Identification Of Force Coefficients Research Articles

Assessment of cutting force coefficient identification methods and force models for variable pitch and helix bull-nose tools

The mechanistic approach is commonly implemented to predict and optimise the cutting forces in milling processes to prevent tool breakages, reduce tool wear, reduce form error, and improve surface quality. To implement this method, the cutting force coefficients (CFCs), that characterise the mechanics of the process, must be calculated. This study compares the accuracy of the predicted cutting forces for variable pitch and helix bull-nose milling tools using a rapid testing (RT) optimisation-based mechanistic CFC identification method that only requires a single angular cut with increasing radial engagement to the traditional mechanistic approach that requires several straight cuts. Along with developing a hybrid technique that combines variation in feed rate and radial engagement. The traditional radial, tangential, and axial (RTA) force model is also compared with the frictional and normal rake face (UV) force model that is independent of the local tool rake and inclination angles which is a necessary for bull nose tools. The RT and the developed hybrid CFC identification method with the UV force model predicted the average Fx, Fy and Fz cutting forces to within 7.1 %, 4.3 %, and 3.8 % error, respectively. These methods were slightly less accurate than the traditional method, however they have significant industrial benefits because they have can be used to identify CFCs with either a single cut, or from any tool-path with chip-load variation, respectively. The RTA force model predicted the average cutting forces similarly to the UV force model, however, the UV force model had lower errors using the rapid RT testing method at the extreme corners of the experimental design space.

Identification of Dynamic Force Coefficients for an Additively Manufactured Hermetic Squeeze Film Bearing Support Damper Utilizing a Pass-Through Channel

Abstract The following paper presents breakthrough experimental results for a new hermetic squeeze film damper (HSFD) concept that is integrally designed within an externally pressurized tilting-pad radial gas bearing support. The flexibly damped gas bearing module was designed for a 7.2″ (183 mm) diameter shaft and fabricated using direct metal laser melting (DMLM); also known as additive manufacturing. The bearing and HSFD were sized based on ongoing studies for oil-free supercritical carbon dioxide (sCO2) power turbines in the 8.5 MW–10 MW power range. The development of the new damper concept was motivated by past dynamic testing on HSFD, which generated frequency-dependent stiffness and damping force coefficients. In efforts to eliminate the frequency dependency, a new HSFD architecture was conceived that adds accumulator volumes and a pass-through channel to previously conceived HSFD flow network designs. The other motivation for the work is the need to develop a cost-effective and reliable oil-free bearing technology that is scalable to large power turbomachinery applications. There were several objectives for the following work. The first objective was to successfully design and fabricate a single piece bearing-damper using additive manufacturing, while dimensionally controlling critical design features. The paper discusses the manufacturing steps and shows cut-ups that reveal adequate clearance control capability with internal damper clearances. The second objective was to perform experimental testing with the new HSFD design in efforts to extract stiffness and damping coefficients for excitation frequencies within 20–160 Hz and peak vibration amplitudes between 0.25 mils (6.35 microns) to 1 mil (25.4 microns). The test results for a single HSFD bearing module indicated that the design modifications to the HSFD architecture were successful in eliminating nearly all the frequency dependencies for the stiffness force coefficient. The dynamic tests yielded a stiffness coefficient that varied between 112 klb/in. (19.6 MN/m) and 96 klb/in. (16.8 MN/m). The damping force coefficient however, exhibited relatively more variation with frequency with values residing between 175 lb-s/in. (31 kN-s/m) to 214 lb-s/in. (37 kN-s/m). Finally, the paper advances a three-dimensional fluid-structure interaction (FSI) model using transient finite element analysis (FEA) coupled to a computational fluid dynamics (CFD) model. The FSI analysis performed between 20 Hz and 80 Hz was used to predict the stiffness and damping of the HSFD using a quarter-section model of the damper. The FSI analysis was able to support test results by showing only a 6–7.4% change in the magnitude of force coefficients. Stiffness predictions agree reasonably well with experiments whereas damping is underpredicted.

