Chordal Deviation Research Articles

An improved path discretization method for automated fiber placement

In the automated fiber placement process, the continuous placement paths need to be discretized into a finite number of path points because the laying head cannot continuously trace the predetermined curved path. However, the discretization of the placement path, which is a spatial curve, will inevitably introduce error. In this paper, an improved path discretization algorithm is proposed for the fiber placement of complex double-curved structures. Firstly, the discrete error was decomposed into normal direction and binormal direction, and they are correlated with the laying process and their influences on the laying quality are discussed, respectively. Secondly, the relationship between the binormal error and the overlap of the tow is analyzed with differential geometry, and the influence of the normal error on laying force is discussed by the pressure experiment and the finite element method. Finally, the improved path discretization algorithm has been verified on double-curved surface and compared with the traditional path discrete algorithms. The results showed that the number of discrete path points decreases by 45.8% on average compared with the chordal deviation discretization algorithm and by 63.1% compared with the equal-arc discretization algorithm.

Research on Influence of CMM Sampling Points on Detection of Feature Parameters for Turbine Blade

Sampling plan is an essential part for measuring profile of turbine blade with coordinates measuring machine(CMM), and the detection of feature parameters is a key component of turbine blade inspection. However, the influence of the sampling strategy on the blade feature parameters evaluation has been rarely studied. In order to understand the correlation between the sampling strategy and the accuracy of blade profile feature parameters, firstly, the extraction methods of turbine blade feature parameters were proposed, and these methods were compiled into an executable program TBGeoInspect. Secondly, based on the level principle, the unified mathematical representations of uniform sampling, curvature-based sampling, chord deviation sampling, weighted curvature-based sampling, and curvature-arc length sampling were given. The effect of these five sampling algorithms on the accuracy of turbine blade profile feature parameters was gained through simulation and experiment results of blade sampling. The results validate that the uncertainty of turbine blade feature parameters and sectional curve fitting error are lowest with curvature-arc length sampling method under the same number of sampling points.

An adaptive sampling methodology for measuring blades with CMM based on dominant feature points

Sampling strategy is one of the most critical components of the contact probing process with coordinate measuring machines (CMMs). The number and location of sampling points have direct impacts on the efficiency and reliability of the measurements. Blades of aviation engines have complex geometry and extremely high precision requirements, but the sampling strategy of blades is still a difficult problem which limits the use of CMMs in blade inspection. To balance the measuring efficiency and accuracy of CMM, an adaptive sampling algorithm based on dominant feature points is proposed. In this algorithm, the points are adaptively sampled through a modified B-spline least-square fitting process with dominant feature points and new dominant points if necessary, and the new dominant points are computed by a new method, namely weighted curvature mass moment method. The sections of the blade to be measured are determined with this adaptive sampling algorithm to be the leading and trailing edge curves, and the points on each section to be measured are determined using dominant feature points of the blade profile. The definition and extraction methods for dominant feature points of the blade profile are also researched. By comparing the reconstruction errors of sampling points for several different blades, this adaptive sampling algorithm is proved to be more efficient and accurate than the equal parameter sampling method, equal arc length sampling method, and chord deviation sampling method.

B-spline contour curve approximation and deformation analysis of complex ceramic core

Complex ceramic core is the critical part for manufacturing hollow turbine blade in the investment casting process. The complex geometry, small inner structures and high-precision requirements of ceramic cores make them difficult to fabricate, and the shape and dimensional accuracy of ceramic cores are very low in factory practice. To understand the deformation characteristics of ceramic cores, a noisy points recognition algorithm, an extraction method of measuring cross-section contour points and a B-spline iterative fitting algorithm using dominant points of chord deviation are proposed. First, the cross-section contour points were provided through registration, slicing and intersection methods. Second, the noisy points were deleted by convex noisy points and concave noisy points recognition algorithms. Third, the cross-section contour curve of the ceramic core was fitted through B-spline iterative fitting method with chord deviation dominant points. The curves fitted with chord deviation points and curves fitted with local maximum curvature points were compared with simulating data and scanning data, respectively, and the results show that B-spline fitting curve needs fewer chord deviation points than local maximum curvature points, 24.4% fewer in simulation validation and 12.5% fewer in experimental validation. In the end, the bending deformation, torsion deformation and shrinkage deformation errors of ceramic core are established by fitting contour curves of serial cross sections of the ceramic core.

