J.R.R. Mayer

Theory and simulation for the identification of the link geometric errors for a five-axis machine tool using a telescoping magnetic ball-bar

The position invariant geometric inaccuracies of a machine tool are the first to influence the quality of machined parts. A systematic approach is presented to identify some of these errors on a five-axis machine tool. The methodology is applied to the link error parameters such as joint misalignments, angular offset and rotary axis separation distance. A method based on the mathematical analysis of singularities of linear systems is used to assist in selecting a minimal but sufficient set of link error parameters for the calibration of a machine tool. A number of criteria are proposed in order to verify that the identified parameters accurately predict the positioning errors of the true machine. Finally, the numerical effectiveness of this method is shown through simulations.

High-resolution of rotary encoder analog quadrature signals

The paper describes a software technique to provide high-resolution absolute angular measurements from the analog quadrature signals of a rotary encoder. The method uses digitized samples of the sinusoidal quadrature signals and the output of a divide-by-four counter circuit. Dynamic measurements on an external trigger signal are possible allowing instantaneous up-to-date angular readings even at high speed. The resolution and hysteresis errors are only dependent on the encoder itself and the bandwidth and resolution of the sampling circuitry. The scheme allows up to 135 degrees of counter hysteresis and delay without loss of precision, thus also affording excellent noise immunity. The theoretical resolution for a 12-bit digital conversion of the analog signals is 1/3360 of a pitch. Experimental results on an encoder built into a laser-tracking measurement system and using 81000 pitches show a unidirectional precision of 0.3 arcsec (rms), a mean bidirectional hysteresis of about 1 arcsec and a worst case variation for a stationary encoder shaft of 0.06 arcsec. >

Touch probe radius compensation for coordinate measurement using kriging interpolation

Abstract Obtaining CAD (computer aided design) descriptions of actual parts having complex surfaces is a key part of the process of reverse engineering. This paper is concerned with the estimation of actual surfaces using coordinate measuring machines fitted with a spherically tipped touch probe. In particular, it addresses in detail the problem of probe radius compensation. A general mathematical model, using kriging, is proposed which first generates the initial probe centre surface and then estimates the compensated or part surface. The compensation is achieved using normal vectors to the initial probe centre surface at each measured point to compensate for the probe radius. The method is validated experimentally on known and free-form surfaces.

Tool path error prediction of a five-axis machine tool with geometric errors

Abstract Predicting the actual tool path of a machine tool prior to machining a part provides useful data in order to ensure or improve the dimensional accuracy of the part. The actual tool path can be estimated by accounting for the effect of the machine tool geometric error parameters. In computer aided design/computer aided manufacture (CAD/CAM) systems, the nominal tool path [or CL (cutter location) data] is directly generated from the curves and surfaces to be machined and the errors of the machine tool are not considered. In order to take these errors into consideration, they must first be identified and then used in the machine tool forward kinematic model. In this paper a method is presented to identify the geometric errors of machine tools and predict their effect on the tool-tip position. Both the link errors (position-independent geometric error parameters) and the motion errors (position-dependent geometric error parameters) are considered. The nominal and predicted tool paths are compared and an assessment is made of the resulting surfaces with respect to the desired part profile tolerance. A methodology is also suggested to integrate this tool within a CAD/CAPP (computer aided process planning)/CAM environment.

Finite element and experimental studies of diametral errors in cantilever bar turning

Abstract An improved model for predicting diametral errors in turning cantilever multi-diameter bars is presented. This model uses the same geometric analysis of the elastic deflections of the machine–workpiece–tool system due to the cutting force as in Ref. [Appl. Math. Model. 24 (2000) 943]. However, an important improvement is made here toward the determination of workpiece deflections in which the part holder stiffnesses are directly included and shear deformation effect is taken into account. It is noted that in Ref. [Appl. Math. Model. 24 (2000) 943], the workpiece deflection is determined using the finite element method with the assumption that the part holders are rigid. Thus, the part holder deflections need to be calculated separately after obtaining the support reactions from the above finite element analysis (FEA). This post-processing step for calculating the part holder deflections is eliminated in this work by taking the stiffness of these part holders into account in the FEA of the workpiece deflection. Here, the part holder stiffnesses include both the transversal and rotational components. As in our previous work related to the workpiece deflections in turning, the same approach to deriving solutions in closed-form is also applied here. The effects of the part holder stiffnesses on the predicted diametral errors are investigated. An experimental validation supports the proposed model.

