Experiment and optimum of the asphalt paver’s parameters to ameliorate the working performance

Abstract

In this paper, the experimental study of the asphalt paver is performed to assess the effect of the vibrational screed system’s operating parameters on the asphalt paver’s working performance. Then, the nonlinear dynamic models of the vibrational screed system and tamper system are built to assess in detail the effect of the working parameters of the vibrational screed system and optimise its working parameters to ameliorate the asphalt paver’s working performance. Both the vertical acceleration and angular acceleration of the vibrational screed system computed via their Root Mean Square (RMS_a) value have been selected as the evaluation indexes. Results showed that the acceleration at the measured points has been unevenly distributed on the vibrational screed system’s length, thus, the working performance of the asphalt paver is quite low. With the vibrational screed system’s working parameters optimised, the average value of RMS_a with optimisation is increased by 7.67% whereas the average deviation of RMS_a between the measurement points with optimisation is greatly reduced by 34.2% in comparison without optimisation. Consequently, the working performance of the asphalt paver has obviously ameliorated.

Keywords

Asphalt paver vibrational screed system nonlinear dynamic model genetic algorithm working performance

Introduction

The structure of the asphalt paver included a vibrational screed system with a length of 12 m used for smoothing the pavement quality and the tamper pairs used for compressing the mixed asphalt. Thereby, the asphalt paver’s working performance was mainly assessed via the compressing performance and pavement quality.^1–5

In the compacting process of the asphalt paver, under the excitations of both vibrator screed and tampers, the acceleration of the vibrational screed system was created and affected the asphalt paver’s performance. Thereby, the working performance of the asphalt paver had been computed and evaluated via the acceleration response and its Root Mean Square (RMS_a) value distributed evenly on the vibrational screed system’s length.^1,3,6,7 In order to calculate the acceleration response and its RMS_a for evaluating the asphalt paver’s working performance, the nonlinear dynamic model of the vibrational screed system had been established. Then, this model was also applied to assess the asphalt paver’s pavement quality under the effect of the moving speed, mass, and excitation of the vibrational screed system.^4,8–10 Research indicated that under the excitations of the vibrational screed system from 12 to 20 Hz, the asphalt paver’s pavement quality was significantly ameliorated. This excitation with other parameters of the vibrational screed system including the eccentric distance and eccentric mass were then optimised to further enhance the pavement quality.^2,3 The asphalt paver’s performance with optimisation was better than that without oprimisation.

However, the working performance of the asphalt paver in the above research was only analyzed via the theoretical and simulation approaches. The asphalt paver’s experiment was ignored. Moreover, in the structure of the asphalt paver’s vibrational screed system, its length was 12 m.^1,3,8 With this length of the vibrational screed system,¹¹ its angular vibrations generated under the excitation of the tampers as well as their eccentricity could also influence the asphalt paver’s performance.^12–14 But this issue has not been assessed in detail.

In this paper, the experimental study of the asphalt paver is performed to assess the effect of the vibrational screed system’s operating parameters on the asphalt paver’s working performance. Then, from the vibrational screed system’s structure of the asphalt paver, the nonlinear dynamic models of the vibrational screed system and tamper system are built to assess in detail the effect of the working parameters of the vibrational screed system as well as optimise its working parameters to ameliorate the asphalt paver’s working performance. Both the vertical acceleration and angular acceleration of the vibrational screed system computed via their RMS values have been selected as the evaluation indexes.

Experiment with the working performance of asphalt paver

Experimental setup of the asphalt paver

To evaluate the effect of the vibrational screed system’s operating parameters on the asphalt paver’s working performance as well as optimise the asphalt paver’s operating parameters, the experimental study of the asphalt paver is performed by:

(1) An asphalt paver in Figure 1(a) has been used for the experiment process to assess the asphalt paver’s working performance.

(2) The working performance of the asphalt paver has been assessed via the values of RMS_a distributed on the screed floor’s length under the excitations of the vibrator screed (f_vs) and tempers (f_t). The vibrational screed system model is shown in Figure 1(b).

