stiffness and damping coefficient
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Fast-actuation cutting systems are in high demand for machining of freeform optical parts. Design of such motion systems requires good balance between structural hardware and controller design. However, the controller tuning process is mostly based on human experience, and it is not feasible to predict positioning performance during the design stage. In this paper, a deterministic controller design approach is adopted to preclude the uncertainty associated with controller tuning, which results in a control law minimizing positioning errors based on plant and disturbance models. Then, the influences of mechanical parameters such as mass, damping, and stiffness are revealed within the closed-loop framework. The positioning error was reduced from 1.19 nm RMS to 0.68 nm RMS with the new controller. Under the measured disturbance conditions, the optimal bearing stiffness and damping coefficient are 1.1×105 N/m and 237.7 N/(m·s−1), respectively. We also found that greater moving inertia helps to reduce all disturbances at high frequencies, in agreement with the positioning experiments. A quantitative understanding of how plant structural parameters affect positioning stability is thus shown in this paper. This is helpful for the understanding of how to reduce error sources from the design point of view.

Abstract The high requirements for sealing performance in high-speed rotating machinery has led to the design of floating seal with annular spiral groove that offer the advantages of low leakage and extended stability. However, efforts to model the dynamic performance of these floating seal have suffered from the great complexity of the flow field. The present work addresses this issue by establishing a transient Reynolds formulation of a floating seal with annular spiral groove in a rotating coordinate system based on the small perturbation method. In addition, the influence of radial eccentricity and film thickness on the solution divergence and calculation accuracy is calculated. The dynamic stiffness and dynamic damping matrixes are built. Then the variation rules of the dynamic stiffness and damping coefficient of the gas film with structure and working conditions are investigated in detail. The results show that the floating ring seal is more suitable for the service conditions of small film thickness, low pressure, high speed and large eccentricity. Accordingly, the results obtained lay a theoretical foundation for evaluating real-world applications of floating ring seal.

High-order and low-order wheel out-of-roundness (OOR) often occur on metro train wheels, which can intensify the wheel–rail dynamic interaction. A vehicle–track rigid-flexible coupled dynamics model is built through combining the dynamics software SIMPACK with the finite element software ANSYS, which is validated by field vibration measurement results of vehicle and track. Two adjacent vehicles with two two-axle bogies for each one are considered in the model. The wheel–rail interactions caused by high-order and low-order wheel OOR are investigated. The influence of the wheel–rail interaction caused by wheel OOR on one wheelset on wheel–rail interactions at other 7 wheelsets is explored. The results show that the wheel OOR can excite the first bending vibration of the wheelset and the P2 resonance at a normal operating speed, which can result in a considerable increase of the wheel–rail dynamic interaction and wheelset vibration. The wheel–rail dynamic interaction can be transmitted from the polygonised wheelset to another wheelset of the same bogie through the rail. However, the transmission is negligible from the path of the bogie. The amplitude of wheel OOR has no effect on the transmission ratio of wheel–rail dynamic interaction, but the vertical stiffness and damping coefficient of fasteners greatly influence the transmission. The two wheelsets on the same bogie should be re-profiled simultaneously if the radial run-out for one wheelset exceeds the limit and for the other does not. The effects of vibration transmission between wheelsets and track flexibility need to be taken into account in a model for predicting the development of wheel OOR.

For improving the performance of an electromagnetic isolation system with reasonable parameters and avoid the parameter tuning problem of a PID controller, an active control method is put forward based on equivalent stiffness and damping coefficient. In this paper, the range of equivalent stiffness coefficient and damping coefficient of the electromagnetic force are calculated based on the required range of dynamic performance indexes. According to the nonlinear expression between electromagnetic force and coil current and gap, the relationships between the coil current and equivalent stiffness coefficient and damping coefficient are established. Then, the equivalent stiffness coefficient and damping coefficient can be satisfied by the controlled current in different gaps for meeting the required dynamic performance indexes. For reducing the maximum overshoot and the number of oscillations of the system, the active control method with the piecewise equivalent stiffness and damping coefficient is proposed based on the piecewise control strategy to realize the variable control parameters of the isolation system. Simulation and experimental results verify that the control method based on the equivalent stiffness and damping coefficient can obtain the desired dynamic performance indexes and the proposed control method with the piecewise strategy can not only reduce the setting time of the system, but also ensure the stability of the system.

