Cross-angle design compared with PCFV - Evaluation of the optimal cross-angle design

9.4 Evaluation of the optimal cross-angle design

9.4.3 Cross-angle design compared with PCFV

It may be interesting to investigate how well the optimal cross-angle design from above, i.e. using a valve plate with ordinary pre-compression angle, per-forms compared with a pre-compression ﬁlter volume, PCFV, without any cross-angle. The PCFV is known to have very low sensitivity to variations in operational conditions, as shown in section 7.1. A valve plate with PCFV design is optimised to minimise peak-to-peak ﬂow ripple at full displacement, at 1700 rpm, at 20 MPa discharge pressure and 0.5 MPa suction port pressure.

Figures 9.8(a) and 9.8(b) show the peak-to-peak flow ripples for the cross-angle design and the PCFV design respectively. Figure 9.8(a) is a reproduction of figure 9.5(b), thus providing both simulated and experimental flow ripples.

The simulated flow ripples from the optimal PCFV design, shown in figure 9.8(b), however, have not been experimentally verified. It should be pointed out here that the PCFV is based upon simulations of a design that is truly optimal at 20 MPa whereas the cross-angle valve plate is optimal for a pressure somewhere between 20 and 25 MPa, as already mentioned. As can be seen, the PCFV produces very low flow ripples for all displacement angles at all pressure levels. At full displacement, the PCFV clearly improves the flow ripples compared with the cross-angle design. At lower displacements however, the cross-angle design with ordinary pre-compression is almost equally good regarding flow ripples as the PCFV design without the cross-angle.

0 4 8 12 16

Figure 9.8 Peak-to-peak ﬂow ripple as function of displacement angle with ordi-nary pre-compression angle and a angle (a), and for a PCFV without cross-angle (b) for diﬀerent discharge pressure levels. The lines represent simulations and the markers are measured values. The dotted line and circles represents 25 MPa, solid line and squares 20 MPa and dashed line and triangles 15 MPa.

It is also interesting to investigate if the two different designs produce differ-ent cylinder pressure rates under varying operational conditions. The diagrams in figure 9.9 are the same as the diagrams in figure 9.6. Thus, they show the peak-to-peak cylinder pressure rates as functions of discharge pressure and dis-placement angle for the valve plates with ordinary pre-compression angles used without the cross-angle (solid lines) and with the cross-angle (dashed lines).

However, ﬁgure 9.9 also includes the simulated peak-to-peak cylinder pressure rate obtained with the PCFV design (dotted lines).

The sensitivity to variations in discharge pressure is substantially reduced with the PCFV compared with the two other designs, see ﬁgure 9.9(a), which was expected.

Consider now the peak-to-peak cylinder pressure rates as functions of dis-placement angle for the three designs, ﬁgure 9.9(b). At full disdis-placement, all three designs produce almost identical peak-to-peak cylinder pressure rates.

As the displacement angle is reduced, vast differences can be observed. As expected, the PCFV clearly improves the sensitivity compared with a valve plate employing ordinary pre-compression and no cross-angle. Interestingly enough, however, the cross-angle design, using a valve plate with ordinary pre-compression angle, is clearly better than the PCFV design. This confirms the statement made in section 6.3.1 that the low flow ripples obtained by the PCFV do not guarantee low peak-to-peak cylinder pressure rates.

A concluding remark from this study is that when using a cross-angle and ordinary pre-compression angle, the sensitivity to varying displacement angles is about the same as that obtained when using a PCFV with a conventional

5 10 15 20 25 30 35

Figure 9.9 Peak-to-peak cylinder pressure rate during pressurisation as function of discharge pressure (a) and as function of displacement angle (b) for ordinary pre-compression angle without cross-angle (solid), for ordinary pre-compression with cross-angle (dashed) and for PCFV without cross-angle (dotted).

swash plate. When also the discharge pressure varies however, the PCFV design is clearly preferable. It is obviously possible to combine the effects of a valve plate PCFV and a swash plate cross-angle in the same unit. Such a design would be superior to any existing design feature, giving effective reduction of flow ripples for all displacement angles and pressure levels.

