The Effect of Front Fork Compliance on the Stability of Bicycles

2015 ◽  
Author(s):  
Alberto Doria ◽  
Luca Taraborrelli ◽  
Nicola Segliani
Keyword(s):  
High Speed ◽  
Degrees Of Freedom ◽  
Experimental Tests ◽  
Specific Method ◽  
Lumped Element ◽  
Small Influence ◽  
Element Approach ◽  
Speed Stability ◽  
The Stability ◽  
Stiffness And Damping

In this paper the effect of front fork compliance on uncontrolled bicycle stability is analyzed. First the benchmark model of a bicycle is improved to take into account either torsion compliance or bending compliance of front fork, a lumped element approach is adopted introducing additional joints restrained by rotational springs and dampers. Two models having three degrees of freedom are developed and implemented in MATLAB codes to perform stability analysis. Then series of experimental tests are carried out on an advanced carbon fork and a standard steel fork, the modal analysis approach is adopted. Experimental methods and results are presented and discussed. A specific method is developed for identifying the stiffness and damping properties from the bending and torsion modes of the forks. Results obtained with the proposed method agree with data presented in literature. Finally, the identified stiffness and damping parameters are implemented in the simulation codes and some numerical simulations are carried out. Results presented in the paper show a small influence of torsion compliance on stability and a large influence of bending compliance on high speed stability.

Synchronous Response to Rotor Imbalance Using a Damped Gas Bearing

2009 ◽  
Author(s):  
Bugra H. Ertas ◽  
Massimo Camatti ◽  
Gabriele Mariotti
Keyword(s):  
High Speed ◽  
Experimental Tests ◽  
Rotor System ◽  
Rotor Imbalance ◽  
High Speeds ◽  
Speed Range ◽  
Speed Stability ◽  
Stiffness And Damping ◽  
Gas Bearing ◽  
Large Rotor

One type of test performed for evaluating bearings for application into turbomachinery is the synchronous bearing response to rotor imbalance. This paper presents rotordynamic tests on a rotor system using a 70mm diameter damped gas bearing reaching ultra-high speeds of 50,000 rpm. The main objective of the study was to experimentally evaluate the ability of the damped gas bearing to withstand large rotor excursions and provide adequate damping through critical speed transitions. Two critical speeds were excited through varying amounts and configurations of rotor imbalance, while measuring synchronous rotordynamic response at two different axial locations. The results indicated a well-damped rotor system and demonstrated the ability of the gas bearing to safely withstand rotor vibration levels while subjected to severe imbalance loading. Also, a waterfall plot was used to verify ultra high-speed stability of the rotor system throughout the speed range of the test vehicle. In addition to the experimental tests, a rotordynamic computer model was developed for the rotor-bearing system. Using the amplitude/frequency dependent stiffness and damping coefficients for the ball bearing support and the damped gas-bearing support, a pseudo-nonlinear rotordynamic response to imbalance was performed and compared to the experiments.

Synchronous Response to Rotor Imbalance Using a Damped Gas Bearing

2009 ◽  
Vol 132 (3) ◽  
Author(s):  
Bugra H. Ertas ◽  
Massimo Camatti ◽  
Gabriele Mariotti
Keyword(s):  
High Speed ◽  
Experimental Tests ◽  
Rotor System ◽  
Rotor Imbalance ◽  
High Speeds ◽  
Speed Range ◽  
Speed Stability ◽  
Stiffness And Damping ◽  
Gas Bearing ◽  
Large Rotor

One type of test performed for evaluating bearings for application into turbomachinery is the synchronous bearing response to rotor imbalance. This paper presents rotordynamic tests on a rotor system using a 70 mm diameter damped gas bearing reaching ultra-high speeds of 50,000 rpm. The main objective of the study was to experimentally evaluate the ability of the damped gas bearing to withstand large rotor excursions and provide adequate damping through critical speed transitions. Two critical speeds were excited through varying amounts and configurations of rotor imbalance while measuring the synchronous rotordynamic response at two different axial locations. The results indicated a well-damped rotor system and demonstrated the ability of the gas bearing to safely withstand rotor vibration levels while subjected to severe imbalance loading. Also, a waterfall plot was used to verify ultra-high-speed stability of the rotor system throughout the speed range of the test vehicle. In addition to the experimental tests, a rotordynamic computer model was developed for the rotor-bearing system. Using the amplitude/frequency dependent stiffness and damping coefficients for the ball bearing support and the damped gas-bearing support, a pseudononlinear rotordynamic response to imbalance was performed and compared with the experiments.

