Estimation of the efficiency of road construction machines in the design

. The reasons for the decrease in the efficiency of road construction machines are fluctuations in speed and load, deviations of which from the optimal value in terms of efficiency and causes an increase in energy losses and a decrease in efficiency. A particularly significant decrease in efficiency is observed in power units with diesel engines equipped with speed controllers that are not designed to control the efficiency of fuel consumption. The increase in energy consumption of power units with internal combustion engines in transient modes requires the creation of energy models and, based on them, the generation of control signals to reduce fuel consumption by working on the economic characteristics of the internal combustion engine. The developed energy model makes it possible to simulate the characteristics of a power unit with an internal combustion engine and develop a management strategy in order to increase the efficiency of road construction machines in transient modes by choosing the optimal ratio of the parameters of high-speed and load modes.


Introduction
The efficiency of the power unit (PU) of road construction machines is one of its most important characteristics.The main dynamic and economic properties of the PU are laid down in the design process when choosing parameters such as the type and power of the engine, the gear ratio of the transmission mechanism.Currently, diesel is chosen as the engine of road construction vehicles as the most economical engine equipped with a speed controller.However, the speed control system is not designed to control fuel economy.In addition, the design of the PU with diesel is particularly difficult, since this type of engine can develop the same power with different combinations of speed and load modes and does not have high efficiency in all operating modes.Moreover, the speed of rotation of the diesel shaft in the mode of minimum specific fuel consumption, as a rule, does not coincide with the speed in the nominal operating mode [1,2].
Additional difficulties in designing the PU of road construction machines are associated with the fact that the diesel engine is an element of the speed control system, the functions of which do not include fuel economy management [3,4].Difficulties in choosing the parameters of the PU also lie in the fact that performance, as a rule, is not constant during operation.A particular difficulty in designing a diesel engine PU is caused by the ambiguous dependence of the specific fuel consumption on the power determined by the speed and torque [5,6].To reduce fuel consumption in operation, it is necessary to choose the optimal rated power of a diesel engine and develop an optimal strategy for managing its power based on ensuring work according to economic characteristics.
The PU of road construction machines is a connection of a diesel engine and a working machine, the main characteristic of which is the gear ratio u12 -the ratio of the speeds of their shafts ω 1 and ω 2 [7].Currently, two types of PU are used, including both their mechanical connection using a gearbox or gearbox or their connection using an electric generator and an electric motor.In both cases, there are similar problems of developing a diesel engine control algorithm based on dynamic and economic criteria to adjust the characteristics of the control system [8].The parameters of the working machine and the transmission mechanism have a significant impact on the efficiency of the fuel consumption of the internal combustion engine, the determining parameter of which is the gear ratio u.Therefore, already at the early stages of the design of road construction machines, in order to reduce fuel consumption in transient modes under operating conditions, it is necessary to develop a management strategy for both the engine and the transmission mechanism.Subsequent calculations based on the criteria of strength and durability, as a rule, do not affect the dynamic qualities of CO and energy consumption in operation, unless there is a significant increase in moving masses [9].

The main economic characteristics of the machine unit
The efficiency of internal combustion engine energy consumption is often estimated in specific units: where P is productivity (energy production per unit of time), G = f(P) -hourly energy consumption (internal combustion engine fuel).With zero productivity P = 0, the specific energy consumption is infinitely large for any type of machine, which makes this estimate inconvenient for engineering calculations.Therefore, it is often replaced by an estimate of the effective efficiency.For example, for internal combustion engines [1,2]: where HH is the lowest specific heat of combustion of fuel, g e = G/W e is the specific energy consumption, which shows how much fuel G consumes the internal combustion engine per unit of effective power We for an hour.
Dependence of hourly energy consumption (internal combustion engine fuel) G = f(P) performance (Figure 2) is based on experimental studies of the internal combustion engine, but for subsequent design purposes of the power unit, its mathematical model of efficiency should be created.The dependence of the specific energy consumption g = f(P) (Figure 1) is obtained by rearranging the dependence of the absolute hourly consumption G = f(P).It has a minimum with optimal performance Popt, which can be obtained as the abcissa of the tangent point of a straight line drawn from the origin to the curve G = f(P).[10,11].
The nature of changes in the specific energy consumption g = f(P).[9,10] is explained by the fact that: 1. the increase in specific energy consumption to the left of the minimum g = f(P) occurs due to a disproportionate increase in specific energy losses due to friction.2. an increase in the specific energy consumption to the right of the optimal Popt performance indicates a decrease in the quality of the working process of the power unit with an internal combustion engine.

