A cutting force model for face milling operations

A procedure for the simulation of the static and dynamic cutting forces in face milling is described. For the static force model, the initial position errors of the inserts and the eccentricity of the spindle are taken into consideration as the major factors affecting the variation of the chip cross-section. The structural dynamics model for the multi-tooth oblique cutting operation is assumed as a multi-degrees of freedom spatial system. From the relative displacement of this system, based on the double modulation principle, the dynamic cutting forces were derived and simulated. The simulated forces were subsequently compared to measured forces in the time and frequency domains.     

A force model for nose radius worn tools with a chamfered main cutting edge

The three-dimensional cutting forces for nose radius tools with a chamfered main cutting edge incorporated with a tool-worn factor are presented in this paper. The variations in shear plane areas occurring in the tool-worn situation are used. The results obtained from the proposed model shows good agreement with the experimental data on both chip formation as well as cutting forces. In the experimental work the throwaway tips are locked onto the pocket of the tool holder. The holders for special tools are designed first. Next, the tool holders are manufactured by using medium carbon-steel bars and the mounting tips are designed based on various specifications. Finally, the nose radius tips mounting in the tool holder are ground to a wear depth, and the worn tool dimensions are measured by using a profile projector. The shear area and the friction area are calculated accordingly. Then the three-dimensional cutting forces will be obtained from those data.     

A three-dimensional analytical cutting force model for micro end milling operation

In the present day manufacturing arena one of the most important fields of interest lies in the manufacturing of miniaturized components. End milling with fine-grained carbide micro end mills could be an efficient and economical means for medium and small lot production of micro components. Analysis of the cutting force in micro end milling plays a vital role in characterizing the cutting process, in estimating the tool life and in optimizing the process. A new approach to analytical three-dimensional cutting force modeling has been introduced in this paper. The model determines the theoretical chip area at any specific angular position of the tool cutting edge by considering the geometry of the path of the cutting edge and relates this with tangential cutting force. A greater proportion of the helix face of the cutter participating in the cutting process differs the cutting force profile in micro end milling operations a bit from that in conventional end milling operations. This is because of the reason that the depth-of-cut to tool diameter ratio is much higher in micro end milling than the conventional one. The analytical cutting force expressions developed in this model have been simulated for a set of cutting conditions and are found to be well in harmony with experimental results.     

Modeling micro-end-milling operations. Part I: analytical cutting force model

A new analytical cutting force model is proposed for micro-end-milling operations. The model calculates the chip thickness by considering the trajectory of the tool tip while the tool rotates and moves ahead continuously. The proposed approach allows the calculation of the cutting forces to be done accurately in typical micro-end-milling operations with very aggressively selected feed per tooth to tool radius (f_t/r) ratio. The difference of the simulated cutting forces between the proposed and conventional models can be experienced when f_t/r is larger than 0.1. The estimated cutting force profile of the proposed model had good agreement with the experimental data.     

A chip formation based analytic force model for oblique cutting

An oblique cutting force model has been developed using an analytic orthogonal force model. The force model uses a thermo-visco-plastic material constitutive law to represent the shear stress during deformation of the material. The strains and strain rates used for defining the shear stress were obtained from chip formation and morphology derived from orthogonal cutting tests and has been extended to oblique cutting. A time domain simulation using the in-cut chip geometry to define the chip load area has been developed. The oblique force model was used to predict the cutting forces during ball milling of hardened AISI D2 tool steel. The predicted forces were verified experimentally and showed good correlation.     

A cutting power model for tool wear monitoring in milling

This paper describes a cutting power model in face milling operation, where cutting conditions and average tool flank wear are taken into account. The cutting power model is verified with experiments. It is shown with the simulations and experiments that the simulated power signals predict the mean cutting power better than the instantaneous cutting power. Finally, the cutting power model is used in a cutting power threshold updating strategy for tool wear monitoring which has been carried out successfully in milling operations under variable cutting conditions.     

A new model for the prediction of cutting forces in micro-end-milling operations

In this work an analytical forces model for real micro-end-milling is developed by regarding the main factors which have influence on the process. The run-out or eccentric deviation of the tool path is taken into account as well as the tool deflection. A linear equation system has to be solved to obtain the forces, so it requires a low computational cost. Size effect is also considered since the chip thickness is comparable to the edge radius and therefore there is chip removal only when it is higher than a certain value. This phenomenon causes variation in the entry and exit angles of the tool in the workpiece. These factors have already been studied in conventional milling. However, since they have not been yet considered for micromilling, the validity of mechanistic models is limited. The model has been developed for two different types of side micromilling: up milling and down milling. Experimental results carried out on Steel and Aluminum show a good correlation with the model. The forces model proposed in this work can be used in a process monitoring in real time as well as in adaptive control of the process.     

