Force Model For Machining Research Articles

Chatter in milling with robots with structural nonlinearity

Stiffness and damping nonlinearities are often negligible in machine tool vibrations, but they are shown to be prominent in industrial robots that are used for milling, mainly due to the several nonlinear phenomenon that occur in the robot’s revolute joints. In this paper, a 2DOF nonlinear vibratory model is presented to study regenerative chatter in robotic milling. The presented model includes cubic stiffness and damping terms to account for the robot’s structural nonlinearities. The machining forces are represented by a combination of periodic forces and delayed vibration terms; the former is generated by the feed motion of the tool and the later by chip regeneration. Furthermore, the machining force model is non-smooth due to (a) periodic entrance and exit of the cutting edges to and from the cutting region, and (b) loss-of-contact at high-amplitude oscillations. The dynamics in the presented model is therefore described by a set of nonlinear Delay Differential Equations with periodic coefficients and non-smooth forces. Numerical continuation with smoothing techniques is used to determine the combinations of spindle speed and axial depth of cut at which the forced periodic vibrations go through secondary Hopf or period doubling bifurcations, causing chatter in the milling process. A KUKA robotic arm with milling end-effector is used as a case study. The presented analysis shows that feedrate, which has no effect on chatter in machine tools with linear dynamics, alters the stability of vibrations in milling systems with nonlinear structural dynamics. Nonlinear systems’ stiffness and damping depend on vibration amplitude. Since feedrate directly influences the amplitude of forced vibrations, the nonlinear system’s damping and stiffness and consequently its chatter stability changes by feedrate.

Mechanisms and predictive force models for machining with rake face textured cutting tools under orthogonal cutting conditions

The cutting performance and mechanisms of rake face textured carbide cutting tools in orthogonal machining of a carbon steel are investigated. Micro-grooves at 15.5 μm top width and different depth-to-width ratios are fabricated on the tool rake face using a femtosecond laser. It is found that the textures can significantly enhance the surface wettability of the cutting tools to an emulsified cutting fluid, and a fast liquid infiltration along the micro-grooves takes place. The machining tests show that cutting tools with the rake face grooves can reduce the thrust force by up to 14.68% in comparison with the untextured cutting tools, as a result of the decreased frictional force between the tool and chip. It is shown that the reduced tool-chip actual contact area due to the rake face textures and reduced tool-chip contact length due to the thinning of chip are the main reasons for this frictional force reduction. It is further found that the ploughing action between the groove edges and chip material tends to increase the frictional force while the chip material deposition to the textural structures reduces the functionality of the textures. Plausible trends of the reduction of the cutting forces with respect to the textural parameters are discussed, from which grooves in parallel to the cutting edge at 0.6 depth-to-width ratio and about 90 μm spacing are found to perform the best. A cutting force model for orthogonal machining using rake face textured cutting tools are then developed using the classical thin shear zone theory and the unified mechanics of cutting approach. The model is finally verified experimentally which shows that the model predictions agree well with the corresponding experimental data for cutting with and without a cutting fluid.

Mechanistic cutting force model for rotary ultrasonic machining of rocks

Cutting force is the predominant output variable in rotary ultrasonic machining (RUM). It dictates other output variables, such as tool wear, cutting temperature, edge chipping, etc. It is desirable to develop a mechanistic model to predict cutting force and reveal the underlying cutting tool-workpiece interaction in RUM. Numerous researchers have developed theoretical approaches to predict cutting force in RUM; nevertheless, the combined effects of material removal on cutting force model have not been investigated. RUM has been used for machining rocks in several recent experimental investigations. However, there are no reports on cutting force model for RUM of rocks. This work bridges the gap and reports an improved mechanistic cutting force model. The model is derived based on the ductile mode removal and brittle fracture mode removal of rock under the indentation of a single abrasive particle. The cutting force model for RUM of rocks is then developed by aggregating the effects of all active abrasive particles bonded to the tool end face. Based on this model, the relationships between input variables (tool rotation speed, feedrate, ultrasonic vibration amplitude, abrasive size, abrasive concentration, and tool size) and cutting force are predicted. Experiments have been conducted and the experimental results agree well with the model predicted trends.