Determination of the optimal mode of operation according to the criterion of specific consumption
Analytically, the optimal P opt mode according to the criterion of specific fuel consumption can be found from the condition that the first derivative of the dependence is equal to zero g�P� = 0: where g min is the minimum specific energy consumption in the optimal mode.Thus, in the mode optimal in terms of specific energy consumption, characterized by optimal performance of P opt , the values of the derivative of the absolute energy consumption function ∂G /∂P(P opt ) is equal to the minimum specific energy consumption g min .This fact of equality is ∂G /∂P(P opt ) = g min has the following physical meaning.The derivative of the absolute energy consumption represents the tangent to the absolute energy consumption function G(P) drawn from the origin.In Figure 1 a family of calculated dependencies G = f(P, g) is plotted for a constant specific energy consumption g = const, in which the dependence of absolute energy consumption on productivity is linear G = gP and represents a straight line passing through the origin with a proportionality coefficient equal to the specific energy consumption g.Consider the upper line G(P, g > g min ) corresponding to a higher specific energy consumption g = const > g min , which corresponds to an increase in specific energy consumption by Δg = g -g min with respect to the minimum specific energy consumption g min .The intersection of the upper line Δg = const > g min with the real characteristic G = f(P) at two points 1 and 3 indicates that between them on the experimental curve G = f(P) there should be a point of optimal performance P opt according to the criterion of energy efficiency with the lowest specific energy consumption g min .
The consumer is interested in minimizing the absolute energy consumption  compared to the minimum possible consumption even with non-optimal parameters of the PU.Let's present such an estimate as the difference between the real absolute energy consumption at the real specific consumption G(P) = gP and the possible one at the minimum specific consumption G = g min P.Such an objective function ΔG(P) is called absolute energy overruns: ΔG�P� = gP -g min P = PΔg�P� (4) where Δg = g -g min is the increase in specific flow compared to the minimum value.
The further from the optimal performance of the P opt the operating mode of the MU will deviate, the greater the energy overruns (i.e., absolute energy losses ΔG) will be compared with the minimum possible costs (i.e., when working with minimal specific energy consumption g min at optimal performance of the P opt : G opt = g min P opt (5) We approximate the dependence of the absolute energy consumption by a quadratic spline [12,13].Then the expression of the specific energy consumption takes the form: G�P� = C 0 +C 1 P+C 2 P 2 (6) where C 0 , C 1 and C 2 are the coefficients of the quadratic spline.
The coefficients of the square polynomial are determined by the experimental characteristic of the energy consumption G(N).For example, consider the working conditions of a road construction machine, the scheme of which is shown in Figure 1: 1. at P = 0 → G�0� = G idle -absolute power consumption at idle; 2. in the optimal mode P = P opt , g = g min ; 3. from where we get G idle P opt 2 .Thus, the above approximating expression of the specific energy consumption  includes the barrier function C 0 /P [1] and will meet the initial condition: When using expressions approximating by a quadratic spline, the change in the specific energy overruns will take the form: If we understand the power of the internal combustion engine -W by the performance P, then the general formula for the PU of a road construction machine with an internal combustion engine takes the form: where K W = W/W nom is the utilization factor of the rated power of the engine, equal to the ratio of the current power W to the rated power W nom, K ec = W ec /W nom is the coefficient characterizing the power ratio in the most economical and rated modes.
The analysis of the dependence of the change in the specific energy overspending (Figure 2) shows that Δg K W as a function of the power utilization factor K W will grow with distance in any direction from the optimal efficiency mode of operation with power: W ec = K ec W nom (10) at which the specific energy overrun is zero Δg K ec .