A comprehensive dynamic cutting force model for chatter prediction in turning

This paper presents a model of the dynamic cutting force process for the three-dimensional or oblique turning operation. To obtain dynamic force predictions, the mechanistic force model is linked to a tool–workpiece vibration model. Particular attention was paid to the inclusion of the cross-coupling between radial and axial vibrations in the force model. The inclusion of this cross-coupling facilitates prediction of the unstable–stable chatter phenomenon which usually occurs in certain cases of finish turning due to process non-linearity. The dynamic force model developed was incorporated into a computer program to obtain time-saving chatter predictions. Experimental tests were performed on AISI 4140 steel workpieces to justify the chatter predictions of the dynamic cutting process model in both the finishing and roughing regimes. Experimental results corroborate the unstable–stable chatter predictions of the model for different cases of finish machining. In addition, experimental results also confirmed the accuracy of chatter predictions for various cases of rough turning.     

Multi-grooved cutting tool to reduce cutting force and temperature during bone machining

The cutting temperature of a cutting tool are required to be low during bone machining for preventing damage to bone cells. However, conventional tools are practically the same as those used for metal cutting, and many operational limitations have been reported. In this study, a dedicated cutting tool was designed for reducing cutting force and temperature. A short contact between the workpiece and the cutting edge leads to a reduction in the cutting force. Furthermore, a straight-line edge improves surface roughness. The effectiveness was evaluated using bovine bone, and the cutting force was found to be decreased by about 40%.     

Generalized dynamic model of metal cutting operations

This paper presents a unified mathematical model which allows the prediction of chatter stability for multiple machining operations with defined cutting edges. The normal and friction forces on the rake face are transformed to edge coordinates of the tool. The dynamic forces that contain vibrations between the tool and workpiece are transformed to machine tool coordinates with parameters that are set differently for each cutting operation and tool geometry. It is shown that the chatter stability can be predicted simultaneously for multiple cutting operations. The application of the model to single-point turning and multi-point milling is demonstrated with experimental results.     

切削温度与切削力综合测量的虚拟仪器

介绍了综合测量切削平均温度和三向切削力并对其进行分析处理的虚拟仪器.利用PCI-1 200卡采集热电偶测温仪和电阻应变式测力仪传输的数据.利用LabVIEW平台开发.具有显示 力和温度波形曲线、热电偶标定和测力仪刻度标定、确定切削温度和切削力指数公式的能力 .提出了基于切削力和切削温度信息的切削状态判定方法.     

切削温度与切削力综合测量的虚拟仪器

介绍了综合测量切削平均温度和三向切削力并对其进行分析处理的虚拟仪器。利用PCI－1200卡采集热电偶测温仪和电阻应变式测力仪传输的数据。利用Lab VIEW平台开发。具有显示力和温度波形曲线、热电偶标定和测力仪刻度标定、确定切削温度和切削力指数公式的能力。提出了基于切削力和切削温度信息的切削状态判定方法。     

Prediction of cutting force for self-propelled rotary tool using artificial neural networks

In this paper, a cutting force model for self-propelled rotary tool (SPRT) cutting force prediction using artificial neural networks (ANN) has been introduced. The basis of this approach is to train and test the ANN model with cutting force samples of SPRT, from which their neurons relations are gradually extracted out. Then, ANN cutting force model is achieved by obtaining all weights for each layer. The inputs to the model consist of cutting velocity V, feed rate f, depth of cut a_p and tool inclination angle λ, while the outputs are composed of thrust force F_x, radial force F_y and main cutting force F_z. It significantly reduces the complexity of modeling for SPRT cutting force, and employs non-structure operator parameters more conveniently. Considering the disadvantages of back propagation (BP) such as the convergence to local minima in the error space, developments have been achieved by applying hybrid of genetic algorithm (GA) and BP algorithm hence improve the performance of the ANN model. Validity and efficiency of the model were verified through a variety of SPRT cutting samples from our experiment tested in the cutting force model. The performance of the hybrid of GA–BP cutting force model is fairly satisfactory.     

Cutting force model for multi-toothed cutting processes and force measuring equipment for face milling

This article presents a mechanical cutting force model for multi-tooth cutting processes, where initial position errors in radial and axial direction, eccentricity and edge wear are taken into account. The cutting forces are presented for each individual cutting edge, and in a system of coordinates where one axis is parallel to the cutting speed vector at any instant. The process parameter cutting resistance, C_r is derived from the measured main cutting force F_M. C_r should be regarded as a parameter since it is always increasing with decreasing values of theoretical chip thickness h₁. A new way of measuring cutting forces in multi-tooth cutting processes is also presented. Eight cutting force components are measured on the tool close to each of the four cutting edges. The aroused signals are filtered, amplified, A/D-converted and put together in a serial stream for transmission through a hollow spindle via a fibre optic cable. The signals are sent from the rotating spindle to the frame of the machine over an air gap with Light Emitting Diodes. They are then demultiplexed, D/A-converted, and stored in a PC-based eight channel oscilloscope. With this measurement equipment it is possible to directly measure the cutting forces acting on each individual cutting edge.     

