Evaluation of the influence of the hydraulic fluid temperature on power loss of the mining hydraulic excavator
Abstract
In the steady state of operation, the temperature of a mining excavator hydraulic fluid is determined by the ambient temperature, hydraulic system design, and power losses. The amount of the hydraulic system power loss depends on the hydraulic fluid physical and thermodynamic properties and the degree of wear of the mining excavator hydraulic system working elements. The main causes of power losses are pressure losses in pipelines, valves and fittings, and leaks in pumps and hydraulic motors. With an increase in the temperature of hydraulic fluid, its viscosity decreases, which leads, on the one hand, to a decrease in power losses due to pressure losses in pipelines, valves and fittings, and, on the other hand, to an increase in volumetric leaks and associated power losses. To numerically determine the level of power losses occurring in the hydraulic system on an example of the Komatsu PC7507 mining excavator when using Shell Tellus S2 V 22, 32, 46, 68 hydraulic oils with the corresponding kinematic viscosity of 22, 32, 46, 68 cSt at 40 °C, the developed calculation technique and software algorithm in the MatLab Simulink environment was used. The power loss coefficient, obtained by comparing power losses at the optimum temperature for a given hydraulic system in the conditions under consideration with the actual ones is proposed. The use of the coefficient will make it possible to reasonably select hydraulic fluids and set the values of the main pumps limit state and other hydraulic system elements, and evaluate the actual energy efficiency of the mining hydraulic excavator. Calculations have shown that the implementation of measures that ensure operation in the interval with a deviation of 10 % from the optimal temperature value for these conditions makes it possible to reduce energy losses from 3 to 12 %.
Introduction
It is well known that in most hydraulic systems, the efficiency does not exceed 75 %. In this case, the input power is spent on overcoming mechanical friction, pressure losses in pipelines, valves and fittings, and internal leakage of the hydraulic fluid. All power losses are converted into heat absorbed by the hydraulic fluid [13]. An increase in the temperature of the working fluid above a certain limit is accompanied by an increase in the aging rate, deterioration of its working properties and significantly affects both the performance of the excavator and the durability of the hydraulic system. Power losses during the operation of mining hydraulic excavators are of particular importance, since they operate in changing external conditions, primarily ambient temperature, and have a powerful drive, which gives large absolute values of the losses of electric energy or diesel fuel [46].
The calculation of power losses will allow you to select the appropriate drive power when designing new equipment, find the conditions for thermal equilibrium, determine the maximum possible oil temperature in the excavator hydraulic system, and correctly select the oil cooler parameters, taking into account the power, mode, and equipment operating conditions. An accurate calculation of the total power losses of а mining excavator hydraulic system is difficult due to the large amount of calculations and the need to take into account the variability of the physical parameters of the substances involved in the process.
Methods
The hydraulic system of the Komatsu PC7507 excavator was chosen as the object of study. Hydraulic fluids Shell Tellus S2 V 22, 32, 46, 68 with the corresponding kinematic viscosity of 22, 32, 46, 68 cSt at 40 °C. Mechanical losses in friction units are assumed to be constant and were not taken into account in the calculations [7, 8].
In a mining excavator hydraulic system, energy losses depend on the operations performed and the temperature of the hydraulic fluid. This is a power expended to overcome resistance in hydraulic lines, fittings, valves etc. and hydraulic fluid leakage in the components of the hydraulic system. To accurately assess the energy loss in the excavator hydraulic system, it is necessary to take into account the dependence of the density and viscosity of the hydraulic fluid on temperature. In manual calculations, it was customary to average the hydraulic fluid physical parameters, since taking into account density and viscosity changes on temperature greatly complicated the calculations.
A change in the hydraulic fluid density and viscosity over a wide temperature range affects the energy intensity of the energy transfer and conversion processes occurring in the hydraulic system of a mining excavator, and to obtain accurate results, these changes should be taken into account. As the temperature changes, the magnitude of each type of power loss changes. With an increase in the temperature of the working fluid, its viscosity decreases, which entails a decrease in power losses due to pressure losses in pipelines, valves and fittings and, at the same time, an increase in power losses due to an increase in the volume of leaks in the elements of the hydraulic system.
A change in the density of the hydraulic fluid in the operating temperature range affects the magnitude of power losses, is linear in nature and can be determined by the formula [911]
where ρ_{0}, ρ_{t} are the hydraulic fluid density at a temperature of t_{0} and t respectively, kg/m^{3}; Δt is the temperature increment, °С; α_{t} is the thermal expansion coefficient of the material, °С^{–1}.
The change in the hydraulic fluid viscosity, when the temperature changes in the range 40110 °C, is determined from the expression
where ν_{0}, ν_{t} are the kinematic viscosity at temperature t_{0} and t, m^{2}/s; n is a coefficient depending on the type and brand of the hydraulic fluid, temperature t_{0}_{ }, and viscosity ν_{0} [9, 10, 12].
In the temperature range from 0 to 40 °C the expression for calculating the kinematic viscosity takes the following form:
where a, b, care the coefficients depending on the temperature and characteristics of the hydraulic fluid are determined from the reference literature or experimentally. Their values for the hydraulic fluid Shell Tellus S2 V 46 in the temperature range up to 40 °C are presented in Table 1.
Table 1
Values of coefficients for hydraulic liquid Shell Tellus S2 V 46
Temperature range t 
Coefficients 

