- Dynamics and Control of Hydraulic Systems
- Energy Efficient Bipedal Robots
- Friction Induced Vibrations in Shift Gearboxes
- Gas Bearings in Rotordynamic Applications
- Influence of Fast Motions on Systems with Dry Friction
- Influence of the Microstructure of Metal Foams on Macroscale
- Regularization of Nonholonomic Constraints in Multibody Systems
- Self-balancing of the planetary moving rotor
- Stochastic Analysis of Geometric Mistuning in Radial Compressor
Dynamics and Control of Hydraulic Systems
Hydraulic valves are known to show interesting dynamic behavior. Nevertheless they have not yet been investigated extensively from the viewpoint of nonlinear dynamics and are not suffciently understood. An elementary hydraulic pressure control valve can be described as a system of third order with a non-smooth nonlinearity.
The transition from an ideally impermeable valve to a valve allowing for leakage ﬂow uncovers an instability mechanism for for certain valve geometries. Leakage changes the character of the equilibrium position from a set-valued equilibrium position to a unique one. A loss of stability of the equilibrium position and the birth of a limit cycle due to leakage can be shown when increasing leakage flow or the working point pressure of the system. A bifurcation analysis reveals the different solution types for the system under external forcing, yielding evidence of period-doubling phenomena up to quasi-periodic solutions.
Building on the findings for the dynamics of the foundational element in hydraulics - the valve - a variable displacement vane pump is currently investigated. This type of pump is frequently used in automotive engineering in order to provide the required pressure for the actuation of a clutch mechanism. A subfunction of the pump is to provide the volume flow required by a cooling unit. The system under investigation shows many aspects which are characteristic for hydraulic systems. In steady state, the valve regulating the system pressure is lapped critically, therefore giving rise to non-smooth dynamics. Apart from analyzing the stability behavior of the pump system in a first step, in a second step control strategies shall be devised that result in a change of the working point of the system. Drawing on the control strategies identified, the task then is to synthesize hydraulic elements and their topology such that the control strategies can be implemented by means of hydraulic action.
The hydraulic consumer provided with volume flow from the variable displacement vane pump is the third field of interest in this research project. As pointed out, it is a clutch actuation mechanism. In order to simulate the dynamics of clutch systems adequately, reasonable estimates of the system parameters have to be known. By means of Kalman filtering, important parameters of the clutch actuation mechanism can be identified. To do so, the clutch actuation system is subjected to transient volume flow excitation. Measurements of the system responses to the transient excitation are then synchronized with a slave model of the consumer, resulting in good estimates of the true parameters to be identified.
Energy Efficient Bipedal Robots
One of the biggest challenges for todays humanoid robots is energy efficiency. To evaluate the efficiency of bipedal locomotion the dimensionless specific energetic cost of transportation, cot = (energy used)/(weight × distance traveled) is used. At a walking speed of 0.4 m/s the state-of-the-art humanoid Honda Asimo with cot = 3.2 is very inefficient compared to humans with cot = 0.2. The main cause for this bad energy efficiency is the control strategy of humanoid robots which fights against gravitation and tries to suppress any natural dynamics. Humans on the other hand walk with gravitation – they use their natural dynamics instead of struggling against it. Their body even consists of springs in the shape of tendons to influence the dynamics and buffer energy during the walking cycle.
Our method to improve the energy efficiency of bipedal walkers consists of a two-track approach. On the first hand an alternative control strategy is used, which allows for evolvement of natural dynamics, based on input–output linearisation. On the other hand the natural dynamics of the underlying mechanical subsystem is optimized by introducing elastic couplings between different links. Numerical optimization is used to determine simultaneously the desired joint trajectories as well as the best elastic coupling.
With elastic couplings the cost of transportation can be reduced significantly. There are mainly two reasons for the energy savings. First of all the natural frequency of the swing leg can be adjusted to the locomotion speed in order to be operated near resonance. The elasticity helps not only to accelerate the swing leg but also to decelerate and to transform kinetic energy into potential energy, which otherwise would get lost for the system during breaking or at the impact. Finally it can be stated that significant gains in energy efficiency can be made by allowing and optimizing the natural dynamics with elastic couplings.
Friction Induced Vibrations in Shift Gearboxes
A shift gearbox is a commonly used element in automotive transmissions, which is needed for two reasons. Firstly, it transmits the driving torque of the motor. Secondly, because a combustion engine works best at its nominal speed, it changes the gears. Experimental data reveal that in a shift gearbox, friction-induced vibrations are possible during the shifting period. The vibrations are visible in the pressure signal of the actuation of the clutch, which implies a coupling with the axial movement of the gear unit input shaft.
The suggested model consists of a pressure plate, a clutch disc, a gear unit input shaft and a tooth contact. The gear unit input shaft is rigidly connected to the gearing and the clutch disc and has translational and rotational degrees of freedom. The tooth contact imposes a kinematic constraint. This is why the sliding friction torque is transformed into forces in axial and radial direction of the shaft. Depending on the gearing parameters and the slip, the contact normal force between clutch disc and pressure plate is amplified (motor accelerating) or reduced (motor slowing down) by the toothing. For both shifting situations, there can be found a region of flutter instability in the parameter space.
