The virtual prototype will be referred to as Unit 1. It distinguishes itself from the commercial pump in several important points, listed in
Table 8. First and foremost, unlike the stock unit, Unit 1 has the aforementioned micro-surface shaping on its cylinder block bushing bore surface, denoted Profile I (to be described in more detail shortly). Second, while the stock unit has a variable guide length (
changes with shaft angle), Unit 1 has a fixed guide length (constant
). This is done because a guide length that varies with shaft angle causes the piston tilt to vary strongly with shaft angle, which causes the manner in which the piston and bore surfaces converge to vary strongly as well. In that case, a surface shape that performs optimally at one shaft angle performs sub-optimally at another.
The third important difference between the stock unit and the prototype is that, in an effort to reduce leakage across the piston–cylinder interface, the minimum piston-bore diametrical clearance of Unit 1 is reduced from that of the stock unit: / = 1.6 m/mm, while /=1.1 m/mm. The fourth difference is that, in aim of enabling the use of harder bushings in the future, their material is set to brass for Unit 1. Fifth, the pistons of the stock unit can have a circumferential groove on them, but not those of Unit 1. Lastly, the swash plate angle of Unit 1 is over higher than that of the stock unit. Consequentially, Unit 1 has a higher piston side load. This makes designing a profile for Unit 1 especially challenging, and demonstrates well the potential of the TPGA.
RKA is the same as the rotating kit of the stock unit, except that the bushing material is changed to a polymer, and represents the baseline to be tested against. RKB, on the other hand, is the sum of the design changes to be tested. On its cylinder block bushing bores, a slightly modified version of the bore profile developed for Unit 1 is implemented, which will be denoted Profile II (see
Figure 18). That is, in order to allow for some variation in the critical slopes at either end of the profile on account of machining tolerances, a small simulation study was conducted, simulating profiles whose slopes deviate a little from those of Profile I. As a result of this study, Profile I has been fine-tuned for manufacturing. The bushing length of RKB, however, is exactly the same as for Unit 1. The piston-bore diametrical clearance of this rotating kit is smaller than that of the stock unit. Specifically, piston and bore diameter measurements for five piston–cylinder interface pairs in the unit exhibit a maximum clearance of
/
= 1.2
m/mm. The measurement of RKA and RKB is intended to show the effects of the described key features: surface shaping, bushing length, and clearance. The remaining features in
Table 8 are the same for RKB as for RKA.
The design of the profile for Unit 1 will now be presented, followed by the corresponding simulation results, and, finally, the measurement results from testing the physical prototype Unit 2.
7.1. Simulation Results for Unit 1
As previously explained, the TPGA designs for a specified operating condition. In designing the bore profile for Unit 1, a “worst-case” operating condition is specified: a high outlet pressure and a low pump speed. At this operating condition, the piston side load is high, and the hydrodynamic pressure is diminished by the low speed. For this, the outlet pressure is set to 120 bar, and the pump speed to 700 rpm (the inlet pressure is 2.5 bar, and the inlet temperature, 20 °C). The hydraulic fluid used for the design process is pure .
The desired profiles at the described operating condition have been generated by feeding the TPGA a set of value combinations for
,
,
,
,
,
, and
. In order to keep the size of the DOE as small as possible,
,
,
,
, and
are each assigned one value, consistent across all combinations. Their values are listed at the top of
Figure 18a. For the critical parameters of
and
, on the other hand, all possible combinations of the values listed in the table of
Figure 18a are employed. As can be seen, the domain of
is set to extend slightly past the nominal
radial piston-bore clearance of
/
= 0.55
/mm. The list of
values do not extend that far—this is because opening up the interface near the DC end of the guide length, where the DC pressure pushing on the piston already widens the piston-bore gap, can drastically increase the leakage.
