Identification Of Cutting Force Coefficients Research Articles

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.

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.

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.

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.

Speed-varying cutting force coefficient identification in milling

Accurate simulation of the machining process is crucial to improve milling performance, especially in High-Speed Milling, where cutting parameters are pushed to the limit.Various milling critical issues can be analyzed based on accurate prediction of cutting forces, such as chatter stability, dimensional error and surface finish. Cutting force models are based on coefficients that could change with spindle speed. The evaluation of these specific coefficients at higher speed is challenging due to the frequency bandwidth of commercial force sensors. On account of this, coefficients are generally evaluated at low speed and then employed in models for different spindle speeds, possibly reducing accuracy of results.In this paper a deep investigation of cutting force coefficient at different spindle speeds has been carried out, analyzing a wide range of spindle speeds: to overcome transducer dynamics issues, dynamometer signals have been compensated thanks to an improved technique based on Kalman filter estimator. Two different coefficients identification methods have been implemented: the traditional average force method and a proposed instantaneous method based on genetic algorithm and capable of estimating cutting coefficients and tool run-out at the same time.Results show that instantaneous method is more accurate and efficient compared to the average one. On the other hand, the average method does not require compensation since it is based on average signals. Furthermore a significant change of coefficients over spindle speed is highlighted, suggesting that speed-varying coefficient should be useful to improve reliability of simulated forces.

Cutting torque and tangential cutting force coefficient identification from spindle motor current

This article presents an enhanced methodology for cutting torque prediction from the spindle motor current, readily available in modern machine tool controllers. This methodology includes the development of the spindle power model which takes into account all mechanical and electrical power losses in a spindle motor for high-speed milling. The predicted cutting torque is further used to identify tangential cutting force coefficients in order to predict accurately the cutting forces and chatter-free regions for milling process planning purposes. The developed model is compared with other studies available in the literature, and it demonstrates significant improvements in terms of the completeness and accuracy achieved. The developed model is also validated experimentally, and the obtained results show good compliance between the predicted and the measured cutting torque. The developed enhanced procedure is very appealing for industrial implementation for cutting torque/force monitoring and tangential cutting force coefficient identification.