Cutting Force Vectors Research Articles

Milling Force Modeling Methods for Slot Milling Cutters

The slot milling cutter is primarily used for machining the tongue and groove of the steam turbine rotor, which is a critical operation in the manufacturing process of the steam turbine rotor. It is challenging to predict the milling force of a groove milling cutter due to variations in rake, rake angles and cutting speeds of the main cutting edge. Firstly, based on a limited amount of experimental data on turning, we have developed an equivalent turning force model that takes into account the impact of the rounded cutting edge radius, the tool’s tip radius and the feed rate on tool’s geometric angle. It provides a more accurate frontal angle for the identification method of the Johnson–Cook material constitutive equation. Secondly, the physical parameters, such as shear stress, shear strain and strain rate on the main shear plane, are calculated through the analysis of experimental data and application of the orthogonal cutting theory. Thirdly, the range of initial constitutive parameters of the material was determined through the split Hopkinson pressure bar (SHPB) test. The objective function was defined as the minimum error between the theoretical and experimental values. The optimal values of the Johnson–Cook constitutive equation parameters A, B, C, n and m are obtained through a global search using a genetic algorithm. Finally, the shear stress is determined by the governing equations of deformation, temperature and material. The axial force, torque and bending moment of each micro-segment are calculated and summed using the unit cutting force vector of each micro-segment. As a result, a milling force prediction model for slot milling cutters is established, and its validity is verified through experiments.

Prediction of Surface Location Error Considering the Varying Dynamics of Thin-Walled Parts during Five-Axis Flank Milling

Surface location error (SLE) caused by forced vibration is a key factor to determine the quality of the finished part. When machining thin-walled structures with sculptured surfaces, the complicated milling process is significantly influenced by the vibration due to the flexibility of the part. The dynamics of the part are dominant and vary with the material removal during machining. This paper presents a prediction method of SLE considering the varying dynamics of thin-walled parts in five-axis flank milling. The in-process part is decomposed into unmachined and machined portions, which are both modelled based on the thin-plate theory. The dynamics models of the two portions are coupled using the substructure method. Coordinate transformation based on the screw theory and the general cutting dynamics model for five-axis flank milling is employed to transform the cutting force vectors and frequency response function (FRF) to the same coordinate system for the prediction of SLE. The proposed method is validated with five-axis flank milling tests and SLE measurements on a thin-walled twisted part. It is shown that the average error of the proposed method for SLE prediction is less than 5 μm, and the calculation is almost 8 times faster than the typical finite element method.

THEORETICAL STUDY OF THE EFFICIENCY OF USING A SPECIAL CUTTER TOOL HOLDER WITH AN ORIENTED POSITION OF CENTER OF RIGIDITY

The theoretical study of vibration resistance of the turning process is effectively carried out using modern mathematical modeling tools, which are characterized by sufficient accuracy of the relationship between input actions or disturbances and the dynamic response of the metal-cutting machine tools. To study and analyze the dynamic processes of a potentially unstable lathe support system during turning, it is important to form a calculation scheme for the processing process and a mathematical model of studies system. The implementation of such a model, which determines the influence of the elastic and dynamic characteristics of a special tool holder with an oriented center of rigidity on the relative vibrations of workpiece and cutter, in general on the main indicator of machine tools dynamic system quality - vibration resistance, is presented. The analytical dependences of tool holders elastic characteristics influence on tool-support system static characteristic, which allow determining its reduced stiffness parameters in main coordinate system directions are presented. Based on the simulation studies results of the cutting process vibration resistance is possible to determine the most rational tool holder elastic parameters, in which the vibration resistance of turning will be relatively increased, taking into account various combinations of the potentially unstable system elastic characteristics of the machine tool carriage during turning. The use of an additional tool holder reduces the overall rigidity in the direction of the cutting force vector and in the direction normal to the workpiece’s surface, while simultaneously increasing the vibration resistance of cutting process due to the reduction of the “coordinate links” negative influence between cutter vibrational movement and the cutting process.

