Investigation of Influence of Hydraulic Parameters on Hydraulic Pump

1. Introduction

Hydraulic systems remain a standard solution wherever high power density, reliable energy transfer, and accurately controlled actuator motion are required. One of their key components is the hydraulic pump, because the pump determines the delivered fluid flow rate and thus directly affects actuator speed, system response, and overall hydraulic performance. Gear pumps still retain an important place in engineering practice due to their simple design, compact dimensions, and relatively low manufacturing cost [1,6]. For a fixed-displacement positive-displacement pump, the theoretical flow rate is primarily determined by the pump displacement and rotational speed [4]. Under real operating conditions, however, the actual delivered flow rate is lower than the theoretical one because part of the displaced volume is lost through internal volumetric losses.

These volumetric losses are mainly associated with fluid leakage through functional clearances inside the pump, including radial, axial, and side leakage paths between moving and stationary parts. Their magnitude depends not only on pump geometry, but also on differential pressure, operating speed, fluid viscosity, and the overall condition of the hydraulic system [2,5]. Increasing pressure raises the driving force for internal leakage, whereas increasing oil temperature reduces viscosity and usually weakens the fluid’s ability to limit backflow. At the same time, rotational speed changes not only the theoretical flow rate but also the relative contribution of volumetric losses to the delivered volume [1,2,3,6,9]. As a result, the flow behaviour of a gear pump cannot be described sufficiently by a single nominal value or a single catalogue characteristic but should be treated as the outcome of coupled operating parameters.

Previous studies have confirmed that hydraulic-fluid properties directly affect the energy efficiency of hydraulic systems [3,9], that the growth of functional clearances reduces the volumetric efficiency of external gear pumps [2], and that pump modelling and experimental evaluation should reflect real operating conditions [5,8]. In this context, temperature-dependent characteristics are particularly important. Stawiński et al. showed that mapping the volumetric efficiency of a gear pump as a function of pressure, rotational speed, and oil temperature provides substantially more practical information than conventional single-point characteristics, and that increasing oil temperature may noticeably deteriorate pump performance [1]. Similarly, our recent published works indicate that viscosity is one of the decisive fluid properties in hydraulic systems and that excessively low viscosity promotes leakage, thereby unfavourably affecting flow behaviour and long-term operating performance [6,7].

Despite this, design practice still often relies on catalogue data related only to a limited number of operating points. For real system design, estimation of hydrostatic actuator speed, diagnostics, and control, such information is frequently insufficient because it does not capture the combined effect of pressure, temperature, and rotational speed on the actual delivered flow rate [1,5,8]. Within the source base used in this study, no directly applicable experimental map of actual flow rate was identified for the GHD 17R pump in the specific operating window corresponding to our laboratory measurements. Therefore, a practically and scientifically relevant task remains: to determine experimentally how the actual flow rate of this pump changes in the operating space defined by rotational speed, pressure, and oil temperature.

The aim of this paper is to investigate experimentally the flow rate of the GHD 17R gear pump as a function of rotational speed, pressure, and oil temperature within the ranges of 500–2500 min⁻¹, 2–10 MPa, and 30–60 °C. The measurements are carried out on a laboratory single-circuit hydraulic test rig equipped with HYDAC sensors, and the resulting data are used to construct flow maps describing the dependence of the measured flow efficiency on rotational speed, pressure, and oil temperature. The main contribution of the paper is an experimentally verified description of the actual flow behaviour of a specific fixed-displacement gear pump, together with an evaluation of the relative influence of the individual operating parameters on flow variation, providing a practical basis for more accurate design, control, and diagnostics of hydraulic systems using this pump type.

