Calculation Of Cutting Forces Research Articles

Development of a Parametric Model for Calculating Cutting Forces in External Cylindrical Turning of 16MNCR5 Steel

The paper presents a mathematical model for calculating cutting forces during the machining of 16MnCr5 steel using the Sandvik CNMG 120408 16P25T tool. The modeling process involved the use of a test rig constructed based on the 16Д25 machine, which enabled the measurement of real values of spindle speed, longitudinal feed, cutting depth, and cutting forces. The results transmitted to a computer through the LTR-EU-8 workstation, equipped with galvanic isolated LTR modules and a synchronization interface. Based on the experimental results, the theoretical model demonstrated a deviation from actual measurements of no more than 4.72%. The study provides evidence that the cutting force calculations commonly presented by leading tool manufacturers are inherently overestimated. he difference in cutting forces can be 9%.

Study on cutting force calculation and optimization strategy of machining spiral bevel gear by using forming method

Study on cutting force calculation and optimization strategy of machining spiral bevel gear by using forming method

Моделирование взаимосвязи силы резания с глубиной резания и объемами снимаемого металла единичными зернами при плоском шлифовании

Introduction. The model for calculating the cutting force is the basis of the modules of CAM-systems related both to the predicting processing errors on metal-cutting machines for specified grinding conditions, and to the optimizing all parameters of the technological mode (parameters of cutting modes, cutting tools, etc.). However, due to the lack of an adequate model for calculating the cutting force presented in engineering form, such modules have not yet been developed not only for flat grinding operations, but also for all other types of metalworking. It is challenging to obtain an adequate cutting force model for flat grinding operations because it is necessary to establish the interrelation between the machine parameters of the macrocutting modes (feed, cutting speed) of the grinding wheel with the parameters of the microcutting modes — the sets of cutting grains of the wheel associated with the plastic deformation of the metal in the shear zone, microvolumes of the metal being removed and the geometry of the cutting part of the abrasive grains. The purpose of this work is to develop a force model establishing the interrelation of the cutting force with the cutting depth and the volumes of the metal being removed by single grains and the wheel as a whole on the basis of the integration of microvolumes and microforces when metal being removed by the wheel grains. Research methods. The subject of the research is the mathematical modeling of the interrelation between the cutting force and cutting modes with the parameters of microcutting by a group of single grains, based on the equality of work when metal being removed of the same volume. The methodological basis of the research is the connection between the work (energy) spent on the plastic deformation of metal by a single grain, the intensity of stresses, the intensity of deformation rates and the volume of the metal being removed by the wheel as a whole, established by S.N. Korchak. Results and discussion. The result of the study is an analytical model that reliably and adequately establishes the interrelation between the cutting force and the cutting depth, cutting modes, wheel characteristics, physical and mechanical properties of the processing material, and other main technological parameters. The field of application of the results is the possibility of using the cutting force calculation model, presented in this paper, as a basis for the development of a module for a CAM-system (a digital twin of the machining), which would allow to perform the calculation and design of optimal technological parameters of the flat grinding operation, as well as cutting modes testing according to the criterion of processing accuracy of a parts batch, considering the influence of various variable factors and real processing conditions within the manufacturing process.

Modeling and methods for gear shaping process and cutting force prediction of variable transmission ratio rack

