A generalized on-line estimation and control of five-axis contouring errors of CNC machine tools

Nonlinear and configuration-dependent five-axis kinematics make contouring errors difficult to estimate and control in real time. This paper proposes a generalized method for the on-line estimation and control of five-axis contouring errors. First, a generalized Jacobian function is derived based on screw theory in order to synchronize the motions of linear and rotary drives. The contouring error components contributed by all active drives are estimated through interpolated position commands and the generalized Jacobian function. The estimated axis components of contouring errors are fed back to the position commands of each closed loop servo drive with a proportional gain. The proposed contouring error estimation and control methods are general, and applicable to arbitrary five-axis tool paths and any kinematically admissible five-axis machine tools. The proposed algorithms are verified experimentally on a five-axis machine controlled by a modular research CNC system built in-house. The contouring errors are shown to be reduced by half with the proposed method, which is simple to implement in existing CNC systems.

Highlights

•Generalized five-axis Jacobian function is derived based on the screw theory.

•On-line estimation of generalized five-axis contouring error method is presented.

•Axis components of contouring errors are evaluated without using forward and inverse kinematics of the five axis machine.

•On-line control and compensation of generalized five-axis contouring errors.

•The accuracy of five axis contouring is improved error by 50% with a simple to implement control method.

A new error measurement method to identify all six error parameters of a rotational axis of a machine tool

a new error measurement method, a Dual Optical Path Measurement Method (DOPMM), to identify error parameters of the rotational axis of a machine tool along its error sensitive directions. The method development was carried out on a motorized rotary stage equipped with a Doppler laser instrument. An error measurement experiment and a machining experiment were conducted on a five-axis machining center with a titling rotary table. It was found that the DOPMM can identify all of the six volumetric error parameters with the simple algebraic operations. Compared with the existing ball bar tests, which need a mathematical error modeling of machine tools to separate the error parameters, the identified process of DOPMM is more simple and easier to understand. And the operation of machine tools during the measurement is much easier than that of the existing ball bar tests. The experimental results showed that the part precision can have a significant improvement of 68% when the identified error parameters are used for error compensation. Hence, the measurement method established in this study is sensible and efficient, and could be used for the error compensation on a wide range of machine tools to improve their machining precision.

Highlights

All the six error parameters inherent to a rotation axis can be identified.

Only the measured axis is moving during the measurement process.

The error identification does not need a volumetric error modeling.

The identified process, a simple algebraic process, is easier to understand.

Development and implementation of a NURBS interpolator with smooth feedrate scheduling for CNC machine tools

Parametric interpolation for Non-Uniform Rational B-Spline (NURBS) curve has become more important than ever before in the control of CNC machine tools. An effective NURBS interpolator not only can obtain accurate contour trajectories, but also have smooth dynamics performance. This paper proposes a numerically efficient NURBS interpolation scheme which consists of two stages namely preprocessing and interpolating. In the stage of pre-processing, the parameter interval is split into several blocks at breakpoints and an iterative numerical quadrature method is applied for each block. By means of the iterative quadrature method, the initial parameter intervals of each block are divided into several subintervals according to the arc length approximation error. Meanwhile, the curvature of each knot and the cubic polynomial coefficients of each subinterval are obtained. Then the critical points with large curvature of each block are found from the candidate points and the tolerated speed of each critical point is calculated according to the constraints of chord error and centripetal acceleration. Hence, the feedrate scheduling based on the S-shaped acceleration profile for each block can be preplanned via the approximate arc length of each subinterval, the tolerated speed of each critical point and kinematics characteristics such as acceleration/deceleration and jerk limits of the machine tools. In the stage of interpolating, the parameter of the next interpolation point can be calculated directly using the cumulative arc length and the cubic polynomial coefficients of each subinterval. Finally, a series of numerical simulations and real machining experiments are conducted, and the simulation and experimental results have showed the good performance of the proposed NURBS interpolator both in efficiency and accuracy.

Highlights

A NURBS interpolator with smooth feedrate scheduling is proposed.

A numerical method is applied to generate jerk-limited feedrate profile.

The stage of interpolating benefits much from the stage of feedrate scheduling.

The proposed method is validated by simulations and experimental results.