2. Materials and Methods

For the experiment, Parallel testing device situated on Slovak university of agriculture is going to be used. This device consists of two separate circuits, but for our test it will be reconfigured to one-circuit use. Energy is delivered into the device via frequency convertor providing stabile current and voltage thus stabile rotational speed of electromotor. This electromotor is directly connected with hydraulic pump by clutch but without change of torque. Hydraulic pump used in this test is gear pump GHD 17R by Jihostroj company. The pump produces fluid flow, which is slowed down by choke valve controlled mechanically, by hand. This enables us to set higher pressures in the circuit and as there is resistance to flow, oil heats up. To facilitate optimal temperature during measurements, cooler is situated on the exit from the circuit, right above the fluid tank. This cooler uses two fans and air-fluid heat exchange, and it is controlled automatically, by computer and algorithm created in graphical programming language LabVIEW when set temperature is reached. Prior to the main experimental phase, a precise calibration of the rotational speed of the motor and the frequency converter Delta VFD-C2000 was performed to verify the linearity of the speed control system. For the independent verification of the actual shaft rotational speed during calibration, a certified and calibrated ALMEMO measurement system was utilized. An automated calibration algorithm was developed in the LabVIEW environment, which systematically increased the control voltage from 0 to 10 V with a step of 0.5 V. To allow full stabilization of the motor shaft speed at each level, a dwell time of 15 seconds was implemented between consecutive voltage steps. Due to the safe operating limits of the attached Jihostroj GHD 17R gear pump, the maximum calibration speed was restricted to 2700 min⁻¹. Hydraulic pump has properties described in Table 1.

A biodegradable synthetic hydraulic fluid based on esters was used as the working medium. According to the manufacturer’s technical data, the typical properties of the fluid are: density at 15 °C of 0.918 g·cm⁻³, kinematic viscosity at 40 °C of 48 mm²·s⁻¹, viscosity index of 184, pour point of −42 °C, Cleveland open-cup flash point of 320 °C, FZG failure load stage of 12, and biodegradability higher than 90%. These properties are relevant for the present experiment because the viscosity and density of the working fluid affect internal leakage, pressure losses, and the resulting volumetric efficiency of the tested gear pump.

Data will be obtained using HYDAC measurement devices particularly EVS 3100 flow meter, HDA 4700 tensometric pressure gauge and ETS 4100 silicon thermometer. All these sensors are connected to HMG 4000 handheld display unit and operator is able to set wanted temperature and pressure, at preset rotational speed, and record flow of the fluid.

Each sensor has its accuracy described by manufacturer. These values are seen in Table 2.

Measurement will be done in five seconds of consecutive measurement, with sampling rate 10ms, thus producing 500 measurements for every point obtained.

Experiment will be carried out as follows: The hydraulic oil will be heated up to 30 °C by choking. After the temperature is risen, frequency converter will be set to produce 500 rounds per minute, and choke valve will be set to create pressure 2MPa. Note that for different operational speeds, different positions of choke valves are required because it does not behave like pressure valve! When parameters are set with required accuracies, flow is recorded. Then experiment proceeds to another combination, 30 °C, 500 min^-1, 4 MPa. This way, all combinations will be worked for pressures 2, 4, 6, 8, 10 MPa, operational speeds, 500, 750, 1000, 1250, 1500, 1750, 2000, 2250, 2500 min^-1 and temperatures, 30, 40, 50, 60 °C.

Figure 1. Hydraulic scheme of the testing device, where: 1. Hydraulic gear pump, 2. Choke valve for loading, 3. Computer, 4. Mechanical safety valve, 5. Choke valve for heating up the circuit, 6. Tank, 7. Cooler, 8. Three-way valve, 9. Electronic safety valve, 10. Clutch, 11. Pressure gauge, 12. Thermometer, 13. HYDAC measurement device, 14. HLB sensor, 15. Bypass for protecting sensors during loading, M—electromotor, FC—Frequency converter. Source: Author’s work (2025).

Figure 1. Hydraulic scheme of the testing device, where: 1. Hydraulic gear pump, 2. Choke valve for loading, 3. Computer, 4. Mechanical safety valve, 5. Choke valve for heating up the circuit, 6. Tank, 7. Cooler, 8. Three-way valve, 9. Electronic safety valve, 10. Clutch, 11. Pressure gauge, 12. Thermometer, 13. HYDAC measurement device, 14. HLB sensor, 15. Bypass for protecting sensors during loading, M—electromotor, FC—Frequency converter. Source: Author’s work (2025).

