Residual Vibration Reduction Research Articles

Optimal placement of inherent zeros in polynomial-based motion profiles for minimizing residual vibration and travel time under system uncertainties

Various industrial processes require motion profiles that determine machine movement over time for workpiece transfer, with the goal of minimizing transfer time to enhance productivity. However, pursuing the maximum speed can trigger excessive motion-induced vibration, which can reduce the manufacturing efficiency, accuracy and operational lifespan of the system. This study proposes a generalized motion profile optimization method that considers the strategic placement of inherent zeros within the motion profile: each inherent zero contributes to the reduction of residual vibration or optimization of arrival time. By offering freedom to the placement of zeros, four optimization options for polynomial-based motion profiles of each order are proposed, expanding on existing work that offered a single option. All proposed optimization options have closed-form solutions, making them easily applicable to industrial applications. The practical applicability of the suggested methodology is demonstrated through case studies and experiments.

Minimum time control of a gantry crane system with rate constraints

This paper focuses on the development of minimum time control profiles for point-to-point motion of a gantry crane system in the presence of uncertainties in modal parameters. Assuming that the velocity of the trolley of the crane can be commanded and is subject to limits, an optimal control problem is posed to determine the bang-off-bang control profile to transition the system from a point of rest to the terminal states with no residual vibrations. Both undamped and underdamped systems are considered and the variation of the structure of the optimal control profiles as a function of the final displacement is studied. As the magnitude of the rigid body displacement is increased, the collapse and birthing of switches in the optimal control profile are observed and explained. Robustness to uncertainties in modal parameters is accounted for by forcing the state sensitivities at the terminal time to zero. The observation that the time-optimal control profile merges with the robust time-optimal control is noted for specific terminal displacements and the migration of zeros of the time-delay filter parameterizing the optimal control profile are used to explain this counter intuitive result. As a comparison to the proposed controller, an acceleration constrained time-optimal control is analyzed which as expected demands a larger maneuver time. A two degree of freedom gantry crane system is used to experimentally validate the observations of the numerical studies and the tradeoff of increase in maneuver time to the reduction of residual vibrations is experimentally illustrated.

Residual Vibration Reduction of High-Speed Pick-and-Place Parallel Robot Using Input Shaping

Because of their elastic links and joints, high-speed parallel robots for pick-and-place operations inevitably suffer from residual vibrations that significantly degrade their positioning accuracy. An effective approach based on the input shaping technique is presented in this paper for suppressing the residual vibration in these parallel robots. After addressing the design principle of an input shaper for a parallel robot with flexible actuated joints, a robust optimal input shaper is developed by considering the configuration-dependent flexible modes and minimizing the maximum percentage of residual vibration at the end-effector. The input shaper allows a good overall performance to be achieved throughout the entire workspace. Experimental results on a 4-DOF SCARA-type parallel robot show that the residual vibration of the end-effector is dramatically reduced and the dynamic positioning accuracy of the robot significantly improved.

Residual vibration reduction in back-and-forth moving systems driven by slider-crank mechanisms working through a dead point configuration

This study proposes an algorithm to construct back-and-forth motion profiles to reduce residual vibrations of 1-dof linear oscillatory systems, driven through a transmission chain made up of a 1-dof linkage mechanism. This set can be advantageous for high transmission ratios, when multistage drive trains are discouraged to prevent a build-up of backlash nonlinearities. We assume that the mechanism: i) is moved by a conventional electric actuator and, ii) is working through a dead point configuration. The solution focuses on the continuity degree Cn of the motion profile to guarantee its feasibility by means of the mentioned actuators. We aim to provide an algorithm to design these profiles. The development meshes several conclusions from other studies: the classical strategies of residual vibration reduction together with an analytical solution, with regard to Cn, of the inverse kinematic problem at a dead point configuration. The development includes an analytical approach to some methods of residual vibration reduction, in addition to numerical simulations. Finally, we present experimental results on a slider-crank mechanism test bed, with a pendulum acting as the oscillatory system.