Dynamics modeling and simultaneous identification of force coefficients for variable pitch bull-nose cutter milling considering process damping and cutter runout

Dynamics modeling and simultaneous identification of force coefficients for variable pitch bull-nose cutter milling considering process damping and cutter runout

An optimized milling force prediction method for multi-axis ball-end finish milling

By accurately predicting milling force in finish milling, simulation of the milling process can be effectively conducted, followed by the provision of effective recommendations on optimization of machining process parameters. The prediction of ball-end milling force poses a significant challenge due to the influence of the cutter workpiece engagement (CWE) calculation and cutting force coefficient identification. This paper proposes a precise approach for predicting milling force, which involves an improved calculation method of CWE and an optimized identification approach for cutting force coefficients based on a mechanistic model. In the calculation of CWE, an optimization method considering the dynamic change of undeformed slice thickness and CWE boundary calculation is proposed. Furthermore, an improved approach incorporating interference signal removal and multiple nonlinear regression fitting methods is utilized for cutting force coefficient identification. Subsequently, the resulting prediction is validated through comparison with measurements and demonstrates a prediction accuracy exceeding 94%. The conclusion drawn is that the proposed prediction method for multi-axis ball-end finish milling force exhibits high accuracy in its predictions.

Mechanistic force model for double-phased high-feed mills

Being able to predict cutting forces, torque and power in machining applications allows to check their influence on the quality of the product, to assess the feasibility of the process and to compare different operations for sustainability purposes. In this paper, the analytical development of a mechanistic model for cutting forces prediction for high-feed mills is carried out. High-feed cutters are featured by extremely low lead angles, leading to a gradual engagement of the cutter inside the workpiece. This fact prevents the mechanistic literature formulation to accurately compute the undeformed instantaneous chip section of each cutter, and thus to correctly predict the spindle torque and power. A closed analytical formulation for the mechanistic cutting force model, including an improved chip thickness formulation with variable entry and exit angles and double-phased cutter geometry, is presented. Experimental cutting tests using double-phased high-feed mills were carried out on Ti6Al4V with variable feed rate per tooth, cutting speed and axial depth of cut. The model was assessed by comparing the performances of the literature model and the developed high-feed one in the identification of specific force coefficients — SFC. The identified SFC resulted to belong to two statistically different populations. SFC 95% confidence intervals were found to be significantly narrower with respect to the literature ones. Kt,c 95% confidence intervals were equal to (1085; 1426) MPa and (970; 2423) MPa for the proposed and literature model, respectively. The validity of the proposed model was assessed in terms of mean forces, mean spindle torque and mean spindle power prediction capabilities. The Root Mean Squared Prediction Error for the proposed model resulted to be remarkably lower (15 N, 0.33 Nm, 29 W) with respect to literature model (41 N, 1.25 Nm, 120 W).

Mill condition monitoring based on instantaneous identification of specific force coefficients under variable cutting conditions

Following the necessity of increased performance and availability requirements for manufacturing systems, research is becoming more and more attracted by monitoring solutions for cutting tools. In this paper, a robust unsupervised strategy for milling tool wear monitoring under variable process parameters and lubrication conditions is presented. The proposed method is completely unsupervised, thus not requiring any kind of training procedure, and is validated on different machine tools. The solution is based upon the online estimation of specific force coefficients (SFC) from instantaneous cutting forces in high-feed milling of Ti6Al4V workpiece. This avoids the need for continuously variable feed per tooth during cutting tests, necessitated for the application of reference literature approach. For this purpose, a novel high-feed mill mechanistic model was conceived and developed. Five run-to-failures were performed in different lubrication conditions – cryogenic and traditional lubrication – with different cutting speeds (50 m/min, 70 m/min and 125 m/min) on two different machine tools. Principal Component Regression was introduced in order to deal with the variability of the estimated coefficients. Self-starting tabular cusum control charts were implemented and demonstrated high accuracy and reliability in the prediction of notch wear phenomena as well as chipping of tool cutting edges for all the cases considered. The solution detected an out-of-control conditions ranging from 166μm to 499μm of maximum flank wear for the analysed tests. The mean prediction error with respect to the 600μm threshold is of −45% with a peak of −72%, whereas reference literature algorithms reach −57% and −66%, respectively. A sensitivity analysis of control chart threshold was performed with reference to the maximum flank wear at the detection point. In a supervised scenario, the threshold can be increased to obtain a less conservative approach: for instance, a mean prediction error of −41% was reached by doubling the threshold.