After having data from all measurements, statistical methods will be used. From pre-set parameters (pressure, temperature), arithmetic mean will be computed, as small fluctuations around nominal value are expected. However, when processing data of hydraulic flow, only 95% of values will be counted into arithmetic mean, as extremes from both sides will be excluded. This can be done in excel by function “trimmean”.

From obtained values of hydraulic flow, we can compute volumetric efficiency using Formula 1. These efficiencies will provide us better insight into quality of work of the hydraulic gear pump, because volumetric efficiency is not directly dependent on rotational speed of gear pump, as hydraulic flow is.

$${\eta }_{vol}={\displaystyle \frac{Q}{V_g·n}}$$

(1)

where:

Q—measured flow [dm³·min^-1]

V_g—geometric volume of the pump [dm³]

n—rotational speed [min^-1]

For practical reasons, especially because the flow is easily measured in practice, we will continue in experiment with two sets of values—flows and volumetric efficiencies, using the same statistical methods.

To determine which input parameter takes the greatest part on change of flow (or on change of flow efficiency), we will compute relative contribution of factor to change ΔQ (respectively Δη), normalized sensibility of system ΔQ/ΔX and relative sensibility, (ΔQ/Q_avg)/(ΔX/X_avg) to determine contributions. After converting relative sensibility to percents, we can have index of relative significance.

Based on data distribution, following table (as in Table 3) will be created, comparing various methods to determine influence of change of respective parameters on hydraulic flow.

For this statistical method, we will need to know difference between maximal and minimal value if only one input parameter changes. (e.g., 30 °C, 2MPa and flow at 2500 min-1–500 min-1). This will be computed from Formula 2.

$$\Delta X=X_{max}-X_{min}$$

(2)

Relative contributions of factor to flow (later efficiency) variations ΔQ_rpm, ΔQ_pres and ΔQ_temp will be computed to assess which parameter changes hydraulic flow the most (in our measurement, neglecting ranges of entrance parameters). ΔQ_rpm is computed as maximal minus minimal value of flow while two impot parameters are stabilized (pressure and temperature, e.g., 30 °C, 2MPa). From all the combinations with these two parameters stabilized we have 9 combinations for different rotational speeds. We take out maximal and minimal values and compute their difference. We will compute these differences for all combinations of two stabilized parameters and then make arithmetic mean, median and trimmean of all ΔQ_rpm values. Analogically, we will proceed for pressure and temperature.

Influence on measured flow will be computed from sum of respective influences and their conversion to %, according to Formula 3:

$$\mathrm{\%}relativecontribution={\displaystyle \frac{\Delta Q}{\Sigma \Delta Q}}·100\mathrm{\%}$$

(3)

The same formula will be used for median values and trimmean values.

Normalized sensitivity will be computed from Formula 4:

$$NS={\displaystyle \frac{\mathsf{\Delta }\mathrm{Q}}{\mathsf{\Delta }\mathrm{X}}}$$

(4)

This formula will be applied for every row in the Table 3 and later, Formula 3 will be applied the same way as before, to convert normalized sensitivities into percent values.

Table can be supplemented with relative sensitivity following Formula 5:

$$RS={\displaystyle \frac{\frac{\Delta Q}{Q_{avg}}}{\frac{\Delta X}{X}}}$$

(5)

where:

ΔQ—average flow of max—min value for two stabilized parameters

Q_avg—average flow of the entire experiment (all combinations)

ΔX—range of measurement

X—average of respective input parameters in the entire experiment

All of the mentioned statistical approaches will be used for flow efficiencies as well, but previous section was for the sake of brevity explained for hydraulic flows only.