Input Shaping for Feed-Forward Control of Cable-Driven Parallel Robots

Abstract This paper deals with the use of input-shaping filters in conjunction with a feed-forward control of cable-driven parallel robots (CDPRs), while integrating cable tension calculation to satisfy positive cable tensions along the prescribed trajectory of the moving platform. This method aims to attenuate the oscillatory motions of the moving platform. Thus, the input signal is modified to make it self-cancel residual vibrations. The effectiveness, in terms of moving-platform oscillation attenuation, of the proposed closed-loop control method combined with shaping inputs is experimentally studied on a suspended and nonredundant CDPR prototype. This confirms residual vibration reduction improvement with respect to the unshaped control in terms of peak-to-peak amplitude of velocity error, which can achieve 72% while using input-shaping filters.

Suppression of robot vibrations using input shaping and learning-based structural models

Industrial robots used in manufacturing processes such as drilling of aerospace structures undergo many rapid positioning motions during each operation. Such aggressive motions excite the structural modes of the robot and cause inertial vibrations at the end-effector, which may damage the part and violate the tolerance requirements. This article presents a vibration avoidance technique based on input shaping combined with a learning-based structural dynamic model. A theoretical dynamic model is first developed for commonly used robotic arms considering the flexibilities of the first three joints of the robot. An artificial neural network is developed and used in conjunction with the dynamic model to predict the natural frequency of the system at any pose in the workspace. Transfer learning techniques are used to extend the trained artificial neural network to account for the mass of the payload with minimal data collection. To reduce the residual vibrations of the robot in rapid motions, zero-vibration derivative shapers are designed and implemented. The effectiveness of the presented methodology has been validated experimentally on a Staubli RX90CR robot with an open-architecture control system developed fully in-house. Experimental results show more than 85% reduction in residual vibrations during aggressive motions of the robot.

A Corrected Adaptive Balancing Approach of Motorized Spindle Considering Air Gap Unbalance

Motorized spindles widely used for high-speed precision machine tools are very sensitive to the mass unbalance of rotors; thus, their balancing problem is always a research hotspot. Although many significant studies were done regarding the theory and application of various rotor balancing technologies for motorized spindles, the particularity of motorized spindles is not carefully considered in the existing balancing approaches. When the rotor unbalance of a motorized spindle occurs in operation, it is subject to both the mass unbalance-induced inertia force and air gap unbalance-induced electromagnetic force, which is an important feature that distinguishes the motorized spindle from a mechanical spindle. This paper describes an investigation into the corrected adaptive balancing approach of a motorized spindle by newly introducing a coefficient representing the removing effect of the air gap unbalance of the motor on the balancing capacity into the balancing formula. The determination of the newly defined coefficient refers to the calculation of electromagnetic force caused by the dynamic air gap eccentricity of motor; thus, much attention is paid to the analytical derivation of the unbalanced magnetic pull (UMP). Finally, a motorized spindle with an electromagnetic ring balancer was developed; then, the balancing tests and vibration signal analysis were done to validate the effectiveness of the newly proposed balancing approach in residual vibration reduction. It can be seen from the test results under different cases that the proposed balancing approach is effective.

Zero-phase velocity tracking of vibratory systems with actuation constraints

In this paper, a novel filter for precise tracking of constant velocity signals is presented, which allows the reduction of residual vibrations along with the compliance with kinematic constraints that affect the actuation system. A technique achieving both these two objectives at the same time is the main contribution of the work. The filter is based on a cascade of smoothers, i.e. dynamic filters that act on the input signal by increasing its continuity level. Unfortunately, when applied to a generic input composed by ramp (and step) functions, the filter introduces a phase delay not acceptable in many applications where moving parts have to be mated, such as high-speed automatic machines. In order to guarantee a perfect synchronization between the original and the filtered reference signal, once the transient is terminated, a proper compensation scheme has been designed. Moreover, the expressions of the smoothers parameters which assure vibration cancellation at specific frequencies and compliance with given bounds on velocity and acceleration have been analytically deduced. By means of an extensive experimental activity, the effectiveness of the proposed approach has been demonstrated, by comparing its performances with the results of well established approaches for vibrations suppression or signal derivatives limitation.

