1. Introduction
Numerical models are important tools in the design of hydraulic circuits for the prediction of their hydrodynamic behavior to evaluate their performance and detect unexpected anomalies, such as pressure oscillations and resonances that may generate instabilities and undesired noises. Moreover, simulation enables to investigate alternative and innovative solutions for improving the sustainability of the systems, such as by evaluating the performance of the circuit operating with eco-friendly innovative fluids instead of petroleum based hydraulic fluids. The hydraulic circuit of the power transmission systems of high-performance cars are generally characterized by strict geometrical constraints, due to the necessity of lightweight and compact systems design, and high speed volumetric pump as supply system, such as Gerotor gear pumps system since they guarantee high performance for the wide operating range of the engine speed.
In this paper, the hydraulic circuit of a Dual-Clutch Transmission (DCT) power transmission system adopted in high performance cars is analyzed by means of lumped and distributed parameters models for the investigation of resonance phenomena due to system design. In fact, these circuits are characterized by several components, such as pumps, valves, pistons, and ducts, which could resonate in specific actual operating conditions. For instance, in [
1], an aeronautical hydraulic pipeline system, which risks resonance due to the excitation of the pump vibration, is analyzed by means of an anti-resonance design approach based on a sensitivity index for the identification of the most significant variables for the circuit design. Gerotor gear pumps are employed in automotive applications, especially when high speed rotation rate is required, and numerical models are implemented to predict their fluid dynamic behavior and therefore to design the hydraulic circuits. Lumped and distributed models demonstrated to be accurate for the investigation and the prediction of the hydraulic behavior of Gerotor pumps, such as in [
2] where a 1D approach is proposed for a Gerotor pump and the comparison with the experimental results proved good agreement by addressing the delivery flow rate prediction as well as the volumetric efficiency and the temperature influence. More detailed results can be obtained simulating the real component geometry with Computation Fluid Dynamics (CFD) numerical tools, such as in [
3], where the fluid dynamics behavior of a double inlet Gerotor pump is analyzed under actual operating conditions by adopting an overset mesh approach. Nevertheless, the computational effort required for the simulation of CFD numerical models is not suitable for the simulation of complex hydraulic circuits and for the investigation of the whole operating conditions domain. Lumped and distributed numerical models are employed to evaluate the dynamic performance of power transmission systems, such as in [
4], where a dynamic model of a DCT’s hydraulic circuit is implemented for the prediction of the circuit characteristic, i.e., clutch filling and lubrication, and good agreement with the experimental results is found.
Figure 1 reports the hydraulic scheme of the DCT power transmission system analyzed in the paper. It presents a Gerotor gear pump actuated by the engine, a Pressure Regulation Valve (PRV) for the regulation of the system pressure, the p
s, which is the system pressure transducer, and three Proportional Valves (PVs) for the actuation of the two clutches and of the differential piston. The two clutches enable power transmission from the engine to the odd and to the even gearsets, while the locking and unlocking of the differential is controlled by actuating the differential piston, based on the vehicle torque requirements. A hydraulic plate (Clutch Control Module) is adopted to manufacture the hydraulic circuit; the pipeline is drilled to design the hydraulic ducts, while the valves are located in their specific housing.
In literature, wave propagation through hydraulic pipeline is deeply theoretically and experimentally investigated to analyze the fluid dynamic behavior. For instance, in [
5], a four-equation model, which assumes 1D liquid flow, is adopted to simulate the fluid-structure interaction of water hammer in a pipeline fastened with a particular support system and it reported a good agreement between numerical and experimental results in terms of pressure oscillations. Hydraulic resonances may be induced by specific operating conditions and they should be generally avoided and constrained to achieve good performance to prevent components failure. For instance, in [
6], the failure of grey cast iron pipe due to resonance phenomenon is numerically investigated by predicting the steady-oscillatory flow and evaluating the maximum stresses in the pipe. Wave attenuation is therefore an important topic and engineering solutions have been developed to reduce pressure oscillations where design constraints oblige to operate in resonant operating conditions. Helmholtz resonators are employed in hydraulic circuits to reduce flow pulsation and numerical models are used to design the resonator frequency, such as in [
7], where a novel lumped parameter model is presented for the prediction of the resonance frequency of a three degrees of freedom Helmholtz resonator in hydraulic system. Numerical tools have been developed to analyze oscillating signals and to highlight their effectiveness by varying the operating parameters. Spectral maps are employed to evaluate instability behaviors in the frequency domain, such as in [
8], where pressure signals recorded at different throttling valve position have been analyzed through spectral maps to describe the process of onset surge of a centrifugal blower. Other methods are also used for vibration analysis, such as the order tracking, which enables to identify speed-related vibrations by using as frequency base running speeds multiples. In [
9], an order tracking method is investigated and the influence of the factors and assumptions are examined to evaluate their effectiveness on the results accuracy. Furthermore, simplified models can be implemented to evaluate and detect resonance behavior through linear response of hydraulic circuit by reducing simulation computational efforts. For instance, in [
10], a modal testing approach is proposed for the experimental identification of the frequency response functions of hydraulic pipelines and results show a good match between experimental and calculated response functions. Numerical models are therefore accurate and reliable tools for pressure wave propagation analysis, but literature lacks numerical methodologies that dynamically predict resonance phenomena and investigate their causes in DCT power transmission systems. Furthermore, numerical tools can be adopted to optimize DCT hydraulic circuits’ design parameters and predict their dynamic behavior by addressing the strict geometrical constraints that characterize this technology.