METHOD FOR SAFE EXPERIMENTAL TESTING OF MACHINE TOOL USABLE SPINDLE POWER

The regenerative chatter during milling is a consequence of the machine tool dynamic compliance and the specific setting of the cutting process. The basic request on the machine structure is to enable a stable cut with dominant portion of the installed spindle power. In order to improve the dynamic properties of newly-designed machine tools, the machine tool structures are optimized using various advanced simulation methods and are made of various advanced materials. The final design should be tested experimentally. The test of usable spindle power provides important feedback on the machine tool design. The testing of large machine tools is time consuming due to the significantly varying machine dynamic compliance dependent on the working space. Due to the installed high power and large diameter tools used, the occurrence of chatter might be dangerous with a high risk of machine tool damage. The article presents a method for the safe and time-effective experimental testing of the machine tool usable spindle power. The method is based on the experimental identification of the cutting force coefficients and the experimental identification of machine tool behavior with the support of extrapolation models based on identified experimental data. The dynamic compliance is measured within a rough network of measurement points in the machine working space. The measured dynamic compliance results are characterized by a model based on modal identification data. Only a few cutting tests are done for the cutting force coefficient identification. Finally, a map of the usable spindle power is calculated. This approach makes it possible to calculate the results with respect to the real machining process and the current machine tool conditions across the whole working space in an acceptable time. The approach is demonstrated on a real case study.

Micro-milling tool wear monitoring under variable cutting parameters and runout using fast cutting force coefficient identification method

Extracting discriminative tool wear features is of great importance for tool wear monitoring in micro-milling. However, due to the dependency on tool runout and cutting parameters, the traditional tool wear features are incompetent to monitor the tool wear condition in micro-milling with significant tool runout and varied cutting parameter interactions. In this study, micro-milling cutting force is represented by a parametric model including variable cutting parameters, tool runout, and tool wear. The cutting force coefficient in the model, which is not only discriminative to the tool wear condition but also independent to the tool runout and cutting parameters, is extracted as the micro-milling tool wear feature. To reduce the computation cost, a fast neural network–based method is proposed to identify the tool runout and the cutting force coefficient from the cutting force signal. Experimental results show that the proposed cutting force coefficient–based approach is efficient to monitor the micro-milling tool wear under varied cutting parameters and tool runout.

Gaussian approach–based cutting force coefficient identification for flat-end milling operation

The identification of appropriate empirical relationships between cutting force coefficients and the uncut chip area is crucial for the successful implementation of mechanistic models in estimating cutting forces for flat-end milling operation. The derivation of empirical relationships necessitates machining experiments to record cutting force components under diverse conditions. The experimental data collected from force sensors (mainly dynamometers) contains outliers and noise that deteriorate the goodness of fit and thereby prediction accuracy of the model. This paper presents an application of the Gaussian approach to refine experimentally measured force data by systematically eliminating outliers and noise, followed by the use of pre-processed data to derive empirical relationships. The proposed methodology is implemented in the form of a computational tool to eliminate irrational data points automatically and obtain meaningful cutting force coefficients relationships using regression models. The outcomes of the study are substantiated further by conducting a set of experiments over a wide range of cutting conditions. The root mean square error (RMSE) of measured and predicted cutting forces is estimated for models with and without a data refining approach, which showed marked improvement in the prediction accuracy. Based on the outcomes of the present study, it can be concluded that the prediction ability of the mechanistic force model can be improved considerably with the augmentation of the Gaussian approach.