Cross-angle is not only interesting for axial piston units. In many variable vane pumps, the eccentricity of the driving shaft axis can be tuned in relation to the cam ring, in the direction that is perpendicular to the normal displacement direction. This is practically achieved by adjusting a knob on the pump housing and the eﬀect obtained is the same as when implementing a swash plate cross-angle in axial piston pumps.

The cross-angle is beneficial for motors as well as pumps. A problem with the cross-angle concept is, however, that the dead-centres will inherently be obtained as functions of the displacement angle, which does not unambiguously improve the behaviour at all operational quadrants¹Figure 9.10 shows which operational quadrants are beneficially influenced by positive and negative cross-angles respectively. As can be seen, the displacement can be changed from positive to negative values, with preserved beneficial influence from the cross-angle. The rotational speed can also be switched. However, when changing pressure port, a cross-angle in the opposite direction is required. The definition of positive displacement direction, positive cross-angle direction and discharge pressure port location is illustrated in figure 9.11. In figure 9.10, negative

1An operational quadrant is defined by one specific displacement direction and one de-fined discharge pressure port. A machine operating with alternating positive and negative displacements and alternating pressure port, thus operates in several operational quadrants.

p_d− pi, i.e. negative y-axis values, imply switched pressure ports. The shaded area in ﬁgure 9.10(a) thus corresponds to the pump quadrant studied in all the measurements and simulations presented in this thesis.

p p

d- i

Pos

Neg Neg

Pos

Counter-clockwise rotation:

9.10(a)

p p

d- i

Pos

Neg Neg

Pos

Clockwise rotation:

9.10(b)

Figure 9.10 Diﬀerent quadrants require positive cross-angle whereas others re-quire negative. Negative pd− pi implies that the pressure ports have switched.

Figure (a) corresponds to counter-clockwise rotation and figure (b) to clockwise rotation. The positive and negative directions are defined in figure 9.11.

BDC when displaced in only -direction

BDC when displaced in only -direction BDC when displaced in bothand -directions

pd p

Figure 9.11 Illustration of positive displacement, positive rotation and dis-charge port location.

10

Discussion and conclusions

T

his thesis showsthat noise primarily originates from pump generated flow ripples, piston forces and bending moments. It is also illustrated that all these noise mechanisms are highly correlated to the design of the valve plate which is thus the key component in noise reduction in hydraulic pumps. The main difficulty when designing a valve plate for noise reduction is to properly rate the different noise generating mechanisms mutually; in some systems, the flow ripples are more important whereas others suffer from noise emitted directly from the pump housing, i.e. from the internal forces and moments. It is also difficult to know whether to emphasise low pulsation peak-to-peak values or well composed frequency spectra of the signals. It is shown that one quantity, known as cylinder pressure rate (dp_c/dt), simultaneously reflects all these objectives.

A low peak-to-peak cylinder pressure rate implies smooth piston forces and bending moments which are in turn also beneﬁcial for noise emissions and housing vibrations. But a low peak-to-peak cylinder pressure rate also implies low ﬂow ripples since no cylinder pressure transients occur when the cylinder links up to the port kidney. Hence, minimisation of peak-to-peak cylinder pressure rate emphasises low overall noise level.

When using an ordinary pre-compression angle, there is a very tight cor-relation between flow ripple and cylinder pressure rate; the pre-compression angle that minimises peak-to-peak flow ripple simultaneously also generates the smoothest piston forces possible, which also gives rise to smooth bending moments. When using a pressure relief groove, the pressurisation is slightly increased due to the discharge fluid being fed into the cylinder before the cylin-der has linked up to the discharge port. On the other hand, the pressure relief grooves provides a better cylinder match at the moment where the cylinder links up to the discharge kidney which gives a slightly smoother cylinder

press-ure rate at this point. In all, the cylinder presspress-ure rates are about the same as when using an ordinary pre-compression angle, and there is still a very tight correlation between flow ripples and cylinder pressure rates. When using a PCFV, however, the flow ripples are poorly correlated to the cylinder pressure rate. The reason is that the pressurisation phase, i.e. when the cylinder is linked up to the PCFV only, may give rise to excessive pressurisation rates, that are not reflected in the discharge flow ripples. When designing PCFV, it is therefore important not only to consider discharge flow ripples. It is shown, however, that the PCFV design studied in this work generally gives both low flow ripples and low cylinder pressure rates throughout the whole range of operational conditions.