Nowadays, environmental compatibility as well as biodegradability are important topics for hydraulic applications. Eco-friendly operating fluids are developed to enhance environmental sustainability for industrial process, such as in [
11], where vegetable oils performance is evaluated for metalworking applications and compared to petroleum based cutting fluid. In the power transmission field, several architectures present hydraulic systems operating with standard mineral oils for the actuation and the lubrication of clutches and gearset, and these applications require oil substitution due to properties degradation. The worldwide diffusion of these systems results into an important environmental impact that can be reduced by adopting eco-friendly compatible fluids.
In this paper, the wave propagation through the actuation circuit of a DCT power transmission system generated by a Gerotor pump supply is numerically investigated. A preliminary steady state model is realized to determine the resonance frequency of the circuit, while lumped and distributed parameter models are developed to numerically predict the dynamic of the pressure oscillations through the real geometrical domain of the pipeline. Resonance phenomena are detected and the influence of design parameters as well as components for the resonance attenuation are evaluated, i.e., pump teeth, hydraulic accumulators, and Helmholtz resonators. The pressure fluctuations are analyzed through spectral maps and order tracking techniques to evaluate resonance frequencies and amplitude as well as the pump orders which generate oscillations. The models are validated by comparing the pressure profiles obtained numerically with the ones measured experimentally on an ad hoc test rig for power transmission system. Furthermore, a linear response analysis of simplified models is investigated, highlighting frequency resonances locations by reducing the simulation computational effort. Finally, the performance of the circuit operating with petroleum-based oil and eco-friendly fluid are compared to evaluate the applicability of biodegradable fluid in the power transmission field to reduce the environmental impact.
4. Conclusions
In conclusion, this paper analyzed wave propagation through the actuation circuit of a power transmission system excited by a Gerotor gear pump by means of numerical approaches. The actuation circuit of a DCT power transmission system has been numerically investigated since numerical models are important tools for the circuit design especially for the engineering applications where strict geometrical constraints and high performance are required. A steady state analysis was conducted to identify resonance behaviors due to circuit lengths and pump frequency excitation based on closed ducts wave propagation theory. By comparing the pump excitation frequency with the circuit lengths, two resonance frequencies were found at 1008 Hz and 1054 Hz, which leads to 5500 rpm and 5750 rpm of the Gerotor pump speed.
Therefore, a dynamic model of the actuation circuit was implemented to investigate the hydraulic behavior of the real geometrical domain of the hydraulic circuit, where CFD-1D pipes were used to address the pressure propagation through the pipelines and the pressure was evaluated at the system pressure transducer location. The numerical model confirmed the resonance behavior at 5220 rpm accordingly to the results of the steady state model. Spectral maps as well as order tracking techniques were adopted to analyze the pressure fluctuations, where the former analysis highlighted the resonance frequency of 957 Hz along the pump excitation strip, while the latter showed that the order 11, which is the internal gear teeth number, was the most influent. Furthermore, three possible design solutions for resonance attenuation were numerically investigated, i.e., a Gerotor pump with a larger number of internal gears, an accumulator and a Helmholtz resonator. A larger number of teeth reduced the flow ripple and only a small resonance behavior was predicted when the excitation frequency resulted comparable with the circuit lengths, 991 Hz and 3130 rpm. By adding an accumulator to the circuit, a significant attenuation of the resonance was found, and the peak moved to lower speed rate. The accumulator requires high volumes that are usually not suitable for high-performance cars’ transmission systems, therefore a more compact solution, a Helmholtz resonator, was designed to suppress the resonance frequency. The results showed the resonance suppression, but the generation of two new resonances at lower and at higher speed rates, where the former had a lower magnitude and can be considered an improvement, while the latter had a significant intensity and may generate instability at high speed rates. A numerical approach, which adopted linear analysis to evaluate the resonance frequency due to the circuit geometrical features, was also implemented to decrease significantly the computational effort required for the simulation of each case. The results showed that the resonance frequencies predicted with the linear analysis agreed with the ones of the dynamic analysis and this result confirmed that linear analysis can be adopted to find optimized solutions, while dynamic analysis is necessary to evaluate the magnitude of the phenomena. Finally, the fluid dynamic behavior of the circuit operating with an eco-friendly fluid was evaluated and by comparing the results with the ones obtained with the ATF, similar performance was obtained. Therefore, eco-friendly fluids are suitable for this application and may improve the eco compatibility of the transmission systems.