Cutting Force Model for Thermal-Assisted Machining of Tool Steel Based on the Taguchi Method

This paper investigates cutting force in thermal-assisted machining (TAM) by induction heating for SKD11 tool steel which is widely used in the mold industry. Experimental studies were first conducted at room and elevated temperatures to evaluate the effectiveness of the heating process on chip morphology and the cutting forces during the thermal-assisted machining and comparing with conventional machining method. The Taguchi method based on orthogonal array and analysis of variance ANOVA method was then used to design the number of experiments and evaluate the influence of cutting speed, feed rate, cutting depth, and elevated temperature on the cutting force. Study results showed a decrease in the cutting force in the TAM process. The optimal condition of parameters obtained for thermal-assisted machining were cutting speed 280 m/min, feed rate 230 mm/min, cutting depth 0.5 mm and temperature 400 °C. Finally, a proposed equation was established to determine the cutting force that was presented as a function of elevated temperatures when milling SKD11 material. A proposed cutting force model was compared, evaluated and confirmed to be in good agreement with experimental results.

Analytical force model for orthogonal machining of unidirectional carbon fibre reinforced polymers (CFRP) as a function of the fibre orientation

Machining of carbon fibre reinforced polymer (CFRP) still represents a significant challenge due to its anisotropic material structure and brittle fracture behaviour. The material causes distinctive tool wear, which results in a significant increase of process forces. Analytical force models are crucial to optimise tool geometries and process parameters for efficient machining of CFRP with various fibre orientations. This research aims to develop an analytical force model for orthogonal machining which considers the influence of fibre orientation, tool geometry and increasing tool wear.The fibre orientation interval from 0° to 180° is sub-divided into four independent sub-models: (1) θ=0°=180°, (2) 15°≤θ≤75°, (3) θ=90° and (4) 105°+γ≤θ≤165°. For machining fibres with orientation (1) θ=0°=180°, the considered chip formation mechanisms are micro-buckling for axial loading and exceeding shear strength for transverse loading. Furthermore, spring back effects due to elastic deformation are taken into account. For fibre orientations in the range of (2) 15°≤θ≤75°, a bending beam surrounded by matrix material is modelled on elastic foundation, using minimum potential energy principle (MPEP) and WINKLER’s elastic foundation approach. After a first crack initiation at initial tool-fibre contact, further potential cracks due to bending of the now unilaterally supported fibres are taken into account. In the third sub-model (3) with the fibre orientation θ=90°, the modelled fibre fracture criterion is the local exceed of the compressive strength due to bending deformation. After the first crack initiation, further potential cracks are considered in the modelling approach, being affected by the varying tool-fibre contact point with progressing cutting motion. Using the same bending beam approach with MPEP for the sub-model (4) 105°+γ≤θ≤165°, the fibres are both axially compressed (buckling) and transversely bent during the cutting process. This superimposed combination results in a “peeling”-removal of the CFRP material.In order to consider tool wear effects, a characteristic description of the cutting edge is proposed using five micro-geometry parameters. The focus of this paper is on the force model, however simulation of tool wear is part of future research. The comparison of the simulated and experimental process forces, depending on the actual wear state and current tool micro-geometry shows a good correlation.

Predictive cutting force model for ductile-regime machining of brittle materials

Ductile-regime machining is a promising technique for processing brittle materials. Although it has been widely investigated, there are few studies on the cutting force in the ductile-regime machining of brittle materials. This paper proposes a predictive cutting force model for ductile-regime machining of brittle materials, with an integration of the elastic recovery of the workpiece on the tool flank face and three parts of material removal on the tool rake face, i.e., the plowing effect, the plastic deformation, and the brittle fracture. Using the predictive cutting force model, it was found that the cutting force caused by the brittle fracture takes a dominant place in the total cutting force in the cutting process. Groove cutting experiments were carried out on the MgF2 (100) crystal to validate the predictive cutting force model. The measured cutting forces showed good agreement with the predicted cutting forces. In addition, it was found that the fluctuation of the measured cutting force increases with the increase of the cutting force caused by the brittle fracture.

