Jan B. Jonker

Penetration control in laser welding of sheet metal

For economical reasons it is desirable to apply the highest possible speed during laser welding. Increasing the welding speed at a certain laser power might result in insufficient penetration of the weld. This work describes the design of a feedback controller, which is able to maintain full penetration in mild steel sheets. An optical detector, which is placed inside the Nd:Yttrium–aluminium–garnet laser source, measures the intensity of the weld-pool radiation through the optical fiber. This sensor signal is used as input of a feedback control system. A model, which describes the dynamic response of the welding process including the sensor and laser source dynamics, has been obtained, using system identification techniques. The input of this model is the laser power and the output is the modeled sensor signal. Based on this dynamic model a feedback controller is designed and implemented. The laser power is used as an actuator. The controller maintains full penetration during welding of tracks with disturbances like sudden artificial power fluctuations and sudden speed changes. This feedback controller opens the possibility to optimize the welding speed without risking lack of penetration

Dynamic Simulation of Planar Flexible Link Manipulators using Adaptive Modal Integration

In this paper a modal integration method is proposed for analyzingthe dynamic behavior of multi-link planar flexible manipulators. Anon-linear finite element method is employed to derive theequations of motion in terms of a mixed set of generalizedcoordinates of the manipulator with rigid links and deformationparameters that characterize flexible deformations of the links.Using a perturbation method the vibrational motion of themanipulator is modeled as a first-order perturbation of thenon-linear nominal rigid link motion. For that purpose theflexible dynamic manipulator model is split into two parts. Arigidified model describes the nominal rigid link motion. Alinear system linearized about the nominal trajectory describesthe vibrational motion. In order to reduce the dimension of thelinearized system, a modal reduction technique is proposed. Thenmodal integration can be applied using only a small number of lowfrequency modes. The mode-acceleration concept is used to accountfor the pseudo static contribution of the high frequency modes.Applied to the motion of a manipulator mechanism the method isreferred to as ‘adaptive modal integration’ since thetime-varying nature of the mode shape functions is taken intoaccount.A flexible two-link manipulator is analyzed to illustrate theperformance of the solution method. Comparisons between solutionsutilizing non-linear and perturbation analyzes with and withoutmodal integration show a good agreement. In a simulation with onlya few modes the accuracy is kept, whereas the computation time isdrastically reduced.

A Perturbation Method for Dynamic Analysis and Simulation of Flexible Manipulators

This paper presents a perturbation method for the dynamicsimulation of flexible manipulators. In this method thevibrational motion of the manipulator is modeled as a first-orderperturbation of the nominal rigid link motion. For that purposethe flexible dynamic model is split into two parts. A rigidifiedsystem describes the nominal rigid link motion of themanipulator. A linear system linearized about the nominaltrajectory describes the vibrational motion. These equations arecomputationally more efficient than the non-linear dynamicequations and offer more insight in the dynamic phenomena of thesystem. The method is based on a full non-linear finite elementformulation which treats the general case of coupled largedisplacements motion and small elastic motion. A planar one linkmanipulator and a spatial two link manipulator with flexiblelinks are used for case studies. A comparison is made between thenon-linear and the perturbation analyzes. The perturbation methodappears to be a very efficient approach for dynamic analyzes offlexible manipulators and yields accurate results even forsystems with low frequency elastic modes.

A FINITE ELEMENT PERTURBATION METHOD FOR COMPUTING FLUID‐INDUCED FORCES ON A CENTRIFUGAL IMPELLER ROTATING AND WHIRLING IN A VOLUTE CASING

A finite element based method has been developed for computing time-averaged fluid-induced radial excitation forces and rotor dynamic forces on a two-dimensional centrifugal impeller rotating and whirling in a volute casing. In this method potential flow theory is used, which implies the assumption of irrotational inviscid flow. In comparison with other analyses of fluid-induced impeller forces, two main features have been included. Firstly, the hydrodynamic interaction between impeller and volute isproperly modelled. Secondly, the variation of the width of the volute has been adequately included in the two-dimensional analysis by a modification of the equation of continuity. A regular perturbation method is used to deal with the effects of the whirling motion of the impeller. The excitation forces are calculated from the zeroth-order problem in which the impeller axis is placed at the volute origin. The rotor dynamic forces associated with the whirling motion of the impeller are derived from the first-order solution. The force components, tangential and normal to the whirl orbit, are predicted as functions of the impeller--volute geometry, the flow conditions and the whirl speed ratio. The method is applied to a centrifugal pump experimentally tested at the California Institute of Technology. Comparisons between predictions and experimental data show the capabilities of the proposed method to reproduce the main features of fluid-induced impeller forces in centrifugal pumps.

