High frequency bandwidth cutting force measurement in milling using capacitance displacement sensors

This article presents a method of measuring cutting forces from the displacements of rotating spindle shafts. A capacitance displacement sensor is integrated into the spindle and measures static and dynamic variations of the gap between the sensor head and the rotating spindle shaft under cutting load. To calibrate the sensing system, the tool is loaded statically while the deflection of the tool is measured with the capacitance probe. With this calibration, the displacement sensor can be used as an indirect force sensor. However, the measurement bandwidth is limited by the natural modes of the spindle structure. If cutting force frequency contents are within the range of the natural modes of the spindle structure or higher, the measurements are distorted due to the dynamic characteristics of the spindle system. In order to increase the bandwidth of the indirect force sensor by compensating for the spindle dynamics, the design of a Kalman filter scheme, which is based on the frequency response function (FRF) of the displacement sensor system to the cutting force, is presented in this paper. With the suggested sensing and signal processing method, the frequency bandwidth of the sensor system is increased significantly, from 350 to approximately 1000 Hz. The proposed indirect force sensor system is tested experimentally by conducting cutting tests up to 12,000 rpm with a five-fluted end mill. Besides cutting forces, the measured displacements can also be affected by factors such as roundness errors, unbalance at different speeds, or dilatation of the spindle shaft due to temperature variations. Methods to compensate for these disturbing effects are also described in the paper.     

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 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.     

Real-time estimation of cutting forces via physics-inspired data-driven model

A method is presented to estimate the cutting forces in real time within machine tools for any spindle speed, force profile, tool type, and cutting conditions. Before cutting, a metrology suite and instrumented tool holder are used to induce magnetic forces during spindle rotation, while on-machine vibrations, magnetic forces, and error motions are measured for various combinations of speeds and forces. A physics-inspired data-driven model then relates the measured accelerations to the magnetic forces, such that during cutting, on-machine measured vibrations are used in the model to estimate the cutting forces in real time.     

Acceleration based indirect force measurement in metal cutting processes

A milling cutter instrumented with a three-component accelerometer is investigated as a sensor of dynamic cutting forces. Two major causes of measurement errors are considered. These causes are: (1) the flexible mode vibrations, and (2) inertial and viscous forces associated with the “rigid body” motion of the spindle. A self-tuning filter consisting of two subsystems is applied to attenuate these errors. The first subsystem converts accelerations from the rotating spindle into stationary coordinates. It also analyses the corrupted signal and calculates an optimal filter structure and the settings for the actual operating conditions. This information is utilized by the second subsystem, a digitally programmable filter, which performs signals correction in real time. Two examples are presented to illustrate performance of the proposed “natural” sensor. In the first example, a periodical force applied from an exciter is reconstructed from the accelerations measured during spindle rotation. The second example deals with estimation of a force impulse generated by means of an impact hammer.     

Chip geometry and cutting force prediction in gear hobbing

This paper presents a tri-dexel geometric engine integrated simulation model for the gear hobbing operation. The process kinematics are modeled and validated using CNC signals from a Liebherr LC500 hobbing machine. Workpiece geometry updating and cutter-workpiece engagement (CWE) calculations are efficiently realized in the tri-dexel engine. 3D force contributions at discretized nodes along the hob's cutting edges are computed considering the localized principal cutting directions, and rake and inclination angles. To measure cutting forces, a rotary dynamometer is successfully adapted and used alongside a Kalman filter to compensate for structural dynamics. The predicted forces agree well with their experimental counterparts.     

