gear on the deviation Rth is determined, assuming a constant Rth value in the five-axis milling process.

Determination of wheel position in flute grinding of cylindrical end-mills considering tolerances of flute parameters

Flute parameters, i.e. rake angle, core radius, and flute width, have significant effects on the cutting performance of an end-mill. These parameters should be controlled within tolerances in flute grinding process by adjusting wheel position properly. Existing methods do not take the tolerances into consideration, resulting in that the wheel position cannot be determined properly in the case where the designed flute parameters are out of the valid range. To solve this problem, this paper proposes a new method of determining the wheel position in flute grinding of cylindrical end-mills considering the tolerances of the flute parameters. The accuracy of rake angle is guaranteed by conjugation of the wheel surface with the flute cutting-edge. Taking error controlling of core radius and flute width as the objective, the problem of wheel-position determination is formulated by an optimization model. On this basis, a search strategy for determining wheel position is proposed to include the effects of the tolerances. Several simulation examples are provided for validation. The simulation results indicate that the new method can determine the wheel position properly and efficiently, and the errors of the flute parameters can be minimized within the tolerances, even though the designed flute parameters are out of the valid range.

A novel approach to wheel path generation for 4-axis CNC flank grinding of conical end-mills

Conical end-mills are widely used in CNC machining and the flank has a great influence on the performance of the end-mill. However, the complex structures of conical flank make it difficult to grind. The traditional method for conical flank grinding is to control the grinding wheel with a 3-axis archimedes helix motion, which cannot guarantee the accuracy of the desired flank parameters, i.e., relief angle and flank angle. To solve this problem, this paper proposed a wheel path generation method for 4-axis CNC conical flank grinding. In this model, the grinding processes were discretized into a finite of cylindrical end-mill grinding. For each cylindrical end-mill, the machined flank parameters could be calculated within the cross-section through the envelope theory. Additionally, the geometrical constraints to avoid interference and abnormal flank profile were developed based on the cylindrical end-mill. The wheel path was obtained by calculating the wheel’s position and orientation for the discretized cylindrical end-mill section by section. Also, an integral procedure was built to optimize and simulate the conical flank grinding. The simulation results showed that the proposed method had a wide range of applications that could provide a general solution for the conical CNC flanking operations and also could be extended to grind the complex surface of end-mills in the future study.

Chatter stability prediction of ball-end milling considering multi-mode regenerations

Ball-end milling has been commonly used in the manufacturing of complex surfaces and structures. In order to improve the machining efficiency and ensure the manufacturing quality, chatter has to be avoided. The stability of cylindrical end mills has been well studied by selecting the most flexible dominant mode. This paper models the chatter stability of ball-end milling cutter with multiple modes and solves it in discrete time domain. Firstly, the multiple degree-of freedom (DOF) vibration model of the tool-workpiece system is established in modal coordinates to decouple the delay differential equations (DDEs). Then, to complete the motion equations of ball-end milling cutter, the cutting force model considering regenerative effect is built by evaluating the dynamic thickness at each cutting point along the cutting edge. Finally, the stability lobe diagram (SLD) of ball-end milling is solved by full-discretization method in discrete time domain. The cutting tests carried out on a machining center verify the prediction accuracy and observe chatter phenomenon caused by different dominant modes.

Dynamics and Stability of Turn-Milling Operations With Varying Time Delay in Discrete Time Domain

Turn-milling machines are widely used in industry because of their multifunctional capabilities in producing complex parts in one setup. Both milling cutter and workpiece rotate simultaneously while the machine travels in three Cartesian directions leading to five axis kinematics with complex chip generation mechanism. This paper presents a general mathematical model to predict the chip thickness, cutting force, and chatter stability of turn milling operations. The dynamic chip thickness is modeled by considering the rigid body motion, relative vibrations between the tool and workpiece, and cutter-workpiece engagement geometry. The dynamics of the process are governed by delayed differential equations by time periodic coefficients with a time varying delay contributed by two simultaneously rotating spindles and kinematics of the machine. The stability of the system has been solved in semidiscrete time domain as a function of depth of cut, feed, tool spindle speed, and workpiece speed. The stability model has been experimentally verified in turn milling of Aluminum alloy cut with a helical cylindrical end mill.

