Jason T. Dreyer

Nonlinear dynamic properties of hydraulic suspension bushing with emphasis on the flow passage characteristics

Hydraulic bushings, which are often employed in vehicle suspension systems, exhibit significant excitation-dependent properties. However, previous analyses were mainly based on the linear system theory. To overcome this void, nonlinear characteristics of common hydraulic bushing configurations are examined in this article, with focus on the component properties as excited by sinusoidal or step displacements of various amplitudes. First, a nonlinear model for a laboratory prototype with a long passage and a short passage (in parallel) is developed using a lumped-parameter approach. Then the system parameters and nonlinearities are identified using experimental and computational methods, with an emphasis on characterization of the flow passage resistances. Steady-state harmonic and transient step experiments are conducted on the prototype, and the dynamic pressures inside two fluid chambers and the force transmitted to the base are measured. Numerical solution of the nonlinear model shows that the proposed model predicts both steady-state sinusoidal responses and transient responses well for single-passage and dual-passage configurations; significant improvement over a corresponding linear model is observed. Finally, approximate analytical and semi-analytical solutions of the nonlinear model are obtained by using the harmonic balance method.

Effect of Disc-Pad Contact Modification on the Brake Judder Source Using a Simplified Elasto-Kinematic Model

The brake torque variation (BTV) generated due to geometric irregularities in the disc surface is generally accepted as the fundamental source of brake judder; geometric imperfections or waviness in a disc brake caliper system is often quantified as the disc thickness variation (DTV). Prior research has mainly focused on the vibration path(s) and receiver(s), though such approaches grossly simplify the source (frictional contact) dynamics and often ignore caliper dynamics. Reduction of the effective interfacial contact stiffness could theoretically reduce the friction-induced torque given a specific DTV, although this method would severely increase static compliance and fluid volume displacement. An experiment is designed to quantify the effect of disc-pad contact modifications within a floating caliper design on BTV as well as on static compliance. The major objective of this experiment is to determine if changes in the disc-pad contact geometry can also reduce BTV without limiting the static compliance of the caliper system. A conceptual half-caliper model is proposed to explain the observed effects of pad modifications. This simplified elastokinematic model uses the elastic center concept on a pad subject to spatially phased periodic displacement inputs (DTV) at the disc-pad interface. It is utilized to determine the effective variation in normal load. The model is finally employed to determine the sensitivity of key physical parameters and to identify trends that might reduce BTV. INTRODUCTION Brake judder is defined as the vibration at frequencies proportional to wheel speed (10-20 Hz) experienced by a driver during a high-speed braking event. The fundamental source of this vibration is believed to be the geometric irregularities on the disc surface (caused by a variety of mechanisms, such as manufacturing process effects, thermal expansion, wear, and misalignments). Disc surface distortions (say quantified by ξ(t) where t is time) cause variations in the normal load at the disc-pad interface and thereby produce variations in brake torque. Some well known causes, observed effects, and analysis methods are summarized by Jacobsson [1] in an extensive review of literature as of 2003. Much of the available literature focuses on the on-vehicle path modifications and on an attenuation of the observed effects at the drivers location. No prior study has explicitly examined the role of caliper dynamics. Using a conventional brake dynamometer, judder is traditionally quantified in terms of BTV ( ) produced by a disc and caliper system during a braking event. Although DTV (ζ(t)) is typically required to produce judder, certain attributes of a disc and caliper system can significantly contribute to . Most mathematical or computational models for brake judder assume a uniform brake disc-pad contact surface [2,3,4]. However, a disc which possesses a wavy braking surface will create a non-uniform contact interface between it and the brake pad. This non-uniformity on the interfacial braking surface can affect heat distribution patterns on the disc surface as well as create a time-varying effective center of pressure [5]. Changes in the center of Effect of Disc-Pad Contact Modification on the Brake Judder Source Using a Simplified ElastoKinematic Model 2013-01-1907 Published 05/13/2013 Jason Dreyer, John Drabison, Jared Liette and Rajendra Singh The Ohio State University Osman Taha Sen Istanbul Technical University Copyright

