Multi-objective optimisation of machine tool error mapping using automated planning

Error mapping of machine tools is a multi-measurement task that is planned based on expert knowledge. There are no intelligent tools aiding the production of optimal measurement plans. In previous work, a method of intelligently constructing measurement plans demonstrated that it is feasible to optimise the plans either to reduce machine tool downtime or the estimated uncertainty of measurement due to the plan schedule. However, production scheduling and a continuously changing environment can impose conflicting constraints on downtime and the uncertainty of measurement. In this paper, the use of the produced measurement model to minimise machine tool downtime, the uncertainty of measurement and the arithmetic mean of both is investigated and discussed through the use of twelve different error mapping instances. The multi-objective search plans on average have a 3% reduction in the time metric when compared to the downtime of the uncertainty optimised plan and a 23% improvement in estimated uncertainty of measurement metric when compared to the uncertainty of the temporally optimised plan. Further experiments on a High Performance Computing (HPC) architecture demonstrated that there is on average a 3% improvement in optimality when compared with the experiments performed on the PC architecture. This demonstrates that even though a 4% improvement is beneficial, in most applications a standard PC architecture will result in valid error mapping plan

Improved Machine Tool Linear Axis Calibration Through Continuous Motion Data Capture

Machine tool calibration is becoming recognised as an important part of the manufacturing process. The current international standards for machine tool linear axes calibration support the use of quasi-static calibration techniques. These techniques can be time consuming but more importantly a compromise in quality due to the practical restriction on the spatial resolution of target positions on the axis under test. Continuous motion calibration techniques have the potential to dramatically increase calibration quality. Through taking several measurement values per second while the axis under test is in motion, it is possible to measure in far greater detail. Furthermore, since machine tools normally operate in dynamic mode, the calibration data can be more representative if it is captured while the machine is in motion. The drawback to measuring the axis while in motion is the potential increase in measurement uncertainty. In the following paper, different methods of continuous motion calibration are discussed. A time-based continuous motion solution is proposed as well as a novel optimisation and correlation algorithm to accurately fuse the data taken from quasi-static and continuous motion measurements. The measurement method allows for minimal quasi-static measurements to be taken while using a continuous motion measurement to enhance the calibration process with virtually no additional time constraints. The proposed method does not require any additional machine interfacing, making it a more readily accessible solution for widespread machine tool use than other techniques which require hardware links to the CNC. The result of which means a shorter calibration routine and enhanced results. The quasi-static and continuous motion measurements showed correlation to within one micrometre at the quasi-static measurement targets. An error of 13 μm was detailed on the continuous motion, but was missed using the standard test. On a larger, less accurate machine, the quasi-static and continuous motion measurements were on average within 3 μm of each other however, showed a standard deviation of 4 μm which is less than 1% of the overall error. Finally, a high frequency cyclic error was detected in the continuous motion measurement but was missed in the quasi-static measuremen

Automated planning to minimise uncertainty of machine tool calibration

When calibrating a machine tool, multiple measurement tasks will be performed, each of which has an associated uncertainty of measurement. International Standards and best-practice guides are available to aid with estimating uncertainty of measurement for individual tasks, but there is little consideration for the temporal influence on the uncertainty when considering interrelated measurements. Additionally, there is an absence of any intelligent method capable of optimising (reducing) the estimated uncertainty of the calibration plan as a whole. In this work, the uncertainty of measurement reduction problem is described and modelled in a suitable language to allow state-of-the-art artificial intelligence planning tools to produce optimal calibration plans. The paper describes how the continuous, non-linear temperature aspects are discretized and modelled to make them easier for the planner to solve. In addition, detail is provided as how the complex uncertainty equations are modelled in a restrictive language where its syntax heavily influences the encoding. An example is shown for a three-axis machine, where the produced plan exhibits intelligent behaviour in terms of scheduling measurements against temperature deviation and the propagation of error uncertainties. In this example, a reduction of 58% in the estimated uncertainty of measurement due to intelligently scheduling a calibration plan is observed. This reduction in the estimated uncertainty of measurement will result in an increased conformance zone, thus reducing false acceptance and rejection of work-piece