A Generalized and Efficient Approach for Accurate Five-Axis Flute Grinding of Cylindrical End-Mills

Wheel position (including wheel location and orientation) in the flute grinding process of an end-mill determines the ground flute's geometric parameters, i.e., rake angle, core radius, and flute width. Current technologies for calculating the wheel position to guarantee the three parameters' accuracy are either time-consuming or only applicable to the grinding wheels with singular points. In order to cope with this problem, this paper presents a generalized and efficient approach for determining the wheel position accurately in five-axis flute grinding of cylindrical end-mills. A new analytic expression of the wheel location is derived and an original algorithm is developed to search for the required wheel position. This approach can apply not only to the wheels with fillets but also to the wheels with singular points. Simulation examples are provided to validate the new approach and compared with the results from other literature. Besides the ability to determine the wheel position, the new approach can evaluate extrema of the core radius and flute width that a specified wheel can generate. Owing to the evaluated extrema, automatic 1V1 wheel customization according to the designed flute is realized in this paper. This work can improve the efficiency and automation degree of the flute grinding process and lay a good foundation for the development of a comprehensive computer-aided design and computer-aided manufacturing system for end-mill manufacturing.

An analytical index relating cutting force to axial depth of cut for cylindrical end mills

In milling processes, the ever-changing cutting force has great effects on machining quality. A novel cutting force model for cylindrical end mills, discretizing the end mill along its circumferential direction, is described in this paper. An analytical index is established for simplifying the prediction for the cutting force and estimating the fluctuation of it based on the model. The influences of the axial depth of cut on the cutting force and the fluctuation are studied based on the proposed index. The predictions of the analytical index are verified by milling experiments.

An accurate method for five-axis flute grinding in cylindrical end-mills using standard 1V1/1A1 grinding wheels

Flute grinding is a critical process in end-mill manufacturing. The wheel geometry and position during the grinding process govern the flute profile and determine the flute parameters (i.e. rake angle, core radius, and flute width). Accuracy of these parameters should be ensured to obtain optimal cutting performance. For a given wheel geometry, the current technologies can only determine the wheel position for the desired rake angle and core radius without consideration of the flute width. This disadvantage seriously restricts the improvement of machining quality and the flexibility of flute grinding. To cope with this problem, this paper presents a novel method of five-axis flute grinding using standard 1V1/1A1 wheels to ensure the accuracy of the three flute parameters. Based on the theories of analytic geometry and envelope, equations for calculating the flute parameters are first derived. Afterwards, a system of nonlinear equations is created to calculate the wheel position for flute grinding. The validity of the proposed method is verified by 3D simulations and machining experiments. Lastly, the sensitivity of the valid flute width with respect to the wheel geometric parameters is further investigated in this work.

A New and Accurate Mathematical Model for Computer Numerically Controlled Programming of 4Y1 Wheels in 2½-Axis Flute Grinding of Cylindrical End-Mills

Solid carbide cylindrical end-mills are widely used in machining, and their helical flutes are crucial to their cutting performance. In industry, the flute is simply defined with four key parameters: the helical angle, the radial rake angle, the fluting angle, and the core radius, which are specified in an end-mill design. The flute shape is not fully defined, while it is often generated by a 1A1 or 1V1 diamond wheel in 2½-axis computer numerically controlled (CNC) grinding. Unfortunately, the two simple wheels cannot make largely different flute shapes, preventing further improvement of the end-mills. Although no research result on how the flute geometry affects the end-mill cutting attribute has come into public yet, it is now necessary to employ more complicated wheels to grind flutes with the specified parameter values but much different flute shapes. For this purpose, the 4Y1 diamond wheel is employed in this work. However, the commercial tool grinding software cannot determine the dimensions and the set-up angle for the 4Y1 wheel. To address this problem, a new mathematical model of the flute parameters in terms of the dimensions and the set-up angle of the 4Y1 wheel is formulated, thus, the 4Y1 wheel can be used in flute grinding. This work lays a foundation of using complex wheels to grind flutes with more shapes in order to improve the end-mill's cutting ability.