а 
b 
c 

010 
0.9 
–30.5 
430 
1020 
0.6 
–28 
435 
2030 
0.14 
–11.3 
285 
3040 
0.04 
–5.4 
198 
The dependence of the viscosity of Shell Tellus hydraulic fluids used in mining hydraulic excavators on temperature is shown in Fig.1.
The calculation of power losses during the operation of a mining hydraulic excavator involves the calculation of pressure losses in hydraulic components (pipelines, valves and fittings), power losses due to hydraulic fluid leaks, primarily of the main pumps and hydraulic motors. The total pressure losses by pipe length are determined by the Darcy – Weisbach formula for a viscous fluid flow
where i is the number of straight sections of the hydraulic pipe; λ_{i} is the flow coefficient for the corresponding hydraulic line; L_{i}, d_{i} are the length and internal diameter of the ith pipeline respectively; v_{i} is the average flow rate of the hydraulic fluid of the ith pipeline [10, 13, 14].
The value of the flow coefficient depends on the type of fluid flow (Laminar and Turbulent). After a long downtime, immediately after starting the hydraulic system, when the fluid has not yet warmed up, laminar flow can be observed in the channels and the flow coefficient is usually calculated using the Poiseuille formula [10, 14, 15]
Further, in a turbulent flow, the Blausius formula is used [1416]
where Re is the Reynolds number of the hydraulic fluid flow in the pipeline.
Losses also occur when the fluid passes through local resistances – fittings, valves, hydraulic control devices. The magnitude of these pressure losses is calculated using the following formula [14, 17]
where K is the pressure drop coefficient. Values are determined from reference literature or experimentally.
The work cycle of the piston chamber of an axial piston pump consists of the processes suction and discharge of the hydraulic fluid. The reason for the hydraulic fluid leakage in the pump is a large pressure difference between the piston chamber and the casing. Volume losses occur when liquid is forced into the pressure line. Fluid leakage from the working chamber consists of the following four components: leakage through the gap between the piston and the piston chamber wall Q_{pc}, through the gap between the piston and the slipper Q_{ps}, through the gap between the slipper and the swash plate Q_{ss} and through the gap between the cylinder block and valve plate Q_{cv} (Fig.2, a).
Hydraulic fluid leakage through the annular gap between the piston and the piston chamber wall is determined by the expression [10, 17, 18]
where d_{p} is the piston diameter, m; h_{pc} is the gap width between the piston and the piston chamber wall, m; P_{1}, P_{0} are the pressure in the piston chamber and in the casing respectively, Pa; μ is the hydraulic fluid dynamic viscosity, Pa·s; l is the length of the piston part in the piston chamber, m; η = e/h_{pc} is the relative eccentricity; e is the eccentricity of the piston relative to the cylinder, m; v – is the speed of the piston in the piston chamber, m/s (Fig.2, b, c) [10].
Hydraulic fluid leaks in the spherical hinge between the piston and the slipper are determined by the expression [10, 17, 18]
where h_{ps}_{ }is the spherical hinge gap width, m; P_{1}, P_{0} are the pressure in the slipper chamber and in the pump casing, respectively, Pa; β_{1}, β_{2} are design angles of the spherical joint of the piston and slipper, rad (Fig.2, d).
Hydraulic fluid leaks through the gap between the slipper and the swash plate are determined by the formula [10, 18, 19]
where h_{ss}_{ }is the width of the gap between the slipper and the swash plate, m; R_{s}_{1} is the groove and R_{s}_{2} is the outer radius of piston slipper, m (рис.2, e).
Hydraulic fluid leaks through the gap between the cylinder block and the valve plate, is determined by the expression [10, 18, 20]
where h_{cv}is the width of the gap between the cylinder block and the valve plate, m; R_{v}_{1}, R_{v}_{2}, R_{v}_{3}, R_{v}_{4} are the valve plate dimensions, m (Fig.2, f).
Summing up the results of formulas (1)(4), taking into account the operating cycle of the piston chambers and the pump construction, we obtain
where z is the number of piston chambers.
Taking into account the assumptions made, the total power loss in the hydraulic system of a mining excavator can be written [2123]
where Q_{w} is the hydraulic fluid flow rate, m^{3}/s; Δp is the pressure loss in the hydraulic system, Pa; Q_{s}_{1} is the total leakage of the hydraulic fluid in pumps and hydraulic motors, m^{3}/s; р is the hydraulic system pressure, Pa.
The mathematical model used for programming calculations in the MatLab Simulink software is based on the considered equations and expressions. The main parameters used in calculations and modeling are the actual parameters of Komatsu PC7507 mining excavator hydraulic system according to the manufacturer's catalog (Table 2).
Table 2
Initial parameters for modeling
Hydraulic system component 
Parameters 
Hydraulic fluid Shell Tellus S2 V 440 
Density at t = 15 °C: ρ = 872 kg/m^{3} 
Main pump HPV160+160 2 pc. 
Piston diameter d_{p} = 22.5 mm 
Piston length L_{p} = 100 mm 