Determination of the optimal mode of operation according to the criterion of specific consumption
The same conclusion can be confirmed by analyzing the idealized parametric characteristics of the diesel engine shown in Figure 3.The purpose of the idealization of characteristics is to refuse to take into account nonessential properties and to identify a clearer influence of essential properties on the solution of the task.The idealization of the characteristics of a road construction machine is a system of accepted assumptions in the field of its descriptions or images, in which the solution of the task is simplified and accelerated.However, the idealization of the characteristics of the engine and MU may be different depending on the purpose of the study.This property of the specific energy overspending function can be traced to an idealized parametric characteristic of a diesel engine.Figure 3 shows the static characteristics reflecting the efficiency of energy consumption, where the point N marks the nominal mode of operation of the internal combustion engine with maximum power, and the point C marks another important mode of operation with minimum specific fuel consumption g min .Parametric closed curves of constant value of specific fuel consumption g > g min are shown around point C. The characteristic is often called parametric because it reflects the influence of several parameters, such as power and specific energy consumption in the coordinate system M 1 is the torque of the engine, ω 1 is the speed of rotation of the motor shaft.The boundaries of this characteristic are: 1 -the external characteristic of the diesel engine, according to which the change in torque occurs at a constant position of the fuel supply body; 2 -the regulatory characteristic, according to which the change in torque occurs when the position of the fuel supply body is changed by an automatic speed controller; 3 -an economic characteristic on which the specific fuel consumption is minimal at the appropriate values of the torque and speed of the engine shaft.The parametric characteristic also shows hyperbolic curves of constant power W corresponding to an ideal "engine": M = W ω (11) Closed curves of constant values of specific fuel consumption g const at some points relate to hyperbolic curves of constant engine power W const  ����� , which form an economic characteristic 3 of a diesel engine on a parametric characteristic in the coordinate system M 1 , ω 1 .Where closed curves of constant specific fuel consumption intersect with curves of constant power on the parametric characteristic of a diesel engine at two points, it shows that the same partial power of a diesel engine W can be realized with different values of specific fuel consumption under operating conditions, but higher than the economic characteristic.Thus, the economic characteristic passes through two points, the point of the nominal mode N with the coordinates M pot , ω pot and the point C of the maximum efficiency mode M 1ec , ω 1ec .The change in MU power under operating conditions is preferably by economic characteristic, since according to it the increase in specific fuel consumption g is minimal compared to g min .
The proportionality coefficient K ec = W ec /W nom depends on the slope of the economic characteristic passing through the points N and C, which may be related to the location of these two characteristic modes of operation of the diesel engine in Figure 3.
The equation of economic characteristics can be described analytically through a secondorder determinant [14,15], where the current values of the engine operation parameters M and ω are interconnected by a direct economic characteristic passing through two points: the point of the nominal mode N and the point C of the maximum efficiency mode: 5 Choosing the optimal engine power Consideration of the issue of choosing the optimal rated power of the engine can be continued according to the idealized characteristic of the diesel engine presented in Figure 3 in order to assess the change in the specific fuel consumption of the work according to the economic characteristic using a second-order determinant.Thus, the proposed solution algorithm is suitable for the steady operation of a diesel engine according to its economic characteristics with minimal absolute fuel consumption.
If we take the specific energy consumption in the nominal mode for 100%, then the increase in specific energy consumption depending on the degree of engine load KW = W/W nom can be represented in the form of Table 1.