Modal parameter identification of general cutter based on milling stability theory

In the field of CNC milling, chatter has been a hot research topic, which is related to machining quality, precision and cost. Stability lobe diagram (SLD) reflects the vibration of the machining system under different process parameters and cutter axis vectors that is significant for optimization. The accurate dynamic characteristics of the machining system is the prerequisite for stability analysis. Finite element simulation is mainly aimed at small diameter cutter system, and accuracy is poor. The most widely used method is hammer test, but the equipment is expensive, the operation is too professional and it cannot reflect the dynamic characteristics of the machining system in working status. This paper proposes an undetermined coefficient method for the general cutter system to identify the modal parameters, that are the natural frequency, stiffness and damping ratio, just based on the very simple experiment of three-axis half-immersion milling in horizontal plane. Firstly, considering the exact in-cut cutting edge and the instantaneous cutting force coefficient corresponding to the axial factor and the chip thickness, the dynamic model of three-axis milling machining for the general cutter is established. Secondly, two implicit conditions of stable critical speed and cutting depth are derived based on feedback control theory in the frequency domain. Thirdly, the two sets of critical cutting depth and the chatter frequency under arbitrary speeds are obtained by using the dichotomy. With the method proposed in this paper, one of the two is used to solve a series of modal parameter sets, and the other of the two is used to extract the optimal modal parameters in the modal parameter sets. Finally, taking the identified modal parameters as known conditions to search the points one by one in the two-dimensional space composed of the rotational speed and the cutting depth, and judge whether it meets the critical conditions. SLD can be obtained by connecting the points that satisfy critical conditions together. Based on the previous experiment of flat-end cutter, it verified the feasibility of the modal parameter identification method in the paper. In the designed three-axis milling experiment of the ball-end cutter, the in-cut cutting edge simulation and the cutting force coefficient identification were carried out, and the modal parameters of the cutter system were also obtained successfully. The plotted lobe diagram was verified by the spectrum analysis result of the vibration signal collected by the acceleration sensor.

Identification of force coefficients in inter-shaft squeeze film dampers utilizing complex vector description and computational fluid dynamics

Squeeze film dampers (SFDs) have been widely used in high-speed turbomachinery to provide external damping to the system to improve stability. An inter-shaft damper (ISD) is a SFD-like device inserted between two shafts of a double spool aircraft engine to provide damping to both internal and external rotors. Compared to SFDs, analysis of ISDs is not well established because of added complexity of the mechanism. A new approach to model ISDs is reported in this paper, which converts an ISD model to a dynamically equivalent SFD model. A systematic analysis method for SFDs subjected to whirling motions of a non-circular orbit is established first because the whirling orbit of the equivalent SFD is always non-circular with two major frequency components. The analysis method utilizes complex vector descriptions of the motion and force, and frequency-domain analysis with double-sided frequency spectrums. The proposed approach is validated by comparing computational fluid dynamics (CFD) analysis results and damping coefficients obtained from the original ISD model and its equivalent SFD model. One significant advantage of the new approach is that all design rules and insights developed for SFDs can be directly applied to ISDs. In addition, the analysis method established in this work enables accurate calculation of damping coefficients of SFDs subjected to non-circular whirling motions, essentially all SFDs in in real operations including SFDs in test rigs.

Plane surface milling force prediction with fillet end milling cutter under pre-determined inclination angle

Fillet end milling is widely used in mould, aerospace, shipping manufacture and other fields. As one of the important parameter in milling machining, milling force is related to machining efficiency and quality, as well as tool wear, but it is difficult to predict. Aiming at fillet end milling under a pre-determined inclination angle, considering cutter run-out, this paper presents a cutting force coefficients identification model related to chip thickness and axial position angle, and then achieve milling force prediction. A parametric relationship among feed direction, cutter axis and to-be-machined surface are established, and then, the analytic expression of previous swept surface, to-be-machined surface and cutter envelope surface is derived. Boundary curves of cutter workpiece engagement (CWE) are established based on spatial surface intersection analytically. The criterion of the cutter edge element involved in cutting is proposed. Judging element along the cutter edge one by one, whereafter the algorithm of in-cut-cutting edge (ICCE) is proposed. Combining mechanical force model with chip thickness considering feed direction and cutter run-out, a milling force prediction model is established. Based on the method of undetermined coefficients, combining average instantaneous measured force, coefficients corresponding to axial position angle and chip thickness are solved. Further instantaneous peak measured force is used to obtain cutter run-out parameters. Simulation and experiments show that CWE agrees well with that of experiment and ICCE is consistent well with that of simulation. Milling force experiments of different machining parameters show the milling force coefficients and run-out parameters can be applied to fillet end milling under pre-determined inclination angle well.