(3) To measure the vertical vibrations on the length L = 12m of the vibrational screed system, the accelerometers have been set at 12 measuring points (P₁₋₁₂) with the distance of x = 1.0 m on the floor of the screed, as shown in Figure 1(b) and (c). Then, the vertical accelerations and RMS_a at the measurement points P₁₋₁₂ are analyzed and computed via the Belgium LMS’s analysis system, as plotted in Figure 1(c).

Figure 1.

The experiment model of asphalt paver. (a) Asphalt paver’s diagram, (b) vibrational screed system’s measurement points, and (c) its experimental setup.

Analysis of the measured results

According to the design parameters of the asphalt paver, two maximum frequencies of the vibrations in the vibrator screed and tamper are f_vs = 45 and f_t = 22 Hz. In the asphalt paving process, the asphalt paver’s working performance is lightly influenced by f_vs whereas it is strongly influenced by f_t. Consequently, under an excitation of f_vs = 22 Hz, the various excitations of tampers including f_t = 4 Hz, f_t = 6 Hz, …, and f_t = 22 Hz have been experimented to determine the vertical accelerometers and their RMS_a at 12 measuring points of P₁₋₁₂. The measurement results of RMS_a are plotted in Figure 2.

Figure 2.

Measured result of RMS_a. (a) Under excitations from 4 to 12 Hz and (b) under excitations from 14 to 22 Hz.

The measurement results of the RMS_a show that the excitation of tampers greatly affects the pavement quality as well as the asphalt paver’s working performance. Under the excitation of f_t below 12 Hz in Figure 2(a), the RMS_a is low, thus, the asphalt paver’s working performance is also low. With the increase of the excitation of f_t in a range of 12 < f_t < 20 Hz, RMS_a has been quickly augmented, thus, the asphalt paver’s working performance has been improved, particularly at 18 Hz. With the increase of the excitation of f_t in a range of 20 ≤ f_t < 22 Hz, RMS_a has been significantly deteriorated (see Figure 2(b)). This is due to the increase of the friction force and the inertia mass of tampers in the vibrational screed system. Thus, the asphalt paver’s working performance is significantly reduced.

Besides, observing the RMS_a at the measurement points P₁₋₁₂ under different excitations of f_t in the same Figure 2, we can see that the value of RMS_a at each measurement point is greatly distorted under all excitations of f_t, especially at the high excitations of f_t from 20 to 22 Hz. This means that the pavement quality is low. To evaluate in detail the influence of f_t on the asphalt paver’s working performance and the pavement quality, the average value of RMS_a and the average deviation of RMS_a between measurement points P₁₋₁₂ have been applied. According to the statistical theory,¹⁵ the average value of RMS_a at the measurement points P₁₋₁₂ and the average deviation of RMS_a between the points P₁₋₁₂ has been calculated via the formulas of $\sum_{j = 1}^{i} R M S_{a} (j) / i$ and $\sum_{j = 2}^{i} | R M S_{a} (j) - R M S_{a} (j - 1) | / (i - 1)$ , i = 12. Thus, based on the measured data of RMS_a at the measurement points P₁₋₁₂ in Figure 2, the average value and average deviation of RMS_a under the various excitations of f_t are computed and plotted in Figure 3(a) and (b).

Figure 3.

Calculated results of RMS_a. (a) Average value of RMS_a and (b) average deviation of RMS_a.

The calculated results in Figure 3(a) and (b) show that the average RMS_a at 18 Hz is the largest while the average deviation of RMS_a is reduced at this frequency. When f_t is increased at 22 Hz, the average RMS_a is reduced by 3.0% whereas the average deviation of RMS_a is increased by 6.3% in comparison with these results at 18 Hz. This means that both asphalt paver’s working performance and pavement quality are reduced by 3.0% and 6.3% in comparison with the excitation at 18 Hz of tampers. The existing research also showed that the angular deviation of the tamper pairs in the vibrational screed system also affected the asphalt paver’s working performance and pavement quality.^2–10,16 However, in this experiment, the effect of the angular deviation of the tamper pairs has been ignored. In order to ameliorate the asphalt paver’s working performance, the maximum RMS_a needs to be achieved and distributed evenly on the length of the vibrational screed system. Therefore, the excitation frequencies of f_t and fvs as well as the angular deviations of the tamper pairs in the vibrational screed system should be researched in detail and optimised to enhance the asphalt paver’s working performance and pavement quality.