Cutting force model for machining of CFRP laminatewith diamond abrasive cutter

The article presents a cutting force model for trimming operations of CFRP laminate with diamond abrasive cutters. Those tools are more and more encountered on industrial applications of CFRP trimming, due to their abrasion resistance and their low cost. Contrary to endmills, they consist of a large number of cutting grits, randomly distributed around the tool. To tackle the issue, a continuous model of tool engagement is proposed. Validity of the approach is verified. A mechanical model of cutting forces, adapted to CFRP laminate, is then presented. The evolution of specific cutting coefficient in relation to fibres orientation is investigated through a piecewise constant model. It leads to the proposal of a sine model for the specific cutting coefficients. The simulated forces are in good agreement with the experimental results of cutting tests, carried out in multidirectional CFRP laminate for different fibres orientation and widths of cut. Cutting mechanisms are finally discussed depending on fibres orientation.

Predictive cutting force model for a cryogenic machining process incorporating the phase transformation of Ti-6Al-4V

Titanium alloys have been attracting interest in aerospace industries because of their high strength-to-weight ratio. However, they are classified as difficult-to-machine materials due to poor tool life in machining processes. Cryogenic machining is a process that uses liquid nitrogen (LN2) as a coolant, and proposed as a method to enhance tool life in the present study. This paper presents a theoretical study to develop a predictive cutting force model for cryogenic machining of Ti-6Al-4V. A modified (in terms of cutting temperature) Johnson-Cook model that considers phase transformation, and a friction coefficient were used as input parameters for inclusion of the cryogenic cooling effect. The predictive cutting force model was validated based on an orthogonal cutting test. The predicted forces showed good agreement with the experimental data, with minimum and maximum error magnitudes of 1.9 and 17.7% for cutting force, and 0.3 and 32.8% for thrust force, respectively. Investigation of the effects of cryogenic cooling on the cutting force, micro-structure, surface integrity and burr height were conducted. The cutting force during cryogenic machining was increased compared to dry machining by a martensitic phase transformation of the work material. There was no effect of cooling condition on the surface roughness. The burr height under cryogenic conditions was decreased by 56.2 and 28.2% compared to the dry and wet conditions, respectively.

Modeling of the dynamic machining force of vibration-assisted nanomachining process

Nanofabrication technology is very important for many emerging engineering and scientific applications. Among different nanofabrication technologies, vibration-assisted nanomachining provides a low-cost easy-to-setup approach for producing structures with nano-scale resolution. It is very important to understand the mechanism for this nanomachining process and predict the involved machining force, so as to provide guidelines to achieve higher productivity and reduce tip wear. In this work, a machining force model for the tip-based nanomachining process was developed and validated. We analyzed the instantaneous engagement between the cutting tool (AFM tip) and the workpiece (PMMA film) during each tip rotation cycle for the vibration-assisted nanomachining process. A discrete voxel method was adopted to calculate the material removal rate at each moment, and an empirical machining force model is developed by correlating the machining force with material removal rate, which is a function of the input parameters of the nanomachining process. The machining force model was verified by experiments over a large range of machining conditions, and the coefficients in the force model were obtained by minimizing the Mean Square Error (MSE) method by comparing the predicted machining force from the model and measured machining force from the experiments. The results show a good fit between the predicted machining force and the measured machining force.

Research on machining characteristic of double-layer elastomer in pneumatic wheel method

For improvement of finishing effect to the laser hardening mold’s free-form surface with high hardness, double-layer elastic mechanics theory of pneumatic wheel based with softness consolidation abrasives (SCA) is analyzed. Under the annular stress around, ratio coefficient m of modulus of elasticity of abrasive layer to modulus of rubber layer and ratio coefficient n of thickness of abrasive layer to radius of stress have been bought in for establishing machining force model and deformation formula of double-layer elastic wheel. After that, a double-layer elastic model of the wheel has been established by ANSYS and the machining process has been simulated. Stress distribution and deformation rule are given by simulation. In the experiments, we use fiber to reinforce inner rubber layer and take binder to hold on abrasive particles. Microscopic analysis demonstrates that pneumatic wheel accords with the situation of double-layer elastic mechanic theory. Moreover, machining platform is established and empirical results show that pneumatic wheel can finish laser hardening mold’s free-form surface efficiently. And conclusion shows pneumatic wheel with lower factor n can help to decrease R a when it faces with concave surface and pneumatic wheel with higher factor n can improve machining efficiency to convex surface.