Variable transmission ratio rack shows great potentials in the automobile industry as a key component of vehicle variable transmission ratio steering gear to balance steering portability and steering sensitivity. The current processing method for variable transmission ratio rack is orbital forging, which has the advantages of high performance and high processing efficiency. However, orbital forging can only process small size rack and its processing accuracy is limited. Therefore, this paper proposes a novel processing method, i.e., gear shaping, to achieve high quality processing of variable transmission ratio rack by overcoming above limits of orbital forging. Firstly, an accurate envelope motion model between the tool and the workpiece is established based on the mapping relation of the speed as well as the feed of each machine axis between envelope motion and actual gear shaping process, so as to envelope final complex changing tooth shape of variable transmission ratio rack. Namely, the speed of each machine axis is determined strictly according to the linkage relationship of each machine axis with a variable transmission ratio function involved. Then, a specific tooth profile mathematical model of variable transmission ratio rack is obtained through simultaneous solution of the envelope motion model and the tool model. Meanwhile, since cutting force is a critical factor of gear shaping process, this paper proposes a new method for cutting force prediction which involves two innovative calculation algorithms for two major components (contact length b and chip area a) of the classical metal cutting force calculation model. Firstly, based on discrete representation, a new calculation algorithm of contact length b including specific dynamic selection criteria of cutting contact points is presented. Secondly, in order to precisely calculate chip area a, this paper proposes a discrete calculation algorithm with two pivotal cutting points selecting criteria involved. Finally, based on the classical metal cutting force calculation model, accurate predictions of cutting force in gear shaping process of variable transmission ratio rack are achieved. Gear shaping experiments as well as cutting force measurements are conducted and errors between the predictions and the experimental measurements of cutting force are obtained, which remain between 1% and 19%. Therefore, it is concluded that the envelope motion model and methods for cutting force prediction in gear shaping process of variable transmission ratio rack presented in this paper are feasible.

Real-time machine simulation using cutting force calculation based on a voxel material removal model

Machining processes must be adjusted regarding tolerances in dimension and shape to fulfill product requirements. For this purpose, machine simulations are used to allow a preliminary characterization of the given process, thus minimizing the number of physical prototypes and scrap parts. However, these simulations are either extremely specialized for single problems, e.g., dynamic machine behavior, or they are simplified to a kinematic simulation of the machine without considering the machine behavior at all. This article presents a new approach for a real-time machine simulation by combining four types of simulations to close this gap. This proposed approach uses a voxel-based material removal inside a kinematic machine simulation as input parameters for a cutting force calculation. Afterwards, the forces are applied to a multi-body simulation of the static machine behavior. Starting point of the simulation is a hardware-in-the-loop coupling of a real CNC and a real-time visualization of a virtual machine tool. The simulation is experimental verified by comparing the simulated cutting forces and displacements with the measured forces during the process and the resulting shape of the manufactured work piece. The presented conclusions show the general applicability of the proposed method for the simulation of milling processes.

A Reliability Statistical Evaluation Method of CNC Machine Tools Considering the Mission and Load Profile

Reliability of the CNC machine tool (abbreviated as machine tool) relates to the product's reliability and has great influence on the manufacturing process. The traditional reliability statistical evaluation method of the machine tool neglects the influence of the mission profile and load profile (M&L), it causes that the evaluation result is not accurate enough to provide accurate references for the reliability-related works under specific M&Ls such as the preventive maintenance, product improvement, etc. To address these defects, this paper proposes an improved reliability statistical evaluation method considering the M&L. Firstly, the machine tool is decomposed by the meta-action decomposition method, and the mission profile of the machine tool is represented by the meta-action chain (MC). Secondly, load profile representation indicators of the machine tool are extracted based on the load composition and cutting force calculation. Then, the mapping model between the M&L and the machine tool's reliability is established using the radial basis function (RBF) neural network. Finally, the improved reliability statistical evaluation method is illustrated and validated by the engineering practical application. Comparing the evaluation results of the two statistical evaluation methods, it shows that the improved reliability statistical evaluation method is more accurate than the traditional reliability statistical evaluation method, under specific M&Ls, so that it can provide more accurate references for the reliability-related works.

The mathematical models for cutting force calculation during structural and corrosion-resistant steels` parts processing

The paper shows that conventional mathematical models for calculating the cutting force components during the turning process, represented in reference guides on engineering, give drastic errors reaching 100 percent or more for various tool-workpiece couples. These errors interfere with applying reference values of the cutting force for any further calculations, equipment selection, workpiece positioning scheme, workpiece deformation value due to the elastic of the technological system elements during processing and etc., because of the insufficient reliability of the results of such calculations. The paper proposes mathematical models obtained as a result of experimental studies, which allow for increasing the accuracy of the calculation of the components of the cutting force by introducing an additional parameter – i.e., the value of thermo EMF of the test running into the calculation formulas. This approach enables to reduce the error in the calculation of the components of the cutting force up to ± 15%. In addition, the need for the development of specific mathematical models for various groups of materials machined is shown, which is due to the peculiarities of contact processes in the machining of various groups of steels, as well as to qualitative and quantitative indicators of the thermo-physical properties of the materials of tool-workpiece contact couples.