Residual vibration reduction for translation unconstrained or partially unconstrained structures by structural optimization

This paper studies residual vibration reduction in translation unconstrained or partially unconstrained structures by structural optimization. Suppression of elastic residual vibration is of great concern in many fields, and several approaches have been proposed to deal with it through structural optimization. However, these approaches are suitable for completely constrained structures, while unconstrained and partially unconstrained structures are not considered in particular. The dynamic responses of the latter include not only elastic responses but also rigid body responses. The rigid body responses make several effective structural optimization approaches inapplicable. This paper proposes two methods to solve the problem arising from the rigid body responses. Then the abovementioned effective approaches based on completely constrained models are applied to study the optimization of translation unconstrained or partially unconstrained structures to minimize the residual vibration. To reduce the computational burden of optimization, model reduction is further applied in this research. Finally, several numerical examples are presented to illustrate the effectiveness of the proposed approaches. The optimized results for residual vibration minimization show superiority over those obtained with classical objective functions.

Model-Based Installation of Viscoelastic Damper Support for Reduction of Residual Vibration

It is necessary to increase the damping of a machine support structure (support damping) to reduce the residual vibrations caused by rocking vibration. The stiffness of the machine support system (support stiffness) is also an important parameter that needs to be considered while designing machine tools, to avoid low frequency vibrations. However, conventional passive damper supports decrease the support stiffness while increasing the damping. In our previous study, a passive viscoelastic non-linear damper system for shear vibrations, where the vertical preload determines its damping coefficient, was developed to increase the support damping without decreasing the stiffness by focusing on the horizontal component of rocking vibration. The magnitude dependency of the damping capacity has been modeled. However, this damper system has a tradeoff relationship between natural frequency and damping capacity caused by changes in the preload distribution. Thus, adjustment of the vertical preload applied on the damper is essential for the model-based installation of this damper system. So far, no method has been proposed considering this issue. The vertical preload has been adjusted by trial and error methods. This study proposes a method to determine the damper preload conditions systematically by considering the tradeoff relationship between natural frequency and damping capacity caused by changes in the preload distribution. This method is described based on the case study of a machining center. First, the relationship between preload distribution and support stiffness is investigated using the support stiffness model. Then, the relationship between damping capacity and vertical preloads on the damper is investigated based on material test results. Based on these investigations, the tradeoff relationships are simulated on a machining center by utilizing the damper model. The simulation results are verified with the experimental results. The results show that the proposed method can estimate the tradeoff relationship between natural frequency and damping capacity caused by the changes in the preload distribution. By utilizing this estimated relationship, the preferred preload condition can be decided depending upon the user’s demand.

An adjoint method of sensitivity analysis for residual vibrations of structures subject to impacts

For structures subject to impact loads, the residual vibration reduction is more and more important as the machines become faster and lighter. An efficient sensitivity analysis of residual vibration with respect to structural or operational parameters is indispensable for using a gradient based optimization algorithm, which reduces the residual vibration in either active or passive way. In this paper, an integrated quadratic performance index is used as the measure of the residual vibration, since it globally measures the residual vibration response and its calculation can be simplified greatly with Lyapunov equation. Several sensitivity analysis approaches for performance index were developed based on the assumption that the initial excitations of residual vibration were given and independent of structural design. Since the resulting excitations by the impact load often depend on structural design, this paper aims to propose a new efficient sensitivity analysis method for residual vibration of structures subject to impacts to consider the dependence. The new method is developed by combining two existing methods and using adjoint variable approach. Three numerical examples are carried out and demonstrate the accuracy of the proposed method. The numerical results show that the dependence of initial excitations on structural design variables may strongly affects the accuracy of sensitivities.

