Impact of the technical condition of main pumps on fuel consumption in a hydraulic excavator

Introduction

Leakage of the working fluid in the discarge mechanism of positive displacement pumps in the hydraulic drive of mining excavators is inherent in the design phase and, on average, accounts for 5% of the operating flow rate at working pressure. A lower leakage volume results in deteriorated lubrication and cooling conditions for the components of the discharge mechanism, leading to overheating and eventual pump failure. The leakage volume is directly dependent on the clearance size in the pump discharge mechanism [1–3]. As the components wear, the clearances in the discharge mechanism increase, leading to higher leakage of the working fluid, a decrease in pump efficiency, and an increase in fuel consumption. The aim of the study was to determine the optimal service life of pumps, taking into account the excess fuel consumption that increases during operation. The impact of increasing leakage on the productivity of a mining excavator can be assessed through the volumetric efficiency of the hydraulic machine. As established in previous studies,the effect of pump wear on energy consumption occurs in two stages: 1. The power reserve of the drive fully compensates for the energy losses caused by increasing internal leakage in the pump. At this stage, the machine's productivity remains unchanged, but the specific energy consumption per cubic meter of mined material increases; 2. The power reserve of the drive is insufficient to compensate for the energy losses due to volumetric leakage in the pump, resulting in a decrease in machine productivity, while the specific energy consumption per cubic meter of mined material continues to rise. During operation, including in axial piston pumps of hydraulic excavators, component wear increases internal clearances, allowing fluid to leak through them. This leads to energy losses and increased (excess) fuel consumption. Replacing pumps based on the increase in excess fuel consumption can help reduce total fuel costs and ownership costs over the pump's operational lifetime. Establishing an optimal service interval for the pump will enable timely replacement planning and better forecasting of future expenses [4–6]. Determining the relationship between "excess" fuel consumption and the technical condition of the pump (leakage volume) will allow for defining the most optimal volumetric efficiency range, considering minimal productivity losses, excess fuel consumption, and ownership costs.

Methods

In a hydraulic excavator, all primary and auxiliary operations are performed using a hydraulic drive. The primary operations, which include digging, swinging to dump, bucket unloading, and swinging back to the face[1], are carried out using variable-displacement axial piston pumps, commonly referred to in technical literature[2] [7–9] as main or primary pumps. Wear of the converting and displacing mechanisms in high-pressure hydraulic pumps leads to increased clearances and distortion of the geometry of components operating in sliding or rolling contacts. As clearances increase, hydraulic fluid leakage rises, causing a decrease in the pump's volumetric efficiency and an increase in energy consumption for performing useful work, as confirmed by previous studies [10–12]. Ultimately, this process results in excess fuel consumption of the internal combustion engine. Replacing the pump resolves the issue of fuel overconsumption but entails additional costs. To achieve the objective of determining the optimal service life of pumps, the following tasks were formulated: developing a mathematical model for pump ownership costs, accounting for fuel overconsumption that increases over time, designing an algorithm and conducting computer modeling in Simulink-Matlab, evaluating the increase in fuel consumption over the pump’s service life.

The study examined the impact of the technical condition of HPV375 axial piston pumps on the fuel consumption of the Komatsu PC2000-8 mining hydraulic excavator. Within the scope of the research, it was assumed that energy losses in the friction pairs of the excavator's mechanisms remain constant and were therefore not considered in the calculations.

The main pumps of the excavator’s hydraulic system supply hydraulic fluid to the hydraulic motors of the working equipment and the swing mechanism. Depending on the phase of the excavator’s work cycle, some hydraulic motors may remain idle or, conversely, operate under maximum load. The load on the excavator’s mechanisms determines the working pressure in the hydraulic system, and, in turn, the magnitude of internal leakage and friction forces in the pump's discharge mechanism changes proportionally to pressure variations. Thus, to accurately assess energy losses in the main hydraulic pumps, it is necessary to consider the properties of the excavated rock mass, the temperature of the hydraulic fluid, the level of fluid leakage, as well as the velocities and accelerations of moving components [13, 14].

Leakage through the clearances of the axial piston pump mechanisms depends on several factors, the most significant being the pressure difference between the inlet and outlet of the clearance and the flow resistance of the clearance, which is determined by its shape and cross-sectional area. Under otherwise identical conditions, leakage increases with rising pressure differential. This occurs during the displacement of hydraulic fluid from the pump’s working chamber. During the filling phase of the working chamber, leakage is nearly absent.