An Automated and Accurate CNC Programming Approach to Five-Axis Flute Grinding of Cylindrical End-Mills Using the Direct Method

In solid carbide end-mills, the flutes significantly affect the tool's cutting performance and life, and the core radius mainly affects the tool's rigidity. The current CNC programming techniques can correctly determine the orientation of the wheel so that it grinds the rake face with the specified rake angle; however, it cannot accurately determine the wheel location for the direct method and, consequently, the desired core radius is not guaranteed. To address this problem, a new CNC programming approach is proposed to accurately calculate the wheel orientation and location (WOL) in 5-axis grinding of the cylindrical end-mill flutes. In this work, a new concept of 5-axis CNC grinding—effective grinding edge (EGE)—is first proposed to represent the instantaneous grinding edge of the wheel, and the parametric equations of the effective grinding edge are formulated. The wheel orientation and location in 5-axis flute grinding are calculated automatically and accurately so that the rake angle of the rake face and the core radius are ensured. The new approach is verified with several examples in this work. Therefore, it can improve the end-mill quality and lays a good foundation for the computer-aided design/computer-aided engineering/computer-aided manufacturing (CAD/CAE/CAM) of end-mills.

Surface topography and roughness in hole-making by helical milling

Helical milling is used to generate holes with a cutting tool traveling on a helical path into the workpiece in which the diameter of the hole can be adjusted through that of the helical path. Based on an improved Z-map model, a 3D surface topography simulation model is established to simulate the surface finish profile generated after a helical milling operation using a cylindrical end mill. The surface topography simulation model incorporates the effects of the relative motion between the cutting tool and the workpiece, in which the effect of the insert runout error of the cutting tool is considered. Furthermore, the roughness parameters are deduced from simulations of the 3D surface topography. The experimental result shows that the proposed simulation algorithm can predict well the surface roughness in a helical milling operation. The surface topography simulation model is used to study the effects of cutting conditions such as the tangential feedrate, the diameter of the cutting tool and the hole, the insert runout error of the cutting tool, as well as the revolution of the cutting tool around the axis of the hole on the surface finish profile. It is found that the surface quality can be improved by optimization of the cutting conditions. As a result, the proposed model will be helpful in determining the cutting conditions to meet surface finish requirements in helical milling operation.

Investigation of Static Failure for Cemented Carbide Cylindrical End Mill

Investigation of the cutting tool failure is one of the important factors in order to optimize the cutting parameters. This paper studies the cutting tool stresses (maximum principal, maximum shear and von Mises) at the shank and at the tip using three failure theories. These stresses are analyzed by means of the finite element method using MSC patran/nastran software and the experimental method using electrical-resistance strain gages. The comparison of the stresses obtained from these two methods for different feed rates and different rotation speeds are depicted in figures.

An Integrated Approach of CAD/CAM for Spatial Cam with Oscillating Cylindrical Rollers

In this paper, an integrated approach of CAD/CAM was presented for the spatial cam with oscillating cylindrical rollers. The relationship between the cam profiles and the meshing element’s surface is established by the conjugate surface theory. In the machining process, the cutter location for the rough and the finish machining using cylindrical-end mill is derived. To avoid interference, the principal curvatures and the principal induced normal curvatures between the cam surface and the cutting tool are analyzed. The geometric error was used as a basis for generating appropriate toolpaths. The postprocessor are developed for converting the cutter location file to the five-axis numerical control program. The generated NC program is verified before actual machining through solid cutting simulation. In order to demonstrate the applicability of the presented method, cam profile was cut using a five-axis machine tool with real material.

The CAM System for Scroll Profile with Three CNC Interpolations

The scroll profile is complex with involute curve and high precision is required. Owing to the interpolation method has significant effects on the dynamic behaviour and to obtain the flexibility of the machining, this paper focuses on the development of a computer-aided manufacturing methodology for precision scroll by the combination of curve fitting and CNC interpolation. In this paper, the method for design and manufacture of the scroll profile is established based on the differential geometry and the enveloping theory. The cutter location using the cylindrical end mill is derived and the cutting path sequences are planned. Three types curve fitting methods: linear fitting, circular biarcs curve fitting, and NURBS curve fitting are adopted to approximate the toolpath of the scroll profile. The error control is used as the basis for generating appropriate toolpath to ensure the machining accuracy. The circular biarcs fitting and NURBS curve fitting can obtain continuous smooth toolpath. In the identical chordal deviation, the circular biarcs curve fitting provides the best performance. The toolpath generated by the proposed method is verified through the solid cutting simulation and the trial-cut on a three-axis machine tool.