Apart from LabView software and excel, Matlab will be used as well. This programme will enable us to create 3D charts from our measurements, showing evolution of flows in various backgrounds. It will be also used to create ANOVA tables to confirm results of our method. From matlab ANOVA tables, parameter η² will be computed and transferred into percents from Formula 6; to assess how big part of variability is explained by respective factor. Partial η² will be computed and transferred into % from Formula 7 to express how strong is particular factor with respect to unexplained error of the model.

$${\eta }^2={\displaystyle \frac{{SS}_{factor}}{{SS}_{total}}}·100\mathrm{\%}$$

(6)

$${partial\eta }^2={\displaystyle \frac{{SS}_{factor}}{\left({SS}_{factor}+{SS}_{error}\right)}}·100\mathrm{\%}$$

(7)

3. Results

The experiment was carried out successfully. During measurement phase we came up against expected accuracy problem: Pressure and temperature were impossible to set at particular value and their values fluctuated.

Temperature was set with accuracy +1 °C, -0.5 °C around nominal value. Pressure was possible to be set with accuracy ±0.1 MPa around nominal value. Rotational speed was dependent on precision of frequency converter Delta VFD-C2000. The dynamic behaviour and stability of the frequency converter control were subsequently verified under heavy-duty operational conditions. When the hydraulic circuit was subjected to random pressure fluctuations induced by the manual throttling valve, the frequency converter reacted smoothly to sustain the set speed. The driven asynchronous motor demonstrated a robust response with only a minimal time delay corresponding to the instantaneous difference between the actual and requested RPM. The precision of controlled speed driven by the frequency converter was under 1% from maximum of the speed range of the motor. thereby confirming the high reliability of the speed control apparatus across the entire experimental range of 500 to 2500 min⁻¹.

Obtained results seen in Figure 2a–d are four graphs from temperature standpoint (each figure shows evolution of combinations at preset temperature):

The same graphical interpretation was done from standpoint of pressures as well, as seen in Figure 3a–e.

The same graphical interpretation was done from standpoint of rotational speed as seen in Figure 4a–e.

During an experiment unexpected phenomenon occurred. Device started vibrating at various rotational speeds, especially 1250 and 1750 min^-1. At these levels of flow, massive fluctuations occurred, which entered our data processing process, thus, to eliminate them, we choose to use trimmmean function at 15%, to exclude fair amount of extreme data from our set. This trimmean function was applied to ΔQ values. For comparison, arithmetic mean without this exclusion and median is done as well. Table 4 shows results and partial results leading to evaluation of normalized sensitivity according to Table 3.

In the Table 4 we can see that change in rotational speed has the biggest relative contribution to change of flow, around 97%. All of three methods, average, median and trimmean led us to very similar results. However, if we consider, that rotational speed was changed in significantly bigger interval, than pressure, or temperature, normalized sensitivity was computed. It describes how strongly system reacts to small change of parameter. And in this case, the system is the most sensitive to change in pressure, with around 73%.

Normalized sensitivity also helped to transfer all values to usable units, because with dividing ${\displaystyle \frac{\Delta Q}{\Delta X}}$ we got: ${\displaystyle \frac{{dm}^3·{min}^{-1}}{MPa}}$, ${\displaystyle \frac{{dm}^3·{min}^{-1}}{°C}}$ and ${\displaystyle \frac{{dm}^3·{min}^{-1}}{{min}^{-1}}}$. These result now express change of flow dependent on change of entrance value by 1 unit, in other words, local sensitivity. However, it is important to notice, that 1MPa shows bigger part of interval than 1 min^-1. For global evaluation, seen in Table 5, relative sensitivity needs to be computed:

Relative sensitivity is a huge benefit for this research, because it better recognises strength of respective intervals of values. Rotational speed was established to 95.80% contribution, pressure to 1.88% and temperature to 2.32%. Even based on uncertainty of measurement (temperature -0.5 °C+1 °C), we can’t consider 2.32% of influence to change in flow as remarkable. This result however indicates dominant influence of rotational speed on flow in entire range, which is expected. For this reason, all statistical approach was recalculated for flow efficiencies as well and it is seen in Table 6.