From the set of values in
Figure 18a, a set of profiles has been generated by the TPGA. One of the most successful of these, Profile I, is shown in
Figure 18b, plotted in the
coordinate system, with the
-coordinates normalized with respect to piston diameter. The ability of this profile to support load can be assessed by simulating the behavior of the piston–cylinder interface in Unit 1, with the profile imposed on its bores, using the interface model from
Section 5.
Figure 18c shows the results, specifically, the magnitudes of the correction forces at control points
and
, plotted against shaft angle. In order for the load on the piston to be fully supported, these forces should be zero. As can be seen, the forces are negligible, indicating full film lubrication.
For comparison,
Figure 18d shows the results for the same simulation run
without any surface shaping imposed on the bushing bores and without wear-in: the piston and bore surfaces are assumed to be perfectly cylindrical. The correction force magnitudes are on the order of
N, indicating the prediction of severe metal-to-metal contact. Simulating the stock unit without surface shaping (i.e., no piston grooves and no wear-in), yields correction forces on the same order of magnitude, but significantly lower, see
Figure 18e. In the absence of surface shaping, the lower swash plate angle, longer guide length, and softer bushing material of the stock unit enable its piston–cylinder interfaces to experience less severe piston-bore contact than Unit 1. With the right surface shaping implemented, however, the tables turn, and Unit 1 is able to deliver the desired performance.
7.2. Experimental Results and Discussion
The measurement procedure for Unit 2 consists of three phases. In the first, all non-rotating kit components are run in, such that they will deliver the same performance for each rotating kit. The second phase comprises a series of measurements, performed by each rotating kit (RKA and RKB) at the operating conditions listed in
Table 9. Measured parameters include the pump speed,
n; the torque transferred through the axle
; the flow out of the pump
; and the inlet and outlet pressures
and
(see
Appendix A for a schematic of the test rig setup and details on sensor accuracy). From these measured parameters, the volumetric, mechanical, and total efficiencies of the pump, respectively,
,
and
, are obtained.
Phase II of the testing procedure also includes taking surface measurements that capture the wear-in process at the piston–cylinder interface. For this, the cylinder block bore and piston surfaces of four such interfaces are measured prior to running the pump, and after each operating condition being tested. Finally, Phase III tests the long-term performance of RKB by retaking the measurements from Phase II after 500 h of run time at OC6.
The first operating condition tested in Phase II is OC1.
Figure 19 shows the volumetric, mechanical, and total pump efficiencies obtained from the measured data at this operating condition; a
-degree polynomial fit serves to highlight the overall trend of the data. From this, it can be seen that RKB is able to achieve a clearly higher volumetric efficiency than the baseline rotating kit, RKA. For the mechanical efficiency, RKA initially performs better. Over the course of the measurement, however, the efficiencies rise: RKB faster than RKA, until the data of the two begins to overlap. This change in mechanical efficiency is most likely due to wear-in.
The resulting total efficiency of RKA and RKB is close. A rigorous comparison of the total efficiency is given in
Figure 20, which plots the average of the total efficiency calculated from the last five minutes of measured data for each operating condition tested (outliers outside (70–100%] are omitted), along with error bars indicating one and two standard deviations. Results from Phase II of the measurement procedure are shown in the left section of the plot, while the right section shows a comparison of the results from Phase II to those from Phase III. The normality of the data used to establish the shown averages and standard deviations has been confirmed via Shapiro–Wilk test. From this plot, it can be seen that at OC1 in Phase II, the core of the data, within one standard deviation of the average, is higher for RKB, but if two standard deviations are taken into account (95% of the data), the error bars overlap.
