Experimental studies of cutting force variation in face milling

The purpose of this paper is to present a developed cutting force model for multi-toothed cutting processes, including a complete set of parameters influencing the cutting force variation that has been shown to occur in face milling, and to analyse to what extent these parameters influence the total cutting force variation for a selected tool geometry. The scope is to model and analyse the cutting forces for each individual tooth on the tool, to be able to draw conclusions about how the cutting action for an individual tooth is affected by its neighbours.A previously developed cutting force model for multi-toothed cutting processes is supplemented with three new parameters; eccentricity of the spindle, continuous cutting edge deterioration and load inflicted tool deflection influencing the cutting force variation. A previously developed milling force sensor is used to experimentally analyse the cutting force variation, and to give input to the cutting force simulation performed with the developed cutting force model.The experimental results from the case studied in this paper show that there are mainly three factors influencing the cutting force variation for a tool with new inserts. Radial and axial cutting edge position causes approximately 50% of the force variation for the case studied in this paper. Approximately 40% arises from eccentricity and the remaining 10% is the result of spindle deflection during machining. The experimental results presented in this paper show a new type of cutting force diagrams where the force variation for each individual tooth when two cutting edges are engaged in the workpiece at the same time. The wear studies performed shows a redistribution of the individual main cutting forces dependent on the wear propagation for each tooth.     

Bandsawing. Part II: detecting positional errors, tool dynamics and wear by cutting force measurement

This article presents a method for measuring individual cutting forces during bandsawing. Methods for detecting errors in cutting edge positions, tool dynamics during machining and geometry changes due to wear have also been developed. The experimental studies that we have conducted show that the cutting forces vary during the tool engagement. These variations in force were then quantified using a previously developed cutting force model for multi-tooth cutting processes including effects of positional errors, tool dynamics and wear.     

A cutting force model for face milling operations

A procedure for the simulation of the static and dynamic cutting forces in face milling is described. For the static force model, the initial position errors of the inserts and the eccentricity of the spindle are taken into consideration as the major factors affecting the variation of the chip cross-section. The structural dynamics model for the multi-tooth oblique cutting operation is assumed as a multi-degrees of freedom spatial system. From the relative displacement of this system, based on the double modulation principle, the dynamic cutting forces were derived and simulated. The simulated forces were subsequently compared to measured forces in the time and frequency domains.     

Bandsawing. Part I: cutting force model including effects of positional errors, tool dynamics and wear

This article presents a mechanical cutting force model for bandsawing. The model describes the variation in cutting force between individual teeth and relates it to initial positional errors, tool dynamics and edge wear. Bandsawing is a multi-tooth cutting process, and the terminology of the cutting action is discussed and compared with other cutting processes. It will also be shown that the setting pattern and the preset feed govern the cutting data.     

A cutting force model for finishing processes using helical end mills with significant runout

Analytical cutting force models play an important role in a wide array of simulation approaches of milling processes. The accuracy of the simulated processes directly depends on the predictive power of the applied cutting force model, which may vary under specific circumstances. End milling processes with small radial cutting depths, e.g. finishing processes, are particularly problematic. In this case, the tool runout, which is usually neglected in established cutting force models, can become quite significant. Within this article, well-known cutting force models are implemented for runout-prone finishing processes and modified by integrating additional parameters. A method is presented for how these additional runout parameters can be efficiently determined alongside commonly used cutting coefficients. For this purpose, a large number of milling experiments have been performed where the cutting forces were directly measured using a stationary dynamometer. The measured cutting forces were compared with the simulated cutting forces to verify and assess the modified model. By using the presented model and calibration method, cutting forces can be accurately predicted even for small radial cutting depths and significant tool runout.     

Dynamic Compensation of Spindle-Integrated Force Sensors

This paper presents a dynamically compensated Spindle-Integrated Force Sensor system to measure cutting forces. Piezo-electric force sensors are integrated into the stationary spindle housing to measure cutting forces in three directions. The transfer function of the spindle structure between the cutting forces acting on the tool tip and the measured forces at the spindle housing are identified. Using the cutting force signals measured at the spindle housing, a Kalman filter is designed to filter the influence of structural modes on the force measurements. The frequency bandwidth of the force measurement system is significantly increased with the proposed sensor and the signal processing method. Milling experiments with tooth passing frequencies up to 1000 Hz are presented with effective removal of cutting force distortions caused by three structural modes of the spindle.     