Dynamics of ultra-high-speed (UHS) spindles used for micromachining

Micromachining dynamics commonly dictate the attainable accuracy and throughput that can be obtained from micromachining operations. The dynamic behavior of miniature ultra-high-speed (UHS) spindles used in micromachining critically affects micromachining dynamics. As such, there is a strong need for effective techniques to characterize the dynamic behavior of miniature UHS spindles. This paper presents a systematic experimental approach to obtain the speed-dependent two-dimensional dynamics of miniature UHS spindles through experimental modal analysis. A miniature cylindrical artifact with 5 mm overhang is attached to (and rotating with) the spindle to enable providing the dynamic excitations to and measuring the resulting motions of the spindle. A custom-made impact excitation system is used to reproducibly excite the spindle dynamics up to 20 kHz while controlling the impact force. The resulting radial motions of the spindle are measured in two mutually perpendicular directions using two independent fiber-optic laser Doppler vibrometers (LDVs). To ensure the mutual orthogonality of the measurements, the two lasers are aligned precisely using an optical procedure. A frequency-domain filtering approach is used to remove the unwanted spindle motion data from the measurements, thereby isolating the dynamic response. The spindle dynamics is then represented in the form of frequency response functions (FRFs). A global curve-fitting technique is applied to identify natural frequencies and damping ratios. The developed approach is demonstrated on a miniature UHS spindle with aerodynamic bearings, and dynamic characteristics are analyzed at different spindle speeds and collet pressures. The spindle speed is shown to have a significant effect on dynamic response, especially at higher spindle speeds, while the collet pressure is observed not to have any significant effect on the spindle dynamics. It is concluded that the presented approach can be used to characterize the dynamics of miniature UHS spindles effectively. Experimental methodology to obtain dynamics of UHS spindles is presented.The motion of the spindle is measured in two mutually perpendicular directions.A custom made impact excitation system enabled repeatable excitations up to 20 kHz.The presented filtering approach is effective to remove unwanted spindle motion data.The spindle speed is shown to have a significant effect on dynamics of spindle.

Numerical study of the solution heat treatment, forming, and in-die quenching

An FE model of the solution heat treatment, forming and in-die quenching (HFQ) process was developed. Good correlation with a deviation of less than 5% was achieved between the thickness distribution of the simulated and experimentally formed parts, verifying the model. Subsequently, the model was able to provide a more detailed understanding of the HFQ process, and was used to study the effects of forming temperature and speed on the thickness distribution of the HFQ formed part. It was found that a higher forming speed is beneficial for HFQ forming, as it led to less thinning and improved thickness homogeneity. A coupled thermo-mechanical FE model of the HFQ forming process is developed. The simulation results are accurate within 5% of the experimental results. A detailed understanding of deformation during the HFQ forming process is provided. For HFQ, improved thickness homogeneity can be achieved with higher forming speeds.

Due to growing concerns about escalating energy prices and the contribution of CO₂ emissions to climate change, fuel efficiency has become the primary driver for technological advancements in road vehicles. Two potential routes to improving efficiency are powertrain optimization techniques and mass reduction. The body structure of an automobile constitutes around a quarter of its mass. By using lightweight materials such as aluminium alloys, this mass can be reduced by over 40%, leading to approximately a 32% increase in efficiency urrently, only 9% of an automobile׳s mass is composed of aluminium parts, which are predominantly cast. Significant research is now being undertaken to expand the use of aluminium into formed sheet parts, such as body panels and bumpers. However, one of the major obstacles to using sheet aluminium alloys is their limited formability at room temperature, which is especially the case for the higher strength alloys . In addition to work being done to develop alloys of improved formability , advanced forming technologies are also being investigated to form complex-shaped parts from these alloys.

Solution heat treatment, forming, and in-die quenching (HFQ) is one such technology [3]. In this process, the blank is first heated up to its solution heat treatment (SHT) temperature. At this elevated temperature, the solid solubility is increased and the alloying elements, or precipitates, fully dissolve into the aluminium matrix. Consequently the yield stress is reduced and the material becomes more ductile due to the fewer obstacles to dislocation movement, enabling more complex shapes to be formed. The blank is then transferred to a cold die, formed at a high speed and held in the cold tool to achieve a rapid cooling rate to room temperature. The fast pace of the process allows a supersaturated solid solution (SSSS) to be obtained. This is a desirable microstructure that is extremely important for the post-form strength of a part, particularly if a heat treatable alloy is used. Valuable research work has been conducted on the effects of solutionising time and quenching rate on an HFQ formed part, which verified the high strength achievable following an appropriate ageing process . Holding the formed part in the cold die after forming minimizes thermal distortion and springback due to the high cooling rate and lower material strength during forming.