Calibration of a Five-Axis Machine Tool for Position Independent Geometric Error Parameters Using a Telescoping Magnetic Ball Bar

Many parameters influence the quality of machined parts on five-axis machine tools. One important family of parameters are the geometric inaccuracies in the relative location of the machine axes. A method is proposed which uses a telescoping magnetic ball bar to identify these error sources. The methodology is applied to position independent geometric error parameters such as joint misalignments, angular offset and axes separation. Simulation results support the effectiveness of the approach.

The hypersingular boundary contour method for two-dimensional linear elasticity

SummaryThis paper presents a novel method called the Hypersingular Boundary Contour Method (HBCM) for two-dimensional (2-D) linear elastostatics. This new method can be considered to be a variant of the standard Boundary Element Method (BEM) and the Boundary Contour Method (BCM) because: (a) a regularized form of the hypersingular boundary integral equation (HBIE) is employed as the starting point, and (b) the above regularized form is then converted to a boundary contour version based on the divergence free property of its integrand. Therefore, as in the 2-D BCM, numerical integrations are totally eliminated in the 2-D HBCM. Furthermore, the regularized HBIE can be collocated at any boundary point on a body where stresses are physically continuous. A full theoretical development for this new method is addressed in the present work. Selected examples are also included and the numerical results obtained are uniformly accurate.

A finite-element model with closed-form solutions to workpiece deflections in turning

Simulation models for workpiece deflections play an important role in determining conditions to maximize the part accuracy in machining processes as well as in analysing the dynamic response of the machining system. In this paper, the crosssectional deflection of the workpiece due to all cutting force components (radial, axial and tangential) is determined using the finite-element method. Three workpiece mounting types generally used in industrial practice are considered. The change in the workpiece diameter during machining can easily be taken into account with this model. Furthermore, the finite-element reponses are derived in closed form which enables rapid and continuous solutions along the part length. Numerical examples are treated for which the workpiece deflections calculated from this model are compared with those computed only from the radial cutting force component as usually done by several simplified models. From the results obtained, the proposed model is generally recommended to improve tur...

Closed door machining error compensation of complex surfaces using the cutting compliance coefficient and on-machine measurement for a milling process

Closed door machining is a strategy for producing a part within tolerance using on-machine measurement and automatic process adjustment as opposed to manual gauging interventions. This paper presents an integrated methodology for compensating errors detected using on-machine probing. In a multi-cut process, intermittent probing which is achieved through replacing the cutting tool with a touch probe, after each cut, can detect machining errors caused by deflection and the tool offset error. A cutting compliance coefficient model is used to estimate corrections to the tool path at the finishing cut based on a finite number of measured errors at discrete locations for previous cuts. The model also anticipates compliance changes and the effect of the compensated depth of cut. The complex surface to be machined is represented by a B-spline model. The compensated tool path is obtained from B-spline deformation techniques applied to the initial tool path according to the discrete corrections. Milling tests are carried out with and without compensation demonstrating a reduction of machining error from +140 to ±20 µm.

A robust method for probe tip radius correction in coordinate metrology

A new algorithm for tip radius correction for the metrology of free-form and two-dimensional contours is proposed. The method is for use in a high-definition coordinate metrology context, as is now possible with scanning probes, where the density of points per scanned distance ensures that the successive probe ball positions overlap partially with each other. The proposed method for correcting measurements can be applied directly to the data collected during a coordinate measuring machine (CMM) measuring process. An additional advantage of the new algorithm is the possibility of detecting the incoherent corrected measured point, a form of validity check. The algorithm performance was verified experimentally on a Zeiss ACCURA CMM with an active VAST Gold scanning probe.