Turning of glass–fiber reinforced plastics materials with chamfered main cutting edge carbide tools

In this paper, the machinability of high-strength glass–fiber reinforced plastics (GFRP) materials in turning with chamfered main cutting edge of P and K type carbide tools have been investigated experimentally. Chip formation mechanisms have been obtained with respect to tip's geometries and nose radii. Experimental results for cutting forces were also taken with GFRP as the workpiece material. Force data from these tests were used to estimate the empirical constants of the mechanical model and verify its prediction capabilities. The results show good agreement between the predicted and measured forces. In this study, the nose radius R = 0.3 mm induces a decrease of the cutting force and the smallest cutting force values was achieved in the case of C_s = 20°, _S1(_S2) = −10°(10°) and R = 0.3 mm. Comparing the different P and K type of tools, K type tool is better than P type of chamfered main cutting edge tools. The theoretical values of cutting forces were calculated and compared with the experimental results; the forces predicted by this model were consistent with the experimental values.     

Why is it hard to identify the onset of chatter? A stochastic resonance perspective

A stochastic dynamical model is presented to identify the difficulties in chatter detection during cutting processes. The theoretical implications are based on measurements related to the stochastic character of the cutting force. The stochastic model is validated in a Hardware-In-the-Loop (HIL) environment where the multiplicative component of the stochastic cutting force is varied parametrically. In case of an industrial machine tool, the stochastic resonance effect is also demonstrated quantitatively by means of high-resolution vibration measurements for various spindle speeds in full immersion milling. The proposed method predicts the noise induced peaks in the spectrum of the vibration signals, which occur already within the chatter-free parameter domains and might be misjudged as chatter.     

Milling force convolution modeling for identification of cutter axis offset

This paper discusses the application of a convolution integral force model to the identification of the geometry of cutter axis offset in milling operations. This analysis builds upon the basis of linear decomposition of elemental local cutting forces into a nominal component and an offset-induced component. The convolution of each elemental local cutting force component with the chip width density in the context of cutter angular position provides an integral expression for the total cutting forces. By virtue of the convolution integration property, the total cutting forces in the frequency domain can be derived as closed-form functions of the cutting pressure constants, various cutting conditions, as well as the cutter offset geometry. Subsequently, the magnitude and phase angle of cutter axis offset are shown to be algebraic and explicit functions of the Fourier series coefficients of cutting forces at the spindle frequency. Following the theoretical analysis, experimental study is discussed to illustrate the implementation procedure for offset identification, and frequency domain data are presented to verify the analytical results. Potential industrial applications of this work include the real-time monitoring of dynamic cutter runout and the in-process compensation for the loss of tolerance or finish using automatic controls based on the feedback information of offset magnitude and phase angle.     

Predictive cutting force model in complex-shaped end milling based on minimum cutting energy

A force model is presented to predict the cutting forces and the chip flow directions in cuttings with complex-shaped end mills such as ball end mills and roughing end mills. Three-dimensional chip flow in milling is interpreted as a piling up of the orthogonal cuttings in the planes containing the cutting velocities and the chip flow velocities. Because the cutting thickness changes with the rotation angle of the edge in the milling process, the surface profile machined by the previous edge inclines with respect to the cutting direction. The chip flow model is made using the orthogonal cutting data with taking into account the inclination of the pre-machined surface. The chip flow direction is determined so as to minimize the cutting energy, which is the sum of the shear energy on the shear plane and the friction energy on the rake face. Then, the cutting force is predicted for the chip flow model at the minimum cutting energy. The predicted chip flow direction changes not only with the local edge inclination but also with the cutting energy consumed in the shear plane cutting model. The cutting processes with a ball end mill and a roughing end mill are simulated to verify the predicted cutting forces in comparison with the measured cutting forces.     

