Mechanistic Force Model Research Articles

Modeling modulated tool path turning using coupled smoothed particle hydrodynamics and finite element method

This paper describes a full-scale, three-dimensional coupled smoothed particle hydrodynamics (SPH) and finite element model for modulated tool path (MTP) turning. The chip breaking mechanism due to modulated motion of the tool is demonstrated by the developed machining model. In contrast, the simulation of conventional turning with the same machining conditions predicts long continuous chips. The cutting force predicted by the simulation is validated with a mechanistic force model based on the instantaneous chip thickness. This work expands the capabilities of machining simulations to predict complex machining phenomena such as MTP turning through a full-scale realistic simulation. The encouraging simulation results show the potential to study more complex phenomena, such as evaluating the parameters of tool path modulation, simulating ultrasonic machining, and studying machining stability.

Chatter prediction for parallel mirror milling of thin-walled parts by dual-robot collaborative machining system

Thin-walled parts with double-sided features are widely used in the aerospace industry, but the machining of such parts still faces great challenges due to their weak rigid structure and the positioning errors caused by turning/re-clamping of the workpiece. For this purpose, a novel machining approach for parallel mirror robotic milling of thin-walled parts is proposed. Different from conventional single-sided milling, it can simultaneously machine both sides of the workpiece while avoiding the above problems and improving machining efficiency. However, the introduction of multiple cutting excitations makes the vibration behavior of the workpiece more complicated, thus making it difficult for the dynamic modeling of the dual-robot machining system. This paper aims to uncover the dynamic mechanism of chatter phenomenon in parallel mirror robotic milling process in consideration of the interaction of tool-workpiece-tool system. A dual-robot collaborative machining system is first developed for the milling of thin-walled workpiece, and the method of synchronous motion planning for dual robots is described. The slave robot synchronously follows the master robot and the two milling cutters mounted on tool flange of the robot are kept in mirror position. Over a tooth passing period, the engagement state of the cutters and the workpiece is analyzed considering the effect of rotation phase lag (RPL) between the twin cutters. After that, the vibration state and the corresponding instantaneous displacement of the workpiece can be expressed explicitly, then the dynamic resultant cutting force acting on the workpiece is calculated according to the mechanistic force model. Comprehensively considering the dynamic interaction of the tool-workpiece-tool system, multi-mode and position-dependent modal characteristics of thin-walled part, a time-varying delay differential equation is constructed and solved to explore the dynamical behavior of parallel mirror milling process. The predicted stability lobe diagram is validated by a series of parallel mirror milling tests on thin-walled PMMA plates. Comparisons of numerical and experimental results show that the dynamic model successfully predicts the chatter stability for the parallel mirror milling of thin-walled parts.

Analysis and modeling of cutting force considering the tool runout effect in longitudinal-torsional ultrasonic vibration-assisted 5 axis ball end milling

The longitudinal-torsional ultrasonic vibration-assisted milling (LTUVAM) can improve the machining quality compared with conventional milling (CM), and the machining quality is closely related to cutting force which is affected by the tool runout effect. In this study, a mechanistic force model for longitudinal-torsional ultrasonic vibration-assisted 5 axis ball end milling considering the tool runout effect is proposed. First, the cutting edge motion model considering the effects of tool runout and ultrasonic vibration is established. Then, based on the analysis of the cutting edge motion relative to the workpiece, the uncut chip thickness (UCT) is computed by means of the geometrical calculation method, and the engaged cutting edge elements are determined according to the Z-map method, the ultrasonic milling force model is established after determining the cutting force coefficients and tool runout parameters through calibration tests. Moreover, the impact of different parameters on dynamic separating characteristics of LTUVAM is studied by the tool-workpiece contact rate. Finally, the verification tests are carried out, and the experimental results show the effectiveness of the ultrasonic milling force model.

Tool wear area estimation through in-process edge force coefficient in trochoidal milling of Inconel 718

The rapid wear and premature failure of the cutting tool are prone to happen due to increased forces during machining difficult-to-cut materials such as Inconel 718. The application of alternative toolpath such as trochoidal milling has significantly improved tool life and reduced the overall cycle time of the process. The wear pattern of the tool has a direct impact on the cutting forces, which increases with tool deterioration. The cutting forces in milling are modeled through the mechanistic force model and can be designated through a set of force coefficients, i.e. cutting and edge representing the shearing and ploughing phenomenon of metal removal. It has been established in the literature that tool wear has a considerable effect on the value of edge force coefficients. This paper aims to determine the in-process edge force coefficients for the trochoidal toolpath and correlates them with the corresponding flank wear area. The proposed correlation will further assist in predicting the level of flank wear area based on the force values in trochoidal milling.