The HFQ process hence presents an opportunity to expand the use of aluminium in complex-shaped sheet parts. However, it is essential that the correct combination of forming parameters, such as temperature, ram speed and blankholding force, are selected. Finite element (FE) process simulations are invaluable for determining and optimizing these parameters, and can reduce the efforts of experimental trials and hence lead times and costs, while ensuring a high quality final part . The feasibility of new, unconventional metal forming processes can also be assessed by running FE simulations .

In recent years, efforts have been made to develop FE models capable of simulating sheet metal forming processes at elevated temperatures accurately, using material models comprised of phenomenological or physically based equations calibrated using the results of uniaxial tension tests . Tabular flow stress data can also be used to describe the material if a sufficient range of values is input, to prevent excessive extrapolation of the data and potentially inaccurate results . A failure criterion is necessary to model the material behaviour upon the nucleation of damage and beyond the point of necking, to accurately simulate the later stages of the forming process  . For non-isothermal processes, coupled thermo-mechanical simulations are conducted using temperature dependent material models, to account for the heat transfer between the blank and the tool parts . The interfacial heat transfer coefficient in such a process can be predicted accurately using numerical methods  If the assumption can be made that the blank׳s temperature field is constant during the forming phase, then it may be calculated in a separate thermal simulation and then input in a purely mechanical simulation to save on computational time . Friction models can also be implemented to improve the results of forming simulations of complex-shaped parts, by accounting for the viscosity of the lubricant used during forming and the surface roughness of the tooling and blank .

To verify the accuracy of the results of a simulation, most authors compared the numerical forming load/displacement curves with the experimental ones Further verification of and confidence in the results was achieved by comparing geometrical aspects of the numerically and experimentally formed parts, such as their draw depth in the case of a square cup drawing process [17], and their thickness distributions 

For the HFQ forming of the aluminium alloy AA5754 into a complex-shaped part, an FE simulation utilizing a physically based material model was run in ABAQUS. The development and application of this simulation is documented in this paper. Ductility and forming tests were first run to acquire data for calibrating the material model and for comparing against the results of the FE simulations, respectively. The viscoplastic damage constitutive equations of the model were then implemented via the user-defined subroutine VUMAT in ABAQUS. The use of a coupled thermo-mechanical simulation meant that the effect of non-uniform temperature could be captured. By comparison of the numerical thickness distribution data with the available experimental data from the forming tests, the results of the simulation were verified. The same simulation set-up could then be used to investigate more detailed aspects of the deformation and to predict part quality under different forming parameters.

The forming tests on the alloy were conducted using the HFQ process on an existing tool for producing stiffener components, designed in the authors׳ laboratory and manufactured by a diemaker. The results of the tests could be used to verify the simulation set-up for the HFQ process.

The tool used, shown in Fig. 3, was mounted onto a 250 kN ESH press which provided the forming load. The test specimen was first heated in a furnace to the target temperature, monitored using a thermocouple wire attached to it, and then quickly and carefully placed in the tool for 10 s, which stamped the specimen when the press was activated. As the load was applied, the top blankholder was displaced downwards, compressing the 1st stage blankholding force (BHF) springs. With the blank held between the top and bottom blankholders, the top die deformed the blank further towards the bottom die, engaging the 2nd stage BHF gas springs. The formed part was then held in the cold die after forming to quench it to room temperature. Subsequently the load was removed and the ejector springs separated the blankholders, enabling removal of the part. Further details about the process are provided in Section 3.1. The die, blankholders and punches of the tool were lubricated before each test using Stuart lubricating oil supplied by Houghton plc.

A method of using turning process excitation to determine dynamic cutting coefficients

Identification of the dynamic cutting force coefficients is an essential work in cutting process modeling. The excitation equipment employed to produce dynamic cutting process is usually sophisticated and may lead to potential error. An alternative method of turning process excitation is proposed to simplify the procedure of cutting dynamics measurement. A cantilever workpiece used in cylindrical turning process has been modeled with a double degree-of-freedom system that supports variable dynamic parameters. The structural dynamics of the equivalent system are analyzed with the theoretical derivation and the finite element simulations. The influence of structural dynamic variation on the chatter frequency is investigated, based on which the self-excited chatter is considered as a method of the turning process excitation. This method is applied in the cutting dynamics tests. The dynamic cutting force coefficients could be measured through a single chattering turning process. Stability analysis is conducted for verification of the measured dynamic cutting coefficients. Chatter is proved to be an effective turning process excitation. The cantilever workpiece is modeled with a double degree of freedom system. The equivalent structural dynamics will change with the cutting point movement. The chatter frequency is controlled by moving the cutting point. The dynamic cutting force coefficients are identified in a single turning process.