Evaluating the effect of asphalt paver’s parameters on the working performance

Nonlinear dynamics model of asphalt paver

From the vibrational screed system’s structure of the asphalt paver given in Figure 1(a) and (c), the nonlinear dynamic models of the vibrational screed system and tamper system including the structure and angular deviation of tampers, dynamic model of the vibrational screed system, and tamper’s dynamic model are built in Figure 4(a)–(c) to calculate the vibration equations and assess the effect of the working parameters of the vibrational screed system on the asphalt paver’s working performance.

Figure 4.

A nonlinear dynamic model of the asphalt paver. (a) Structure and angular deviation of tampers,³ (b) vibrational screed system’s model, and (c) tamper’s dynamic model.

In Figure 4, Z, ϕ, and M are the vertical vibration, the rolling angle, and the mass of the vibrational screed system. The angles of φ₁, φ₂, and φ₃ are the deviations of left/right tampers, first/second tampers, and between tamper pairs. K_1,2 are the stiffness parameters and C_1,2 are the damping parameters of the mixed asphalt at the left and right sides of the vibrational screed system. Z_1j are the vertical vibration of first tampers and Z_2j are the vertical vibration of second tampers. M_1j are the first tampers’ mass and M_2j are the second tampers’ mass. K_t1,_t2 are the stiffness parameters and C_t1,_t2 are the damping parameters of the mixed asphalt under the first/second tampers. F_vs is the vibrator screed’s vertical excitation force and F_tj is tampers’ vertical excitation force. x_tj are the tamper’s distances. x₁,₂ are vibration screed system’s distances, j = 1−8.

From the vibrational screed system’s dynamic model in Figure 4(b), the mathematical equations of the vibrational screed system have been written as:

[\begin{array}{l} M & 0 \\ 0 & I \end{array}] {\begin{cases} \ddot{Z} \\ \ddot{ϕ} \end{cases}} = {\begin{cases} \bar{F} \\ \bar{M} \end{cases}}

(1)

where

\bar{M} = F_{1} x_{1} + \sum_{j = 1}^{4} F_{t j} x_{t j} - F_{2} x_{2} - \sum_{j = 5}^{8} F_{t j} x_{t j}

and

\bar{F} = \sum_{j = 1}^{8} F_{t j} + F_{v s} - F_{1} - F_{2}

The vertical force response F_vs in the same Figure 4(b) is expressed as:

F_{v s} = ε_{v s} M_{v s} ω_{v s}^{2} \sin ω_{v s} t

(2)

where ω_vs = 2π × f_vs is the vibrator screed’s vibration excitation, ε_vs is the vibrator screed’s eccentricity, and M_vs is the vibrator screed’s eccentric mass.

The left force F₁ and right force F₂ of the interaction between the mixed asphalt and vibration screed system are determined as follows:

{\begin{cases} F_{1} \\ F_{2} \end{cases}} = [\begin{array}{l} C_{1} & C_{1} x_{1} \\ C_{2} & - C_{2} x_{2} \end{array}] {\begin{cases} \dot{Z} \\ \dot{ϕ} \end{cases}} + [\begin{array}{l} K_{1} & K_{1} x_{1} \\ K_{2} & - K_{2} x_{2} \end{array}] {\begin{cases} Z \\ ϕ \end{cases}}

(3)

Besides, the vertical force response F_tj in the tamper’s pairs impacting the vibrational screed system is also determined via the dynamic model of tampers, as shown in Figure 4(c). Based on this tampers’ dynamic model, the vertical force response F_tj is determined as follows:

\begin{array}{l} {F_{t j}} = [- M_{1 j} C_{t 1} K_{t 1}] {{\ddot{Z}}_{1 j} {\dot{Z}}_{1 j} Z_{1 j}}^{T} + \\ + [- M_{2 j} C_{t 2} K_{t 2}] {{\ddot{Z}}_{2 j} {\dot{Z}}_{2 j} Z_{2 j}}^{T} \end{array}