Modulated orthogonal cutting system realized by piezo stack actuation and linear guide coupling

Modulation-assisted machining (MAM) employs low-frequency feed-direction tool vibration to enhance conventionally continuous cutting processes such as turning, drilling, and boring operations. The development of a suitable tool vibration system is critical for the success of MAM. In this paper, a tool vibration system realized by using piezo stack actuation and linear guide coupling was designed and constructed. The performance of the system was evaluated by conducting orthogonal tube face turning tests on AISI 1045 steel using a range of cutting and modulation conditions. Cutting forces and tool vibration displacement were measured and analyzed. A mechanistic force model based on the variable uncut chip thickness was used to predict the variable primary cutting and feed forces in MAM which showed good agreement with the measured forces. Furthermore, It was found that the vibration amplitude with cutting was reduced when compared to the vibration amplitude without cutting. The reduction in vibration amplitude was predictable as it depends on the feed force and the stiffness of the system. The results indicate good control ability of the tool vibration system across a wide range of cutting and modulation conditions.

Neural Network-based Model Parameter Estimation for End Milling of Carbon Fiber Reinforced Polymer (CFRP) Composites

A predictive cutting force model is critical during the end milling of Carbon Fiber Reinforced Polymer (CFRP) composites to achieve optimum fiber delamination, tool wear, and surface accuracy. The mechanistic force model showed robust prediction abilities; however, cutting constant estimation is challenging due to the involvement of multiple variables resulting in higher-order mathematical formulations. This paper presents augmenting the Feed Forward Neural Network (FFNN) with a mechanistic force model to approximate independent relationships of the chip load and edge contact length with shearing and rubbing constants. The prediction abilities of the proposed approach are compared with the traditional Fourier fitting model and experimentally measured values over diverse cutting conditions. It has been demonstrated that the proposed approach can accurately estimate cutting forces during the end milling of CFRPs.

Bayesian approach to determine force model parameters for the prediction of cutting forces in turning operations

The prediction of cutting forces is a major topic in predesigning turning operations. An efficient method to predict cutting forces are machining simulations taking mechanistic force models into account. However, their accuracy highly depends on the model parameters, whose calibration requires numerous time- and cost-consuming experiments. In order to calibrate model parameters with low experimental effort, this study presents a Bayesian Makrov Chain Monte Carlo (MCMC) method. Force model parameters are conditioned to only few measurements of turning experiments and lead to accurate results of machining simulations. Due to low experimental effort, this approach is of major interest for industrial applications.

Physics-informed Bayesian machine learning case study: Integral blade rotors

This paper provides a physics-informed Bayesian machine learning (PIBML) description and case study. The PIBML approach applies three physics-based models to establish the initial beliefs before testing to determine the probability of milling stability (or prior). These include: receptance coupling substructure analysis (RCSA) prediction for the tool tip frequency response functions; finite element software prediction of the mechanistic force model coefficients; and a spindle speed-dependent power law model for process damping. Testing was then performed to identify optimal stable machining conditions using an expected improvement in material removal rate criterion. The prior probability of stability was updated using the test results to determine the posterior probability of stability. The test results were compared to the parameter recommendations provided by the endmill manufacturer. A demonstration integral blade rotor was machined at the optimal stable machining conditions for 304 stainless steel and 6061-T6 aluminum. The disagreement between manufacturer recommendations and milling performance in both materials tested emphasizes the need for broad implementation of PIBML approaches to increase machining productivity and efficiency.

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).

Analysis of cutting forces at different spindle speeds with straight and helical-flute tools for conventional-speed milling incorporating the effect of tool runout

This paper is concerned with the experimental investigation and mechanistic prediction of cutting forces for flat-end milling with tool runout. The effects of the tool geometry, the workpiece material and cutting parameters such as spindle speed, tool engagement and cutting direction are investigated. The mechanistic force model uses the trochoidal flute path to calculate the undeformed chip thickness. Average cutting force and linear regression model are applied for identifying the coefficients of the force model, and tool runout parameters are established from the radii of all flutes at the free end of the cutting tool. A series of milling processes are conducted on AZ31 Magnesium (Mg) alloy and titanium alloy (Ti6Al4V) to analyze the instantaneous cutting force curves, amplitudes of cutting forces and peak forces over a wide range of conventional spindle speeds, namely 600, 1200 and 3000 rev/min. It is found that the values of the cutting force coefficients are higher at lower spindle speed and decrease with an increase in spindle speed, especially when machining Ti6Al4V alloy. For the edge force coefficients, it is observed a slight variation when using cutting tools with different helix angles. Besides, the cutting force amplitudes strongly depend upon the workpiece material. The helix angle has a significant influence on the transverse force amplitude at the spindle speed of 600 rev/min. The cutting forces obtained mechanistically are also substantiated by comparison with measurements.