Dynamic characterization of the rectangular piston seal in a disk-caliper braking system using analytical and experimental methods

A new simplified, yet representative experiment of a floating dual-piston disk-caliper braking system is designed to isolate the rectangular seal and the piston–bore chamber from the complexities of a braking system. The physical sources of the stiffness and damping mechanisms associated with the seal during an applied pressure event are identified and quantified under harmonic excitation. A tractable analytical model of the experiment that incorporates the identified dynamic seal properties is proposed. This linear time-invariant model describes the governing equations of both the hydraulic brake system components and the mechanical caliper components and provides some insights into a seemingly nonlinear system. For a range of pressure amplitudes and brake configurations, excellent agreement between predictions and measurements is obtained for the peak-to-peak values of the piston–bore chamber pressure, the force transmitted by the pistons, and the caliper displacement. The proposed model and experiment could be utilized in brake control, vibration, and pedal feel studies.

Suppression of Multiple Order Friction Torque Fluctuations with Modulated Actuation Pressure

The goal of this article is to examine the effect of modulated actuation pressure on the friction torque response of a disc brake system. First, a dynamic friction experiment, consisting of a flywheel, shaft and brake assembly, is built and instrumented accordingly. The actuation pressure is modulated with a solenoid valve located in the hydraulic line. During the experiment, the modulation frequency is kept intact, and the shaft torque is measured as the system slows down; an amplification of the dynamic torque is observed as the system passes through the resonance. Second, a nonlinear mathematical model of the brake experiment is developed, and the dynamic torque response is numerically calculated for various modulation schemes, such as with constant frequency and sweeping modulation frequency with single harmonic content. Predicted results are compared with measurements. Finally, the outcome of this study is related to the brake judder problem, and some solutions for the reduction of dynamic torque are briefly discussed.

Effects of Preloads on Vibration Transmission Through Double Row Angular Contact Ball Bearings

This work investigates the role of double row angular contact ball bearings as a vibration transmitter in shaft-bearing assemblies. In our analyses the double row bearings are represented as five dimensional stiffness elements (with associated damping) through an extension of the stiffness matrix concept described by Lim and Singh (1989) for single row bearings to double row angular contact ball bearings. In particular, the effects of bearing preloads on dynamic characteristics of double row angular contact ball bearings are first numerically explored. The dynamic responses of face-to-face, back-to-back and tandem arrangements are evaluated on a comparative basis under various preloads. The nature and extent of preloads significantly affect the vibration characteristics of the bearing assembly due to major changes in the diagonal and off-diagonal elements of the stiffness matrix, and these effects vary for alternate configurations. The dynamic effects of bearing preloads are then experimentally investigated for a wheel bearing assembly containing double row angular contact ball bearings (with back-to-back arrangement) under two different preloading mechanisms. Experiments show that the mechanism and amount of bearing preloads significantly affect the system natural frequencies, mode shapes and vibration amplitudes, thus altering the vibration behavior of the bearing assembly. Suggestions for further work and applications will be briefly mentioned.© 2011 ASME

Active and Passive Vibration Control Using Compact Damping Patches: Assessment of a Reduced Order Model for an Euler Beam

Concurrent placement of compact active and passive damping patches for vibration reduction is a developing area of research. Analytical and computational models to evaluate alternate patch configurations and structural geometries are not widely available. To overcome this void, this paper presents a simplified discrete-system model for vibrations of a beam-like structure. A disturbance input is included in the model, along with a control input from an active patch. Localized structural damping resulting from a passive patch is modeled with an equivalent loss factor. Results from the simplified model are verified using a more detailed analytical formulation, which is based on the Ritz approximation. Verification studies include the effect of a passive damping patch on modal loss factors and broadband attenuation. Finally, a few case studies are proposed which show the efficacy of the reduced-order model for parametric design studies. These studies include determining the effect of localized damping on the control system parameters that are required for attenuation of localized and global motions. The effect of patch locations on system response is also studied. This work has potential applications in industry since compact damping patches are attractive NVH treatments that add minimal weight and complexity.© 2015 ASME