Piston pitch radius R_{p} = 49.5 mm 

Swash plate angle γ = 19.5° 

Minimum piston length in piston chamber l_{0} = 45 mm 

Number of piston chambersz = 9 

Shaft speedn = 2400 min^{–1} 

Piston chamber working pressure P_{s} = 31 MPa 

Pump casing pressure P_{0} = 1.5 MPa 

Piston slipper design dimensions R_{s}_{1} = 8 mm; R_{s}_{2} = 13° 

Design angles of the piston and slipper spherical b_{1} = 14°; b_{2} = 119° 

Valve plate design dimensions R_{v}_{1} = 29 mm; R_{v}_{2} = 38 mm; R_{v}_{3} = 50 mm; R_{v}_{4} = 60 mm; a_{0} = 193° 

Swing motors (axial piston) 2 pc. 
Displacement q_{1} = 255 cm^{3} 
Shaft speed260 min^{–1} 

Working pressure 28.4 MPa 

Power 31.4 kWt 

Mechanical efficiency η_{mc} = 0.98 

Volumetric efficiency η_{vl} = 0.96 

Boom lift cylinders 2 pc. 
Flow rate at: 
digging 0.0018 m^{3}/s 

swing load 0.0013 m^{3}/s 

loading 0.0014 m^{3}/s 

swing empty 0.00144 m^{3}/s 

Hydraulic pipe inner diameter d_{pBl}_{in} = 19.05 mm 

Hose length L_{pBl} = 13.4 m 

Arm cylinders 2 pc. 
Flow rate at: 
digging 0.002 m^{3}/s 

swing load 0.00014 m^{3}/s 

loading 0.00105 m^{3}/s 

swing empty 0.001903 m^{3}/s 

Hydraulic pipe inner diameter d_{pAc}_{in} = 19.05 mm 

Hose length L_{pAc} = 23 m 

Bucket cylinders 1 pc. 
Flow rate at: 
digging 0.00191 m^{3}/s 

swing load 0.001804 m^{3}/s 

loading 0.0021 m^{3}/s 

swing empty 0.00115 m^{3}/s 

Hydraulic pipe inner diameter d_{pBc}_{in} = 19.05 mm 

Hose length L_{pBc} = 23 m 

Oil cooler 1 pc. 
Oil cooler oval pipes dimensions: a = 22.1 mm; b = 6 mm; δ_{pp} = 0.75 mm 
Number of pipe rows z_{row} = 3 