A unified instantaneous cutting force model for flat end mills with variable geometries

A new and unified instantaneous cutting force model is developed to predict cutting forces for flat end mills with variable geometries. This model can routinely and efficiently determine the cutting properties such as shear stress, shear and normal friction angles (SSSNFAs) involved in the cutting force coefficients by means of only a few milling tests rather than existing abundant orthogonal turning tests. Novel algorithms are developed to characterize these properties using following steps: transformation of cutting forces measured in Cartesian coordinate system into a local system on the normal plane, establishment of explicit equations to bridge SSSNFAs and the transformed cutting forces, determination of SSSNFAs by solving the equations and fitting SSSNFAs as functions of process geometries. Results definitely show that shear stress can be treated as a constant whereas shear and normal friction angles should be characterized by Weibull functions of instantaneous uncut chip thickness. Experiments verify that the proposed unified model is effective to predict the cutting forces in flat end milling in spite of cutter geometries and cutting conditions.     

Mechanistic cutting force model in band sawing

In order to establish a mechanistic model of cutting force, specific cutting pressure was first obtained through cutting experiments. The band sawing process is similar to milling in that it involves multi-point cutting, so it is not an easy matter to evaluate specific cutting pressure. This was achieved by making the thickness of workpiece smaller than one pitch of the saw tooth, analogous to fly cutting in the face milling process. Then the cutting force was predicted by analysing the geometric shape of a saw tooth. The tooth shape used was the raker set style that is generally used in band sawing. A set of teeth comprises three teeth, ranked as left, straight, and right. The mechanistic model developed in the research considered the shape of each tooth in a set. The predicted cutting forces coincided well with those measured in the validation experiment. Therefore, the predicted cutting forces in band sawing can be used for the adaptive control of saw-engaging feed rate in band sawing.     

A method for measuring cutting forces in boring operations

In boring operations, two methods of measuring cutting forces are possible: measurement of forces exerted on the tool, by means of a dynamometric boring bar, or measurement of forces exerted on the workpiece, by means of a dynamometric table.In the second method, it is difficult to read the three components of the cutting force (tangential, radial and axial force), because the tool is rotating with respect to the workpiece. A three-component dynamometer on which the workpiece is clamped gives the axial (feed) force directly. The other two outputs, instead, are projections on two fixed axes of a force that is the sum of the radial and tangential components, and that rotates at spindle speed.This paper describes a simple, reliable method for solving the problem of obtaining the single components of the rotating force. Tangential and radial forces are measured continuously by means of an electrical resolver and lowcost electronic equipment.     

A cutting force model for finishing processes using helical end mills with significant runout

Analytical cutting force models play an important role in a wide array of simulation approaches of milling processes. The accuracy of the simulated processes directly depends on the predictive power of the applied cutting force model, which may vary under specific circumstances. End milling processes with small radial cutting depths, e.g. finishing processes, are particularly problematic. In this case, the tool runout, which is usually neglected in established cutting force models, can become quite significant. Within this article, well-known cutting force models are implemented for runout-prone finishing processes and modified by integrating additional parameters. A method is presented for how these additional runout parameters can be efficiently determined alongside commonly used cutting coefficients. For this purpose, a large number of milling experiments have been performed where the cutting forces were directly measured using a stationary dynamometer. The measured cutting forces were compared with the simulated cutting forces to verify and assess the modified model. By using the presented model and calibration method, cutting forces can be accurately predicted even for small radial cutting depths and significant tool runout.     

Simulation based model for tool life prediction in bevel gear cutting

Due to unpredictable tool life behavior in bevel gear cutting, unexpected production stops for tool changes occur. These lead to additional manufacturing costs. Because of its complexity, it is currently not possible to analyze the bevel gear cutting process sufficiently regarding tool life. This restriction leads to an iterative process design and determination of the ideal process parameters by using a trial-and-error approach. As a matter of fact, there is no concept to predict tool life in bevel gear cutting. Thus, a project has been initiated in order to develop a tool life model based on cutting simulation. This report presents the tool life model which combines a manufacturing simulation for bevel gear cutting with a regression model. The data of the regression model are determined by analogy trials. The combination of manufacturing simulation and regression model allows a local tool life prediction along the cutting edge.