This thesis also addresses the importance of investigating the operational point sensitivity of a design proposal. A compact and informative technique for visualising the sensitivity to variations in all operational conditions simul-taneously is proposed. For a pump designer, such sensitivity diagrams reveal directly how good a certain solution really is. For a system designer, choos-ing between different pumps from different suppliers, such information would facilitate more well-founded decisions about which pump satisfies certain re-quirements better than others. The sensitivity technique is employed to show the importance of the size of the pre-compression filter volume (PCFV). It is shown that a rather small PCFV is enough to significantly reduce flow ripples as well as cylinder pressure rates compared with ordinary pre-compression an-gle and pressure relief grooves. The behaviour is further improved by larger PCFV sizes, but the improvement compared with a small PCFV is not as considerable.

The design of the cross-angle conducted in this thesis clearly illustrates the applicability and reliability of simulation-based optimisation. When introduc-ing a cross-angle, a complex behaviour is obtained and it is very difficult to find the optimal cross-angle design and a matching valve plate without simulation-based optimisation. For the particular pump studied, the optimisations carried out propose a compromise cross-angle value of 2^◦. Excellent results are obtained when using the cross-angle; optimal pre-compression and decompression can be retained throughout the whole range of displacement angles. It is shown that when using a valve plate with ordinary pre-compression angle together with a cross-angle, the peak-to-peak values of the flow ripples and the cylinder pressure rates are reduced to about the same extent as when using a PCFV together with conventional swash plate designs, i.e. without the cross-angle. Experimental investigations of manufactured hardware show very good agreement between simulations and experiments which reveal that the predicted optimum is very close to the real optimum, already for the first prototype manufactured. The small divergence obtained is a consequence of a slightly under-estimated bulk modulus in the simulation model used for the optimisation. This information can be used to re-design primarily the valve plate, which will result in an even better design.

Also measured sound levels from pump housing, with and without the cross-angle, verify the beneﬁts gained from using the cross-angle. At low displace-ment angles, the sound level is reduced by about 3-5 dB when impledisplace-menting the cross-angle, which is considerable.

Since the dead-centres are obtained as functions of the displacement an-gles, the cross-angle is unable to compensate for varying discharge pressure level. The cross-angle is therefore an ideal design feature in constant pressure variable displacement pumps. On the other hand, the sensitivity to varying discharge pressure does not deteriorate when using the cross-angle compared with conventional swash plate design. To reduce the sensitivity to varying dis-charge pressure, it can be supplemented with conventional valve plate design features such as pressure relief groove and PCFV. There is reason to believe that many future variable pumps will proﬁt from the preferable characteristics obtained with the cross-angle, especially since the implementation is simple and inexpensive.

The cross-angle is beneficial for pumps as well as motors. A problem with the cross-angle concept, however, is that the piston bottom dead-centre moves only up to almost ±90^◦ from the swash axis when the displacement angle varies between maximum positive and maximum negative displacement. It is shown that one cross-angle value can be beneficial for machines switching between positive and negative displacements and also between positive and negative rotation directions, given a specified discharge pressure port. If the pressure ports are switched, a negative cross-angle, i.e. a cross-angle in the other direction, is required. With a revolving valve plate, the timing can be adjusted arbitrary, independently of the displacement angle. Such a design is more appealing, but would require on-line measurements of pressures and displacement angle and external control devices for valve plate control. A revolving valve plate also implies a higher implementation cost.

Another issue that needs to be considered in the cross-angle design is the forces obtained along the swash axis due to the additional swash plate incline.

Even though the cross-angle is only a few degrees, this axial force reaches thou-sands of Newton. In addition, this axial force pulsates due to the alternating number of cylinders connected to the discharge port. Special bearings capable of withstanding forces in this direction must therefore be considered.