A chatter mitigation technique in milling based on H∞-ADDPMS and piezoelectric stack actuators

Chatter is a kind of self-excited vibration which may occur in the milling process and has several negative effects such as poor surface quality and severe tool wear. This paper presents an active chatter control method based on H∞ almost disturbance decoupling problem with measurement feedback and with internal stability (H∞-ADDPMS) and piezoelectric stack actuators. First, a milling process model considering regenerative effect is constructed to find out the milling conditions when chatter occurs. Then, the whole active control system and constructing procedure of an active controller based on H∞-ADDPMS is proposed. Next, the milling process is simulated and the H∞-ADDPMS controller is calculated based on cutting force coefficient identification, frequency response experiments, and modal analysis technique. Finally, the active control experiment is carried out on a computer numerical control (CNC) milling machine to verify the feasibility and effectiveness of the proposed active control strategy.

An identification model of cutting force coefficients for five-axis ball-end milling

Five-axis ball-end milling is widely used in energy, ship, aerospace, and other fields. As one of the difficulties in milling research, milling force is often critical to the processing efficiency and quality of part. For predicting the milling force of the five-axis ball-end milling better, this paper presents a cutting force coefficients identification model which is related to the instantaneous chip layer thickness and axial position angle considering the cutter run-out. For five-axis ball-end milling of the oblique plane, the relationship of feed direction, cutter axis vector, and machined surface is parameterized. The boundary curves of cutter workpiece engagement (CWE) are determined by intersecting spatial surfaces. The boundary curves are discretized, and an algorithm of in-cut cutting edge (ICCE) is proposed by defining the distance between discrete points and the cutting edge. Combining the instantaneous chip thickness considering arbitrary feed direction and cutter run-out, the five-axis milling force model of ball-end mill is established. Based on the undetermined coefficient method and the instantaneous average milling force of teeth, the cutting force coefficients identification model corresponding to the instantaneous chip layer thickness and the axial position angle is established. Furthermore, cutter run-out parameters are obtained combined with instantaneous measured milling force of single tooth. The experimental and simulation examples demonstrate that the CWE determined by the spatial surfaces is consistent with the experimental results. The ICCE is in good agreement with the simulation results based on the solid modeling method. A large number of milling experiments under different processing parameters show that the cutting force coefficients and cutter run-out parameters identification model can be effectively applied to five-axis ball-end milling.

Analytical Calculation of Cutting Forces in Ball-End Milling with Inclination Angle

The traditional analytical cutting force prediction method for ball-end milling ignores the effect of the inclination angle on cutting forces. In this paper, a new experimental method for cutting force prediction methods considering the inclination angle in the ball-end milling process is proposed. First, the actual immersion ranges of cutter in the ball-end milling process with and without an inclination angle are analyzed by a geometrical method and the cutting force prediction model with an inclination angle is developed by a numerical integration method. Second, considering that entry and exit angles of cutting zones for different cutter layers vary due to the inclination angle, a milling force coefficients identification approach for different cutter layers is established by experimental calibration. Comparing the traditional analytical cutting force prediction method that ignores the inclination angle, the numerical simulation results show that the prediction force values calculated by the proposed method have a better consistency with the measured values.