Numerical and Experimental Approaches to Investigate the Stability of a Motorcycle Vehicle

2006 ◽  
Author(s):  
Federico Cheli ◽  
Marco Bocciolone ◽  
Marco Pezzola ◽  
Elisabetta Leo
Keyword(s):  
Degrees Of Freedom ◽  
Structural Parameters ◽  
Experimental Tests ◽  
Roll Angle ◽  
Longitudinal Motion ◽  
Reference Trajectory ◽  
Steering Angle ◽  
Steady State Condition ◽  
The Stability ◽  
Linearized Model

The study of motorcycle’s stability is an important task for the passenger’s safety. The range of frequencies involved for the handling stability is lower than 10 Hz. A numerical model was developed to access the stability of a motorcycle vehicle in this frequency range. The stability is analysed using a linearized model around the straight steady state condition. In this condition, the vehicle’s vertical and longitudinal motion are decoupled, hence the model has only four degrees of freedom (steering angle, yaw angle, roll angle and lateral translation), while longitudinal motion is imposed. The stability was studied increasing the longitudinal speed. The input of the model can be either a driver input manoeuvre (roll angle) or a transversal component of road input able to excite the vibration modes. The driver is introduced in the model as a steering torque that allows the vehicle to follow a reference trajectory. To validate the model, experimental tests were done. To excite the vehicle modes, the driver input was not taken into account considering both the danger for the driver and the repeatability of the manoeuvre. Two different vehicle configurations were tested: vehicle 1 is a motorcycle [7] and vehicle 2 is a scooter. Through the use of the validated model, a sensitivity analysis was done changing structural (for example normal trail, steering angle, mass) and non structural parameters (for example longitudinal speed).

Investigation of Gyroscopic Effect on the Stability of High Speed Micromilling via Bifurcation Analysis

2021 ◽  
Vol 5 (4) ◽  
pp. 130
Author(s):  
Rinku K. Mittal ◽  
Ramesh K. Singh
Keyword(s):  
High Speed ◽  
Degrees Of Freedom ◽  
Multistep Method ◽  
Gyroscopic Effect ◽  
High Rotational Speed ◽  
Micro Tool ◽  
The Stability ◽  
Delay Differential ◽  
Stability Limits ◽  
Micro Tools

Catastrophic tool failure due to the low flexural stiffness of the micro-tool is a major concern for micromanufacturing industries. This issue can be addressed using high rotational speed, but the gyroscopic couple becomes prominent at high rotational speeds for micro-tools affecting the dynamic stability of the process. This study uses the multiple degrees of freedom (MDOF) model of the cutting tool to investigate the gyroscopic effect in machining. Hopf bifurcation theory is used to understand the long-term dynamic behavior of the system. A numerical scheme based on the linear multistep method is used to solve the time-periodic delay differential equations. The stability limits have been predicted as a function of the spindle speed. Higher tool deflections occur at higher spindle speeds. Stability lobe diagram shows the conservative limits at high rotational speeds for the MDOF model. The predicted stability limits show good agreement with the experimental limits, especially at high rotational speeds.

scholarly journals Simulation analysis of efficiency and stability for vehicle’s ABS control on combined steering and braking maneuvers

2019 ◽  
Vol 272 ◽  
pp. 01024 ◽  
Author(s):  
Feng YU ◽  
Jun XIE
Keyword(s):  
High Speed ◽  
Control Algorithm ◽  
Degrees Of Freedom ◽  
Simulation Analysis ◽  
Stability Control ◽  
Vehicle Stability ◽  
Slip Ratio ◽  
Braking Performance ◽  
Braking System ◽  
The Stability

Eight degrees of freedom vehicle model was established. Using the method of fuzzy control, the ABS control algorithm was designed based on slip ratio. Simulation analysis was done at speed of 15m/s, 20m/s, 25m/s under turning braking. The results show that the vehicle braking performance and vehicle stability at middle or low speed was improved by using the ABS controller, but qualitative analysis shows that phenomenon of vehicle instability was appeared at high-speed conditions. The turning braking stability under ABS controller was judged quantificationally by the stability judging formula. The results show that the requirements of stability control could not meet with only Anti-lock Braking System.