Analyzing Table 1, it can be noted that with a decrease in the degree of loading K W of the internal combustion engine from 100% to 75% of the nominal capacity, it causes a decrease in the specific overspending of energy consumption up to 23%.compared to the nominal.When the degree of loading K W of the machine decreases from 100% to K ec , it causes a decrease in the specific energy consumption to zero.A further decrease in the degree of PU loading does not cause a decrease, but an increase in specific energy overruns.For example, a decrease in the degree of MA loading to 10% of the nominal one causes an increase in the specific energy consumption by about 15 times compared to its value at the nominal load.Such characteristics of the specific energy consumption are explained by the fact that the design of the PU of a road construction machine with an internal combustion engine is carried out in such a way that the operating mode indicated as nominal does not coincide with its most economical mode, as shown in Figure 3.The rated power of the internal combustion engine installed in the PU, as a rule, is selected based on the need to reduce the acceleration time or for short-term peak load reception, therefore it turns out to be obviously greater than it is necessary to operate in a steady-state operation mode.However, a significant reserve of internal combustion engine power may not lead to energy overspending due to its operation at steady state in the area of increased efficiency when operating according to economic characteristics.Such an increase in the efficiency of energy consumption in steady-state modes is possible due to the choice of the optimal nominal installed power of the internal combustion engine due to the approximation of the steady-state operation mode to the minimum specific energy consumption mode.
The influence of the characteristics of the transmission mechanism on the economic indicators of the PU road construction machine should be considered taking into account the characteristics of the internal combustion engine.Figure 4 shows the dependence of the torque on the rotational speed on the output shaft of a diesel engine with a diesel engine at different gear ratios.These dependences are obtained using the idealized diesel characteristics shown in Figure 3.
Curve 1 represents the trajectory of the point N of the nominal diesel mode when the gear ratio changes (with an optimal gear ratio of the gearbox, which ensures the passage of a linearly increasing moment of resistance through N1).Other inclined beams of the moments of resistance pass through the points N1 and N2 of the nominal mode at gear ratios other than optimal: These rays intersect curve 3, on which the minimum specific fuel consumption is ensured, i.e. curve 3 is the trajectory of point C when the gear ratio changes and in a sense is an economic characteristic of a diesel engine as part of a road construction machine.Curve 2 flows equidistant to curve 3 and is the accepted acceptable limit for reducing efficiency.Thus, in the upper part of Figure 4, two curves 1 and 2 highlight the area of operation with acceptable efficiency at different values of the gear ratio.Figure 5 shows the dependence of the machine's performance on the gear ratio with the linear nature of the change in the moment of resistance corresponding to the nominal speed mode.This dependence has a maximum at the point N 1 of the nominal mode in Figure 4 and corresponds to the optimal gear ratio.A decrease in performance occurs when the gear ratio deviates from the optimal one in any direction.But with a decrease in the gear ratio below the optimal, there is a decrease in fuel economy, and with an increase in the gear ratio above the optimal, there is a less significant decrease in fuel economy, since the work takes place near the external characteristics of the diesel.The main factor causing a decrease in the efficiency of a power unit with a diesel engine in operating conditions is an unfavorable characteristic of the control system, which determines the change in fuel supply when the speed changes and does not introduce fuel supply correction depending on the load.An exception to this rule are automatic regulators

Figure 1
Figure 1 shows the structural diagram of the PU of road construction machines with a mechanical transmission mechanism (a) and with an electric transmission mechanism representing the electrical connection of an electric motor and a generator (b).

Fig. 1 .
Fig. 1.Structural diagram of PU road construction machines with a mechanical transmission mechanism (a) and with an electric transmission mechanism (b).

Fig. 4 .
Fig. 4. Parametric characteristics of the power unit from a diesel engine with a gearbox: 1characteristic of the nominal operating modes of the diesel engine; 2 -lower permissible limit of specific fuel consumption; 3 -economic characteristic passing through the point C of the minimum specific fuel consumption; 5 -linear characteristic of the moment of resistance corresponding to the nominal speed mode.

Fig. 5 .
Fig. 5.The dependence of the machine's performance on the gear ratio with a linear characteristic of the moment of resistance corresponding to the nominal speed mode.

Table 1 .
Increase in energy consumption depending on the degree of engine load.