A Generic Multi-Axis Post-Processor Engine for Optimal CNC Data Creation and Intelligent Surface Machining

This paper focuses on the development of a multi-axis post-processor engine with a curvature-based feed adaptation module, capable of extracting generic CNC data for high precision machining. The motivation of this work stems from the drawback of standard and commercial post-processors to modify their internal source codes so as to be implemented to newly-developed functions which integrate modern CNC units. The multi-axis post-processor proposed in this work operates as a stand-alone function of an artificial intelligent module that optimizes machining parameters for standard swept cut multi-axis surface tool-paths. The post-processor developed receives APT source files previously been optimized by means of a genetic algorithm that handles cutting tool selection; radial cut engagement; maximum discretization step; lead and tilt angles. The algorithm optimizes the aforementioned machining parameters towards the minimization of the number of cutter locations found in a specific APT source file as well as the surface machining error as a combined effect of chordal deviation and scallop height. The final APT output is then properly handled by the post-processor engine so as to extract the final ISO code for a double-pivoted head 5-axis CNC machine and compute optimal values for feed rate in each NC block considering the interpolation error and curvature analysis given the surface properties. To simulate and verify our proposals, the MAZAK Vortex 1000 gantry-type 5-axis CNC machine tool equipped with a Fanuc 15i CNC unit has been selected as the manufacturing resource corresponding to the final CNC output that the proposed post-processor computes. A benchmark sculptured part is created and used for the virtual material removal simulation in CATIA® V5 R18. For that part, both the proposed post-processor engine and a commercially available post-processor were employed to extract G-code data whilst it was shown that identical outputs were obtained.

A practical sampling method for profile measurement of complex blades

Blade is one of the most important parts in turbine machinery. The complex geometry of blades not only makes them difficult to fabricate, but also leads them difficult to inspect. Typically, the surface of blades is measured by using coordinate measuring machine (CMM). Since the measurement time and cost increase proportionally as the increase of measurement points, it is essential to sample measurement points which can represent entire blade with sufficient confidence and accuracy. In order to achieve a certain allowable deviation with a suitable set of points, a practical sampling method for surface measurement of blades was studied. Firstly, the leading edge curve and trailing edge curve were supposed to represent the twisted and bend information of blades. A sampling method based on maximum chordal deviation for leading edge curve and trailing edge curve was researched. Further, a fusion approach for sampling points on both edge curves, which determine the cross-sections, was proposed. Secondly, the inspection points sampling method for sectional curves were investigated. Finally, two simulation and one experimental examples were used to demonstrate the sampling methodology. The results indicated that the approach of this study can ensure the measurement precision at high curvature potion by measuring a small number of points.

Performance evaluation of CUDA programming for 5-axis machining multi-scale simulation

5-Axis milling simulations in CAM software are mainly used to detect collisions between the tool and the part. They are very limited in terms of surface topography investigations to validate machining strategies as well as machining parameters such as chordal deviation, scallop height and tool feed. Z-buffer or N-buffer machining simulations provide more precise simulations but require long computation time, especially when using realistic cutting tools models including cutting edges geometry. Thus, the aim of this paper is to evaluate Nvidia CUDA architecture to speed-up Z-buffer or N-buffer machining simulations. Several strategies for parallel computing are investigated and compared to single-threaded and multi-threaded CPU, relatively to the complexity of the simulation. Simulations are conducted with two different configurations including Nvidia Quadro 4000 and Geforce GTX 560 graphic cards.

Path-Planning of Laser Quenching of 5-Axis Laser Machine Tool

This paper presents a path-planning method of laser tool in 5-axis laser quenching for complicated surface. In this method, two main factors are concerned which include: (1) Planning the CC paths on the complicated surface quenched to maintaining laser tool scanning speed constant easily in quenching process; (2) Diminishing the chord deviation between the actual value and its approximation by choosing different interpolation methods according to the curvature radius of CC points which is being quenched. This method effectively ensures the part’s laser quenching quality.

Numerical interpolators to maintain discretisation step under constant minimum chord error for spiral-type surfaces

This paper proposes a simple philosophy of machining 2D spiral-type sculptured surfaces by analysing a given mathematical expression which describes such surfaces and then generating a shape interpolator via the implementation of already known numerical techniques for CNC machining such as linear and circular approximation. An algorithm discretises the ideal curve of a given surface so as to maintain the lowest possible value in terms of chordal deviation existed between the theoretical curve and the real tool path trajectory. The algorithm is applied to 2D geometries only and is going to be developed in the near future. Nevertheless, experiments conducted in CAM software simulations to approximate the curve of a centrifugal impeller's blade as a paradigm for three axis machining, have show promising directions for building an entire software-based optimisation system integrated to cutting edge manufacturing systems.