Mechanistic force model for machining process—theory and application of Bayesian inference

This work discusses the Bayesian parameter inference method for a mechanistic force model for machining. Bayesian inference methods have gained popularity recently owing to their intuitiveness and ease with which empirical knowledge may be combined with experimental data considering the uncertainty. The first part of the paper discusses Bayesian parameter inference and Markov Chain Monte Carlo (MCMC) methods. MCMC method effectiveness has been further analyzed by (1) changing the number of particles in MCMC estimation and (2) changing the MCMC move step size. The second part of the paper discusses two example applications as nonlinear mechanistic force model coefficient identification. The Bayesian inference scheme performs prediction of the cutting force coefficients from the training data. Using these coefficients and input parameters to the model, the cutting force is predicted. This prediction is validated using experimental data, and it is demonstrated that with very few parameter updates the predicted force converges with the measured cutting force. The paper is concluded with the discussion of future work.

Rotary ultrasonic face grinding of carbon fiber reinforced plastic (CFRP): a study on cutting force model

Carbon fiber reinforced plastic (CFRP) offers excellent mechanical properties, such as high strength, light weight, which makes it widely used in aerospace, transportation, machineries, and industrial applications. However, because of its anisotropic mechanical properties, high hardness, high strength, and poor thermal conductivity, the traditional processing methods are gradually unable to meet the processing needs. Except delamination, glitches, and tearing during processing, there are also other defects, like severe tool wear, larger cutting force, and higher cutting temperature, which make the tool life shortened. The machinability of CFRP materials using conventional machining (CM) techniques has seen a limited improvement over the years. Rotary ultrasonic machining (RUM) is an advanced machining process, which has shown to have specific advantages especially in the machining of CFRP. Many experimental investigations on cutting force in RUM of CFRP have been reported. However, in the literature, there are no reports on the development of a cutting force model for flat surface rotary ultrasonic machining, i.e., rotary ultrasonic face grinding (RUFG). In order to reveal the mechanism of grinding force reduction in RUFG of CFRP, based on material properties of CFRP, the brittle fracture theory approach was adopted and a cutting force model was developed for CFRP in RUFG process. The experiments were carried out and found the affect of the input variables for the cutting force in RUFG. The results were analyzed and discussed. The trends of predicted effects of input variables on cutting force agree well with the trends determined experimentally. Compared with the experimental results, the developed cutting force model was regarded as reasonable.

0517 Experimental design of a cutting force model for machining of thin-walled parts

0517 Experimental design of a cutting force model for machining of thin-walled parts

Effects of cutting parameters on ductile material removal mode percentage in rotary ultrasonic face machining

Rotary ultrasonic machining is an excellent method for processing hard brittle materials and has been investigated extensively via theoretical and experimental studies. However, there are few researches about rotary ultrasonic machining of ceramic matrix composite materials. Material removal mode presents both ductile-mode and brittle-fracture when machining hard brittle materials. The ratio of ductile-mode and brittle-fracture has a significant impact on processing status and processing quality. In this article, we developed a cutting force model for rotary ultrasonic face machining of ceramic matrix composite materials. Based on this model, we investigated the effects of cutting parameters on ductile-mode percentage of ceramic matrix composite materials. The cutting depth, feedrate and spindle speed are assumed to be three main factors that affect the ductile-mode percentage in rotary ultrasonic face machining. The primary aim of this article is to verify the correctness of the assumption using a three-variable three-level orthogonal experiment array. The experimental results agreed well with the assumption. The main factors deciding the ductile-mode percentage were found to be cutting depth and feedrate.

Characterization of shear stresses in nickel-based superalloy Mar-M247 when orthogonal machining with coated carbide tools

Mar-M247 is a nickel-based alloy which is well known as difficult-to-machine material due to its characteristics of high strength, poor thermal diffusion and work hardening. Calculation of shear stress by an analytical force model to indicate the effect of coating material, cutting speed, feed rate on tool life and surface roughness was conducted experimentally. Cutting tests were performed using round inserts, with cutting speeds ranging from 50 to 300 m/min, and feed rates from 0.1 to 0.4 mm/tooth, without using cooling liquids. The behavior of the TiN and TiCN layers using various cutting conditions was analyzed with orthogonal machining force model. Cutting results indicate that different coated tools, together with cutting variables, play a significant role in determining the machinability when milling Mar-M247.

