To find a trade-off design that works fairly well over the whole operational range rather than a design that works excellently but only in a narrow region of operational conditions, sensitivity can be considered in the formulation of the optimisation problem. This is practically accomplished by determining the ob-jective function for different operational conditions. For each operational con-dition it is also investigated whether the optimisation constraints are violated or not. This obviously expands the optimisation problem to a multi-objective kind. Such optimisation problems can be solved by employing multi-objective optimisation algorithms and Pareto optimality, as described in section 6.2. In this study, however, an aggregated objective function approach is employed.
The different regions considered to be more important than others are given higher weights in the aggregated objective function.
Suppose for instance that a pump designer has no budget or room inside the pump housing that allows a pre-compression filter volume design. Still, low flow ripples are desired in the regions where low power is demanded, i.e.
along ε=0 and along pd=0.1 MPa. The best alternative to a PCFV is then a pressure relief groove. Figure 7.4(a), which is the same as figure 7.1(c), illustrates the flow ripple sensitivity to varying operational conditions when using a pressure relief groove. This particular groove design is optimised for minimising peak-to-peak flow ripple at full displacement, 2000 rpm, 20 MPa discharge pressure and 0.5 MPa suction port pressure, see section 5.2. Two points are marked out with stars. At point 1, the discharge pressure is 35 MPa and the displacement angle is zero. At point 2, the discharge pressure is 0.1 MPa and the fraction of displacement is 1. The goal is now to find a new groove design that simultaneously minimises the peak-to-peak flow ripples at these two operational points. For illustrative purposes, point 2 is considered to be 10 times more important than point 1 in this study. Thus, the aggregated objective function is formulated as:
ftot= (max(qd,1) − min(qd,1)) + 10 · (max(qd,2) − min(qd,2)) (7.3) As for the optimisation for the first groove design, no constraints are accounted for. The sensitivity surfaces of the new pressure relief groove design are shown in figure 7.4(b). As can be seen, the peak-to-peak flow ripples at both these points are improved with the new groove design. At point 1, the peak-to-peak flow ripple is reduced by≈ 16%, and at point 2 with ≈ 34%. The trade-off for this improvement, however, is a deterioration in the region of the point that the previous design was optimised for (full displacement, 2000 rpm, 20 MPa discharge pressure and 0.5 MPa suction pressure). At this specific operational point, the peak-to-peak flow ripple is increased by as much as 22% compared with the initial groove design. Since the new groove design emphasises noise reduction in the low power regions, this design will very likely be perceived as less noisy than the first groove design.
0
Figure 7.4 Figure (a) illustrates the peak-to-peak flow ripple for varying oper-ational conditions when using a pressure relief groove. This design is optimised for minimising peak-to-peak flow ripple at full displacement, 2000 rpm, 20 MPa discharge pressure and 0.5 MPa suction port pressure. Figure (b) shows the same thing but for a groove design optimised for minimising peak-to-peak flow ripple at points 1 and 2 simultaneously. In both these points, the flow ripples are reduced. The trade-off, however, is increased flow ripples in the region that was previously optimal.
8
Measurement of fluid-borne noise
I
n previous chapters, it has been shown how the fluid dynamics from the pump can be modelled on a very high level of detail. It is also shown how these simulation models can be used for design optimisation considering a variety of objectives and constraints under varying operational conditions. Obviously, the practical use of such simulations and optimisations is very limited before the results of the simulation model have been confirmed experimentally. Therefore, this section focuses on different methods for measuring fluid-borne noise from hydraulic pumps. Drawbacks and advantages of the different methods are discussed, and for some methods extensions are proposed.A generally accepted, but nevertheless often misleading quantity for rating fluid-borne noise from hydraulic pumps, is the system pressure ripples. System pressure ripples are not produced by the pump alone, but appear as a sys-tem response when the pump generated flow ripples interact with the external hydraulic system. It is thus not possible to reveal how much of the pressure rip-ples originates from the pump and how much is caused by system interference.
Therefore, measured pressure ripples should only be used as a comparative figure of merit for rating fluid-borne noise from pumps operating in identical external systems. It is however not possible to verify a pump simulation model with this quantity.