High frequency bandwidth cutting force measurement in milling using capacitance displacement sensors

This article presents a method of measuring cutting forces from the displacements of rotating spindle shafts. A capacitance displacement sensor is integrated into the spindle and measures static and dynamic variations of the gap between the sensor head and the rotating spindle shaft under cutting load. To calibrate the sensing system, the tool is loaded statically while the deflection of the tool is measured with the capacitance probe. With this calibration, the displacement sensor can be used as an indirect force sensor. However, the measurement bandwidth is limited by the natural modes of the spindle structure. If cutting force frequency contents are within the range of the natural modes of the spindle structure or higher, the measurements are distorted due to the dynamic characteristics of the spindle system. In order to increase the bandwidth of the indirect force sensor by compensating for the spindle dynamics, the design of a Kalman filter scheme, which is based on the frequency response function (FRF) of the displacement sensor system to the cutting force, is presented in this paper. With the suggested sensing and signal processing method, the frequency bandwidth of the sensor system is increased significantly, from 350 to approximately 1000 Hz. The proposed indirect force sensor system is tested experimentally by conducting cutting tests up to 12,000 rpm with a five-fluted end mill. Besides cutting forces, the measured displacements can also be affected by factors such as roundness errors, unbalance at different speeds, or dilatation of the spindle shaft due to temperature variations. Methods to compensate for these disturbing effects are also described in the paper.     

Acceleration based indirect force measurement in metal cutting processes

A milling cutter instrumented with a three-component accelerometer is investigated as a sensor of dynamic cutting forces. Two major causes of measurement errors are considered. These causes are: (1) the flexible mode vibrations, and (2) inertial and viscous forces associated with the “rigid body” motion of the spindle. A self-tuning filter consisting of two subsystems is applied to attenuate these errors. The first subsystem converts accelerations from the rotating spindle into stationary coordinates. It also analyses the corrupted signal and calculates an optimal filter structure and the settings for the actual operating conditions. This information is utilized by the second subsystem, a digitally programmable filter, which performs signals correction in real time. Two examples are presented to illustrate performance of the proposed “natural” sensor. In the first example, a periodical force applied from an exciter is reconstructed from the accelerations measured during spindle rotation. The second example deals with estimation of a force impulse generated by means of an impact hammer.     

Cutting force modeling for flat end milling including bottom edge cutting effect

This study proposes a novel mechanistic cutting force model for flat end milling. The prominent feature of this model lies in that the overall cutting forces contributed by both the flank edge and the bottom edge cuttings are simultaneously taken into consideration. In the model formulation, to reflect the size effect in flank cutting, the flank cutting force coefficients are treated as an exponent function of instantaneous uncut chip thickness and are identified by nonlinear least-square algorithm. With the help of the calibrated flank cutting force coefficients, the bottom cutting force coefficients are instantaneously calibrated by the force component that is obtained by subtracting the flank force component from the total measured force. It is shown that the bottom cutting force coefficients can be treated as constants. The validity of the proposed cutting force model is also experimentally demonstrated over a relatively wide range of cutting conditions. It turns out that the bottom edge cutting has a remarkable effect on total cutting forces, when the axial depth of cut is relatively small.     

Static rigid force model for 3-axis ball-end milling of sculptured surfaces

Static rigid force model is used to estimate cutting forces of sculptured surface in a straightforward way, without considering tool deflection, machine tool dynamic behavior and any vibration effects. Two programs were used for calculations, “ACIS” the 3-D geometric modeler and “VISUAL BASIC”. Two programs were edited and used to perform the calculations, the scheme program to model the work piece, tool and cutting edge and to obtain the geometric data and the VISUAL BASIC program design to use ACIS geometric data to calculate the cutting forces. The engaged part of the cutting edge and work piece is divided into small differential oblique cutting edge segments. Friction, shear angles and shear stresses are identified from orthogonal cutting database available in literature. The cutting force components, for each tool rotational position, are calculated by summing up the differential cutting forces. Laboratory tests were conducted to verify the predictions of the model. The work pieces were prepared from CK45 steel using an insert-type ball-end cutter. No coolant was used in any of the experimental works. The cutting forces predicted have shown good agreement with experimental results.     