Iso-parametric tool-path planning for point clouds

Due to the compute-intensiveness and the lack of robustness of the algorithms for reconstruction of meshes and spline surfaces from point clouds, there is a need for further research in the topic of direct tool-path planning based on point clouds. In this paper, a novel approach for planning iso-parametric tool-path from a point cloud is presented. Since such planning falls into the iso-parametric category, it intrinsically depends on the parameterization of point clouds. Accordingly, a point-based conformal map is employed to build the parameterization. Based on it, formulas of computing path parameters are derived, which are much simpler than the conventional ones. By regularizing parameter domain and on the basis of the previous formulas, boundary conformed tool-path can be generated with forward and side step calculated against specified chord deviation and scallop height, respectively. Experimental results are given to illustrate the effectiveness of the proposed methods.

Synthesis and Simplification of Fractal Profile

In order to import a synthesized fractal profile into finite element software, the profile synthesized by discrete Fourier transform was studied. The synthesized profile was filtered in frequency domain in order to filter its high frequency components and to make it smooth, and then the chord deviation algorithm was used to reduce its redundant data in space domain. It was found that: after filtering, the profile is smooth but with lots of redundant data; the chord deviation algorithm can simplify the profile which is redundant in space domain; the time needed in the process of importing a profile into finite element software can be reduced greatly after profile simplification.

The CAM System for Scroll Profile with Three CNC Interpolations

The scroll profile is complex with involute curve and high precision is required. Owing to the interpolation method has significant effects on the dynamic behaviour and to obtain the flexibility of the machining, this paper focuses on the development of a computer-aided manufacturing methodology for precision scroll by the combination of curve fitting and CNC interpolation. In this paper, the method for design and manufacture of the scroll profile is established based on the differential geometry and the enveloping theory. The cutter location using the cylindrical end mill is derived and the cutting path sequences are planned. Three types curve fitting methods: linear fitting, circular biarcs curve fitting, and NURBS curve fitting are adopted to approximate the toolpath of the scroll profile. The error control is used as the basis for generating appropriate toolpath to ensure the machining accuracy. The circular biarcs fitting and NURBS curve fitting can obtain continuous smooth toolpath. In the identical chordal deviation, the circular biarcs curve fitting provides the best performance. The toolpath generated by the proposed method is verified through the solid cutting simulation and the trial-cut on a three-axis machine tool.

Development of an improved CNC interpolator and performance evaluation in terms of chordal error and feedrate deviation

The parametric interpolators of modern CNC machines use Taylor's series approximation to generate successive parameter values which, after substituting into the curve equation, gives the x, y, z coordinates of the tool positions. In order to achieve greater accuracy, higher order derivatives are required which complicates the calculation when the curve is represented by NURBS curve. This method calculates the chordal error on a given segment by estimating the curvature which neglects a fraction of the error. In order to avoid calculating higher derivatives and make the calculations easier the classical fourth-order Runge-Kutta (RK) method is proposed in this research, which only requires the first derivative to be calculated, but achieves the accuracy of Taylor's approximation with higher order terms. This paper also proposes the estimation of chordal error on the average value of the parameters at the end points of a given curve segment, which does not require calculation of curvature at every segment. Finally computer simulation is performed on different types of spline curves to show that the proposed method results in reduced chordal error and less fluctuation in feedrate.

Determination of Geometry-Based Errors for Interpolated Tool Paths in Five-Axis Surface Machining

Five-axis computer numerical control (CNC) machining is characterized with a multitude of errors. Among them an important component comes from the computer-aided manufacturing software known as the geometry-based errors. A new and accurate method to determine these errors is presented in this paper as opposed to the conventional chordal deviation method. The present method allows establishing the exact linearly interpolated tool positions between two cutter contact points on a given tool path, based on the inverse kinematics analysis of the machine tool. A generic procedure has been developed to ensure wide applicability of the proposed method. Analytical derivation of the geometry-based errors provides insights regarding the origin of these errors and their affecting parameters. Due to the highly non-linear characteristics of the problem, analytical solutions can only be obtained for simple surface geometry. Numerical computation is able to determine the errors for general surface shapes but it would be difficult to uncover further insightful information from the calculated error values. Besides the local surface geometry, the configuration of the kinematic chain of the CNC machine has been found to be the primary factor controlling the resulting value and type of the geometry-based errors. Implementations with a typical complex free-form surface demonstrated that the conventional chordal deviation method was not reliable and could significantly underestimate the geometry-based errors.