On-line cutting force coefficients identification for bull-end milling process with vibration

The foundation of newest cutting forces models still is cutting force coefficients that represent material behaviors. They are combined with cutter-workpiece contact algorithms, material properties and so on in the model to accomplish the prediction. Even though cutting force coefficients are significant, identification methods are still involved with onerous experiments, over-idealized measurement conditions, serious results fluctuation caused by many unquantifiable factors. To enlarge cutting database for the optimization of cutting process, utilizing the abundant real-time process monitoring data is a possible choice, in which novel identification methods are needed. To settle this problem, this paper proposed an online identification method considering stiffness property of cutter-holder-spindle system. This investigation considers the fluctuation of cutting forces caused by cutter vibration in two steps: First, a cutting force model that is combined with dynamic undeformed chip thickness is built for bull-end milling. Second, on the foundation of previous step, a corresponding identification method is developed, in which the dynamic undeformed chip thickness is obtained using measured data and utilized in cutting force coefficient identification. The comparison of experimental results and predicting results proves the reliability of cutting force model. Under different conditions, the application of identification method output promising results. In this section, the results show that it is possible to use new method in realizing real-time identification and eliminating machine tool stiffness effect. Also, the shortcomings of the method and the potential improvements are discussed.

A comparative study on the cutting force coefficient identification between trochoidal and slot milling

Cutting force modeling is of great importance to understanding the mechanistic behavior of the milling process. Through the understanding of cutting forces the potential for process improvement by way of tool life, surface finish, dimensional accuracy and machining time is opened. The basis for establishing cutting force models lies in the method of gathering cutting force coefficients, of which literature has two main approaches, both of which occur under full engagement: linear-direction slotting cuts. The geometry of the uncut chip has a strong dependency on the toolpath, particularly for trochoidal milling techniques, where the chips do not exhibit the repeating and somewhat invariant thickness profile that occurs in slotting. Gathering cutting force coefficients for trochoidal milling remains largely unexplored and is the focus of this paper, particularly to establish an understanding of cutting parameters and coefficient values among different toolpath techniques. It was found that matching the tool feed and speed between trochoidal and slotting toolpaths produces large differences, which are reduced when using slotting parameters based on trochoidal milling chip geometry conditions, with the closest agreement resulting from matching the maximum chip thicknesses. Furthermore, the method of gathering coefficients produces similar results between single and double flute trochoidal, which are both less than the coefficients resulting from slotting tests.

Upgraded stability analysis of milling operations by means of advanced modeling of tooling system bending

The problem of undesired self-excited chatter vibrations in milling is very common. However, only in the last two decades some significant achievements for the theoretical understanding of this intricate phenomenon have been accomplished. Nevertheless, state of the art dynamic models are still not able to completely explain milling dynamics and chatter onset during some conventional milling operations performed by conventional cutting tools. In this research work, a revolutionary model of tooling system dynamics and of the regenerative effect in milling will be presented. The new model introduces a significant correction to the predicted stability borders when the cutter diameter is relatively large in comparison with tooling system overhang and when curved or inclined cutting edges are applied. Accordingly, the new approach may be of great interest for many industrial applications. The model has been successfully validated by performing experimental modal analysis, cutting force coefficient identification and stability lobes diagram determination, through many specific cutting tests. In the considered case study, where the afore mentioned geometrical features of the tooling system were still moderate, a significant shift of the stability borders of about +25% was experimentally observed and correctly predicted by the new approach.

Milling Force Coefficient Identification of Ball-End Milling Based on Instantaneous Milling Forces

Milling Force Coefficient Identification of Ball-End Milling Based on Instantaneous Milling Forces

Determining cutting force coefficients from instantaneous cutting forces in ball end milling

The precise prediction of cutting forces helps in improving the machining performances. This involves the modelling of cutting force components in tangential, radial and axial directions and determination of respective specific cutting force coefficients. In the present work, an improved method of identification of specific cutting force coefficient is proposed for ball end milling cutter using semi-mechanistic force model. The cutter is discretised into a finite number of axial discs along the axis of the cutter. Using the geometry of ball end milling cutter, true uncut chip thickness is modelled based on the trochoidal trajectory of a cutting edge element. Specific cutting force coefficients have been determined through inverse method. Also, a fourth order polynomial curve fitting method has been employed to establish a mathematical relationship between the said coefficients and axial depth of cuts. Several experiments have been carried out at different feed rate and axial depth of cut to determine the specific cutting force coefficients based on the proposed identification method. Validation results show good agreement between predicted and experimental results. Compared to conventional identification model, the specific force coefficient identification process discussed in the present paper is fast, convenient and accurate.