Number of pipes in a row m_{row} = 51 

Hose length L_{pOc} = 1290 mm 

Filters 5 pc. 
Pressure drop coefficients 512 
Directional control valves 3 pc. 
Pressure drop coefficients 35 
Throttle valves 3 pc. 
Pressure drop coefficients 0100 
Elbows 90° 34 pc. 
Pressure drop coefficients 1 
Check valves 5 pc. 
Pressure drop coefficients 15 
Pump suction line dimensions 
Diameter 35 mm 
Length 2.5 m 
Numerical modeling of physical processes has found wide application in the field of studying the processes of mining hydraulic excavators, since it allows taking into account a large number of quantities that change according to nonlinear dependencies and solving previously considered problems with much greater accuracy [2426]. For computer simulation of power losses in a hydraulic system, the developed calculation method and a software algorithm implemented in the MatLab Simulink environment were used.
Discussion of the results
The preparation of a numerical experiment required an analysis of the Komatsu PC7507 mining hydraulic excavator operating cycle [2729]. The accurate values of flow rates in various sections of the hydraulic lines, as well as in individual devices of the hydraulic system of the excavator, were calculated, which is important for accurately determining energy losses [3032]. As a result of the simulation, the values of power losses during the execution of work operations at various temperatures were obtained, presented in Table 3.
Table 3
Power loss during work operations, kWt
Hydraulic fluid temperature t, °C 
Digging 
Swing load 
Loading 
Swing empty 
Volumetricleakages 
0 
390.2 
110.3 
269.3 
222.5 
1.6 
20 
126.3 
41.73 
90.08 
76.23 
5.99 
30 
90.78 
32.44 
65.92 
56.42 
9.64 
40 
71.43 
27.51 
52.34 
45.74 
15.2 
50 
58.41 
24.34 
43.69 
38.73 
24 
55 
54.66 
23.39 
41.16 
36.68 
28.71 
60 
51.87 
22.69 
39.28 
35.15 
33.56 
70 
48.04 
21.71 
36.69 
33.04 
43.51 
80 
45.54 
21.07 
35.02 
31.67 
53.62 
90 
43.8 
20.61 
33.85 
30.71 
63.76 
110 
41.52 
20.02 
32.33 
29.45 
83.78 
Figure 3 shows power losses due to hydraulic fluid leakage and pressure losses in hydraulic components (lines, valves etc.) depending on the hydraulic fluid temperature for the working cycle operations: digging, swing load, loading, swing empty.
From the presented graphical dependences it is clearly seen that the energy losses during various working operations differ significantly from each other, which does not contradict the previously published results [3335]. As the temperature of the liquid increases, the power loss caused by to hydraulic losses due to the properties of pipelines and associated resistances will decrease, while the increase in power due to the volume of leaks increases.
The values of the total power loss ∆N for different operations of the excavator working cycle differ in value, but they all have a common feature, which is that the total power loss decreases with an increase in the hydraulic fluid temperature from 0 to 3035 °C, reaching the lowest value in the temperature range from 35 to 55 °C. After 55 °C, the power loss increases rapidly with the temperature rise. Since leaks in the control devices of the hydraulic system were not taken into account at this stage of the research, power losses with increasing temperature in the example under consideration will be the lower limit of values.
The total power loss versus temperature for various hydraulic fluids is shown in Fig.4. The presented graphic dependences clearly show a significant energy overspending when working on unheated hydraulic oil and the need to warm it up to 3040 degrees before starting work.
It follows from these dependencies that when the excavator is operating in winter conditions, it is more advisable to use hydraulic fluids with a lower viscosity, and when working in a hot climate, for example, in the conditions of the Socialist Republic of Vietnam, it is advisable to use hydraulic fluids with increased viscosity. The optimal temperature value depends on the viscosity and other characteristics of the fluid, but it also depends on the hydraulic system elements technical condition and mining operating factors that affect the duration of the working cycles. Therefore, absolute value of power losses in certain conditions, are not an informative indicator.
To assess the energy efficiency of the mining excavator hydraulic system, a power loss coefficient is proposed. It is defined as the ratio of the minimum possible power losses in the hydraulic system in the considered operating conditions to the actual ones:
where ΔN_{min} is the minimum possible power loss in given conditions; ΔN_{f} is the actual power loss.
The value of the power loss coefficients when using various hydraulic fluids is shown in Fig.5. The concept of “temperature range of power loss – T_{rpl}” is proposed – the temperature interval between the minimum and maximum temperatures, corresponding to the value of the power loss coefficient.
The temperature range at the value of the power loss coefficient of 0.8; 0.9; 0.95 for liquids with different viscosities in the conditions under consideration is presented in Table 4: ν is the hydraulic fluid kinematic viscosity; t_{opt}is the temperature value for the lowest energy losses; t_{–}_{А}, t_{+}_{А}_{ }are the smallest and largest temperature values in the interval under consideration; t_{–Ot}, t_{+Ot} are the value of the temperature interval from t_{opt} to t_{–A}, t_{+A}; t_{+}t_{–} are the value of the temperature interval from t_{–A} to t_{+A}.
Table 4
The value of the temperature range for different viscosities of hydraulic fluids
ν, cSt 
t_{opt} 
K_{pl} = 0.8 
K_{pl} = 0.9 
K_{pl} = 0.95 