A Freeform Surface Modelling System Based on Laser Scan Data for Reverse Engineering

Reverse engineering technology starts with a measurement process, inspecting the surface contour of the object, and applies a CAD geometric modelling technique to construct the surface model. The purpose of this study is to develop a freeform surface modelling system involving the functions of data reorganisation and surface construction of reverse engineering. An important task in reverse engineering is the process of reducing the large amount of coordinate data derived by measurement devices. Reduction methods in common use include uniform deviation, division by a factor, spatial sampling, chordal deviation and interpolated sampling. Each of the above modes has its advantages and weaknesses, and suitable application areas. A new data reduction mode, which integrates the space concept and height characteristic, is proposed, called the height decision method. This method can achieve the aim of data simplification while maintaining the curve characteristics of the model. The CAD modelling system is developed by an AutoLISP program with MDT v4.0 software. An egg model is presented in this paper for explanation and verification.

A Surface Based Approach for Constant Scallop HeightTool-Path Generation

The machining of sculptured surfaces like molds and dies in 3-axis milling relies on the chordal deviation, the scallop height parameter and the planning strategy. The choice of these parameters must ensure that manufacturing surfaces respect the geometrical specifications. The current strategies of machining primarily consist in driving the tool according to parallel planes which generates a tightening of the tool paths and over quality. The constant scallop height planning strategy has been developed to avoid this tightening. In this paper, we present a new method of constant scallop height tool path generation based on the concept of the machining surface. The concept of the machining surface is exposed and its use to generate constant scallop height tool paths. The approach is confronted with existing methods in terms of precision and in particular its aptitude to treat curvature discontinuities.

A New Tool-Path Generation Method Using a Cylindrical End Mill for 5-Axis Machining of a Spatial Cam with a Conical Meshing Element

The geometry of a spatial cam is normally generated using a form-milling cutter and a special multi-axis machine and software. The general purpose CAD/CAM software can generate the cutter location file of this class of product only by the sculpturing method. Because of the limited choice of cutting tool when using the generating method, this paper presents a new toolpath generating method which combines the advantages of the generating and sculpturing methods for machining a spatial cam. In the machining process, the cutter location is derived for rough and finish machining using a cylindrical end mill. The guidelines for choosing cutter diameter for the machining process are discussed. To avoid interference, the principal curvatures and the principal induced normal curvatures are analysed. The mathematical errors including chordal deviation and scallop height are used as the basis for generating appropriate tool-paths. Cutting simulation of a solid model was performed to verify the proposed tool-path generation method.

Tool path generation and error control method for multi-axis NC machining of spatial cam

In this paper, based on the homogeneous coordinate transformation and conjugate surface theory, a tool path generation method is developed for generating spatial cam in order to establish the interface between the design and manufacture of this class of product. The mathematical error (chordal deviation) between the design and manufacture surface has been analysed and used as a basis for selecting the tool path control point. Moreover, the developed tool path generation method is verified through a cutting simulation software with solid model. It is also verified through the trial cut with model materials on a five-axis numerical controlled machine. The results show that the mathematical error of the cam surface can be controlled within given tolerance by the proposed method.

A new machine strategy for sculptured surfaces using offset surface

A new CNC tool path planning method is developed for accurate and efficient finishing cutting of sculptured surfaces. The proposed method generates CNC tool paths based on an offset surface of an object instead of the actual surface. The new algorithm consists of two main computational techniques: offset surface generation technique and offset CNC tool path planning technique. In offset surface generation, approximate parametric offset surfaces are generated accurately from an original parametric surface by employing bi-cubic surface patch, surface conversion, and surface subdivision algorithms. In offset CNC tool path planning, the precise geometric models of chordal deviation and cusp height on an offset surface are established. The effectiveness of this proposed CNC tool path planning method is verified by geometric simulation and verification which detect and identify errors in CNC tool paths.

The Profile Determination and Machining of Camoids with Oscillating Spherical Followers

A simple procedure, that can be used to determine the complicated camoid profile with an oscillating spherical follower and to decide the cutter path with the predictable surface roughness, is presented. In the profile design stage, it employs the theory of envelope for a family of surfaces with two independent parameters to derive the camoid contour. Also, the pressure angle is investigated by means of the analytical expression of the camoid. The results are compared to those obtained by using the principle of contact point between the camoid and the follower. Based on the chordal deviation and the scallop height, the surface roughness is analyzed in the machining process. An example is given to illustrate the application of the proposed method.