Response Surface Methodology's Steepest Ascent and Step Size Revisited

Response Surface Methodology (RSM) searches for the input combination maximizing the output of a real system or its simulation.RSM is a heuristic that locally fits first-order polynomials, and estimates the corresponding steepest ascent (SA) paths.However, SA is scale-dependent; and its step size is selected intuitively.To tackle these two problems, this paper derives novel techniques combining mathematical statistics and mathematical programming.Technique 1 called 'adapted' SA (ASA) accounts for the covariances between the components of the estimated local gradient.ASA is scale-independent.The step-size problem is solved tentatively.Technique 2 does follow the SA direction, but with a step size inspired by ASA.Mathematical properties of the two techniques are derived and interpreted; numerical examples illustrate these properties.The search directions of the two techniques are explored in Monte Carlo experiments.These experiments show that - in general - ASA gives a better search direction than SA.response surface methodology

A holistic integrated dynamic design and modelling approach applied to the development of ultraprecision micro-milling machines

Ultraprecision machines with small footprints or micro-machines are highly desirable for micro-manufacturing high-precision micro-mechanical components. However, the development of the machines is still at the nascent stage by working on an individual machine basis and hence lacks generic scientific approach and design guidelines. Using computer models to predict the dynamic performance of ultraprecision machine tools can help manufacturers substantially reduce the lead time and cost of developing new machines. Furthermore, the machine dynamic performance depends not only upon the mechanical structure and components but also the control system and electronic drives. This paper proposed a holistic integrated dynamic design and modelling approach, which supports analysis and optimization of the overall machine dynamic performance at the early design stage. Based on the proposed approach the modelling and simulation process on a novel 5-axis bench-top ultraprecision micro-milling machine tool – UltraMill – is presented. The modelling and simulation cover the dynamics of the machine structure, moving components, control system and the machining process, and are used to predict the overall machine performance of two typical configurations. Preliminary machining trials have been carried out and provided the evidence of the approach being helpful to assure the machine performing right at the first setup

Design of a five-axis ultra-precision micro-milling machine—UltraMill. Part 2: Integrated dynamic modelling, design optimisation and analysis

Using computer models to predict the dynamic performance of ultra-precision machine tools can help manufacturers to substantially reduce the lead time and cost of developing new machines. However, the use of electronic drives on such machines is becoming widespread, the machine dynamic performance depending not only on the mechanical structure and components but also on the control system and electronic drives. Bench-top ultra-precision machine tools are highly desirable for the micro-manufacturing of high-accuracy micro-mechanical components. However, the development is still at the nascent stage and hence lacks standardised guidelines. Part 2 of this two-part paper proposes an integrated approach, which permits analysis and optimisation of the entire machine dynamic performance at the early design stage. Based on the proposed approach, the modelling and simulation process of a novel five-axis bench-top ultra-precision micro-milling machine tool—UltraMill—is presented. The modelling and simulation cover the dynamics of the machine structure, the moving components, the control system and the machining process and are used to predict the entire machine performance of two typical configurations