Leakage in the working chambers of the HPV375+375 pump's discharge mechanism can be represented as four main components: fluid bypass in the annular clearance between the plunger and the working chamber wall Q_pc, leakage in the spherical joint connecting the plunger base to the slipper pad, leakage through the flat clearance between the slipper pad and the swashplate, leakage at the contact surface between the cylinder block and the valve plate Q_bp. These leakages are not only unavoidable by design but also essential, as the hydraulic fluid lubricates component surfaces subjected to forces generated by working pressure, thereby reducing wear.

When calculating fluid bypass through the clearance between the plunger and the working chamber wall, it is essential to consider that due to lateral forces arising during the transmission of torque from the drive shaft to the plunger group, the plunger assumes an eccentric position in the working chamber, despite tight tolerances and high manufacturing precision. The fluid flow rate in the eccentric annular clearance is determined by the following equation [15, 16]:

where d_p – pump plunger diameter, m; h_pc – average clearance between the plunger and the working chamber wall, m; p_c, p₀ – working pressure of the pump and casing pressure, respectively, Pa; μ – dynamic viscosity of the working fluid, Pa·s; λ = e/h_pc – relative eccentricity of the plunger in the working chamber; e – plunger eccentricity relative to the cylinder walls, m; v – plunger velocity, m/s; l – length of the plunger section inside the cylinder at a given moment, m:

                                                         l = l₀ + R(1 – cos ωt) tg γ,                                     (2)

where l₀ – average length of the plunger section inside the cylinder, m; R – radius of the working chamber axes, m; ω – angular velocity of the cylinder block, rad/s; γ – tilt angle of the swashplate, degrees.

The axial velocity of an individual piston relative to the cylinder is determined by:

                                                                v = ωR tg γ sin ωt.                                              (3)

Leakage of the working fluid through the clearance between the piston and the slipper is calculated using the following expression [17]:

where h_bp – clearance between the piston and the slipper, m; p₁, p₀ – pressure in the slipper chamber and in the pump casing chamber, respectively, Pa; β₁, β₂ – design angles of the piston and slipper, rad.

Leakage calculations for other components of the axial piston pump follow a similar approach.

The current GOST 13823–78 standard specifies failure criteria only for fixed-displacement axial piston pumps and does not establish limits for variable-displacement pumps with a control system powered by the main flow. However, according to existing engineering practices, there comes a point when further operation of a variable-displacement axial piston pump becomes impractical, including due to excessive fuel consumption. For mining hydraulic excavators, the failure threshold of variable main pumps should be determined considering both mining-technical and economic operating conditions [18].

[1] GOST R 55165–2012. Mining equipment. Open-pit single-bucket excavators with a bucket capacity exceeding 4 m³. General technical requirements and test methods.

[2] Zang K. K. Substantiation and selection of hydraulic system cooler parameters for a mining hydraulic excavator operating in the Socialist Republic of Vietnam. [Author’s abstract of the dissertation for the degree of Cand. Sci. (Eng.)]. Moscow: MISIS; 2021. 21 p.

Results and discussion

A comprehensive mathematical model, incorporating the listed leakage formulas for the critical components of the fluid discharge mechanism in axial piston pumps of the hydraulic system in a mining excavator, was developed in Simulink-Matlab. In recent years, Simulink-Matlab, along with other popular CAD and CAE systems, has been widely and successfully used for digital prototyping of equipment operating processes in the mining industry [19]. Additionally, the model included constraints and conditions that directly and indirectly affect the leakage volume of the working fluid in the clearances. These include: pump working chamber cycle parameters, design parameters of the discharge mechanism, time and load parameters of the mining hydraulic excavator's duty cycle, temperature of the hydraulic fluid.

As part of the numerical experiment, the volumes of hydraulic fluid leakage were determined for high-pressure pumps in the hydraulic system of a mining hydraulic excavator, considering different levels of discharge mechanism wear: from a new pump (clearances h_рс = h_сv = h_рs = h_ss = 5 µm) to a pump in operation for several years (clearances h_рс = h_сv = h_рs = h_ss = 20 µm).

The fuel overconsumption values corresponding to pump leakage losses are presented in Table 1. The graphs showing the dependence of fuel overconsumption on hydraulic fluid temperature for four levels of discharge mechanism wear (Fig. 1) indicate that as clearances increase, fuel overconsumption rises exponentially. For example, at a hydraulic fluid temperature of 70°C, increasing the clearance size in the discharge mechanism of an axial piston pump by a factor of 2, 3, and 4 results in fuel overconsumption due to hydraulic fluid leakage increasing by factors of 8, 27, and 64, respectively. This relationship can be expressed by the function x = y³.