Experimental investigation on milling of hardened steel Cr12

Hardened steel Cr12 test piece with hardness HRC50 is designed with special shape by means of Buda method. The effect of cutting speed and feeding per tooth on chip deformation and shear angle can be investigated comprehensively. The shear angle increases significantly with the increasing of cutting speed. So that, chip deformation becomes less and less with the increasing of cutting speed. The cutting power becomes greater with increasing of cutting speed, cutting temperature rises, and then the friction coefficient between tool-chip becomes smaller, so the shear angle has a gradually increasing trend. The shear angle increases significantly with the increasing of feeding per tooth. As feeding rate increases, cutting force increases, cutting temperature rises, friction coefficient decreases, thus, the shear angle has the trend of increasing. The cutting force investigation has been done by means of multi-factor orthogonal test method with four factors and four levels. The calculation equations for cutting forces have been deduced by means of the mixed algorithm of least-square method fitting and Monte Carlo fitting. It follows from the significant test results of regression analysis of cutting force calculation equations and coefficients based on 99% confidence that the equations for cutting force calculation are of excellent significance. Cutting speed is minor factor to impact cutting forces. Feeding per tooth and axial depth of cut are the most important parameters to impact cutting forces.

Расчет сил резания при обработке пластичных материалов в широком диапазоне толщин срезаемого слоя

Расчет сил резания при обработке пластичных материалов в широком диапазоне толщин срезаемого слоя

Vibrations of Flat‐End Cutter Entering Workpiece Process: Modeling, Simulations, and Experiments

During all the machining process, the milling cutter has to enter the workpiece either from the boundary or from the machined/unmachined surface, due to the change of machining sequence/cutter or the variation of cutting depth. Unlike the stable cutting process, the contact between cutter and machined workpiece changes significantly in the entering process, resulting in vibration and leaving marks on the machined surface. Aiming at in‐depth understanding the mechanism of this phenomenon, this paper presents a novel time‐domain simulation model to predict the dynamic response of the cutter during the entering process. Two typical entering conditions, including entering from the workpiece boundary and from the machined surface along the cycle path, are modeled based on the dynamic cutting force calculation by considering dynamic undeformed chip thickness created by consequential teeth engagement. Then, it is synthesized with the time‐varying immersion angle and exit angle of cutter teeth in the entering process to simulate the dynamic cutting forces and cutter vibrations. To validate the developed model, eight conditions in boundary entering and six conditions in cycle path entering are carried out by comparing the collected data and the predicted results. Results show that the developed model could precisely predict the dynamic cutting forces and cutter vibration, especially the forces and displacements under the varied cutter‐workpiece contact.

Chip volume and cutting force calculations in 5-axis CNC machining of free-form surfaces using flat-end mills

This paper presents two new methods and associated algorithms for numerically modeling chip geometry and calculating cutting force for parts with free-form surface during 5-axis CNC machining using a flat-end mill. Extending the computational geometry-based Alpha shape method that can only predict cutting chip geometry, a parallel slice local volume modeling approach has been added to predict cutting forces as well. To demonstrate the validity and capability of these new methods, simulation of the cutting and chip forming process of 5-axis CNC machining on a free-form surface has been carried out. Physical validation experiment in controlled conditions has been carried out on a 3-axis micro CNC machine with the two cutter rotation angles set to be zero. The predicted and measured cutting forces are in reasonably good agreement both in trend and magnitude. The presented chip volume and cutting force method can be used to perform cutting force estimation for generating optimal tool path and orientation during 5-axis milling. The method requires longer computational time than traditional analytical methods, but it supports the ultimate goal of chip volume modeling and calculation—accurate dynamics cutting force prediction.