Modal Frequency Response of a Four-Pad Tilting Pad Bearing With Spherical Pivots, Finite Pivot Stiffness and Different Pad Preloads

2010 ◽  
Author(s):  
Timothy W. Dimond ◽  
Amir A. Younan ◽  
Paul E. Allaire ◽  
John C. Nicholas
Keyword(s):  
Frequency Response ◽  
High Speed ◽  
Degrees Of Freedom ◽  
Natural Frequencies ◽  
Theoretical Calculations ◽  
Leading Edge ◽  
Damping Coefficients ◽  
Tilting Pad ◽  
The Subject ◽  
Stiffness And Damping

Tilting pad journal bearings (TPJBs) provide radial support for rotors in high-speed machinery. Since the tilting pads cannot support a moment about the pivot, self-excited cross-coupled forces due to fluid-structure interactions are greatly reduced or eliminated. However, the rotation of the tilting pads about the pivots introduces additional degrees of freedom into the system. When the flexibility of the pivot results in pivot stiffness that is comparable to the equivalent stiffness of the oil film, then pad translations as well as pad rotations have to be considered in the overall bearing frequency response. There is significant disagreement in the literature over the nature of the frequency response of TPJBs due to non-synchronous rotor perturbations. In this paper, a bearing model that explicitly considers pad translations and pad rotations is presented. This model is transformed to modal coordinates using state-space analysis to determine the natural frequencies and damping ratios for a four-pad tilting pad bearing. Experimental static and dynamic results were previously reported in the literature for the subject bearing. The bearing characteristics as tested are considered using a thermoelastohydrodynamic (TEHD) model. The subject bearing was reported as having an elliptical bearing bore and varying pad clearances for loaded and unloaded pads during the test. The TEHD analysis assumes a circular bearing bore, so the average bearing clearance was considered. Because of the ellipticity of the bearing bore, each pad has its own effective preload, which was considered in the analysis. The unloaded top pads have a leading edge taper. The loaded bottom pads have finned backs and secondary cooling oil flow. The bearing pad cooling features are considered by modeling equivalent convective coefficients for each pad back. The calculated bearing full stiffness and damping coefficients are also reduced non-synchronously to the eight stiffness and damping coefficients typically used in rotordynamic analyses and are expressed as bearing complex impedances referenced to shaft motion. Results of the modal analysis are compared to a two degree-of-freedom second-order model obtained via a frequency-domain system identification procedure. Theoretical calculations are compared to previously published experimental results for a four-pad tilting pad bearing. Comparisons to the previously published static and dynamic bearing characteristics are considered for model validation. Differences in natural frequencies and damping ratios resulting from the various models are compared, and the implications for rotordynamic analyses are considered.

Dynamic Characteristics of Spiral-Grooved Opposed-Hemisphere Gas Bearings

2016 ◽  
Vol 139 (3) ◽  
Author(s):  
Guangwei Yang ◽  
Jianjun Du ◽  
Weiping Ge ◽  
Tun Liu ◽  
Xiaowei Yang
Keyword(s):  
Dynamic Characteristics ◽  
Degrees Of Freedom ◽  
Dynamic Stiffness ◽  
Translational Motion ◽  
Coupling Coefficients ◽  
Dynamic Coefficients ◽  
Large Eccentricity ◽  
The Stability ◽  
Stiffness And Damping ◽  
Gas Bearing

The traditional eight-coefficient bearing model only considers the translational motion of the bearings and neglects the tilting motion and coupling effects between them. In this paper, the dynamic characteristics of the spiral-grooved opposed-hemisphere gas bearing considering five degrees-of-freedom are studied, and 50 dynamic coefficients including the translational, tilting, and coupling components are completely calculated. The Reynolds equations and their perturbed equations are solved by the finite element method to obtain the dynamic stiffness and damping coefficients. The effects of the tilting motion on the dynamic coefficients and response are analyzed, respectively. The results show that the coupling coefficients between the translational and tilting motions, which have been neglected in most previous studies, are significant at large eccentricity ratio. But these coupling coefficients have little effect on the dynamic response. On the other hand, the influences of the tilting motion on the synchronous response and natural frequency are remarkable and will decrease the stability of the rotor bearing system.