Relative contribution to change of flow is divided more evenly in efficiency analysis, with maxima still at rotational speed, however with higher variation between respective methods. Normalized sensitivity than reduces this variability, picking pressure as most significant contributor, when change od 1 unit of parameter changes. As mentioned before, because units are not comparable, relative sensitivity was computed to gain global picture of sensitivities. This is illustrated in Table 7:

Relative sensitivity describes rotational speed as biggest contributor to change in flow efficiency with contribution almost 55%. Interesting take is, that within our range of measurement, temperature influences efficiency more, than pressure. This result may vary with different hydraulic pumps and different measurement ranges.

Anova method computed in matlab programme was used to confirm validity of our approach. Three-way ANOVA confirmed that pressure, temperature and rotational speed have statistically significant effect on flow rate with p values < 0,05, as seen in Table 8 and Table 9. Size of their effects was determined using η².

In Table 10, comparison of relative sensitivity method to ANOVA based effect size method is illustrated.

Comparing ANOVA based effect size method to relative sensibility, we observed similar trend—when assessing hydraulic flow, the rotational speed was the most significant contributor to variance. But when assessing volumetric efficiencies, the rotational speed’s contribution fell to 68%, 54% respectively. However, comparing pressures and temperatures, relative sensibility tells us that temperature is bigger contributor to overall change of output parameter, but ANOVA effect size tells the opposite. This could be explained by interactions, which ANOVA method deals with separately, while our approach using relative sensitivity neglects these interactions.

4. Discussion

The results of the present study confirm that the flow rate of the GHD 17R gear pump is mainly controlled by rotational speed. This agrees with Toet et al. [4], who describe the theoretical flow of positive-displacement pumps as a function of displacement volume and rotational speed. In the present experiment, rotational speed contributed approximately 96% to the direct change in measured hydraulic flow when the ΔQ-based evaluation was used. This confirms its dominant role over the whole measured range. A similar relationship between pump speed and flow behaviour was also considered by Corvaglia et al. [11] for external gear pumps.

The obtained results also support the approach of Stawiński et al. [1], who emphasized that pump performance should be evaluated using maps including pressure, rotational speed and oil temperature. Their study focused mainly on volumetric efficiency and temperature effects, while the present study applies a similar mapping approach to both measured hydraulic flow and flow efficiency of the GHD 17R pump. This is also consistent with Torrent et al. [5], who highlighted the need to evaluate gear pumps under real operating conditions.

When the direct change in measured hydraulic flow was evaluated using arithmetic mean, median and 15% trimmed mean, rotational speed was clearly the dominant parameter. Depending on the statistical method, its contribution to ΔQ was approximately 96%, while the contributions of pressure and temperature were much smaller. This result is expected for a fixed-displacement gear pump, because theoretical flow is directly proportional to pump displacement and rotational speed. Therefore, even though pressure and temperature influence internal leakage and fluid properties, their direct effect on total measured flow was much smaller than the effect of rotational speed in the investigated operating range.

The normalized sensitivity evaluation provided a different interpretation. After dividing the flow change by the investigated interval of each parameter, pressure showed the highest normalized sensitivity, followed by rotational speed and temperature. This does not contradict the dominant absolute influence of rotational speed. Rather, it indicates that a unit change of pressure had a stronger local effect on measured flow than a unit change of rotational speed or temperature. This is also expected because 1 MPa represents a much larger part of the investigated pressure interval than 1 min⁻¹ represents in the rotational-speed interval. The high normalized sensitivity of pressure is physically reasonable because increasing pressure promotes internal leakage through functional clearances inside the gear pump.