Cutting force calculation for gear slicing with energy method

A calculation method for cutting force in gear slicing is proposed based on energy method. In view of the particularity of gear slicing, the cutting edge on a cutter tooth is divided into three sections: cut-in edge, top edge, and cut-out edge. Then, the concept of micro-section edge is proposed for the three curved edges. The cutting force on micro-section edge is calculated according to oblique cutting theory. The vector sum of cutting forces on micro-section edges make up the cutting force on one section of the cutting edge. Then, the cutting force on single cutter tooth is obtained by the vector sum of cutting forces on the three sections of the cutting edge. For the calculation of whole cutting force acting upon the cutter, the number of cutter teeth participating in cutting is determined based on coincidence degree. As a result, the whole cutting force is obtained by the vector sum of cutting forces on the cutter teeth participating in cutting. The feasibility of this cutting force calculation method is proved by a calculation example and the effectiveness of this method is verified by finite element simulation.

A combination method of the theory and experiment in determination of cutting force coefficients in ball-end mill processes

AbstractIn this paper, the cutting force calculation of ball-end mill processing was modeled mathematically. All derivations of cutting forces were directly based on the tangential, radial, and axial cutting force components. In the developed mathematical model of cutting forces, the relationship of average cutting force and the feed per flute was characterized as a linear function. The cutting force coefficient model was formulated by a function of average cutting force and other parameters such as cutter geometry, cutting conditions, and so on. An experimental method was proposed based on the stable milling condition to estimate the cutting force coefficients for ball-end mill. This method could be applied for each pair of tool and workpiece. The developed cutting force model has been successfully verified experimentally with very promising results.Highlights By investigation of the stable cutting conditions in milling process, the linear function of average cutting force and feed per flute was successfully verified. A combined theoretical-experimental method was proposed with an effective model for the determination of cutting force coefficients in ball-end mill process.

Cutting force models for Fe–Al-based coating processed by a compound NC machine tool

The arc-spraying Fe–Al-based coating cutting process is a spindle-tool-workpiece vibration system dependent upon the machine tool's dynamic performance, cutting tool vibration, the coarse coating surface and its thin cutting depth. To investigate the cutting force, this research indicates the coating cutting fundamental mechanics; furthermore, it represents two cutting steps and cutting force models in the machining process avoiding an analysis of the natural vibration parameters of the machine tool itself. In the first cutting step, there is a transient cutting force due to forced vibration of the rough surface; the second cutting step has a steady machining feature based on the first cutting surface and the reduced hardness of the inhomogeneous region. According to the different characteristics of each cutting step, this research presents dynamic cutting calculation models including cutting parameters, tool vibration and cutting depth effects in the first cutting step. A steady cutting model is based on three cutting parameters including cutting velocity, cutting feed and cutting depth. Piezoelectric force and acceleration sensors were used to obtain accurate experimental data. Then, response surface methodology (RSM) and the principle of least squares estimation of polynomial regression (PLSEPR) were applied to analyse the resultant cutting data. The results showed that cutting force calculation models were suitable for the coating machining.

Optimization of cutter posture based on cutting force prediction for five-axis machining with ball-end cutters

In process planning for five-axis machining, the key issue is the determination of cutter postures (orientations). In this paper, a simulation-based method is proposed to identify cutter postures that produce minimum deflection cutting force. The method applies to the finish machining process, where only the ball part of the cutter will be engaged with the workpiece. For ball-end cutters, with change of cutter postures, the shape of the engagement region between the cutter and workpiece remains the same. Only the distribution of the engagement region on the cutter surface will change. Based on this principle, a method to transform engagement information between cutter postures is proposed, to eliminate the demand for repeated engagement calculation for different cutter postures. As a result, the computational loads of cutting force calculation for different cutter postures are greatly reduced, which enables us to deploy evolutionary algorithms to search for the optimal cutter posture at a reasonable computational cost.