(4)

where

{\begin{cases} Z_{11} = ε_{11} \sin (ω_{t} t + φ_{3}) \\ Z_{12} = ε_{12} \sin (ω_{t} t + φ_{3}) \\ Z_{13} = ε_{13} \sin (ω_{t} t + φ_{3}) \\ Z_{14} = ε_{14} \sin (ω_{t} t + φ_{3}) \\ Z_{15} = ε_{15} \sin (ω_{t} t + φ_{1} + φ_{3}) \\ Z_{16} = ε_{16} \sin (ω_{t} t + φ_{1} + φ_{3}) \\ Z_{17} = ε_{17} \sin (ω_{t} t + φ_{1} + φ_{3}) \\ Z_{18} = ε_{18} \sin (ω_{t} t + φ_{1} + φ_{3}) \end{cases}

${\begin{cases} Z_{21} = ε_{21} \sin (ω_{t} t + φ_{2} + φ_{3}) \\ Z_{22} = ε_{22} \sin (ω_{t} t + φ_{2} + φ_{3}) \\ Z_{23} = ε_{23} \sin (ω_{t} t + φ_{2} + φ_{3}) \\ Z_{24} = ε_{24} \sin (ω_{t} t + φ_{2} + φ_{3}) \\ Z_{25} = ε_{25} \sin (ω_{t} t + φ_{1} + φ_{2} + φ_{3}) \\ Z_{26} = ε_{26} \sin (ω_{t} t + φ_{1} + φ_{2} + φ_{3}) \\ Z_{27} = ε_{27} \sin (ω_{t} t + φ_{1} + φ_{2} + φ_{3}) \\ Z_{28} = ε_{28} \sin (ω_{t} t + φ_{1} + φ_{2} + φ_{3}) \end{cases}$ , ω_t = 2π × f_t is the tampers’ vibration excitation, ε_1j is the first tampers’ eccentric distance, and ε_2j is the second tampers’ eccentric distance, j = 1−8.

By using the vibration equation of the vibrational screed system determined from equations (1) to (4), both the vertical acceleration ( $\ddot{Z}$ ) and angular acceleration ( $\ddot{ϕ}$ ) of the vibrational screed system have been calculated. Additionally, Rood Mean Square (RMS) accelerations of $\ddot{Z}$ and $\ddot{ϕ}$ are also computed as follows:^17–19

{\begin{cases} R M S_{\ddot{Z}} = \sqrt{T^{- 1} \int_{0}^{T} {\ddot{Z}}^{2} (t) d t} \\ R M S_{\ddot{ϕ}} = \sqrt{T^{- 1} \int_{0}^{T} {\ddot{ϕ}}^{2} (t) d t} \end{cases}

(5)

Thereby, the screed floor’s RMS acceleration in the vertical direction at the measurement points P₁₋₁₂ in Figure 1(b) could be determined via the screed floor’s dynamics model in Figure 4(b) and computation results in equation (5) as follows:

{\begin{cases} R M S_{a (P 1 - 6)} = R M S_{\ddot{Z}} + x_{(P 1 - 6)} \times R M S_{\ddot{ϕ}} \\ R M S_{a (P 7 - 12)} = R M S_{\ddot{Z}} - x_{(P 7 - 12)} \times R M S_{\ddot{ϕ}} \end{cases}

(6)

Equation (6) shows that the screed floor’s RMS acceleration at points of P₁₋₁₂ is affected by $R M S_{\ddot{Z}}$ and $R M S_{\ddot{ϕ}}$ . In order to ameliorate the working performance of the asphalt paver, the values of $R M S_{a (P 1 - 12)}$ should be increased and distributed evenly on the vibration screed system. To achieve these two goals, the value of $R M S_{\ddot{ϕ}}$ should be decreased whereas the value of $R M S_{\ddot{Z}}$ should be augmented. Thus, the maximum $R M S_{\ddot{Z}}$ and minimum $R M S_{\ddot{ϕ}}$ have been selected as objective investigations for assessing the asphalt paver’s working performance.