t_{–}_{A} 
t_{–}_{Ot} 
t_{+}_{A} 
t_{+}_{Ot} 
t_{+}t_{–} 
t_{–}_{A} 
t_{–}_{Ot} 
t_{+}_{A} 
t_{+}_{Ot} 
t_{+}t_{–} 
t_{–}_{A} 
t_{–}_{Ot} 
t_{+}_{A} 
t_{+}_{Ot} 
t_{+}t_{–} 

22 
35 
12 
23 
68 
33 
56 
20 
15 
52 
17 
32 
25 
10 
45 
10 
15 

32 
44 
24 
20 
79 
35 
55 
30 
14 
62 
18 
32 
32 
12 
53 
9 
21 

46 
55 
30 
25 
100 
45 
70 
38 
17 
80 
35 
42 
42 
13 
70 
15 
28 

68 
68 
40 
28 
> 110 
> 45 
80 
48 
20 
108 
50 
60 
52 
16 
95 
27 
43 
From the graphical dependencies and the data presented in Table 4, it follows that with an increase in viscosity, the difference in the values of the high and optimal temperatures increases, as well as the value of the “power loss interval” corresponding to the specified K_{pl} value.
Conclusion
A method for calculating power losses in the hydraulic system of a mining hydraulic excavator depending on temperature is proposed. The method is implemented using the MatLab Simulink program on the example of Shell Tellus SV 2 46 hydraulic fluid and the hydraulic system of the Komatsu PC7507 excavator.
 In the range from zero to 3050 degrees, 7080 % of power losses are pressure losses in hydraulic components (lines, valves etc.), which decrease in a quadratic relationship with a decrease in the hydraulic fluid viscosity caused by an increase in temperature. After 3050 degrees, with a further decrease of hydraulic fluid viscosity, due to an increase in hydraulic fluid leaks in pumps and hydraulic motors, the main power losses increase according to a dependence close to a straight line, the angle of inclination of which is determined by the technical condition of the hydraulic motors and pumps, primarily the main pumps, the parameters of the hydraulic fluid, and mining factors of operation.
 A criterion for estimating energy losses in the hydraulic system of a mining hydraulic excavator depending on the hydraulic fluid temperature is proposed – the power loss coefficient K_{pl}, obtained by comparing the minimum possible losses at the optimum temperature in given conditions with energy losses at the actual temperature. The use of the proposed coefficient will allow estimating “excessive” energy losses when deviating from a range close to the optimal temperature of the hydraulic fluid in the conditions under consideration and hydraulic systems of other machines.
 The concept of “temperature range of power loss – T_{rpl}” is proposed – the temperature interval between the minimum and maximum temperatures, corresponding to the value of the power loss coefficient.
 Calculations have shown that the implementation of measures that ensure operation in the interval with a deviation of 10 % from the optimal temperature value (K_{pl} ≥ 0.9) for these conditions, can reduce energy losses from 3 to 12 %.
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