Application of a Novel Method to Identify Multi-axis Joint Properties

This article is motivated by the widespread use of shaped elastomeric body mounts that undergo broadband, multi-axis loading; whereas often in application, the principal direction mount properties are measured separately at single frequencies. An inverse method is applied to a new experiment that is constructed with an elastic metal beam end-supported by two elastomeric mounts. Due to a judiciously selected attachment location relative to the neutral axis of the beam as well as the shape of the mount, the in-plane transverse and longitudinal beam motions are found to be coupled. This method utilizes the sensitivity of the beam modal parameters, including natural frequency, mode shapes, and damping ratio, to support properties at each end to identify the multi-axis mount properties. The dynamic stiffness and loss factors of the elastomeric mounts are directly measured in a commercial elastomer test machine and agreement is found between the inverse and direct methods at small displacements. Further, this article helps provide insight into multi-axis properties with new benchmark experiments on off-the-shelf mounts that permit comparison between inverse system and direct component identification methods of the dynamic multi-axis elastomeric mount properties.

Forced Response of a Nonlinear Translating Brake Band in the Presence of Friction Guides

The goal of this article is to investigate the response of a nonlinear translating brake band system under different external loading and constraint conditions. A friction bench experiment is designed, built, and instrumented accordingly. In this experiment, an actuation body (supported by the friction guides) is pushed against a translating brake band over a prescribed actuation cycle. Therefore, two friction regimes are generated; one between the actuation body and brake band, and another one between the actuation body and friction guide(s). Locations of the friction guides and external load application points are varied and all possible cases are experimentally and computationally studied. First, the effect of the center of contact force shift on the forced response is investigated, and conditions that lead to this shift are examined. Second, a nonlinear mathematical model is utilized to explain the relationship between the center of contact force location and the forced system response, as well as to observe certain trends. Finally, such trends are confirmed by measurements, and a better understanding of the effect of external load and constraint locations on a variation in the friction force is obtained. Some of the findings are briefly linked to the vehicle brake judder problem.

Comparative signal processing analyses of a speed-dependent problem as motivated by brake judder problem

The goal of this paper is to investigate a transient problem using several digital signal processing techniques. First, a simple linear mathematical model, where a point mass is connected to a roller through a contact interface, is developed and the dynamic interfacial force is analytically calculated as a function of the speed. In this model, the contact interface is described with a linear spring and viscous damper, and the system is excited with a base excitation, as defined by the undulations on the roller surface. Due to the time-varying speed characteristics of the roller, the resulting response is transient. Second, the dual-domain analyses of the calculated system response is carried out by using short-time Fourier and wavelet transforms, since single-domain representation leads to a loss of information due to signals transient characteristics. Third, the Hilbert transform is applied and the envelope curves of the interfacial force response are successfully obtained. Finally, this problem is brie...

Estimation of room absorption of acoustic cones based on impedance tube measurements

Acoustic cones are often the primary absorption treatment choice for constructing anechoic chambers. Reverberation chamber estimation of room absorption will most accurately represent the actual effect of three‐dimensional treatments, such as cones. However, for low frequencies, large reverberation chambers are often required, which may not be available due to space and cost constraints. Impedance tubes measurements are more accurate than reverberation chamber measurements in terms of sound absorption coefficient. Conversely, due to the two‐dimensional nature of impedance tubes, room absorption of three‐dimensional objects is difficult to estimate. Absorption coefficient of the material is a function of not only surface area but also material thickness. This paper proposes a technique to estimate the room absorption of three‐dimensional treatments based on measured absorption coefficient of different thickness treatment specimens by impedance tube. This extrapolation of impedance tube measured absorption ...