In the hydraulic-flow analysis based on ΔQ and normalized sensitivity, oil temperature showed the weakest influence among the three investigated parameters. Although the investigated temperature interval was larger than the pressure interval, its contribution to the direct change in measured flow remained low. This behaviour can be explained by the indirect nature of the temperature effect. Temperature does not change the theoretical displacement flow directly, as rotational speed does, but affects the hydraulic system mainly through changes in oil viscosity. A decrease in viscosity may reduce flow resistance in pipes and throttling elements, but at the same time it may increase internal leakage in the pump clearances and therefore reduce volumetric efficiency. In the present hydraulic-flow evaluation, these viscosity-related effects were smaller than the dominant effect of rotational speed and the normalized pressure effect within the investigated range.

The pressure-related interpretation is consistent with Szwemin and Fiebig [2], who showed that radial and axial clearances significantly affect the volumetric efficiency of external gear pumps. The present study did not measure internal clearances directly, but the observed pressure sensitivity supports the same general mechanism: increasing pressure increases the driving force for leakage and reduces the actual delivered flow. This mechanism is also consistent with the gear-pump analyses of Mazzei et al. [12] and Orlandi et al. [13], where leakage and internal flow behaviour are important factors in gear pump performance.

For a global evaluation of parameter importance, relative sensitivity was also calculated. In this evaluation, rotational speed remained the dominant parameter affecting measured hydraulic flow. It accounted for 95.80% of the relative sensitivity, while temperature and pressure contributed only 2.32% and 1.88%, respectively. Therefore, within the investigated operating range of 500–2500 min⁻¹, 2–10 MPa and 30–60 °C, the measured hydraulic flow was influenced primarily by rotational speed, followed by oil temperature, while pressure had the lowest relative contribution. This confirms that the direct speed-dependent displacement flow dominated the measured hydraulic flow, whereas viscosity-related temperature effects and pressure-induced leakage had only minor global influence on the flow rate.

A different but more informative result was obtained when flow efficiency was evaluated instead of measured flow. In this case, rotational speed accounted for 54.73% of the relative sensitivity, followed by temperature with 26.08% and pressure with 19.19%. This shows that, after the direct proportional effect of rotational speed on theoretical flow was reduced through the efficiency calculation, the influence of temperature and pressure became more visible. Nevertheless, rotational speed remained the most influential parameter even for flow efficiency. The final order of relative importance was therefore the same for both measured hydraulic flow and flow efficiency: rotational speed had the strongest influence, followed by temperature, while pressure had the lowest relative contribution.

The observed influence of rotational speed on flow efficiency is consistent with the general behaviour of positive-displacement pumps and with the results of Kosiba et al. [14]. In their laboratory testing of a GHD-type gear hydraulic pump using an environmentally friendly hydraulic fluid under controlled pressure and temperature conditions, pump behaviour was evaluated together with hydraulic-fluid properties. Their work supports the interpretation that operating speed is an important factor influencing pump flow characteristics and volumetric efficiency. This is consistent with the present result, where rotational speed had the strongest influence not only on measured hydraulic flow but also on flow efficiency.

The finding that temperature had a higher relative influence than pressure in both final relative-sensitivity evaluations is physically reasonable. Oil temperature changes the viscosity of the hydraulic fluid, and viscosity directly affects leakage, friction losses and the energy behaviour of hydraulic systems. Michael et al. [3] showed that viscosity loss is connected with hydraulic system performance, while Rydberg [9] emphasized that hydraulic-fluid properties, including viscosity, have a direct impact on energy efficiency. Therefore, the higher contribution of temperature compared with pressure can be explained by temperature-induced changes in fluid viscosity. These changes affect not only internal leakage in the pump but also the hydraulic resistance of the circuit.

The present findings are also related to the work of Stawiński et al. [1], who reported a pronounced influence of hydraulic oil temperature on variable-speed pump performance and emphasized the need for temperature-dependent pump maps. In comparison with their results, the temperature effect in the present study was not dominant. However, it was still the second most important parameter in the final relative-sensitivity evaluation of both measured hydraulic flow and flow efficiency. This confirms that temperature should not be neglected, although its relative importance depends on the investigated pump, working fluid, operating range and evaluation method.