Cylinder pressure is one measurement quantity that can be employed for simulation model verification. Practically, cylinder pressure measurements can be conducted by mounting a pressure transducer inside the cylinder bore in the rotating barrel. The measured pressure signal is fed out via telemetry elements in the driving axis [104]. Obviously, a drawback with the technique is the complicated practical implementation of pressure transducer inside the rotating cylinder barrel. If different pumps are to be compared, this is also a
time-consuming technique. Another approach to measure the cylinder pressure allows the pressure transducer to be mounted in a fixed part in the pump [82]. A drilled channel connects the pressure transducer to the cylinder and a mathematical model compensates for the dynamics of this channel. The adequacy of this mathematical compensation is debatable.
Another drawback with cylinder pressure measurements is the inability to measure the source impedance, which is required for a complete description of the fluid dynamics from a pump. The following sections treat mainly methods for measuring the source characteristics, i.e. both source flow and source im-pedance, since these quantities are entirely system independent and together capable of completely describing the fluid dynamics of the pump.
8.1 Source characteristics
The pump source flow Qsis a theoretical and completely system-independent flow created in the close vicinity of the valve plate. The fact that the source flow is system-independent implies that it is constant for any dynamic pressure outside the valve plate. It is however very sensitive to the stationary discharge pressure level, as shown in chapter 7. The source impedance Zscan be seen as a transfer function describing the geometry of the outlet channel of the pump, i.e.
the geometrical compartment between the valve plate and the pump flange. A generally accepted model for describing source characteristics of pumps where the valve plate is located close to the pump flange is illustrated in figure 8.1.
The source flow can hence be seen as driving two parallel impedances, Zsand Z1where the latter represents the quotient between dynamic pressure and flow
Q
sQ
1Zs Z1
P
1Pump External system
Figure 8.1 Impedance representation of pump outlet channel if valve plate is located close to pump flange.
at the pump flange, i.e. the point impedance at the pipe entry. Due to the obvious analogy between fluid dynamics and electricity, Norton equivalents are henceforth used for establishing relationships between pressures and flows in
the frequency domain. The impedance model illustrated in 8.1 can thus be formulated mathematically as:
Qs = Q1+P1
Zs (8.1)
1
Z1 = Qs P1 − 1
Zs (8.2)
The understanding of this source model representation is essential since it forms the basis for all existing measurement techniques for capturing source flow and source impedance. The outlet channels, and thereby the source impedance, often become much more complex than what is illustrated in figure 8.1. These complex outlet channels are, however, mathematically re-configured into the shape given by figure 8.1 and can therefore be treated in a similar manner.
More on complex outlet channels can be found in section 8.5.
Often, when the valve plate is located close to the pump flange, the source impedance Zs is modelled as a volume and a laminar restrictor, as shown in figure 8.2. The volume Vs can be seen as the sum of all cylinder volumes connected to the discarge channel and the volume between the valve plate and
Q Q
P1
Z Q1 Q1
V P1
s s
kc s s
Figure 8.2 The impedance Zsis often modelled using a volumeVsand a laminar restrictor kc. The volume represents the total volume comprised within the outlet channel, also including the cylinder volumes for all cylinders connected to the discharge port. The laminar restrictor accounts for the leakage occurring between cylinder and piston wall and between the valve plate and the cylinder barrel.
the pump flange. The laminar restrictor, kc, represents the total leakage from the volume Vs, i.e. the leakage between pistons and cylinder walls and between valve plate and cylinder barrel etc. The circuit in figure 8.2 is mathematically determined as:
Zs= 1
Vs
βes+ kc
(8.3) Due to the high-frequency nature of the fluid dynamics, direct measurement of flow ripples is practically impossible. Attempts to develop dynamic flow ripple sensors have been carried out [105], using a membrane type of sensor.
The dynamic response of this specific flow transducer, however, is only about
300 Hz which corresponds to the first and possibly also the second harmonic frequency in normal industrial and mobile applications. Hence, such low sen-sor dynamics are insufficient for source flow measurements from pumps. In addition, the reported accuracy is rather low. Instead, indirect methods based upon dynamic pressure measurements along rigid measurement pipes are em-ployed. Via mathematical models of the measurement pipe, dynamic flows can be determined.