The harmonic fitting method for the assessment of the substitute geometry estimate error. Part I: 2D and 3D theory

The dimensional inspection of a part consists of the measurement of several points on the manufactured surface and the fitting of a substitute geometry. The estimated parameters of the substitute geometry, which are related to the position and dimensions of the measured surface, are then compared with the specifications, leading to the acceptance or rejection of the manufactured part. Consequently, the reliability of the dimensional inspection depends on the precision of the estimated substitute geometry. The error that affects the estimate (estimate error) is a function of several factors (number and distribution of sampled points, measurement error, machining deviations, etc.), but the analytic expression of this relationship is still unknown.The first part of this work presents the Harmonic Fitting Method (HFM) for the assessment of the estimate error. It will be demonstrated that with the HFM the closed analytic relationship between the estimate error and the most important factors can be determined. This relationship is extremely simple when using the matrix notation, since the estimate error can be expressed as the product of different matrices, each one accounting for a single factor. In the first part of the work the general theory of the HFM will be presented and discussed for 2D features (line and circle) and 3D features (plane, cylinder and cone). In the second part the statistic approach and the machining process analysis will be presented, which are the basis for the practical use of the HFM for the inspection plan optimisation. The HFM will be applied to real data to optimise the inspection of circular geometric elements, which are particularly relevant for the mechanical industry.     

Dimensional errors in longitudinal turning based on the unified generalized mechanics of cutting approach.: Part II: Machining process analysis and dimensional error estimate

The model presented in the first part of this work is used here to estimate the diameter error in the most common turning operations. In fact, the diameter error is considered as a variable depending on the deflections of the tool, workpiece holder and workpiece, which are considered the main factors responsible for the machining accuracy. The proposed model has been applied to the three most common turning schemes related to workpiece fixturing, where the workpiece is clamped in a chuck, or supported between two centers, or clamped in a chuck at the spindle and supported on a center at the tailstock. Some numerical examples have been computed using the proposed model to predict the diameter error along the workpiece and the cutting force along the workpiece axis, as well as the influence of the cutting force components on the error prediction. The results provide additional insight into error formation in the turning process. Finally, some experimental tests have been carried out in order to validate the developed model. Good agreement has been obtained between numerical and experimental results. The proposed model represents a first step towards accuracy control in machining operations and, thus, towards optimization of the manufacturing process.     

The prediction of dimensional error for sculptured surface productions using the ball-end milling process. Part 1: Chip geometry analysis and cutting force prediction

The study of machining errors caused by tool deflection in the balkend milling process involves four issues, namely the chip geometry, the cutting force, the tool deflection and the deflection sensitivity of the surface geometry. In this paper, chip geometry and cutting force are investigated. The study on chip geometry includes the undeformed radial chip thickness, the chip engagement surface and the relationship between feed boundary and feed angle. For cutting force prediction, a rigid force model and a flexible force model are developed. Instantaneous cutting forces of a machining experiment for two 2D sculptured surfaces produced by the ball-end milling process are simulated using these force models and are verified by force measurements. This information is used in Part 2 of this paper, together with a tool deflection model and the deflection sensitivity of the surface geometry, to predict the machining errors of the machined sculptured surfaces.     

A new method and device for motion accuracy measurement of NC machine tools. Part 2: device error identification and trajectory measurement of general planar motions

This paper describes in two parts a new method and device for measuring motion accuracy of NC machine tools. In the first part, the measurement principle and the characteristics of the prototype device have been presented and discussed. In the second part, an efficient and practical approach to identifying the errors of the proposed device after assembly is developed and evaluated. The approach ensures realising the aim of the investigation, i.e. to measure the most items of the motion accuracy, especially, to measure and assess the trajectory accuracy of a general planar motion of NC machine tools. The result of the identification experiment by using the prototype device on a machining centre for the prototype device is presented and it well verifies the validity and practicality of the approach. Some measurement results for the general planar motions of the machining centre are also shown, which sufficiently demonstrate the desirable capability of the proposed method and device.     

Measurement methods for the position errors of a multi-axis machine. Part 1: principles and sensitivity analysis

Accurate measurement of errors is an essential part of error compensation. By using telescoping ball-bars, two measurement methods, characterized by low cost, simplicity of setup, and quick measurements are developed to directly identify the total position errors at the tip of the tool of a multi-axis machine tool without the use of an error model. The first method uses the well known triangulation principle that requires three reference points. The second, referred to as the single socket method, utilizes a single reference point, offering thereby a higher degree of dexterity and flexibility. In addition, sensitivity analysis is used to investigate the accuracy of the two methods with respect to two error factors: errors of the ball-bar system, and location errors of the reference point.     

The prediction of dimensional error for sculptured surface productions using the ball-end milling process. Part 2: Surface generation model and experimental verification

This paper presents a surface generation model for sculptured surface productions using the ball-end milling process. In this model, machining errors caused by tool deflections are studied. As shown in Part 1 of this paper, instantaneous horizontal cutting forces can be evaluated from the cutting geometries using mechanistic force models. In this paper, a tool deflection model is developed to calculate the corresponding horizontal tool deflection at the surface generation points on the cutter. The sensitivity of the machining errors to tool deflections, both in magnitude and direction, has been analyzed via the deflection sensitivity of the surface geometry. Machining errors are then determined from the tool deflection and the deflection sensitivity of the designed surface. The ability of this model in predicting dimensional errors for sculptured surfaces produced by the ball-end milling process has been verified by a machining experiment. In addition to providing a means to predict dimensional accuracy prior to actual cutting, this surface generation model can also be used as a tool for quality control and machining planning.     

Scientific and technological fundamentals for the development of the controlled short-circuiting MIG/MAG welding process: a review of the literature. Part 2 of 3. Metal droplet formation,shield gases,penetration mechanisms,heat input and economical aspects

The second part of this series deals with the metal transfer modes of most interest to the MIG/MAG process, regarding the development of the controlled short-circuiting MIG/MAG welding process (CCC). The primary intention is to study pulsed arc and short-circuiting arc welding, both of which are the basis for the CCC. Also in relation to the metal transfer dynamics, the drop formation and the forces acting on it are reviewed. To provide a more complete understanding, aspects regarding shielding gases are described, including economic issues. Since they are important characteristics for any weld, information concerning short-circuiting MIG/MAG welding penetration and heat input are also provided.