Robust motion profiles for the residual vibration reduction of an undamped system

This paper proposes two robust motion profiles to reduce the residual vibration of an undamped system: Trigonometric and trapezoidal acceleration motion profiles. The proposed motion profiles are defined by the total traveling, accelerating, and rising times in acceleration for each profile. Due to their simplicity, implementation of the proposed motion profiles is relatively easier when compared to previous input-shaping motion profiles. Furthermore, the proposed profiles are more robust in terms of system modelling errors than previous s-curve motion profiles. It is found in this paper that the zero vibration and robustness conditions are satisfied if the total traveling, accelerating, and rising times are half-integer multiples of the natural period for the trigonometric profile and integer multiples for the trapezoidal profile.

Modelling of viscoelastic damper support for reduction in low frequency residual vibration in machine tools

Residual vibrations deteriorate the accuracy and productivity of precision machine tools. Rocking vibration is excited by feed motion. Rocking vibration is the mode in which the entire machine vibrates and is the main source of residual vibrations at low frequencies. The characteristics of rocking vibration are influenced by the characteristics of the machine support structure. Thus, it is necessary to increase the damping of the machine support structure to reduce the residual vibrations caused by rocking vibration. In addition, it is important for machine tools to be stiff to reduce vibrations caused by the acceleration of feed drives. Conventional passive damper supports decrease the stiffness of a machine support structure while increasing the damping. Consequently, a passive viscoelastic damper system is developed to increase support damping without decreasing stiffness by focusing on the horizontal component of rocking vibration. However, the proposed damper damping capacity has a magnitude dependency. This makes it difficult to quantitatively determine the damper area in machine tools to reduce rocking vibrations to the required level. In this study, the developed damper is modeled using a viscoelastic four element model. Because of the nonlinearity of the model, an iterative time domain calculation method is introduced for the simulation. This method enables us to quantitatively estimate the effect of the damper on the machine tool. Based on the model proposed in this study, the proposed damper system can be applied to various machine tools to reduce the residual vibration without adjusting the damper area on the machine tool by a trial and error method.

Reduction of Residual Vibration of Piezoelectric Actuator Driven by Series of Current Pulses

Reduction of Residual Vibration of Piezoelectric Actuator Driven by Series of Current Pulses

Reduction of vibrations of passively-isolated ultra-precision manufacturing machines using mode coupling

Ultra-precision manufacturing (UPM) machines are used to fabricate and measure complex parts having micrometer-level features and nanometer-level tolerances/surface finishes. Therefore, random vibration of the machine due to ground excitations and residual vibration stemming from onboard disturbances must be mitigated using vibration isolation systems. A long-standing rule of thumb in vibration isolation system design is to locate the isolators in such a way that the vibration modes of the isolated machine are decoupled. However, prior work by the authors has demonstrated that coupling vibration modes of passively-isolated UPM machines could provide conditions for drastic reduction of residual vibrations compared to decoupling. The authors’ analysis was based on the restrictive assumption that the isolated machine was modally damped. The key contribution of this paper is in investigating the effect of mode coupling on the residual vibrations of UPM machines with non-proportional (NP) damping—which is more realistic than modal damping. It also analyzes the effects of mode coupling on the reduction of ground vibrations (i.e., transmissibility). The analyses reveal that, even though NP damping changes the vibration behavior of the machine compared to modal damping, mode coupling still provides ample opportunities to reduce residual vibration and transmissibility. Guidelines for properly designing a UPM machine to best exploit mode coupling for vibration reduction are provided and validated through simulations and experiments. Up to 40% reduction in residual vibration and 50% reduction in transmissibility are demonstrated.

Discrete-time command profile for simultaneous travel and hoist maneuvers of overhead cranes

A strategy for generating optimal shaped command-profile for the reduction of residual vibrations in rest-to-rest crane maneuvers is proposed. The technique used is based on generating discrete-time shaped acceleration profile. This profile accommodates simultaneous travel and hoist maneuvers in the presence of damping. The discrete-time acceleration profile is derived analytically using finite step segments. These segments are integrated into an input matrix coupled with a response matrix through a time varying equation of motion of the system. The input acceleration matrix is then optimized to satisfy specific rest-to-rest maneuver conditions. Several parameters are incorporated in the proposed strategy including maneuver time, time step, hoisting speed, damping, and maximum travel velocity and acceleration. Unlike traditional command shapers, the proposed strategy matches the discrete command signal steps to the machine minimum time step of the control hardware used. To achieve an optimum maneuvering time, the shaped command utilizes the full system acceleration and velocity capabilities. The resulting shaped command profile is capable of eliminating travel and residual oscillations. Successful performance of the proposed command shaping strategy is validated through numerical simulations and experiments on a scaled model of an overhead crane.