The conventional measurement methods for capturing source characteristics from hydraulic pumps require a tuned model of the source impedance, i.e. the pump outlet channel geometry, to obtain the true source ﬂow. Experimental studies have shown that for pumps with well-deﬁned outlet channels, that can be modelled fairly easily, this principle works well. Often, however, variable displacement pumps have more complex outlet channel geometries, partly due to the regulator channel that connects to the stroking piston and partly due to the often long outlet channel with varying cross-sectional area and shape.

Such complex outlet channels are very diﬃcult to model with required accuracy, which in turn implies that the source ﬂow is obtained incorrectly.

A new measurement method, called the source admittance method, is inves-tigated. The strength of this method is that the source flow can be obtained without any source model. The method, however, requires an additional press-ure transducer to be mounted at the source flow origin, which enables the complete outlet channel dynamics to be identified. Generally, the quality of the source flow measurements is fairly good. However, in some frequency re-gions, severe unexpected oscillations appear. One plausible reason for this is that the varying cross-sectional area and shape of the outlet channel are not perfectly represented by the linear relationship between the dynamic flows and pressures that is assumed by the source admittance method. This could also imply that the circuit reciprocity, i.e. h₁₂= h₂₁, which is another assumption required by the method, does not hold. Another source of error may be that the source pressure sensor is not exactly located at the origin of the source flow, which is required. In general, the method seems promising but more research is required to examine possibilities, limitations and possible improvements.

To obtain satisfactory measurement quality for verification of the theories outlined in this thesis, the regulator channel was mechanically blocked using a plug. The source characteristics are then measured using the two-microphone method. The plugged regulator channel implies a fairly well defined source impedance using a valve plate with ordinary pre-compression angle. It is pos-sible to obtain a satisfactory source model but only up to around 1500 Hz. For good valve plate timing, the flow ripples are dominated by the low-frequency oscillations and thus, that the rather poor match between source model and measured source impedance at higher frequencies is of minor importance. For valve plates with inadequate timing on the other hand, the high-frequency source flow contribution is substantial which implies that the high-frequency source flow components are determined incorrectly. When transformed back into the time domain, this gives rise to high-frequency oscillations superim-posed onto the source flow, as can be observed in the diagrams in appendix A. Truncations of the measured pressure spectra also contribute to this effect.

The good measurement quality up to 1500 Hz implies however that the general shapes of the time domain source ﬂows are obtained satisfactorily.

The poor match between measured and modelled source impedance is most likely due to the varying cross-sectional area and shape of the outlet chan-nel between valve plate and pump flange. The first resonant frequency of the measured source impedance thereby appears at about 1.5 times the first anti-resonant frequency. Normally, the non-negligible distance between valve plate and pump flange is modelled using a constant diameter rigid pipe element.

With such a model, the first resonant frequency of the source impedance is obtained at exactly twice the first anti-resonance frequency. A more represen-tative model, accounting for the varying cross-sectional area and shape between the valve plate and the pump flange, is thus needed. Such a model, however, is difficult to obtain with the conventional modelling techniques outlined in this thesis.

Even though the plugged regulator channel provides a fairly well-defined source impedance for a valve plate with ordinary pre-compression angle, prob-lems are encountered when measuring source characteristics for a valve plate with a large PCFV. The source impedance obtained is very unpredictable and hence difficult to model. One plausible reason for this is that the PCFV is connected to the source impedance for only a fraction of the period time. As a consequence, the source impedance becomes time-variant. The source imped-ance varies to some extent in all pumps. This variation, however, is normally negligible which means that the source impedance can be approximated as time-invariant. Hence, an input signal at one frequency only affects the output signal at the same frequency, which is also the definition of a time-invariant system.

Thereby, the frequency dependent quantities can be solved frequency-wise, as is done in all the conventional measurement methods such as the secondary source method and the two-microphone method. For time-variant systems, however, an input signal at one speciﬁc frequency aﬀects the output signal at all frequencies. Thus, for time-variant outlet channels, the source impedance cannot be represented by a transfer function and the dynamic equations can

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