Brief paper: A computationally efficient algorithm of iterative learning control for discrete-time linear time-varying systems

Iterative Learning Control (ILC) improves the tracking accuracy of systems that repetitively perform the same task. This paper considers model-based ILC for linear time-varying (LTV) systems. The applied feedforward iteratively minimises a quadratic norm of the feedforward update and the error in the next iteration as predicted by the model. The optimal feedforward update can be derived straightforwardly using a matrix description of the system dynamics. However, the implementation of the resulting matrix equation is demanding in terms of computation time and memory. In this paper it is shown that an efficient algorithm can be derived directly from the matrix equation using the associated state-equations. The ILC algorithm is applied to an industrial robot. The configuration dependent robot dynamics can be approximated as LTV for small tracking errors from the large-scale motion along the desired trajectory. It is shown that a substantial reduction of the tracking error at the robots tip can be realised by ILC using an LTV model of the robot dynamics and the same reduction cannot be accomplished using an LTI model that ignores the variation of the robot dynamics along the trajectory.

Model-based iterative learning control applied to an industrial robot with elasticity

In this paper model-based iterative learning control (ILC) is applied to improve the tracking accuracy of an industrial robot with elasticity. The ILC algorithm iteratively updates the reference trajectory for the robot such that the predicted tracking error in the next iteration is minimised. The tracking error is predicted by a model of the closed-loop dynamics of the robot. The model includes the servo resonance frequency, the first resonance frequency caused by elasticity in the mechanism and the variation of both frequencies along the trajectory. Experimental results show that the tracking error of the robot can be reduced, even at frequencies beyond the first elastic resonance frequency.

Calculations on the Time-Dependent Potential Flow in a Centrifugal Pump

In this paper a finite element based method is presented for the calculation of two-dimensional time-dependent potential flows through a rotor/stator configuration. An algorithm was developed that numerically evaluates the time derivative of all relevant field quantities. For that purpose the computational domain was split into a region containing the rotor and one containing the stationary parts, each region being treated in a different coordinate system. The corresponding finite element grids are matched by an interface consisting of connect-elements which move in time. The pressure field was then obtained from the unsteady Bernoulli equation. The Kutta condition was imposed by a method using the linear property of the operators. The algorithm was in particular applied to calculate the two-dimensional quasi-steady flow through a volute laboratory pump which made an experimental verification possible. For various mass flows the lateral fluid forces, the axial moment, the total head of the pump were computed and analyzed. The agreement with the experimental data, with respect to the quantities in the volute, was reasonable. The deviation was quantitatively greatest at low mass flow, the maximum deviation in the velocity being 10%. The overall behavior of the pump could be well predicted.Copyright

A superelement-based method for computing unsteady three-dimensional potential flows in hydraulic turbomachines

A numerical method is presented for the computation of unsteady, three-dimensional potential flows in hydraulic pumps and turbines. The superelement method has been extended in order to eliminate slave degrees of freedom not only from the governing Laplace equation, but also from the Kutta conditions. The resulting superelement formulation is invariant under rotation. Therefore the geometrical symmetry of the flow channels in the rotor can be exploited. This makes the method especially suitable to performing fully coupled computations of the unsteady flow phenomena in both rotor and stator, the so-called rotor-stator interaction. The developed numerical method is used to simulate the unsteady flow in an industrial mixed-flow pump. Two types of simulation are considered: one in which unsteady wakes behind the trailing edges of the rotor blades are taken into account and one in which these are neglected. Results are given that show the importance of unsteady flow phenomena. However, the computed head-capacity curve is hardly influenced by whether or not unsteady wakes are taken into account.

ITERATIVE LEARNING CONTROL FOR IMPROVED END-EFFECTOR ACCURACY OF AN INDUSTRIAL ROBOT

Abstract In this paper Iterative Learning Control is used to improve the tracking accuracy of the end-effector of an industrial robot. The learning control algorithm is based on a straightforward robot model and an optimisation criterium. The algorithm is tested on an industrial robot, where the end-effector motion is measured relative to a weld seam using a seam tracking sensor based on optical triangulation. The experiments show that the tracking error can be reduced considerably in a few iterations.

Modelling of Joint Friction in Robotic Manipulators with Gear Transmissions

This paper analyses the problem of modelling joint friction in robotic manipulators with gear transmissions in the sliding regime, i.e. at joint velocities varying from close to zero until their maximum appearing values. It is shown that commonly used friction models that incorporate Coulomb, (linear) viscous and Stribeck components are inadequate to describe the friction behaviour for the full velocity range. A new friction model is proposed that relies on insights from tribological models. The basic friction model of two lubricated discs in rolling-sliding contact is used to analyse viscous friction and friction caused by asperity contacts inside gears and roller bearings of robot joint transmissions. The analysis shows different viscous friction behaviour for gears and pre-stressed bearings. The sub-models describing the viscous friction and the friction due to the asperity contacts are combined into two friction models; one for gears and one for the pre-stressed roller bearings. In this way, a new friction model is developed that accurately describes the friction behaviour in the sliding regime with a minimal and physically sound parametrisation. The model is linear in the parameters that are temperature dependent, which allows to estimate these parameters during the inertia parameter identification experiments. The model, in which the Coulomb friction effect has disappeared, has the same number of parameters as the commonly used Stribeck model. The model parameters are identified experimentally on a Staubli Rx90 industrial robot.