Adaptive cutting force control for a machining center by using indirect cutting force measurements

This paper presents an adaptive cutting force controller for the milling process, which can be attached to most commercial CNC machining centers in a practical way. The cutting forces of x, y and z axes are measured indirectly from the use of currents drawn by a.c. feed-drive servo motors. A typical model for the feed-drive control system of a horizontal machining center is developed to analyze cutting force measurement from the drive motor. The pulsating milling forces can be measured indirectly within the bandwidth of the current feedback control loop of the feed-drive system. It is shown that indirectly measured cutting force signals can be used in the adaptive controller for cutting force regulation. The robust controller structure is adopted in the whole adaptive control scheme. The conditions under which the whole scheme is globally convergent and stable are presented. The suggested control scheme has been implemented into a commercial machining center, and a cutting experiment on face milling process is performed.     

An analytical finite element technique for predicting thrust force and torque in drilling

An analytical finite element technique was developed for predicting the thrust force and torque in drilling with twist drills. The approach was based on representing the cutting forces along the cutting lips as a series of oblique sections. Similarly, cutting in the chisel region was treated as orthogonal cutting with different cutting speeds depending on the radial location. For each section, an Eulerian finite element model was used to simulate the cutting forces. The section forces were combined to determine the overall thrust force and drilling torque. Good agreement between the predicted and measured forces and torques was found in orthogonal and oblique cutting and in drilling tests. The drilling tests were performed on AISI 1020 for several drill diameters, spindle speeds, and feed rates. An extension of the technique for predicting drill temperatures has also been described.     

圆片刀超声切削蜂窝芯材料试验研究

为提高加工Nomex蜂窝芯材料的质量和效率,采用试验方法对超声切割时的切削力进行测量,研究其影响因素和变化规律,并对切削后蜂窝芯的表面进行观察。使用回归分析法分析不同振幅和切削深度下的切削力,推导切削力的经验公式。结果显示:切削力F_y,F_z与切削深度a_p,圆片刀底部边缘处振幅A呈指数关系。通过对比切削力拟合结果和试验数据,发现误差在10%内。切削后蜂窝芯表面平整、毛刺更少。      

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.     

Cutting force prediction of sculptured surface ball-end milling using Z-map

The cutting force in ball-end milling of sculptured surfaces is calculated. In sculptured surface machining, a simple method to determine the cutter contact area is necessary since cutting geometry is complicated and cutter contact area changes continuously. In this study, the cutter contact area is determined from the Z-map of the surface geometry and current cutter location. To determine cutting edge element engagement, the cutting edge elements are projected onto the cutter plane normal to the Z-axis and compared with the cutter contact area obtained from the Z-map. Cutting forces acting on the engaged cutting edge elements are calculated using an empirical method. Empirical cutting mechanism parameters are set as functions of cutting edge element position angle in order to consider the cutting action variation along the cutting edge. The relationship between undeformed chip geometry and the cutter feed inclination angle is also analyzed. The resultant cutting force is calculated by numerical integration of cutting forces acting on the engaged cutting edge elements. A series of experiments were performed to verify the proposed cutting force estimation model. It is shown that the proposed method predicts cutting force effectively for any geometry including sculptured surfaces with cusp marks and a hole.     

Identification of the specific cutting force for geometrically defined cutting edges and varying cutting conditions

Cutting force modeling is a major discipline in the research of cutting processes. The exact prediction of cutting forces is crucial for process characterization and optimization. Semi-empirical and mechanistic force models have been established, but the identification of the specific cutting force for a pair of tool and workpiece material is still challenging. Existing approaches are depending on geometrical idealizations and on an extensive calibration process, which make practical and industrial application difficult. For nonstandard tools and five axis kinematics there does not exist a reasonable solution for the identification problem.In this paper a co-operative force model for the identification of the specific cutting forces and prediction of integral forces is presented. The model is coupled bidirectionally with a multi-dexel based material removal model that provides geometrical contact zone information. The nonlinear specific forces are modeled as polynomials of uncut chip thickness. The presented force model is not subjected to principal restrictions on tool shape or kinematics, the specific force and phase shift are identified with help of least square minimization. The benefit of this technique is that no special calibration experiments are needed anymore, which qualifies the method to determine the specific forces simultaneously during the machining process. In this paper, experiments with different cutting conditions are analyzed and systematically rated. Finally, the method is validated by experiments using different cutting conditions.