M.F. Golnaraghi

Experimental Research and Modeling of Magnetorheological Elastomers

In this paper, new methods for fabricating magnetorheological (MR) elastomers are introduced. Two different MR elastomers, one made of polyurethane and the other made of natural rubber, are successfully fabricated. The experimental results show that the modulus of polyurethane MR elastomers can increase by 28% under a strong magnetic field. Comparatively, the rubber MR elastomer has low modulus change ability. A mathematical model to represent the stress-strain relationship of MR elastomers is presented. The model takes into account all the dipole interactions in a chain and the nonlinear properties of the host composite. The analytical results of the model are in agreement with experimental data.

Active Structural Vibration Control: A Review

In this paper we review essential aspects in- volved in the design of an active vibration control system. We present a generic procedure to the design process and give selective examples from the literature on relevant ma- terial. Together with examples of their applications, various topics are briefly introduced, such as structure modeling, model reduction, feedback control, feedforward control, con- trollability and observability, spillover, eigenstructure assign- ment (pole placement), coordinate coupling control, robust control, optimal control, state observers (estimators), intelli- gent structure and controller, adaptive control, active con- trol effects on the system, time delay, actuator-structure interaction, and optimal placement of actuators.

Semi-active Vibration Control Schemes for Suspension Systems Using Magnetorheological Dampers

Three semi-active control methods are investigated for use in a suspension system using a commercial magnetorheological damper. The three control methods are the limited relative displacement method, the modified skyhook method, and the modified Rakheja-Sankar method. The method of averaging has been adopted to provide an analytical platform for analyzing the performance of the different control methods. The analytical results are verified using numerical simulation, and further are used to assess the efficiency of different control methods. An experimental test bed has been developed to examine the three control methods under sinusoidal and random excitations. Both analytical and experimental results confirm that the Rakheja-Sankar control and modified skyhook control methods significantly reduce the root-mean-square response of both the acceleration and relative displacement of the sprung mass, while the limited relative displacement controller can only control the relative displacement of the suspension system.

Initial calibration of an inertial measurement unit using an optical position tracking system

A reliable calibration procedure of a standard six degree-of-freedom inertial measurement unit (IMU) is presented. Mathematical models are derived for the three accelerometers and three rate gyros, taking into account the sensor axis misalignments, accelerometer offsets, electrical gains, and biases inherent in the manufacture of an IMU. The inertial sensors are calibrated using data from a 3D optical tracking system that measures the position coordinates of markers attached to the IMU. Inertial sensor signals and optical tracking data are obtained by manually moving the IMU. Using vector methods, the quaternion corresponding to the IMU platform orientation is obtained, along with its acceleration, velocity, and position. Given this kinematics information, the sensor models are used in a nonlinear least squares algorithm to solve for the unknown calibration parameters. The calibration procedure is verified through extensive experimentation.

A quaternion-based orientation estimation algorithm using an inertial measurement unit

This paper presents a real-time orientation estimation algorithm based on signals from a low-cost inertial measurement unit (IMU). The IMU consists of three MEMS accelerometers and three MEMS rate gyros. This approach is based on relationships between the quaternion representing the platform orientation, the measurement of gravity from the accelerometers, and the angular rate measurement from the gyros. Process and measurement models are developed, based on these relations, in order to implement them into an extended Kalman filter. The performance of each filter is evaluated in terms of the roll, pitch, and yaw angles. These are derived from the filter output since this orientation representation is more intuitive than the quaternion representation. Extensive testing of the filters with simulated and experimental data show that the filters perform very accurately in the roll and pitch angles, and even significantly corrects the yaw angle error drift.

Frequency response and jump avoidance in a nonlinear passive engine mount

This paper explores a model for a nonlinear one-degree of freedom passive vibration isolator system, known as a smart engine mount. Nonlinearities are employed to analyze and possibly improve the behavior of the optimal linear mount. Nonlinear damping and stiffness rates of the isolator have interacting effects on the dynamic behavior of the mount. The frequency response of the system is obtained using the averaging perturbation method, and a parametric analysis shows that the effect of nonlinear stiffness rate on frequency response is opposite to that of the nonlinear damping rate. Stability of the steady state periodic response has also been analyzed. Jump avoidance criteria are introduced, and the conditions for jump avoidance are studied. Closed form solutions for the absolute acceleration and relative displacement frequency responses are derived, since they are essential to use of the RMS optimization method.