Besides the stationary solution, also periodic orbits are possible. E.g. there exists a stable piecewise-continuous limit cycle for a slowing down motor: During one period, the contact between the clutch disc and the pressure plate opens shortly. This limit cycle depends on parameters (masses, stiffnesses, ...) as well as on operation conditions.
Contact: Prof. A. Fidlin
Gas Bearings in Rotordynamic Applications
The two major advantages of gas bearings compared to other lubricated bearings are inherently low viscosities and their chemical stability over a wide temperature range. Furthermore, the usage of gas lubrication can lead to auxiliary benefits, depending on the application. For example, a simpler lubrication supply, a contamination free environment, less maintenance and less noise generation. All these reason could additionally lead to reduced manufacturing- and maintenance costs.
Unfortunately, in gas bearing mounted rotors are prone for instabilities. Reasons are, for example, the low viscosity of the fluid film, resulting in a low damping characteristic and self-excited vibrations, caused by the bearing reacting forces. Consequently, a proper designing- and dimensioning process of the rotor-bearing system can be very extensive.
In order to identify the physical effects, derivate design guidelines for rotor-bearing-systems and detect the limitations of gas bearing technology, gas bearing – rotor interactions are studied. Currently, the focus is on time-efficient nonlinear bearing modelling for rotor dynamic simulation, as well as stability- and bifurcation analysis of the rotor.
Journal Bearings with Variable Geometry
Influence of Fast Motions on Systems with Dry Friction
Undesired phenomena in systems with dry friction are well known. Especially for low relative velocities, non-smooth properties and velocity dependence of dry friction may lead to friction induced vibrations or stick-slip motion.
By imposing high-frequency vibrations to a system, the effective friction characteristics can be smoothed and, consequently, undesired friction induced phenomena can be quenched.
Considering for example revolute joints in positioning applications, high-frequency excitation may be provided using piezoelectric transducers. Smoothing the friction characteristics can reduce break-away forces significantly and thus improve accuracy.
In order to get deeper insight in the mechanism of smoothing dry friction, several aspects such as the direction, amplitude and frequency of excitation, pre-stress or material properties have to be studied. Focusing on different frictional materials, contact compliance and therefore dynamic properties of friction may become important. Dynamic friction models can be used in order to improve modeling and thus achieve better agreement with experimental results.
Influence of the microstructure of metal foams on macroscale
Metal foams and their applications are of increasing interest in the area of research and development. High stiffness in conjunction with low density, high percentage of free surface within the volume, capacity of high energy absorbation and good damping properties of metal foams are relevant for light weight construction, chemical reactions, crash elements and vibration damping. Metal foams are used for example as car body elements, crash absorbers, fast moving vibrating devices, heat exchangers, catalysts, heat shieldings.
In dynamic applications it is necessary to describe eigenfrequencies and damping properties of metal foams. Due to the strongly developed inhomogenities of the microstructure of metal foams the material parameters and properties fluctuate.
The influence of the inhomogenities at the micro level to the macroscopic behavior is being researched. Two aspects are of main interest: The size effect and the standard deviation of the material parameters. The aim is to develop a simulation model that depicts the influence of the microstructural inhomogenities on the macroscopic behavior.
Contact: Prof. C. Proppe
Self-balancing of the planetary moving rotor
The phenomenon of self-balancing of rigid rotors is well known and investigated for rotors with fixed bearings. However, in some technical devices the rotor performs complex motions. An example of such system is a computed tomography scanner. Its anode rotates very fast in the housing of the X-ray tube. At the same time the X-ray tube itself rotates rather slowly around the patient’s body. It is very important for CT scanner to keep the minimal possible level of vibrations in order to obtain good image quality. The objective is to investigate how and to which extent the self-balancing devices can be used for reducing vibrations in a planetary moving rotor.
The model to consieder consists of the rotor of mass M, which is fixed on the end of the regid carrier. The other end of the carrier is elastically suspended with radial spring-dampers of a certain stiffness c and damping b. The carrier rotates around it’s point of suspension with a constant velocity Ω. At the same time the rotor rotates around its symmetry axis with a given velocity ω. Its centre of mass has an offset relative to the rotation axis. Two pendulum balancers of mass m, moment of inertia J and length r are placed on the rotation axis of the rotor.
Stochastic Analysis of Geometric Mistuning in Radial Compressors
Radial compressor in turbochargers is often considered in theory as periodic system, but in fact it features inevitable small imperfections caused by material defects and manufacturing tolerances which break the cyclic periodicity. This is called mistuning. The loss of periodicity changes drastically the dynamic behavior of the compressor. Typically the forced response level of the mistuned bladed disk is larger than the tuned design. Because of the random nature of mistuning, the determination of the largest resonant response at any frequency has to be considered as a stochastic problem.
Mistuning receives significant attention from the research community since the late 1960s. Models using coupled lumped mass oscillators have allowed the fundamental phenomena of mistuning to be understood. More recently finite element model are used to explore with a better precision the behavior of mistuned compressor. To minimize the computational costs the finite element model has to be reduced first before performing a Monte Carlo Analysis. In the last decade several model reduction methods were developed. The way in which mistuning is implemented depends on the used reduction method and the vast part of them accounts only for a frequency mistuning model or a proportional mistuning model, in which the ideal tuned configuration is not modified.
Today a key topic is to combine this reduction methods with a more realistic introduction of mistuning, such as geometric mistuning. In other words, it will be tried to take directly random geometry modifications into consideration in a stochastic problem.