Experimental investigation of drilling damage and stitching effects on the mechanical behavior of carbon/epoxy composites

The main purpose of composite materials drilling is the need to put together different parts of a structure, in aeronautics for example. Machining generates damages which affect mechanical properties and have to be taken into account during manufacturing process. The objective of this study is to experimentally analyze the influence of drilling on a carbon/epoxy composite, to investigate the relationships among damages, cutting forces, mechanical properties of the drilled specimens and crack propagation. Stitching and a range of spindle speed and feed have been tested when drilling with a classic twist drill. The effect of each parameter has been assessed in terms of thrust force, moment (during machining) and defects, and then linked to mechanical test results. Experimental results have shown significant influences of feed and composite configuration on delamination. Furthermore, cyclic tensile tests have shown that reducing damage and using stitching help increasing tensile strength. Cutting forces and damages rise significantly with the feed. Stitching allows reducing damages generated inside the hole. Minor defects generate higher fracture strength for the unstitched composite. Fracture strength for stitched specimen is greatly higher than for unstitched one. Sudden and progressive fractures are noted for unstitched and stitched laminates respectively.

Feed speed scheduling method for parts with rapidly varied geometric feature based on drive constraint of NC machine tool

A sub-regional processing method with variable machining parameters is proposed.The proposed approach is suitable for parts with rapidly varied geometric feature. The generation mechanism of the machining error is studied. The relation between the programmed feed speed and the curvature is established.The drive constraint is taken into account in the NC machining method As the existence of rapidly varied geometric feature and during the NC manufacturing process of this kind of parts, the actual moving speed of the workbench of the NC machine tool cannot reach the feed speed set in the NC program timely due to the drive constraint of NC machine tool. Furthermore, the machine tool would vibrate violently with the drive constraint when employing the constant machining parameter to process the parts with rapidly varied geometric feature, which seriously restricts the improvement of processing this kind of parts with high quality and high efficiency. In order to manufacture such parts with high quality and high efficiency, a sub-regional processing method with variable machining parameters is proposed. Firstly, the generation mechanism of the machining error is studied, and its mathematical model is built. Then the change rule of the machining error influenced by the curvature and the NC programmed feed speed is found out. Finally, taking the drive constraint and the machining error requirement into account, the relationship between the programmed feed speed and the curvature is established, and the corresponding programmed feed speeds to different curvatures are obtained. Taking the NC machining of the edge line of spiral microstrip antenna, which is an equiangular spiral, for example, the experiment results show that compared with the machining result with constant machining parameter, the maximum machining error of the sub-regional processing method with variable machining parameters decreases by 35.51% and the average value of the machining error decreases by 46.65%. For another example, the clover rose line is machined and the processing quality is also improved. This study proves that the method distributing the programmed feed speeds based on the curvature variation can improve the machining precision and ensure processing efficiency, and provides an effective method to manufacture parts with rapidly varied geometric feature.

Validation of volumetric error compensation for a five-axis machine using surface mismatch producing tests and on-machine touch probing

Validation of G-code compensation for 5-axis machine tools by mismatch producing tests. Seven slots are machined, one half-slot at a time using alternative indexations.Surface mismatches are touch probe measured by the erroneous machine itself. “All on-machine” and fully automated validation strategy in a single setup.Machining patterns are sensitive to seven out of eight geometric link errors.In order to validate volumetric error compensation methods for five-axis machine tools, the machining of test parts has been proposed. For such tests, a coordinate measuring machine (CMM) or other external measurement, outside of the machine tool, is required to measure the accuracy of the machined part. In this paper, a series of machining tests are proposed to validate a compensation strategy and compare the machining accuracy before and after the compensation using only on-machine measurements. The basis of the tests is to machine slots, each completed using two different rotary axes indexations of the CNC machine tool. Using directional derivatives of the volumetric errors, it is possible to verify that a surface mismatch is produced between the two halves of the same slot in the presence of specific machine geometric errors. The mismatch at the both sides of the slot, which materializes the machine volumetric errors is measured using touch probing by the erroneous machine itself and with high accuracy since the measurement of both slot halves can be conducted using a single set of rotary axes indexation and in a volumetric region of a few millimetres. The effect of a compensation strategy is then validated by comparing the surface mismatch value for compensated and uncompensated slots.

http://www.sciencedirect.com/science/journal/08906955/87