Automatic planning for machine tool calibration: A case study

Machine tool owners require knowledge of their machine’s capabilities, and the emphasis increases with areas of high accuracy manufacturing. An aspect of a machine’s capability is its geometric accuracy. International Standards and best-practice guides are available to aid understanding of the required measurements and to advise on how to perform them. However, there is an absence of any intelligent method capable of optimising the duration of a calibration plan, minimising machine down-time. In this work, artificial intelligence in the form of automated planning is applied to the problem of machine tool pseudo-static geometric error calibration. No prior knowledge of Artificial Intelligence (AI) planning is required throughout this paper. The authors have written this paper for calibration engineers to see the benefits that automated planning can provide. Two models are proposed; the first produces a sequential calibration plan capable of finding the optimal calibration plan. The second model has the additional possibility of planning for concurrent measurements, adding the possibility of further reducing machine down-time. Both models take input regarding a machine’s configuration and available instrumentation. The efficacy of both models is evaluated by performing a case study of a five-axis gantry machine, whereby calibration plans are produced and compared against both an academic and industrial expert. From this, the effectiveness of this novel method for producing optimal calibration plan is evaluated, stimulating potential for future work

Improved dynamic cutting force model in peripheral milling - Part 2 : experimental verification and prediction

“The original publication is available at www.springerlink.com”. Copyright Springer. DOI: 10.1007/s00170-003-1797-5 [Full text of this article is not available in the UHRA]Cutting trials reveal that a measure of cutter run-out is always unavoidable in peripheral milling. This paper improves and extends the dynamic cutting force model of peripheral milling based on the theoretical analytical model presented in Part I [1], by taking into account the influence of the cutter run-out on the undeformed chip thickness. A set of slot milling tests with a single-fluted helical end-mill was carried out at different feed rates, while the 3D cutting force coefficients were calibrated using the averaged cutting forces. The measured and predicted cutting forces were compared using the experimentally identified force coefficients. The results indicate that the model provides a good prediction when the feed rate is limited to a specified interval, and the recorded cutting force curves give a different trend compared to other published results [8]. Subsequently, a series of peripheral milling tests with different helical end-mill were performed at different cutting parameters to validate the proposed dynamic cutting force model, and the cutting conditions were simulated and compared with the experimental results. The result demonstrates that only when the vibration between the cutter and workpiece is faint, the predicted and measured cutting forces are in good agreement.Peer reviewe

Improved dynamic cutting force model in ball-end milling. Part 1: theoretical modelling and experimental calibration

An accurate cutting force model of ball-end milling is essential for precision prediction and compensation of tool deflection that dominantly determines the dimensional accuracy of the machined surface. This paper presents an improved theoretical dynamic cutting force model for ball-end milling. The three-dimensional instantaneous cutting forces acting on a single flute of a helical ball-end mill are integrated from the differential cutting force components on sliced elements of the flute along the cutter-axis direction. The size effect of undeformed chip thickness and the influence of the effective rake angle are considered in the formulation of the differential cutting forces based on the theory of oblique cutting. A set of half immersion slot milling tests is performed with a one-tooth solid carbide helical ball-end mill for the calibration of the cutting force coefficients. The recorded dynamic cutting forces are averaged to fit the theoretical model and yield the cutting force coefficients. The measured and simulated dynamic cutting forces are compared using the experimental calibrated cutting force coefficients, and there is a reasonable agreement. A further experimental verification of the dynamic cutting force model will be presented in a follow-up paper

Determination of the quark coupling strength vertical bar V-ub vertical bar using baryonic decays

In the Standard Model of particle physics, the strength of the couplings of the b quark to the u and c quarks, vertical bar V-ub vertical bar and vertical bar V-ub vertical bar, are governed by the coupling of the quarks to the Higgs boson. Using data from the LHCb experiment at the Large Hadron Collider, the probability for the Lambda(0)(b) baryon to decay into the p mu(-)(nu) over bar (mu) final state relative to the Lambda(+)(c)mu(-)(nu) over bar (mu) final state is measured. Combined with theoretical calculations of the strong interaction and a previously measured value of vertical bar V-ub vertical bar, the first vertical bar V-ub vertical bar measurement to use a baryonic decay is performed. This measurement is consistent with previous determinations of vertical bar V-ub vertical bar using B meson decays to specific final states and confirms the existing incompatibility with those using an inclusive sample of final states