Experimental studies of cutting force variation in face milling

The purpose of this paper is to present a developed cutting force model for multi-toothed cutting processes, including a complete set of parameters influencing the cutting force variation that has been shown to occur in face milling, and to analyse to what extent these parameters influence the total cutting force variation for a selected tool geometry. The scope is to model and analyse the cutting forces for each individual tooth on the tool, to be able to draw conclusions about how the cutting action for an individual tooth is affected by its neighbours.A previously developed cutting force model for multi-toothed cutting processes is supplemented with three new parameters; eccentricity of the spindle, continuous cutting edge deterioration and load inflicted tool deflection influencing the cutting force variation. A previously developed milling force sensor is used to experimentally analyse the cutting force variation, and to give input to the cutting force simulation performed with the developed cutting force model.The experimental results from the case studied in this paper show that there are mainly three factors influencing the cutting force variation for a tool with new inserts. Radial and axial cutting edge position causes approximately 50% of the force variation for the case studied in this paper. Approximately 40% arises from eccentricity and the remaining 10% is the result of spindle deflection during machining. The experimental results presented in this paper show a new type of cutting force diagrams where the force variation for each individual tooth when two cutting edges are engaged in the workpiece at the same time. The wear studies performed shows a redistribution of the individual main cutting forces dependent on the wear propagation for each tooth.     

KDP晶体切入角度对切削力和表面粗糙度影响试验

KDP晶体具有各向异性,使得沿不同晶向切入时切削力的大小和作用效果发生改变,进而可能影响表面质量。利用高精度三向测力仪搭建了KDP切削力测试平台,对其沿不同晶向的切削力进行了测试。结果表明:切削力沿特定的角度呈一定的规律分布,与理论计算有一定的吻合,同时表面粗糙度值在不同的晶向也呈典型的周期分布。在切削力测试基础上,开展了表面粗糙度优化试验,在50 mm×50 mm工件上实现了S_q1.8 nm的超光滑表面加工。     

金刚石绳锯切割混凝土的锯切力实验研究

对烧结金刚石串珠绳锯在锯切混凝土过程中锯切力的变化进行了跟踪检测实验,研究了锯切力随锯切参数及锯切长度的变化规律.实验结果表明:锯切过程中,工件上所承受的锯切力(水平力Fh和垂直力Fv)随着线速度vs的提高而减低,随着进给速度vf的提高而增加.锯切力随着锯切中工件长度L的增加而增加.垂直力与水平力之间存在着良好的对应关...     

Indirect cutting force measurement in multi-axis simultaneous NC milling processes

There have been many research works for the indirect cutting force measurement in machining process, which deal with the case of one-axis cutting process. In multi-axis cutting process, the main difficulties to estimate the cutting forces occur when the feed direction is reversed. This paper presents the indirect cutting force measurement method in contour NC milling processes by using current signals of servo motors. A Kalman filter disturbance observer and an artificial neural network (ANN) system are suggested. A Kalman filter disturbance observer is implemented by using the dynamic model of the feed drive servo system, and each of the external load torques to the x and y-axis servo motors of a horizontal machining center is estimated. An ANN system is also implemented with a training set of experimental cutting data to measure cutting force indirectly. The input variables of the ANN system are the motor currents and the feedrates of x and y-axis servo motors, and output variable is the cutting force of each axis. A series of experimental works on the circular interpolated contour milling process with the path of a complete circle has been performed. It is concluded that by comparing the Kalman filter disturbance observer and the ANN system with a dynamometer measuring cutting force directly, the ANN system has a better performance.     

Real time monitoring and diagnosis system development in turning through measuring a roundness error based on three-point method

A real time monitoring and diagnosis system to measure spindle center displacement (roundness error) during turning operation is introduced in this paper. The system was developed based on the three-point method. The error generated during cutting process was monitored and diagnosed by using a system equipped with a designed DSP (Digital Signal Processor) board and FFT (Fast Fourier Transform) algorithm. The system could estimate cutting force and predict other cutting characteristics such as chattering and tool wear. Using the spindle center fluctuation, i.e. a roundness error movement from the center, the relationship between the cutting force and the roundness error could also be investigated. The roundness error that eliminated geometric shape error and eccentric error from the measured signals in the frequency domain proved to be a dominating factor in determining cutting characteristics.     