Interference-Free Multi-Axis NC Machining of Cylindrical Cam Using Enveloping Element

To obtain the flexibility of choice of cutting tool and to compensate the wear of the cutting tool, this paper presents an interference-free toolpath generating method for multi-axis machining of a cylindrical cam. The notion of the proposed method is that the cutting tool is confined within the meshing element and the motion of the cutting tool follows the meshing element so that collision problem can be avoided. Based on the envelope theory, homogeneous coordinate transformation and differential geometry, the cutter location for multi-axis NC machining using cylindrical-end mill is derived and the cutting path sequences with the minimum lead in and lead out are planned. The cutting simulations with solid model are performed to verify the proposed toolpath generation method. It is also verified through the trial cut with model material on a five-axis machine tool.

A novel cutting force modelling method for cylindrical end mill

This paper proposes a new and simplified method for the calibration of cutting force coefficients and cutter runout parameters for cylindrical end milling using the instantaneous cutting forces measured instead of average ones. The calibration procedure is derived for a mechanistic cutting force model in which the cutting force coefficients are expressed as the power functions of instantaneous uncut chip thickness (IUCT). The derivations are firstly performed by establishing mathematical relationships between instantaneous cutting forces and IUCT. Then, nonlinear algorithms are proposed to solve the established nonlinear contradiction equations. The typical features of this new calibration method lie in twofold. On the one hand, all derivations are directly based on the tangential, radial and axial cutting force components transformed from the forces which are measured in the workpiece Cartesian coordinate system. This transformation makes the calibration procedure very simple and efficient. On the other hand, only a single cutting test is needed to be performed for calibrating the cutting force coefficients that are valid over a wide range of cutting conditions. The effectiveness of the proposed method in developing cutting force model is demonstrated experimentally with a series of verification cutting tests.

Extracting cutting constants via harmonic force components for a general helical end mill

Mechanistic cutting constants serve well in predicting milling forces, monitoring the milling process as well as in helping to understand the mechanistic phenomena of a machining process for a unique pair of workpiece and cutter materials under various types of cutting edge geometry. This paper presents a unified approach in identifying the six shearing and ploughing cutting constants for a general helical end mill from the dynamic components of the measured milling forces in a single cutting test. The identification model is first presented assuming the milling force is measured with a known phase angle of the cutter spindle. When the phase angle of the cutter rotation is not available, as is the case for most milling machines, it is shown that the true phase angle can be identified through the theoretical phase relationship between the different harmonic components of the milling forces measured with an arbitrary phase angle. The numerical simulation and the experimental results for ball and cylindrical end mills are presented to demonstrate and validate the identification methods.

Mechanistic identification of specific force coefficients for a general end mill

The paper presents expressions for semi-empirical mechanistic identification of specific cutting and edge force coefficients for a general helical end mill from milling tests at an arbitrary radial immersion. The expressions are derived for a mechanistic force model in which the total cutting force is described as a sum of the cutting and edge forces. Outer geometry of the end mill is described by a generalized mathematical model valid for a variety of end mill shapes, such as cylindrical, taper, ball, bull nose, etc. The derivations follow a procedure originally proposed for a cylindrical end mill. The procedure itself is improved by including the helix angle in evaluation of the average edge forces. The resulting expressions for the specific force coefficients are verified by simulations and experiments.

A New Tool-Path Generation Method Using a Cylindrical End Mill for 5-Axis Machining of a Spatial Cam with a Conical Meshing Element

The geometry of a spatial cam is normally generated using a form-milling cutter and a special multi-axis machine and software. The general purpose CAD/CAM software can generate the cutter location file of this class of product only by the sculpturing method. Because of the limited choice of cutting tool when using the generating method, this paper presents a new toolpath generating method which combines the advantages of the generating and sculpturing methods for machining a spatial cam. In the machining process, the cutter location is derived for rough and finish machining using a cylindrical end mill. The guidelines for choosing cutter diameter for the machining process are discussed. To avoid interference, the principal curvatures and the principal induced normal curvatures are analysed. The mathematical errors including chordal deviation and scallop height are used as the basis for generating appropriate tool-paths. Cutting simulation of a solid model was performed to verify the proposed tool-path generation method.