The next two operating conditions tested, OC2 and OC3, differ from OC1 only in terms of pump speed: 700 rpm for OC1, 1100 rpm for OC2, and 1500 rpm for OC3. As can be seen in
Figure 20, with increasing speed, RKA increasingly outperforms RKB in terms of total efficiency. The volumetric efficiency of RKB (see
Appendix B) is consistently higher than that of RKA—but RKB is experiencing significant wear-in, most likely due to the piston groove scraping over the edge of the bushing near the DC. This wear can be seen in
Figure 21, which shows measurement traces taken lengthwise along the surface of one of the measured bores in RKA, and one in RKB. The traces correspond to two representative circumferential locations (one for RKA and one for RKB). These traces were taken using industry grade 3k measurement equipment that records the (x,y,z) coordinates of the center of a zirconia sphere moving over surface to be mapped along a predefined path, with force feedback sensors ensuring contact between the sphere and surface. The 3-D global calibration tolerance of the machine is ±2
m; however, it should be noted that the local point-to-point tolerance is lower than this.
For each rotating kit, the traces have been aligned via cross-correlation and stacked in order of measurement, such that the change in shape of the bore surface along each trace over time may be observed. For RKB, in order to show how the manufactured surface profile compares to the the theoretical bore shape, the nominal profile (Profile II) has been aligned with the case end of the measured profile. It should be noted that, as is evident from the section of the nominal profile shown, the measurements do not reach fully to the DC end of the bushing. It can nevertheless be seen that at the circumferential location the RKB plot corresponds to, heavy wear-in occurs on the end of the measurements nearest the DC ( = 0%), while at the other end (the “case end” at = 100%), the profile remains consistent. Although the wear-in is not circumferentially symmetric and wear does occur at the case end for other circumferential locations, the slope of the surface in that region remains relatively consistent with that of the nominal profile. These results suggest that elimination of the piston grooves could drastically improve the mechanical and total efficiencies of RKB. Furthermore, while the case end of the measured traces captures the slope of the nominal profile fairly well, improvements in the manufacturing technique, allowing the measured profile to come closer to the nominal profile, could also make a significant difference the performance of the piston–cylinder interface.
However, RKB does already offer an advantage over RKA in terms of wear. As can be seen from
Figure 21, RKA also experiences wear, in the form of a deep pit carved into the bushing surface. This pit can be detrimental to the operation of the interface, because the pump is intended for use with seawater: even with filtering, this will bring small hard particles into the interface, which are likely to catch in the pit. The buildup of such particles can turn the soft bore surface into hard sandpaper, which then wears away at the piston. Piston wear, in turn, increases the thickness of the piston–cylinder interface fluid film, thereby driving up the leakage rate. For RKB, with its fixed guide length on the other hand, the piston can only brush up against the slopes at either end of the bore, which show no such pits.
Moreover, while RKB was able to run at the subsequently tested high-pressure operating condition, OC4, RKA had to be shut down part-way through the measurement in order to prevent large-scale damage to the pump, and was then tested at OC5 instead. Although the measurement results of these two operating conditions cannot be compared directly, notably, the total efficiency measured for RKA at OC4 is on par with that measured for RKB at the lower operating pressure. On account of the failure of RKA to run at
=100 bar, the next operating condition, OC6, is of lower pressure, and higher speed.
Figure 20 shows that as before, the higher speed effects a higher total efficiency for RKA. As the last step of measurement Phase II, RKB is tested at OC5, showing the total efficiency of RKB to be on par with that of RKA.
Overall, in Phase II, the best performance of RKB is delivered at low-speed operating conditions; however, Phase III demonstrates that running the unit over a longer stretch of time can effect drastic improvements through higher pump operating speed. The right column of
Figure 19 shows this by plotting the efficiency measurements taken at OC6 both during Phase II, and after 501 h of run time (at the end of Phase III). As can be seen, the volumetric efficiency does not change significantly from Phase II to the end of Phase III. The mechanical efficiency, however, increases significantly. This suggests that by the end of Phase III, the wear-in process has eliminated a significant percentage of the piston-bore friction that was present in Phase II.
Over the last five minutes of measurement, an average total efficiency of 95.8%, with a standard deviation of 0.26%, is achieved by RKB at OC6. The stock unit, tested in a comparable setup, typically attains a total efficiency of up to 92% [
33]. While individual units may reach 1–2% higher than this, still, a noteworthy improvement is achieved with RKB.