Strain field analysis and sensor design for monitoring machine tool spindle bearing force

The fluctuating strain field produced by the rolling motion of the spindle bearing is analyzed by an elastic model and verified with experimental data. This strain field analysis is of considerable practical significance because of its close correlation to spindle bearing preload, cutting forces, and bearing running conditions. Based on the model, a conventional sensing scheme with strain gages mounted in a groove ground around the bearing outer ring is optimized by selecting proper sensor sizes, locations, and configurations such that signal cross-over error is minimized. In addition, the feasibility of a non-invasive sensing scheme achieved by attaching high sensitivity sensors on the outside surface of the spindle housing is studied. From the strain model, it is found that the level of strain field at the housing surface is substantially lower, and its distribution is not concentrated. Therefore, high sensitivity sensors and different sensing schemes are needed. Simulation results show that, compared with the conventional scheme, the output of this scheme requires less signal processing when the force acting on the bearing is fluctuating.     

A new method of cutting force measurement based on command voltages of active electro-magnetic bearings

In this paper, a new indirect method of measuring dynamic cutting forces is proposed. Milling tests have been performed on a five-axis machine, Gambin 120CR, fitted out with an electro-spindle with magnetic bearings developed by the company S2M, and named SMB30. These bearings are not affected by friction and wear. An experimental approach has been developed to determine the cutting forces as a function of the measured command voltages of the milling spindle’s magnetic bearings. The spindle is treated as a “black box”, where the transfer functions linking the unknown cutting force with command voltages are established experimentally. The cutting forces calculated from the command voltages of magnetic bearings are in good agreement with the ones measured with a Kistler four-component dynamometer. This indirect method of cutting force determination provides a useful way to estimate tool wear and monitor product quality in high-speed milling on-line.     

Cutting performance of diamond tools during ultra-precision turning of electroless-nickel plated die materials

This study is an attempt (a) to observe the wear characteristic of diamond tool with 200 km cutting distance and to study the effects of wear on the surface roughness and cutting forces and (b) to optimize various cutting parameters such as depth of cut, feed rate, spindle speed and phosphorus content. The experimental results showed that tool wear was not so significant although some defects on rake face were observed after cutting 15.6 km. Further cutting showed that the surface roughness increases with cutting distance, and that the cutting forces were larger than thrust force at the beginning of cutting, but after cutting 130 km, thrust force became larger and increased rapidly. It was also observed that forces increase with the increase of depth of cut, spindle speed and feed rate, and decrease with the increase of phosphorus content of the plating. Depth of cut has no significant effect on surface roughness, while it increases with increase of feed rate and decreases with the increase of percentage of phosphorus content in the workpieces. In case of spindle speed, surface roughness decreases with the increase of spindle speed up to a certain value and then starts to increase with the increase of spindle speed.     

Forces and hole quality in drilling

Drilling is one of the most commonly used machining processes in various industries such as automotive, aircraft and aerospace, dies/molds, home appliance, medical and electronic equipment industries. Due to the increasing competitiveness in the market, cycle times of the drilling processes must be decreased. Moreover, tight geometric tolerance requirements in designs demand that drilled hole precision must be increased in production.In this research, a new mathematical model based on the mechanics and dynamics of the drilling process is developed for the prediction of cutting forces and hole quality. A new method is also proposed in order to obtain cutting coefficients directly from a set of relatively simple calibration tests. The model is able to simulate the cutting forces for various cutting conditions in the process planning stage. In the structural dynamics module, measured frequency response functions of the spindle and tool system are integrated into the model in order to obtain drilled hole profiles. Therefore, in addition to predicting the forces, the new model allows the determination and visualization of drilled hole profiles in 3D and to select parameters properly under the manufacturing and tolerance constraints. An extensive number of experiments is performed to validate the theoretical model outputs with the measured forces and CMM hole profiles. It is observed that model predictions agree with the force and CMM measurements. Some of the typical calibration and validation results are presented in this paper.     