Analyzing simulation results

Because the pairs of tampers between the left tamper and right tamper of the vibrational screed system are designed symmetrically, the vibration of the vibrational screed system is insignificantly affected by the angular deviation φ₃, thus, the effect of φ₃ on the system’s vibration is ignored. To evaluate the effect of working parameters in the vibrational screed system on the asphalt paver’s working performance, from the asphalt paver’s dynamics parameters provided in Table 1,³ the influence range of the asphalt paver’s working performance including 1.0 ≤ f_t ≤ 22 Hz, 0 ≤ f_vs ≤ 45 Hz, 0 ≤ φ₁ ≤ 180°, and 0 ≤ φ₂ ≤ 180° is then simulated, respectively. The results of

R M S_{\ddot{Z}}

and

R M S_{\ddot{ϕ}}

under the effect of f_vs, f_t, and φ₁, ₂ have been illustrated in Figures 5 and 6.

Table 1.

Asphalt paver’s designed parameters.

Parameter	Value	Parameter	Value
M/kg	3.083	ε_1j,_2j/m	3 × 10⁻³
M₁₁,₁₈/kg	78.0	K₁,₂/N m⁻¹	3.57 × 10⁶
M₁₂,₁₇/kg	110.0	K_t1,₂/N m⁻¹	3.06 × 10⁶
M₁₃,₁₆/kg	70.0	C₁,₂/Ns m⁻¹	58 × 10³
M₁₄,₁₅/kg	69.0	C_t1,₂/Ns m⁻¹	68 × 10³
M₂₁,₂₈/kg	80.0	φ₁/^o	120
M₂₂,₂₇/kg	114.0	φ₂/^o	90
M₂₃,₂₆/kg	71.0	φ₃/^o	90
M₂₄,₂₅/kg	72.0	f_{t max}/Hz	22.0
x₁,₂/m	6.0	f_vs _max/Hz	45.0
ε_vs/m	2.5 × 10⁻³	x/m	25 × 10⁻³

Figure 5.

Effect of f_vs and f_t on the vibration of vibrational screed system. (a) Value of $R M S_{\ddot{Z}}$ , (b) value of $R M S_{\ddot{ϕ}}$ .

Figure 6.

Effect of φ_1,2 on the vibration of vibrational screed system. (a) Value of $R M S_{\ddot{Z}}$ , (b) value of $R M S_{\ddot{ϕ}}$ .

Effect of the vibration frequency (f_t, f_vs)

The result in Figure 5(a) reveals that $R M S_{\ddot{Z}}$ of the vibrational screed system is obviously influenced by excitations of f_t and f_vs. Under the low excitation of 2.0 < f_t < 11 Hz, the result of $R M S_{\ddot{Z}}$ is very low, so the asphalt paver’s working quality is also low. With the excitation of f_t increased from 11 < f_t < 20 Hz, $R M S_{\ddot{Z}}$ has been quickly augmented. Especially, the value of $R M S_{\ddot{Z}}$ is maximum at f_t = 17.5 Hz. Thus, the obtained pavement quality is also the best at this excitation frequency. With the excitation of f_t increased from 20 < f_t < 22 Hz, $R M S_{\ddot{Z}}$ has been lightly decreased. This may be due to the friction in the vibrational screed system is increased. Thereby, the pavement quality is lightly reduced. These results are also similar to the measured results in the section “Experiment of the working performance of asphalt paver”. In order to achieve the maximum $R M S_{\ddot{Z}}$ , the excitation of 11 ≤ f_t ≤ 21 Hz needs to be used for the asphalt paver.