Correction to: Experimental verification of mechanistic force models for endmilling: the impact of the size effect on cutting coefficients

Correction to: Experimental verification of mechanistic force models for endmilling: the impact of the size effect on cutting coefficients

Experimental verification of mechanistic force models for endmilling: the impact of the size effect on cutting coefficients

Experimental verification of mechanistic force models for endmilling: the impact of the size effect on cutting coefficients

Novel crescent drill design and mechanistic force modeling for thrust force reduction in bone drilling

Bone drilling tends to cause mechanical damages and thermal necrosis in the vicinity of the drilled hole, which can deteriorate the surgery quality and patients’ recovery. Understanding the cutting forces generation mechanism is crucial in controlling thrust force and bone temperature for optimum tool design. In this study, a novel crescent drill bit featuring an improved positive rake angle distribution was designed to reduce the thrust force and temperature elevation. On this basis, a mechanistic model for predicting thrust force and torque was proposed for drill bits with different geometries (twist drill and crescent drill). The proposed model was established in the polar coordinate system to precisely calculate the curvilinear integral of the crescent cutting edges. Drilling experiments were carried out using two types of drill bit under different cutting conditions and results showed that our proposed model agrees well with the experimental data. The experimental results also demonstrated that our tool design can significantly reduce the thrust force and reduce the bone temperature below the thermal threshold without coolant, providing a clinical option for coolant free drilling.

Long Short-Term Memory-Based Cutting Depth Monitoring System for End Milling Operation

Abstract The technologies related to manufacturing processes monitoring, optimization, and control are becoming prevalent to achieve autonomous operations in Smart Manufacturing. The present work establishes an edge-level system based on the long short-term memory (LSTM) model for monitoring significant variations of cutting depths during end milling of near-net-shaped components. The proposed system consists of a trained LSTM model that decodes force data to identify cutting depths and an edge-level interface for displaying abnormal changes to the operator. The LSTM model development requires considerable labeled data consisting of cutting force sequences and corresponding depth classes generated using machining experiments. The present work proposes to develop the LSTM model using synthetic datasets generated using the mechanistic force model to minimize experimental efforts. The optimum configuration was derived by investigating the effect of network parameters and adaptive learning methods. The performance of an optimal network was substantiated by conducting tests using previously unseen synthetic datasets derived from the mechanistic model. The optimal network architecture was integrated with a dynamometer and an edge-level system to capture end milling force data and display cutting depth information. A set of end milling experiments are carried over a range of parameters to examine the efficacy of the proposed approach in estimating cutting depth deviations. It has been demonstrated that the approach can be effectively used as an edge-level system to capture significant cutting depth variations during the end milling and alert machine operators.

INSTANTANEOUS PARAMETER IDENTIFICATION FOR MILLING FORCE MODELS USING BAYESIAN OPTIMIZATION

The comparison between measured and simulated machining forces enables the evaluation of workpiece quality, process stability, and tool wear condition. To compute the machining forces that occur, mechanistic cutting force models are typically used. The cutting force coefficients (CFCs) of mechanistic force models are directly linked to the mechanics of chip formation and, thus, depend on the tool-workpiece combination and on the prevailing cutting conditions. CFCs are usually identified via the average cutting force identification method, which requires the execution of cutting tests under defined test conditions. Hence, determining CFCs for different cutting conditions is time-consuming and expensive. In this paper, the performance of an instantaneous CFC identification approach based on Bayesian Optimization during the machining of arbitrary workpiece geometries is studied. Bayesian Optimization is well suited for global optimization problems with computationally expensive cost functions. The simulated cutting forces are calculated using a dexel-based cutter workpiece engagement simulation and the actual cutting forces are measured during the machining process using a dynamometer. Thus, an efficient identification of CFCs could be achieved.

A model-based sustainable productivity concept for the best decision-making in rough milling operations

There is a need in manufacturing as in machining of being more productive. However, at the same time, workshops are also urged for lesser energy waste in cutting operations. Specially, rough milling of impellers and bladed integrated disks of aircraft engines need an efficient use of energy due to the long cycle times. Indeed, to avoid dramatic tool failures and idle times, cutting conditions and operations tend to be very conservative. This is a multivariable problem, where process engineers need to handle several aspects such as milling operation type, toolpath strategies, cutting conditions, or clamping systems. There is no criterion embracing productivity and power consumption.In this sense, this work proposes a methodology that meets productivity and sustainability by using a specific cutting energy or sustainable productivity gain (SPG) factor. Three rough milling operations -slot, plunge nad trochoidal milling- were modelled and verified. A bottom-up approach based on data from developed mechanistic force models evaluated and compared different alternatives for making a slot, which is a common operation in that king of workpieces. Experimental data confirmed that serrated end milling with the highest SPG value of 1 is the best milling operation in terms of power consumption and mass removal rate (MRR). In the case of plunge milling technique achieve an SPG < 0.51 while trochoidal milling produces a very low SPG value.