Dynamic response analysis in end milling using pre-twisted beam finite elements

This paper develops an analytical model for estimating the dynamic responses in end milling, i.e. dynamic milling cutter deflections and cutting forces, by using the finite-element method along with an adequate end milling-cutting force model. The whole cutting system includes the spindle, the bearings and the cutter. The spindle is modelled structurally with the Timoshenko-beam element, the milling cutter with the pre-twisted Timoshenko-beam element due to its special geometry, and the bearings with lumped springs and dampers. Because the damping matrix in the resulting finite-element equation of motion for the whole cutting system is not one of proportional damping due to the presence of bearing damping, the state-vector approach and the convolution integral is used to find the solution of the equation of motion. To assure the accuracy of prediction of the dynamic response, the associated cutting force model should be sufficiently precise. Since the dynamic cutting force is proportional to the chip thickness, a quite accurate alogorithm for the calculation of the variation of the chip thickness due to geometry, run-out and spindle-tool viration is developed. A number of dynamic cutting forces and tool deflections obtained from the present model for various cutting conditions are compared with the experimental and analytical results available in the literature, good agreement being demonstrated for these comparisons. The present model is useful, therefore, for the prediction of end milling instability. Also, the tool deflections obtained using the pre-twisted beam element are found to be smaller than those obtained using the straight beam element without pre-twist angle. Hence neglecting the pre-twist angle in the structural model of the milling cutter may overestimate the tool deflections.     

Modeling of spindle-bearing and machine tool systems for virtual simulation of milling operations

This paper presents a general, integrated model of the spindle bearing and machine tool system, consisting of a rotating shaft, tool holder, angular contact ball bearings, housing, and the machine tool mounting. The model allows virtual cutting of a work material with the numerical model of the spindle during the design stage. The proposed model predicts bearing stiffness, mode shapes, frequency response function (FRF), static and dynamic deflections along the cutter and spindle shaft, as well as contact forces on the bearings with simulated cutting forces before physically building and testing the spindles. The proposed models are verified experimentally by conducting comprehensive tests on an instrumented-industrial spindle. The study shows that the accuracy of predicting the performance of the spindles require integrated modeling of all spindle elements and mounting on the machine tool. The operating conditions of the spindle, such as bearing preload, spindle speeds, cutting conditions and work material properties affect the frequency and amplitude of vibrations during machining.     

An analytical finite element technique for predicting thrust force and torque in drilling

An analytical finite element technique was developed for predicting the thrust force and torque in drilling with twist drills. The approach was based on representing the cutting forces along the cutting lips as a series of oblique sections. Similarly, cutting in the chisel region was treated as orthogonal cutting with different cutting speeds depending on the radial location. For each section, an Eulerian finite element model was used to simulate the cutting forces. The section forces were combined to determine the overall thrust force and drilling torque. Good agreement between the predicted and measured forces and torques was found in orthogonal and oblique cutting and in drilling tests. The drilling tests were performed on AISI 1020 for several drill diameters, spindle speeds, and feed rates. An extension of the technique for predicting drill temperatures has also been described.     

Precompensation of machine dynamics for cutting force estimation based on disturbance observer

Complex machine-structure dynamics of a movable stage affects observer-based cutting force estimation. A dynamic compensation approach based on the concept of machine-in-the-loop learning is proposed to enhance the accuracy of cutting force estimation based on a disturbance-observer. Machine dynamics induced estimation errors are pre-compensated by modifying a digital filter representing an inverse disturbance transfer function. The order and parameters of the filter are self-optimized to enhance the estimation accuracy during iterative pre-milling tests with various rotational spindle speeds. The experimental results show that the proposed self-optimized filter achieves accurate wide-band cutting force estimation in milling process.     

An examination of the fundamental mechanics of cutting force coefficients

In metal cutting, the cutting force is the key factor affecting the machined surface, and is also important in determining reasonable cutting parameters. The research and construction of cutting force prediction models therefore has a great practical value. The accuracy of cutting force prediction largely depends on the cutting force coefficients of the material. In the average cutting force model, cutting force coefficients are considered to be constant. This study makes use of experiments to investigate the cutting force coefficients in the average cutting force model, with a view to accurately identifying cutting force coefficients and verifying that they are related only to the tool–workpiece material couple and the tool geometrical parameters, and are not affected by milling parameters. To this end, the paper first examines the theory behind identifying cutting force coefficients in the average cutting force model. Based on this theory, a series of slot-milling experiments are performed to measure the milling forces, fixing spindle speeds and radial/axial depths of cutting, and linearly varying the feed per tooth. The tangential milling force coefficient and the radial milling force coefficient are then calculated by linearly fitting the experimental data. The obtained results show that altering the milling parameters does not change the milling force coefficients for the selected tool/workpiece material combination.