Residual vibration reduction of white-light scanning interferometry by input shaping.

White-light scanning interferometry is widely used for precision metrology of engineering surfaces. It needs a mechanical scanning for capturing an interferogram that determines where the surface of a measured sample is located. The residual vibration during the scanning procedure distorts the interferogram and it reduces the accuracy and the precision of the system. The residual vibration becomes bigger as the proportional gain gets higher for the fast response. So it is hard to achieve the fast and precise measurement simultaneously. In this study, input shaping which convolves a reference signal with the input shaper is investigated to reduce the residual vibration of the scanning system. The step response data is analyzed using Continuous Wavelet Transform (CWT) to design the input shaper. Using proposed method, the residual vibration of the white light scanning interferometry is reduced and it achieved both faster measurement speed and more accurate measurement.

Residual vibration reduction of a flexible beam deploying from a translating hub

Abstract This paper presents a method for reducing the residual vibration of a flexible beam deployed from a translating hub. Whereas previous studies have discussed reducing vibration in translating constant-length beams, this study investigates a vibration reduction method for translating beams of variable length. The partial differential equation of motion for a translating beam is derived and transformed into a variational equation. Based on the discretized equations from the variational equation, the dynamic responses of the flexible beam under translation are analyzed. A vibration reduction method is proposed that is effective for both constant- and variable-length deploying translating beams.

Feedforward Input Generation Based on Neural Network Prediction in Multi-Joint Robots1

Learning feedforward control based on the available dynamic/kinematic system model and sensor information is generally effective for reducing the tracking error for a learned trajectory. For new trajectories, however, the system cannot benefit from previous learning data and it has to go through the learning process again to regain its performance. In industrial applications, this means production line has to stop for learning, and the overall productivity of the process is compromised. To solve this problem, this paper proposes a feedforward input generation scheme based on neural network (NN) prediction. Learning/training is performed for the NNs for a set of trajectories in advance. Then the feedforward torque input for any trajectory in the predefined workspace can be calculated according to the predicted error from multiple NNs managed with expert logic. Experimental study on a 6-DOF industrial robot has shown the superior performance of the proposed NN based feedforward control scheme in the position tracking as well as the residual vibration reduction, without any further learning or end-effector sensors during operation.

Nonlinear analysis and vibration suppression control for a rigid–flexible coupling satellite antenna system composed of laminated shell reflector

In this paper, a nonlinear dynamic modeling method for a rigid–flexible coupling satellite antenna system composed of laminated shell reflector is proposed undergoing a large overall motion. For the study of the characteristics of the reflector using laminated shell structure, the displacement field description of a point in a 3-noded shell element is acquired in conjunction with the length stretch, lateral bending and torsional deformation. Hence, a nonlinear dynamic model of the satellite antenna system is deduced based on Lagrange's equations. The complete expressions of nonlinear terms of elastic deformation and coupling terms between rigid motion and large deflection are considered in the dynamic equations, and the dynamic behavior of the rigid–flexible coupling system is analyzed using linear model and nonlinear model, respectively. In order to eliminate the system vibration, the PD with vibration force feedback control strategy is used to achieve its desired angles and velocity in a much shorter duration, and can further accomplish reduction of residual vibration. Then, the asymptotic stability of the system is proved based on the Lyapunov method. Through numerical computation, the results show that the linear model cannot capture the motion-induced coupling terms and geometric nonlinearity variations. However, the nonlinear model is suitable for dealing with large deformation rigid–flexible problem undergoing large overall motions. Hence, the satellite antenna pointing accuracy would be predicted based on the nonlinear model. Furthermore, the results also show that the proposed control strategy can suppress system vibration quickly. The above conclusions would have important academic significance and engineering value.