Purpose Currently, there is a lack of fast and highly accurate on analytical solution of Reynolds equation for evaluating the characteristics of surface textured bearing. This paper aims to develop such an analytical solution of Reynolds equation for an effective analysis of the characteristics of surface textured bearings. Design/methodology/approach By using the separation of variables method and mean eigenvalue method, the analytical solution is constructed. The CFD simulations and experimental results are used to validate the correctness of the analytical solution. Findings The analytical solution can accurately evaluate the characteristics of textured bearings. It is found that the larger the eccentricity ratio and aspect ratio, the greater the oil film force. It also found that the smaller the eccentricity ratio, the larger the Sommerfeld number S. When eccentricity ratio e = 0.65, the attitude angles of different oil boundaries are same. The effect of different aspect ratios on dynamic stiffness and damping coefficient generally follows a same trend. It is numerically shown that the critical speed of rotor-bearing is 3500 rpm. Originality/value The analytical solution provides a simple yet effective way to study the characteristics of surface textured bearings.

In this study, the music-inspired Harmony Search (HS) algorithm is modified for the optimization of active tuned mass dampers (ATMDs). The modification of HS includes the consideration of the best solution with a defined probability and updating of algorithm parameters such as harmony memory, considering rate and pitch adjusting rate. The design variables include all the mechanical properties of ATMD, such as the mass, stiffness and damping coefficient, and the active controller parameters of the proposed proportional–integral–derivative (PID) type controllers. In the optimization process, the analysis of an ATMD implemented structure is done using the generated Matlab Simulink block diagram. The PID controllers were optimized for velocity feedback control, and the objective of the optimization is the minimization of the top story displacement by using the limitation of the stroke capacity of ATMD. The optimum results are presented for different cases of the stroke capacity limit of ATMD. According to the results, the method is effective in reducing the maximum displacement of the structure by 53.71%, while a passive TMD can only reduce it by 31.22%.

In this paper, we investigate the design of an integrated system consisting of two non-rigidly connected bodies: A floating buoy and an emerged offshore structure. When waves excite the buoy to oscillate, the relative motion between the two bodies are converted to useful energy through a spring damper system, resulting in wave energy being absorbed. The parameter to design includes the mass and underwater shape of the buoy. The spring stiffness of the power take-off (PTO) system is constrained to be non-negative with the concerns of complexity in implementation and system stability. Results suggest that a larger mass of the buoy is advantageous due to smaller optimal spring stiffness and damping coefficient of the PTO system, more absorbed wave power, and less motion amplitude of the two bodies. A favorable underwater shape of the buoy is characterized by large diameter to draft ratio, with the section profile preferring a circle or square rather than an equilateral triangle. Investigations on the designed buoy in irregular waves show that the integrated system presents its peak power absorption within the common range of energy period, and the motion amplitude of the offshore structure is larger than the wave amplitude in a certain range of sea states.

Tire vertical stiffness is influenced by many factors. The inflation pressure, tire dimension, and usage of run-flat tire are considered in this paper. Robust multi-objective optimization technique is used to optimize the suspension performance considering the variation of the tire vertical stiffness. Three objective functions, discomfort, road holding, and working space are used to evaluate the dynamic behavior of the suspension considering a two-degree-of-freedom quarter-car model excited by a random road profile. The Pareto-optimal solutions in terms of suspension spring stiffness and damping coefficient are obtained and compared with the one computed by means of a deterministic approach. Solutions obtained by means of the robust optimization method are proven to be less sensitive to the possible variations of the tire vertical stiffness without influencing significantly the expected performance.

The measurement results of various nitrile butadiene rubber (NBR) O-Ring sizes are presented, and reduced-order models are developed in order to predict the stiffness and damping coefficient as a function of O-Ring geometry, Shore hardness, squeeze, and excitation frequency. The results show that the curvature ratio d/D needs to be considered in the reduced-order models. The assessment of the model suggests a maximum deviation of 30% in predicted stiffness compared to the measurement data. However, taking into account the typical Shore hardness tolerance given by O-Ring manufacturers and other measurement uncertainties, the proposed model enables the prediction of various O-Rings with a good accuracy in the frequency range of 1.5–3.75 kHz, which corresponds to typical gas bearing supported rotor applications.