Table 1

Fuel overconsumption during primary duty cycle operations depending on the clearance between the piston and cylinder block

Fig. 1. Power losses at different clearance widths: 1 – 5 µm; 2 – 10 µm; 3 – 15 µm; 4 – 20 µm

Fig. 2. Fuel overconsumption during working operations: а – digging; b – swing to dump; c – bucket unloading; d – swing to face

The fuel overconsumption during working operations, depending on the clearance between the piston and the cylinder block at different hydraulic fluid temperatures, is shown in Fig. 2.

The impact of hydraulic fluid temperature on power losses in a hydraulic excavator was analyzed in [20]. However, that study did not consider the effect of pump technical condition on power losses.

It should be noted that a power loss of 1 kWh results in an excess fuel consumption of 207–218 g.

In Chan V. H.'s study[3], a mathematical model was developed to calculate the ownership cost of the main hydraulic excavator pump and the expenses associated with excess fuel consumption:

where Z_e – pump operating costs, RUB/h; Z_g – fuel costs at the initial moment of operation, RUB/h; C – pump replacement cost, RUB; η_n – volumetric efficiency of the pump at the initial moment of operation; v_η – rate of volumetric efficiency degradation, %/h; Т – service life, h.

Based on the proposed model, an expression was derived to determine the replacement interval:

Using the calculated replacement interval will help minimize pump acquisition costs and fuel consumption throughout the pump’s operational life until replacement.

From the equation, it is evident that the replacement interval increases proportionally to the square root of the pump replacement cost and decreases with lower fuel costs and higher volumetric efficiency degradation rates during operation.

Furthermore, the equation indicates that the fixed operating costs of the pump do not affect the optimal replacement interval (Fig. 3).

Fig. 3. Impact of the replacement interval for main pumps: а – on fuel overconsumption; b – on fuel costs and pump replacement costs: 1 – v_n = 0.5∙10⁻³ %/h; 2 – v_n = 1∙10⁻³ %/h; 3 – v_n = 1.5∙10⁻³ %/h; 4 – v_n = 1∙10⁻³ %/h, C_zn = 800,000 RUB, D = 35 RUB/L; 5 – v_n = 1∙10⁻³ %/h, C_zn = 800,000 RUB, D = 70 RUB/L; 6 – v_n = 1∙10⁻³ %/h, C_zn = 1,600,000 Rub., D = 35 RUB/L

To evaluate fuel overconsumption, the study proposes the K_ef, indicator, which characterizes excess fuel consumption and is determined by the ratio of the difference between the actual fuel consumption per cubic meter of excavated material G_f and the fuel consumption at the initial volumetric efficiency G_n to the fuel consumption at the initial volumetric efficiency:

The K_ef value is zero when the nominal and actual fuel consumption are equal, i.e., at the initial moment of operation. If the actual fuel consumption becomes twice the nominal value (which is not permissible in operation), the coefficient reaches one.

Using the proposed fuel efficiency coefficient and the derived equation for pump replacement intervals will enable data-driven decisions regarding the definition of critical pump conditions and optimal replacement timing. This approach can reduce total pump ownership and fuel costs by up to 17%, depending on the economic and mining-technical operating conditions.

[3] Chan V. H. Optimization of pump replacement intervals for mining hydraulic excavators operating in Vietnam. [Author’s abstract of the dissertation for the degree of Cand. Sci. (Eng.)]. Tver; 2024. 21 p.

Conclusion

1. Using the developed algorithm and computer modeling in Simulink-Matlab, a relationship was established between fuel overconsumption, hydraulic fluid viscosity, and clearance size in the HPV375 axial piston pump of the Komatsu PC2000-8 excavator.
2. A mathematical model was developed for pump ownership costs, accounting for increasing fuel overconsumption over the pump's service life. Based on this model, an expression was derived to determine the optimal pump service life, aimed at minimizing pump acquisition and fuel costs, while considering the technical condition of the main pumps, its degradation rate, fuel price, and pump replacement costs.
3. A new indicator was proposed to characterize fuel overconsumption, defined as the ratio of the difference between actual fuel consumption per 1 m³ of excavated material and the fuel consumption at the initial pump efficiency to the fuel consumption at initial efficiency.
4. 4. Implementing the proposed fuel overconsumption indicator and the equation for pump replacement intervals will allow for more accurate planning of replacement timing and future expenditures. Additionally, this approach can reduce total pump ownership and fuel costs by up to 17%, depending on economic and mining-technical operating factors.