Rotordynamic Behavior of 225 kW (300 HP) Class PMS Motor–Generator System Supported by Gas Foil Bearings

2015 ◽  
Vol 137 (9) ◽  
Author(s):  
Bok Seong Choe ◽  
Tae Ho Kim ◽  
Chang Ho Kim ◽  
Yong Bok Lee
Keyword(s):  
Axial Length ◽  
High Speed ◽  
Load Capacity ◽  
Stability Margin ◽  
Generator System ◽  
Thrust Bearings ◽  
Foil Bearings ◽  
Speed Up ◽  
The Stability ◽  
Stiffness And Damping

This paper presents the dynamic behavior of a 225 kW class (300 HP), 60,000 rpm, permanent magnet synchronous (PMS) motor–generator system supported on gas foil bearings (GFBs). The rotor of a 225 kW PMS motor is supported by two identical gas foil journal bearings (GFJBs) and one pair of gas foil thrust bearings (GFTBs). The total weight and axial length of the coupled rotors are 272 N and 1042 mm, respectively. During the speed-up test to 60,000 rpm, unexpected large subsynchronous rotor motions appear at around 120–130 Hz above 35,040 rpm. After disassembling the motor, an inspection of the top foils of the GFJBs reveals significant rotor rubbing. Thus, the GFJBs are redesigned to have a smaller load capacity by reducing their axial length to 45 mm. In addition, three 50 μm thick shims are installed in the GFJBs at 120 deg intervals for reducing the swirl speed of air and producing bearing preloads. The modification delays the onset speed of subsynchronous motions to 43,200 rpm and decreases the amplitude of the subsynchronous motions from 20 to 15 μm. These results indicate that the modification improves the stability margin of the high-speed rotor system with increasing stiffness and damping. In addition, the logarithmic decrement trends are in good agreement with the test results.

scholarly journals Dynamic Modelling, Experimental Identification and Computer Simulations of Non-Stationary Vibration in High-Speed Elevators

2021 ◽  
Vol 67 (6) ◽  
Author(s):  
Radomir Đokić ◽  
Jovan Vladić ◽  
Milan Kljajin ◽  
Vesna Jovanović ◽  
Goran Marković ◽  
...  
Keyword(s):  
Dynamic Model ◽  
High Speed ◽  
Dynamic Behaviour ◽  
Dynamic Modelling ◽  
Control Program ◽  
Specific Method ◽  
Unique Method ◽  
Stationary Vibration ◽  
Vertical Vibrations ◽  
Stiffness And Damping

Modelling the dynamic behaviour of elevators with high lifting velocities (contemporary elevators in building construction and mine elevators) is a complex task and an important step in the design process and creating conditions for safe and reliable exploitation of these machines. Due to high heights and lifting velocities, the standard procedures for dynamic exploitation are not adequate. The study presents the method of forming a dynamic model to analyse nonstationary vibrations of a rope with time-varying length with nonholonomic boundary conditions in the position where the rope is connected with the cabin (cage) and in the upcoming point of its winding onto the pulley (drum). A unique method was applied to identify the basic parameters of the dynamic model (stiffness and damping) based on experimental measures for a concrete elevator. Due to the verification of this procedure, the experiment was conducted on a mine elevator in RTB Bor, Serbia. Using the obtained computer-experimental results, the simulations of the dynamic behaviour of an empty and loaded cage were shown. In addition, the study shows the specific method as the basis for forming a control program that would enable the decrease in vertical vibrations during an elevator starting and braking mode.

On the High-Speed Porpoising Instability of a Prismatic Hull

1984 ◽  
Vol 28 (02) ◽  
pp. 77-89 ◽  
Author(s):  
Peter R. Payne
Keyword(s):  
Skin Friction ◽  
High Speed ◽  
Degrees Of Freedom ◽  
Transient Solution ◽  
Delta Wings ◽  
Closed Form Solutions ◽  
Wetted Area ◽  
The Stability ◽  
Transient Forces ◽  
Vertical Impact

Simple closed-form solutions are obtained for the steady-state and transient forces and moments on a prismatic hull at speeds high enough for hydrostatic forces to be negligible and the chines to be above the undisturbed water surface ("chines dry"). We first show that this solution can be transformed to get the correct results for other hydrodynamic problems, such as the vertical impact of a wedge, a slender foil, or the two-dimensional planing of a flat plate. We then show that the full transient solution is essentially identical with Ribner's [1]2 equations for delta wings, except for terms which depend on the reduction in wetted width with heave. These results are employed to study the stability of such a hull on the assumption that only heave and pitch degrees of freedom are important, following the reasoning of Per̂ing [2]. In contradistinction to all four previous studies [2–5], the effect of skin friction is included and is found to be very powerful. If the center of gravity is above the centroid of the wetted area (which it generally is), then the effect of skin friction is stabilizing.

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