Root mean square optimization criterion for vibration behaviour of linear quarter car using analytical methods

In this paper, a linear two-degree-of-freedom quarter car model is used to derive a number of analytical formulae describing the dynamic behaviour of passively suspended vehicles running on a harmonically bumped road. The linearity of the system allows us to analytically investigate the steady-state response characteristics. We derive analytical expressions for the root mean square (RMS) of the sprung mass absolute acceleration and relative displacement. This paper demonstrates the shortcomings of existing classical optimization methods. Hence we introduce a new optimization method based on minimizing the absolute acceleration RMS with respect to the relative displacement RMS. The RMS optimization method is applied for the symbolic derivation of analytical formulae featuring the best compromise among conflicting performance indices pertaining to the vehicle suspension system, i.e., sprung mass acceleration and working space. The proposed optimization technique is utilized to find the optimal damping and stiffness curves for the main suspension. The RMS optimal values are used to create design charts for suspension parameters, which are very useful particularly in the presence of physical constraints such as a limit on relative displacement. We introduce a numerical example to illustrate the optimality of the obtained solutions.

Large free vibrations of a beam carrying a moving mass

Abstract The focus of this work is to develop a technique to obtain numerical solution over a long range of time for non-linear multi-body dynamic systems undergoing large amplitude motion. The system considered is an idealization of an important class of problems characterized by non-linear interaction between continuously distributed mass and stiffness and lumped mass and stiffness. This characteristic results in some distinctive features in the system response and also poses significant challenges in obtaining a solution. In this paper, equations of motion are developed for large amplitude motion of a beam carrying a moving spring–mass. The equations of motion are solved using a new approach that uses average acceleration method to reduce non-linear ordinary differential equations to non-linear algebraic equations. The resulting non-linear algebraic equations are solved using an iterative method developed in this paper. Dynamics of the system is investigated using a time-frequency analysis technique.

A vector-based gyro-free inertial navigation system by integrating existing accelerometer network in a passenger vehicle

Modern automotive electronic control and safety systems, including air-bags, anti-lock brakes, anti-skid systems, adaptive suspension, and yaw control, rely extensively on inertial sensors. Currently, each of these sub-systems uses its own set of sensors, the majority of which are low-cost accelerometers. Recent developments in MEMS accelerometers have increased the performance limits of mass-produced accelerometers far beyond traditional automotive requirements; this growth trend in performance will soon allow the implementation of a gyro-free inertial navigation system (GF-INS) in an automobile, utilizing its existing accelerometer network. We propose, in addition to short-term aid to GPS navigation, a GF-INS can also serve in lieu of more expensive and less reliable angular rate gyros in vehicle moment controls and inclinometers in anti-theft systems. This work presents a modified generalized GF-INS algorithm based on four or more vector (triaxial) accelerometers. Historically, GF-INS techniques require strategically-placed accelerometers for a stable solution, hence inhibiting practical implementations; the vector-based GF-INS allows much more flexible system configurations and is more computationally efficient. An advanced attitude estimation technique is presented, utilizing coupled angular velocity terms that emerged as a result of the intrinsic misalignment of real vector accelerometers; this technique is void of singularity problems encountered by many prior researchers and is particularly useful when error due to the integration of angular accelerations is prominent, such as in low-speed systems or long-duration navigations. Furthermore, an initial calibration method for the vector-based GF-INS is presented. In the experimental setup, four vector accelerometers, based on Analog Devices accelerometers, are assembled into a portable, one cubic-foot, rigid structure, and the data is compared with that of a precision optical position tracking system. Finally, the feasibility of a GF-INS implementation in an automobile is assessed based on experimental results.

Practical Frequency and Time Optimal Design of Passive Linear Vibration Isolation Mounts

Summary In this paper we examine a linear one-degree of freedom vibration isolator mount. The linearity of the system allows us to analyze its frequency and time response characteristics analytically. Optimal damping and stiffness values for the isolator are obtained by minimizing certain cost functions, which are the Root Mean Square (RMS) of the absolute acceleration and the relative displacement. These RMS cost functions are used to create a design chart for the isolator parameters. This is very useful particularly in the presence of physical constraints such as a limit in relative displacement. The time response of the system for a unit step input is also considered to gain an insight into the transient characteristics of the system. We obtain an optimal value for the damping ratio of the system in order to minimize the transmitted acceleration. Combining the frequency and time response analyses leads to an optimal value for the mount natural frequency and damping ratio satisfying both time and frequency domains. The results are verified numerically using measured acceleration as input.