A New Approach for Chatter Prediction in Robotic Milling Based on Signal Processing in Time Domain

Robotic machining is an attractive, cost-effective, and flexible alternative for basic machining applications. Having these characteristics, industrial robots are assumed to be the next generation of machine tools. But, due to weaker structure of robotic manipulators in comparison to conventional CNC machines, robotic machining processes are more subject to unwanted detrimental vibrations. At this work, simulations are realized in Time-Domain using the linearized robot structure model as transfer function of chatter block diagram and end milling force as machining force model. This article presents a new technique for simulating and analyzing the possibility of happening chatter vibrations at different values of machining parameters considering structure and configuration of the studied robot. Results show that limit of chatter occurrence is dramatically affected by changing robotic machining configuration.

Mathematical model for cutting force in rotary ultrasonic face milling of brittle materials

Rotary ultrasonic machining of brittle materials, such as glass, ceramics, silicon, and sapphire, has been ex- plored in a large number of experimental and theoretical investigations. Mechanistic models have been developed to predict the material removal rate or cutting force in the rotary ultrasonic machining of brittle materials. However, most merely describe the rotary ultrasonic machining process of drilling holes in brittle materials. There are no reports on the development of a cutting force model for flat surface rotary ultrasonic machining, i.e., rotary ultrasonic face milling. This paper presents a mathematical model for the cutting force in the rotary ultrasonic face milling of brittle materials under the assumptionthatbrittlefractureremovalistheprimarymodeof material removal. Verification experiments are conducted for the developed cutting force model and show that the trends of input variables for the cutting force agree well with the trends of the developed cutting force model. The developed cutting force model can be applied to evaluate the cutting force in the rotary ultrasonic face milling of brittle materials.

Determination of stress state in chip formation zone when orthogonal machining nickel-based superalloy Inconel 718

An analytical force model with shearing and ploughing mechanisms is established for orthogonal machining of nickel-based superalloy Inconel-718. The force balance is conducted on the main boundary of the deformation zone, leading to the machining force model. These machining force components are distinct functions of the shear angle and tool edge radius. Increasing the tool edge radius will influence the average rake angle and lead to the increment of chip formation and ploughing forces. Using the machining force model in calculating shear stress on the main boundary of the deformation zone will demonstrate the influence of the size effect when using edge radius tools in machining Inconel 718. This is attributed to the larger chip formation component at a lower shear angle and deformation below the tool. TiCN coating proved to be more suitable for milling Inconel 718 than TiN coating due to the fact that lower shear stress was presented.

A cutting force model for rotary ultrasonic machining of brittle materials

Knowing cutting force in rotary ultrasonic machining (RUM) can help optimizing input variables. RUM of brittle materials has been investigated both experimentally and theoretically. However, there are no reports on cutting force models for RUM of brittle materials. This paper presents a mechanistic model for cutting force in RUM of brittle materials. Assuming that brittle fracture is the primary mechanism of material removal in RUM of brittle materials, the cutting force model is developed step by step. On the basis of this mechanistic model, relationships between cutting force and input variables (such as spindle speed, feed rate, ultrasonic vibration amplitude, abrasive size, and abrasive concentration) are predicted. Experiments are conducted for model verification and experimental results agree well with model predictions.

Cutting force prediction in ball end milling of sculptured surface with Z-level contouring tool path

This paper presents an approach to predict cutting force in 3-axis ball end milling of sculptured surface with Z-level contouring tool path. The variable feed turning angle is proposed to denote the angular position of feed direction within tool axis perpendicular plane. In order to precisely describe the variation of feed turning angle and cutter engagement, the whole process of sculptured surface milling is discretized at intervals of feed per tooth along tool path. Each segmented process is considered as a small steady-state cutting. For each segmented cutting, the feed turning angle is determined according to the position of its start/end points, and the cutter engagement is obtained using a new efficient Z-map method. Both the chip thickness model and cutting force model for steady-state machining are improved for involving the effect of varying feed turning angle and cutter engagement in sculptured surface machining. In validation experiment, a practical 3-axis ball end milling of sculptured surface with Z-level contouring tool path is operated. Comparisons of the predicted cutting forces and the measurements show the reliability of the proposed approach.