This paper reviews the state-of-the-art of wavelet analysis for tool condition monitoring (TCM). Wavelet analysis has been the most important non-stationary signal processing tool today, and popular in machining sensor signal analysis. Based on the nature of monitored signals, wavelet approaches are introduced and the superiorities of wavelet analysis to Fourier methods are discussed for TCM. According to the multiresolution, sparsity and localization properties of wavelet transform, literatures are reviewed in five categories in TCM: time–frequency analysis of machining signal, signal denoising, feature extraction, singularity analysis for tool state estimation, and density estimation for tool wear classification. This review provides a comprehensive survey of the current work on wavelet approaches to TCM and also proposes two new prospects for future studies in this area.

Wavelet analysis of sensor signals for tool condition monitoring: A review and some new results

In this paper, a dynamics-based interpolator with real-time look-ahead (DBLA) algorithm is proposed to generate a smooth and jerk-limited acceleration/deceleration (ACC/DEC) feedrate profile. The interpolator consists of three modules: geometric, dynamics-based, and jerk-limited modules. The geometric module can detect the local maximum/minimum (max/min) curvatures, and divide a NURBS curve into small segments according to the information of sharp corners. The feedrates at the sharp corners are determined based on confined chord errors and curvatures of the curve. The dynamics-based module utilizes a dynamics feedrate modification equation (DFME) to estimate contour errors at the sharp corners and adjusts the feedrates at the locations of the sharp corners. The jerk-limited module plans the feedrate profile of the curve according to the segments’ length and the given jerk limit. Simulations are performed to verify real-time performance of the look-ahead algorithm. Experiments using a PC-based motion controller and an X–Y table are conducted to demonstrate that high-accuracy can be achieved with the proposed dynamics-based interpolator as compared to the adaptive-feedrate and the curvature-based feedrate interpolation algorithms.

Development of a dynamics-based NURBS interpolator with real-time look-ahead algorithm

Monitoring and processing signal applied in machining processes – A review

This article presents a new format of tool path polynomial interpolation in 5-axis machining. The linear interpolation usually used produces tangency discontinuities along the tool path, sources of decelerations of the machine tool whereas polynomial interpolation reduces the appearance of such discontinuities. The new format involves a faster tool path and a better surface quality. However, it imposes a modification of the process so as to take the interpolation format and the inverse kinematics transformation (necessary to 5-axis machining) into account. This article deals with the geometrical problem of tool path calculation. Validation tests are detailed. They show that profits concern the reduction of machining time as well as the quality of the machined surfaces. Indeed, the trajectory continuity avoids the appearance of marks and facets.

A new format for 5-axis tool path computation, using Bspline curves

This paper proposes an off-line feedrate scheduling method of CNC machines constrained by chord tolerance, acceleration and jerk limitations. The off-line process for curve scanning and feedrate scheduling is realized as a pre-processor, which releases the computational burden in real-time task. The proposed method first scans a non-uniform rational B-spline (NURBS) curve and finds out the crucial points with large curvature (named as critical point) or G^0 continuity (named as breakpoint). Then, the NURBS curve is divided into several NURBS sub-curves using curve splitting method which guarantees the convergence of predictor-corrector interpolation (PCI) algorithm. The suitable feedrate at critical point is adjusted according to the limits of chord error, centripetal acceleration and jerk, and at breakpoint is adjusted based on the formulation of velocity variation. The feedrate profile corresponding to each NURBS block is constructed according to the block length and the given limits of acceleration and jerk. In addition, feedrate compensation method for short NURBS blocks is performed to make the jerk-limited feedrate profile more continuous and precise. Because the feedrate profile is established in off-line, the calculation of NURBS interpolation is extremely efficient for CNC high-speed machining. Finally, simulations and experiments with two free-form NURBS curves are conducted to verify the feasibility and applicability of the proposed method.