Pressure showed the lowest relative sensitivity in the final relative-sensitivity evaluation, with 1.88% for measured hydraulic flow and 19.19% for flow efficiency. This does not mean that pressure is unimportant in gear pump operation. Increased pressure promotes internal leakage through functional clearances, which is why pressure becomes more visible in the flow-efficiency analysis than in the direct flow analysis. However, within the investigated pressure range of 2–10 MPa, its global relative contribution was lower than the contribution of temperature and rotational speed. This result is therefore valid mainly for the selected operating range and should not be generalized to substantially higher pressure ranges.

From the point of view of practical operation, the results confirm that measured flow and flow efficiency should be interpreted together. The measured flow rate is important for practical design, actuator speed estimation and system control, but it is mainly governed by rotational speed. Flow efficiency provides deeper information about pump operation because it better reflects losses caused by pressure-dependent leakage and temperature-dependent viscosity changes. The importance of monitoring hydraulic oil condition and temperature is also supported by Hong and Jeon [15], who showed that integrated oil sensors measuring viscosity, density and temperature can provide useful information about hydraulic oil and machine condition.

The use of arithmetic mean, median and 15% trimmed mean led to very similar conclusions, which supports the reliability of the observed trends. The trimmed mean was appropriate because flow fluctuations occurred at selected rotational speeds, especially around 1250 and 1750 min⁻¹. The importance of experimental validation under real operating conditions is also emphasized by Ketelsen et al. [8] and Wang et al. [16].

Overall, the present study confirms that the GHD 17R pump should be evaluated by experimentally determined flow and efficiency maps rather than by a single nominal value. This conclusion is consistent with Stawiński et al. [1], Torrent et al. [5] and Kučera et al. [17], who emphasize the importance of evaluating hydraulic pumps under variable operating conditions. The main contribution of this study is therefore the experimental quantification of how rotational speed, pressure and temperature influence the actual flow rate and flow efficiency of the GHD 17R pump in the selected operating range.

5. Conclusions

This study successfully quantified the simultaneous influence of rotational speed, operating pressure, and oil temperature on the flow behavior and volumetric efficiency of the GHD 17R external gear pump. The experiments were conducted using an environmentally friendly biodegradable synthetic ester hydraulic oil, which enabled a comprehensive assessment of how fluid properties affect internal losses under variable conditions. To ensure data robustness against flow fluctuations caused by pump vibrations at selected speeds, a 15% trimmed mean statistical approach was applied, which proved highly reliable when compared to standard arithmetic mean and median values.

The results demonstrated that the evaluation of actual flow rate alone is insufficient for a complete understanding of positive-displacement pump mechanics. When evaluating raw flow rate directly, relative sensitivity indicated that rotational speed is the dominant factor (accounting for 95.80% of global influence), while pressure and temperature showed minimal absolute impacts. However, recalculating the dataset into volumetric efficiencies eliminated the directly proportional effect of speed on theoretical volume. Under this approach, the relative significance of temperature and pressure rose to 26.08% and 19.19%, respectively, highlighting the critical role of temperature-dependent viscosity changes and pressure-driven leakage across internal clearances.

To validate the findings, a three-way ANOVA was utilized to identify the effect size (η² and partial η²) of each parameter and their cross-interactions. The ANOVA confirmed that all primary parameters and their interactions are statistically significant (p < 0.05). While relative sensitivity highlighted temperature as a stronger direct contributor to global variance, ANOVA highlighted the absolute significance of pressure (η² = 10.24% vs. 3.98% for temperature), revealing that parameter cross-interactions play an essential role in pump loss mechanics.

The main contribution of this work is the generation of experimentally verified, coupled flow and volumetric efficiency maps for the GHD 17R pump using a high-performance bio-lubricant. These multi-dimensional maps offer significantly more detailed input than conventional catalogue single-point characteristics and provide a practical foundation for the precise design, simulation, and real-time thermal diagnostics of modern hydraulic systems. Future research will extend this methodology to long-term pump wear tracking and wide-range fluid degradation analysis.