METHOD FOR CALCULATING CUTTING FORCES BY MODELING CAD WITH A SYSTEM OF GEOMETRIC CUTTING PARAMETERS WITH RADIAL MILLS

The accuracy of processing surfaces of a complex profile largely depends on the selected processing strategy, which will allow creating the same, within certain limits, power characteristics of the shaping process at the intervals of the programmed tool path. In this case, it becomes possible to include tuning modules in programs for CNC machines that form vector values of corrections in certain areas, as reactors for elastic deformations of the cutting process. Therefore, it is especially important to know the modulus and direction of the resulting cutting force vector, which does not necessarily coincide with the feed direction.
 The purpose of this work is to build a method for calculating cutting forces by modeling the geometric parameters of a cut with a CAD system, a cutter with a nonlinear generatrix. Solid modeling of the process is based on the Boolean operations of "intersection" and "subtraction" of 3D objects: the teeth of a radius cutter with a helical cutting edge and a workpiece "moving" at a feed rate. The tool for the implementation of this method is a software module created on the basis of API functions, the input data for which are: a 3D tool and a workpiece, the equation of the trajectory of its movement and the parameters of the infeed movement. Targeting API properties, the application makes it possible to simulate various trajectories, helical or trochoidal, when machining complex surfaces. In the future, it is possible to take into account the plastic deformation processes in the chip formation zone in the model by connecting external modules.
 In the course of the conducted research on milling with radial end mills with a helical cutting edge, when two or more teeth are within the arc of contact, it was determined by 3D modeling how much thickness and width the layer cuts off each of the teeth during the feed per revolution. Consequently, in the process of shaping, normal and tangential cutting forces, which are different in direction and modulus, are present as a function of the angle of rotation of the cutter. Therefore, the concept of "circumferential force on the cutter", accepted in the theory of cutting, as a certain constant component of the process, can introduce an error when considering the causes of the excitation mechanism of vibrations of different nature that arise in the processing zone.

Effect of Vibration Direction of Ultrasonic Vibrating Cutting Edge on Internal Stress Fluctuation of Workpiece

The aim of this study is to investigate the dynamic phenomenon of ultrasonic vibration-assisted cutting by utilizing a stress distribution visualization system. The vibrating cutting-edge is considered to be a cause of dynamic changes in the cutting force at ultrasonic frequencies. However, many researchers have explained the effect of ultrasonic vibration-assisted cutting by evaluating the time-averaged cutting force, because existing dynamometers are unable to measure the dynamically changing cutting force at ultrasonic frequencies. There are some reports that the vibration direction of cutting edge strongly affects tool wear. However, in practical ultrasonic cutting, the vibration of the cutting edge has yet to be measured in a production environment. In this study, the instantaneous stress distribution on the workpiece was visualized by a photoelastic method that combines a pulsed laser emission synchronized with tool vibration. The developed photographic system can capture 360 frames in one ultrasonic vibration period. The dynamic cutting force was calculated by Flamant’s stress distribution theory. It was experimentally confirmed that the stress distribution under vibration-assisted conditions showed periodical changes synchronized with vibration. Because these results are compatible with well-known vibration-cutting theories, the imaging system was able to show the periodic changes in stress distribution in the ultrasonic frequency band. This indicates that the dynamic change in cutting force during the ultrasonic vibration period affects intermittent cutting conditions. In this report, the vibration direction was adjusted from −9.5° to +9.5° along the cutting direction. When the tool moved in upwards for the cutting phase and downwards for withdrawal phase, the stress distribution was continuously observed over one tool vibration period; no intermittent cutting was observed. The locus of the cutting force vector was affected by the ultrasonic vibration direction and rake angle of the cutting tool. A negative rake angle showed that the direction of the cutting force vector shifted toward the workpiece side near the most advanced position of the cutting edge.

Optimization of the cutting force vector during counter milling

The process of counter milling with cylindrical and end mills is investigated. It was found that in order to improve the accuracy and quality of processing by counter milling, when choosing the cutting depth, it is necessary to take into account the diameter of the cutter and its rigidity. Keywords counter milling, mating surfaces, accuracy, machining quality, cylindrical and end mills, depth of cut, cutter diameter. bsv_sfmai@mail.ru

Twin-cutter form turning of commutator rings using cutters’ progressive motion piezoelectric engines

The option of realization of the technological scheme of twin-cutter form turning via use of piezoelectric engines of progressive motion is hereby proposed. The cutting force vector constitutes the external perturbation effect. The scheme, design, transfer function of the cutter's piezoelectric engine of progressive motion is hereby presented.