Generic Mathematical Model for Efficient Milling Process Simulation

The current challenge in metal cutting models is to estimate cutting forces in order to achieve a more accurate and efficient machining process simulation and optimization system. This paper presents an efficient mathematical model for process simulation to evaluate the cutting action with variable part geometries of helical cutters and predict the cutting forces involved in the process. The objective of this paper has been twofold: to improve both the accuracy and computational efficiency of the algorithm for cutting force estimation in peripheral milling. Runout effect and the real tool tooth trajectory are taken into account to determine the instantaneous position of the cutting flute. An expression of average chip thickness for the engaged flute in the cut is derived for cutting force calculations resulting in a more efficient process simulation method in comparison with previous models. It provides an alternative to other studies in scientific literature commonly based on numerical integration. Experiments were carried out to verify the validity of the proposed method.

A prediction method of cutting force coefficients with helix angle of flat-end cutter and its application in a virtual three-axis milling simulation system

Predicting the quality of a machined component is the grandiose signification in manufacturing industry. Calculation of the cutting force is one of the most important elements to predict the quality of machined parts. In this paper, a linear force model is developed in which the cutter’s helix angle is incorporated to calculate the cutting force coefficients for the milling process. On the effect of cutter’s helix angle, all derivations of cutting forces are directly based on the tangential, radial, and axial cutting force components. In the developed mathematical model, with the stable milling condition, the average cutting forces are expressed as a linear function of the feedrate, and the cutting force coefficient model is formulated by a function of average cutting force and cutter geometry such as cutter diameter, number of flutes, cutter’s helix angle. An experimental method is proposed based on the stable milling condition to estimate the cutting force coefficients. This method can be applied to each pair of cutter and workpiece. The developed cutting force calculation model has been successfully verified by both simulation and experiment with very promising results. Integrated application with a virtual three-axis milling machining simulation system has also been implemented to demonstrate potential utilization of this developed model.

Cutting Data Modeling Based on Artificial Neural Network

Cutting force is usually obtained based on the experimental data which is conducted under certain cutting condition with certain cutters because metal cutting mechanism study is not mature. As the data are numerous, in different types, and the relationships between them are complex, the commercial database can be used directly. A new approach based on ANN is introduced here for unstructured and discrete data modeling, which transfers the unstructured and discrete data into ANN topology and net weight matrix. In this paper, the experimental data of union cutting force modification are taken as examples for verifying the feasibility of the ANN model. The ANN modeling, inputs, outputs and ANN training are discussed. Compared with other modeling approaches, this model is general and can process discrete data with unified data structure. This model can be used for cutting force calculation as well as intelligent and general CAPP.

Investigating Eccentricity Effects in Turn-milling Operations

Manufacturing of parts made out of difficult-to-cut materials presents many challenges. Reduced productivity and increased cost due to low machinability and tool life are main problems in these applications. Turn-milling may offer important advantages in solving these problems. Turn-milling combines conventional turning and milling processes providing lower cutting temperatures, higher process flexibility and productivity. Turn–milling processes have additional parameters one of which is the eccentricity between the tool and workpiece axes. The objective of this study is to develop a process model for eccentricity effects on orthogonal turn-milling operation. Process model includes chip geometry and cutting force calculations. In addition, effect of eccentricity on tool wear is also investigated in this paper. Although intermitted characteristics of turn-milling provide benefits such as lower cutting temperature and longer tool life, there are some drawbacks which have to be taken into consideration. In this direction, analytical definitions related to surface quality such as circularity, surface roughness and cusp height under the effect of eccentricity are also investigated. Experiments were carried out on a multi tasking CNC machine tool. Analytical solutions and experimental results are compared to verify the process model.

An enhanced method for cutting force estimation in peripheral milling

A new model for cutting force estimation is presented in this paper. It is based on the specific cutting force coefficient, which is defined as a function of chip thickness. The distinguishing feature of the proposed cutting force model is the use of average chip thickness for cutting force calculation on each position of the cutting tool, in such a way that only one iteration is needed on every angular position of the tool. This model is based on the actual workpiece–tool interaction which provides information about the real position of the cutting edge. It provides an alternative to other studies in scientific literature commonly based on numerical integrations. With this model, it is possible to estimate the cutting forces not only under steady-state conditions but also under variable machining conditions of axial and radial depth of cut.