https://ir.nctu.edu.tw:443/bitstream/11536/23168/1/000291337300006.pdf

The feedrate scheduling of NURBS interpolator for CNC machine tools

Parametric interpolation has many advantages over linear interpolation in machining curves. Real time parametric interpolation research so far has addressed achieving a uniform feed rate, confined chord errors and jerk limited trajectory planning. However, simultaneous consideration of confined chord errors that respect the acceleration and deceleration capabilities of the machine has not been attempted. In this paper, the offline detection of feed rate sensitive corners is proposed. The velocity profile in these zones is planned so that chord errors are satisfied while simultaneously accommodating the machine's acceleration and deceleration limits. Outside the zone of the feed rate sensitive corners, the feed rate is planned using the Taylor approximation. Simulation results indicate that the offline detection of feed rate sensitive corners improves parametric interpolation. For real time interpolation, the parametric curve information can be augmented with the detected feed rate sensitive corners that are stored in 2×2 matrices.

A parametric interpolator with confined chord errors, acceleration and deceleration for NC machining

Tool wear identification and estimation present a fundamental problem in machining. With tool wear there is an increase in cutting forces, which leads to a deterioration in process stability, part accuracy and surface finish. In this paper, cutting force trends and tool wear effects in ramp cut machining are observed experimentally as machining progresses. In ramp cuts, the depth of cut is continuously changing. Cutting forces are compared with cutting forces obtained from a progressively worn tool as a result of machining. A wavelet transform is used for signal processing and is found to be useful for observing the resultant cutting force trends. The root mean square (RMS) value of the wavelet transformed signal and linear regression are used for tool wear estimation. Tool wear is also estimated by measuring the resulting slot thickness on a coordinate measuring machine.

Tool wear monitoring in ramp cuts in end milling using the wavelet transform

Wavelets permit multiresolution analysis of curves and surfaces. A complex curve can be decomposed using wavelet theory into lower resolution curves. The low-resolution (coarse) curves are similar to rough-cuts and high-resolution (fine) curves to finish cuts in NC machining. In this paper, we investigate the applicability of multiresolution analysis using B-spline wavelets to NC machining of contoured 2D objects. High-resolution curves are used close to the object boundary similar to conventional offsetting while lower resolution curves are used farther away from the object boundary. Experimental results indicate that wavelet-based tool path planning improves machining efficiency. Tool path length is reduced, sharp corners are smoothed out thereby reducing uncut areas and larger tools can be selected for rough-cuts.

https://lib.dr.iastate.edu/cgi/viewcontent.cgi?article=1735&context=rtd

Multiresolution analysis as an approach for tool path planning in NC machining

This paper investigates new wavelet-based multiresolution modeling techniques in CAD Models in the system are represented by endpoint-interpolating B-spline functions Wavelet deformation techniques are extended to include synthesis editing and detail blending from previous sweep editing and fractional editing methods Application of multiresolution editing to multiple patches of complex topology is investigated An algorithm for multi-patch deformation is developed by enforcement of G0 continuity between adjacent patches After editing G1 continuity may be recaptured by numerical optimization of the error vectors along boundary seams A simple CAD interface is implemented for B-spline patch acquisition based on reverse engineered data and layer based modeling and a moving cursor plane is used for three-dimensional (3D) editing Design examples are presented to illustrate the 3D wavelet editing capability The developed wavelet deformation techniques can be a useful complement to current CAD systems by providing powerful new modeling and editing capabilities

Multiresolution modeling techniques in CAD

A complex curve can be decomposed using wavelet-based multiresolution analysis into lower resolution curves. In this paper B-spline wavelet theory is applied to NC machining of contoured 2D objects. High-resolution curves are used close to the object boundary, while lower resolution curves are used farther away from the object boundary. This reduces tool path length and sharp corners are smoothed out thereby reducing uncut areas. The wavelet curves are clipped against a loose convex hull of the 2D object contour to further improve the efficiency of the generated tool paths. Simulation results indicate that the wavelet based tool paths and clipping improves machining efficiency.

Ranga Narayanaswami

Papers

A parametric interpolator with confined chord errors, acceleration and deceleration for NC machining

Tool wear monitoring in ramp cuts in end milling using the wavelet transform

Multiresolution analysis as an approach for tool path planning in NC machining

Multiresolution modeling techniques in CAD

Multiresolution offsetting and loose convex hull clipping for 2.5D NC machining