A SPINE SURGERY SIMULATOR BASED ON VOLUMETRIC MODELS

A volume based surgery simulator described herein provides cutting simulations for diverse tools used in spine surgery and morphological simulations of bone reposition, deletion and fusion. A tool coordinate based method is used to obtain constant and simple surface equations for representing the tools. Such representations give efficient computations for cutting surface changes and calculate pre-computed transformations for fast summating the cutting force vectors along the haptic device axes from chip removal loads on a tool surface. This study extends the traditional one-scalar volume with geometric and topologic data. Real-time cutting simulations for predicting tissue surface changes and cutting forces can be achieved by manipulating extended geometric volume data. The manipulation of extended topological volume data can detect new separate bones generated during the cutting simulations and enables morphological simulations of repositioning, deleting or fusing the separate bones. Realistic 3D images with fine tissue surface features obtained from simulating three typical surgeries located on the cervical, thoracic and lumbar spine respectively demonstrate that the proposed simulator can be an excellent tool for planning, confirming and rehearsing various complex spine surgeries such as abnormal tissue removal, spine decompression and morphology correction.

Optimization of Cutting Path for Minimizing Workpiece Displacement at the Cutting Point: Changing the Material Removal Process, Feed Direction, and Tool Orientation

The vibrations of a workpiece during machining shorten the tool life and deteriorate the surface roughness in cases where the workpieces have a low stiffness (as is the case with artificial hip joints). In this paper, we propose a method to reduce the vibrations of the workpiece at the cutting point; this method is based on an algorithm that generates a cutting path to minimize workpiece displacements. The generation of the cutting path takes into account the workpiece stiffness, cutting force vectors, the material removal process, feed directions, and tool orientation. The cutting path generation algorithm generates cutting path strategies based on the relationships among cutting force vectors, feed directions, and tool orientation, all of which are measured with machining experiments.

Design method of material removal process for minimizing workpiece displacement at cutting point

In the machining of flexible workpieces, the workpiece displacements caused by cutting forces become larger, which may deteriorate machining accuracy and reduce tool life. In this paper, we propose a design method to minimize the workpiece displacements at cutting points. The calculation method directly designs the material removal sequence, feed direction and tool orientation taking the varying static stiffness of the workpiece and cutting force vectors into account. The method is verified with the process design for the milling of a titanium alloy cantilever.

Configuration of the cutting-force vector in turning plastic metals

A method is proposed for determining the angle of the cutting-force vector in turning plastic metals by a hard-alloy tool at maximum productivity (maximum profit), on the basis of a mathematical model of the dissipation rate in chip formation as a function of the cutting parameters.

Cutting Process Design for Minimizing Workpiece Displacement at Cutting Point

Vibrations of a tool or a workpiece in cutting shorten tool life and deteriorate a surface roughness. In this research, we propose a method to reduce vibrations of the workpiece at a cutting point. An algorithm that generates a cutting path to minimize workpiece displacements at a cutting point is developed. In this algorithm, the cutting path is generated with changing feed directions, tool posture and material removal process by considering workpiece compliance matrices and cutting force vectors. Feed directions and tool posture are changed to control the direction of the cutting force vector. Material removal process is changed to control the change of the workpiece compliance. FEM (Finite Element Method) is used to calculate workpiece compliance matrices. SVD (Singular Value Decomposition) is used to calculate the direction which has the lowest compliance in the workpiece compliance matrices. Minimum workpiece displacement at a cutting point is calculated from these calculated results. The algorithm is applied to the cutting path of end milling for a simple bar and the cutting path is compared with two conventional cutting paths by conducting a simulation and a cutting test. As a result, mean values of workpiece displacement were reduced by applying the algorithm.

A Mechanistic Model of Cutting Forces in Micro-End-Milling With Cutting-Condition-Independent Cutting Force Coefficients

Complex three-dimensional miniature components are needed in a wide range of industrial applications from aerospace to biomedicine. Such products can be effectively produced by micro-end-milling processes that are capable of accurately producing high aspect ratio features and parts. This paper presents a mechanistic cutting force model for the precise prediction of the cutting forces in micro-end-milling under various cutting conditions. In order to account for the actual physical phenomena at the edge of the tool, the components of the cutting force vector are determined based on the newly introduced concept of the partial effective rake angle. The proposed model also uses instantaneous cutting force coefficients that are independent of the end-milling cutting conditions. These cutting force coefficients, determined from measured cutting forces, reflect the influence of the majority of cutting mechanisms involved in micro-end-milling including the minimum chip-thickness effect. The comparison of the predicted and measured cutting forces has shown that the proposed method provides very accurate results.