Application of mechanistic force models to features of arbitrary geometry at low material removal rate

This paper presents a workpiece discretization method to apply existing cutting force models to predict the forces generated during low material removal rate robotic machining operations of features with arbitrary geometry. Two machining operations along a straight edge which are modelled using this feature discretization method are shown, a chamfer pass on a sharp corner and the removal of a trapezoidal cross section. The workpiece features are measured using a high-resolution laser profile scanner to obtain the volume of the features to be removed. The identified features are discretized into rectangular sections such that the cutting force models can be applied to predict the cutting forces. A linear and an exponential mechanistic model which relate tool immersion and feed rate to the cutting force are applied to the scanned workpiece features. The linear and nonlinear models show good agreement with the measured data, with the exception that the linear model occasionally over predicts the forces depending on the radial depth of cut.

Rigidity Regulation Approach for Geometric Tolerance Optimization in End Milling of Thin-Walled Components

Abstract This article presents a novel approach to optimize geometric tolerances (flatness and cylindricity) by manipulating the rigidity among finishing and roughing cutting sequences during end milling of thin-walled components. The proposed approach considers the design configuration of the thin-walled component as an input and aims to determine semi-finished geometry such that the geometric tolerance parameters are optimized while performing a finish cutting sequence. The objective is accomplished by combining mechanistic force model, finite element (FE) analysis-based workpiece deflection model, and particle swarm optimization (PSO) technique to determine optimal disposition of material along the length of component thereby regulating rigidity. The algorithm has been validated by determining the rigidity-regulated semi-finished geometries for thin-walled components having straight, concave, and convex configurations. The outcomes of the proposed algorithm are substantiated further by conducting a set of end milling experiments for each of these cases. The results of the proposed strategy are compared with a traditional approach considering no change in the rigidity of component along length of the cut. It is demonstrated that the proposed approach can effectively optimize geometric tolerances for thin-walled components during end milling operation.

An image-based approach to predict instantaneous cutting forces using convolutional neural networks in end milling operation

Cutting force detection can contribute to predicting the productivity and quality of end milling operations. Instantaneous cutting force prediction of digital twins in end milling operations should be near real-time and accurate. This paper proposes an image-based approach that can contain more useful information due to a higher dimension and simplify the complexity of computing geometric data. The cutter frame image (CFI) is utilized as one of the inputs of a convolutional neural network (CNN) to predict instantaneous cutting forces. Considering the convenience of capturing massive data, the approach uses cutting forces generated from a mechanistic force model instead of experimental cutting forces to train the CNN. The correlation coefficient R2 value between predicted results and simulated results is 0.9999 and the average time cost per image is 0.057 s in a cutting condition, which validates the possibility to use the image-based method to predict instantaneous cutting forces accurately and efficiently in the digital twin.

Propagation of Johnson-Cook flow stress model uncertainty to milling force uncertainty using finite element analysis and time domain simulation

This paper describes the propagation of uncertainty in the parameters for a 6061-T6 aluminum Johnson-Cook flow stress model to, first, the uncertainty in the corresponding mechanistic cutting force model obtained by orthogonal cutting finite element simulation and, second, the milling force predicted by time domain simulation using the force model. The approach includes five key elements: 1) a literature review to identify the means and standard deviations for the 6061-T6 aluminum Johnson-Cook model parameters; 2) structured light scanning to measure an endmill’s cutting edge macro-geometry along the tool axis; 3) structured light scanning to identify the cutting edge cross-sectional rake and relief profiles for the same endmill; 4) orthogonal cutting finite element analysis to determine the mechanistic force model coefficients that relate the force components to chip area and width using the tool’s rake and relief profiles and random samples from the Johnson-Cook parameter distributions; and 5) time domain simulation with inputs that include the measured cutting edge macro-geometry, uncertain finite element-based force model, and measured structural dynamics. Distributions for milling force predictions are determined by Monte Carlo simulation and compared to in-process measurements for an indexable endmill-collet holder to demonstrate the approach. It is observed that 95% confidence intervals on the predicted forces bound the measured time-dependent force profile peaks in over half of the cases tested. It is also seen that the Johnson-Cook flow stress model-based force predictions performed as well as predictions based on a calibrated mechanistic force model.