Model-Based Cutting Simulation System for Prediction of Cutting States.

This paper describes a cutting simulation system which has the function of physical simulations as well as geometrical simulations. In the geometrical simulation, changes in workpiece geometry in the course of cutting processes are evaluated based on a solid modeling system. In the physical simulation, physical parameters of cutting processes are evaluated based on physical models. Instantaneous cutting force can be estimated by composing cutting force vectors acting on infinitesimal parts of flutes. Cutting error is then estimated based on tool deflections induced by the cutting force. A system for simulating the cutting process using a square end mill cutter has been developed based on a geometric modeler with boundary representations. A number of cutting experiments were conducted for various tools and cutting conditions. The results of experiments proved the accuracy of estimations by the simulation system.

エンドミルによるコーナ部加工に関する研究 （第２報） 切削力の加工精度に及ぼす影響と精度改善について

This paper deals with influence of cutting force on machining accuracy and improving method of the accuracy in corner cut by end mill. Errors by corner cut are extremely greater than that of steady state cutting. When a cutter radius is equal to a radius of curvature of the corner, maximum machining error becomes 13 to 22 times as large as that of steady state cutting. Describing the position of maximum error by rotating angle φ from start point of corner cut, the position by the angle is φ=10° in down milling and φ=0°in up milling. And also cutting forces in corner cut are measured, and machining accuracy is analysed by a simple error generating model that depends upon cutting force vector and resulting stiffness of machine-tool-workpiece system. Calculated values or shape errors are almost coincident with that of experimental values. To improve machining accuracy, plunge and twice looped path cutting are recommended. But under the experimental conditions, difference of accuracy between steady state cutting and corner cut is smaller by diameter 17 mm in down milling and 14 mm in up milling.

Prediction of Chatter Vibration by Means of a Model-Based Cutting Simulation System

This paper describes a system for predicting charter vibration in ad milling operation. The system estimates instantaneous cutting force vectors based on geometric models of a workpiece and a tool. The vibration of the tool induced by cutting forces is calculated by using a lumped-parameter model with two degrees of freedom. Considering changes in cutting volume due to tool deflections and regenerative effects, the numerical simulation of dynamic tool movement is conducted to check the occurrence of chatter vibration. To reduce the evaluation time, a simplified stability criterion is introduced to exclude apparently stable conditions. A number of cutting experiments were carried out to verify he effectiveness of the system.

A Cutting Simulation System for Machinability Evaluation Using a Workpiece Model

This paper describes a cutting simulation system to be used in the evaluation of machinability of products at various stages of the manufacturing processes. The system developed consists of geometric simulation and physical simulation. The geometric simulation is performed by using extended Z buffer models representing a workpiece and a tool swept volume. In the physical simulation, instantaneous cutting force vectors acting on a square end mill are computed based on the am of chip element removed by a thin divided section of a flute. The tool deflection induced by the cutting force is then calculated. The result is used to estimate the machining error caused by tool deflection. A series of cutting experiments are conducted to verify the effectiveness of the system.

微小切削における切削開始の条件について (第2報)

In the previous paper a cutting-beginning-model was experimentally proposed, in which chip formation begins when the end of contact of piled-up material at the rounded part of cutting edge reaches the same height as the center of that rounded part.In this paper, the validity of the model is investigated by varying the rake angle of tool and utilizing the cutting force vector diagram. And then, the flow behavior is discussed from the variation of fractional friction force acting on the successively increased contact area with the advance of tool.The main results as follows.(1) In the range of positive rake angle, rake angle has no effect on the cutting force and sliding length, before the cutting-beginning-point. After this point the cutting force changes in accordance with the magnitude of rake angle.(2) The direction of cutting force vector at the cutting-beginning-point is constant irrespective of the magnitude of roundness radius, material hardness and rake angle. But, the magnitude of vector is proportional to roundness radius and material hardness.(3) It is shown from the result of friction force analysis that the piled-up material begins to flow as a chip at the cutting-beginning-point.

二段掬角の効果

One of the distinguished traits of CSM cutter is double radial raking of blades. Double radial raking not only directs the cutting force vector to the centre line of a cutter but also reduces cutting powers. Double radial raking forces the contact lengths between chip and blades to shorten, and it is the cause of reduction of cutting powers.