Similarly, under the low excitation of 0 < f_sv < 18 Hz, $R M S_{\ddot{Z}}$ is low and the asphalt paver’s working quality is also low. With f_sv increased from 18 < f_sv ≤ 36 Hz, $R M S_{\ddot{Z}}$ has been quickly augmented, especially, $R M S_{\ddot{Z}}$ is maximum at f_sv = 36 Hz. The pavement quality is also the best at this excitation. When f_sv is increased from 36 < f_sv < 45 Hz, $R M S_{\ddot{Z}}$ is lightly decreased. In order to achieve the maximum $R M S_{\ddot{Z}}$ , the excitation of 22 ≤ f_sv ≤ 43 Hz should be optimised for the asphalt paver.

Besides, Figure 5(b) shows that $R M S_{\ddot{ϕ}}$ is insignificantly influenced by the excitations of f_vs whereas this value is strongly influenced by f_t. This is due to the excitation of f_vs had been generated at the vibrational screed system’s centrer. Therefore, the rolling angle ϕ of the vibrational screed system is insignificantly influenced by the F_vs, as shown in Figure 4(b). In order to achieve the minimum $R M S_{\ddot{ϕ}}$ , the excitation of f_t should be reduced.

Based on the analyses results of the influence of f_vs and f_t on the pavement quality, to achieve both maximum $R M S_{\ddot{Z}}$ and minimum $R M S_{\ddot{ϕ}}$ , the values of f_vs and f_t should be optimised in the operating ranges of 22 ≤ f_sv ≤ 43 Hz and 11 ≤ f_t ≤ 21 Hz.

Effect of the angular deviation (α₁, α₂)

The result in Figure 6(a) indicates that $R M S_{\ddot{Z}}$ is also remarkably influenced by both α₁ and α₂. With the increase of φ₁,₂, the value of $R M S_{\ddot{Z}}$ is reduced, conversely, with the reduction of φ₁,₂, $R M S_{\ddot{Z}}$ is augmented. In order to achieve the maximum $R M S_{\ddot{Z}}$ , the angular deviations φ₁,₂ should be designed in a range of 0° ≤ φ₁,₂ < 60°.

Besides, Figure 6(b) also shows that $R M S_{\ddot{ϕ}}$ is also remarkably influenced by both φ₁,₂. With the increase of φ₁ and reduction of φ₂, the $R M S_{\ddot{ϕ}}$ is reduced, conversely, with the reduction of φ₁ and increase of φ₂, the $R M S_{\ddot{ϕ}}$ is augmented. In order to achieve the minimum $R M S_{\ddot{ϕ}}$ , the parameters of φ₁,₂ should be operated at a range of 0° < φ₁ ≤ 60° and 90° ≤ φ₂ ≤ 180°.

Based on the analyses results of the influence of φ₁,₂ on the pavement quality, to achieve both maximum $R M S_{\ddot{Z}}$ and minimum $R M S_{\ddot{ϕ}}$ , the values of φ₁ and φ₂ should be optimised in the operating ranges of 0° < φ₁ ≤ 60° and 0° ≤ φ₂ ≤ 180°.

Optimum of parameters of asphalt paver

Optimisation approach

The genetic algorithm was used to optimise the design parameters of the mathematical models via the natural selection approach.^20–23 Genetic algorithm has been defined as searching a = [a₁, a₂, …, a_x]^T to achieve the maximum or minimum G(a) as follows:

G (a) = {[G_{1} (a), G_{2} (a), \dots, G_{x} (a)]}^{T}

(7)

with $p_{n} (a) = 0, n = 1, 2, 3, \dots, N$

$q_{m} (a) < 0, m = 1, 2, 3, \dots, M$

Based on the genetic algorithm, the vibrational screed system’s parameters including f_t, f_vs, and φ₁,₂ need to be optimised to ameliorate the asphalt paver’s working parameters based on two values of maximum $R M S_{\ddot{Z}}$ and minimum $R M S_{\ddot{ϕ}}$ . The genetic algorithm is designed as follows:

(1) Initial population and encoding process: Based on the analyzed result of asphalt paver’s working parameters (f_t, f_vs, and φ₁,₂) with their boundary limits including 11 < f_t < 21 Hz, 22 < f_vs < 43 Hz, 0 < φ₁ < 60°, and 0 < φ₂ < 180°, the parameters of f_t, f_vs, and φ₁,₂ have been then linked to chromosome a = [a₁, a₂, a₃, a₄]^T. Besides, each internal chromosome a_x in a has been also encoded as follows:

{\begin{cases} a_{1} = [22, 22.5, . . ., f_{v s}^{j - 1}, f_{v s}^{j}, f_{v s}^{j + 1}, . . ., 42.5, 43] \\ a_{2} = [11, 11.5, . . ., f_{t}^{j - 1}, f_{t}^{j}, f_{t}^{j + 1}, . . ., 20.5, 21] \\ a_{3} = [0, 2, . . ., φ_{1}^{j - 1}, φ_{1}^{j}, φ_{1}^{j + 1}, . . ., 58, 60] \\ a_{4} = [0, 2, . . ., φ_{2}^{j - 1}, φ_{2}^{j}, φ_{2}^{j + 1}, . . ., 178, 180] \end{cases}

(8)

Then, a has been optimized to obtain the maximum value in G ( a ) = [G₁( a ), G₂( a )]^T. Here, G₁( a ) = maximum $R M S_{\ddot{Z}}$ and G₂( a ) = maximum $R M S_{\ddot{ϕ}}^{- 1}$ . The initial population in the genetic algorithm is setup by 200 populations. Besides, each individual a_x in an initial population and each gene in a_x has been created randomly from equation (8).

(2) Fitness values: In order to achieve the maximum $R M S_{\ddot{Z}}$ and minimum $R M S_{\ddot{ϕ}}$ of the vibrational screed system, their fitness values (O₁,₂) in the genetic algorithm have been defined by:²³

{\begin{cases} O_{1} = maximum (R M S_{\ddot{Z}}) \\ O_{2} = maximum (R M S_{\ddot{ϕ}}^{- 1}) \end{cases}

(9)

The optimisation process of the asphalt paver’s working parameters in the genetic algorithm including the input values, encodes, genetic operations, and fitness values have been described and illustrated in Figure 7.

(3) Genetic algorithm model and genetic operations: With the asphalt paver’s model in Figure 3, vibrational screed system’s parameters in Table 1, and genetic algorithm written in MATLAB, the optimisation of the parameters of f_t, f_vs, and φ₁,₂ has been illustrated in Figure 8. In order to optimise these parameters, the probabilities of the mutation process and crossover in the genetic operation are set up by 0.05 and 0.95. The optimisation process is performed in 1500 generations. After the optimisation is finished, the fitness values (O₁,₂) with their optimised parameters will be saved in MATLAB’s workspace.

Figure 7.

Encoded chromosome and optimisation model of the genetic algorithm.

Figure 8.

Model of the genetic algorithm.

Optimised results

By applying the genetic algorithm program written in MATLAB and asphalt paver’s mathematical equations, the vibrational screed system’s working parameters are then optimised. The optimization result of O₁,₂ is plotted in Figure 9.

Figure 9.

Optimisation result of the fitness values of O₁,₂.

Figure 9 reveals that the values O₁,₂ in the genetic algorithm have been quickly increased from the generation of 0 to 1200. Then, the values O₁,₂ are insignificantly increased from the generation of 1200 to 1433. From the generation of 1433 to 1500, the values O₁,₂ are unchanging and stable. This means that the optimised parameters of f_t, f_vs, and φ₁,₂ at the generation of 1433 could be accepted. From the optimised parameters of f_t, f_vs, and φ₁,₂ at the generation of 1433 saved in MATLAB’s workspace, these optimised parameters have been then saved and provided in Table 2. By using the optimised parameters of the vibrational screed system, the asphalt paver with optimisation has been then tested to compare the asphalt paver without optimisation. The measured result of RMS_a at the measurement points (P₁₋₁₂) with optimisation and without optimisation are compared and shown in Figure 10.

Table 2.

Vibrational screed system’s working parameters optimized.

Parameter	Value	Parameter	Value
f_t/Hz	18.2	f_vs/Hz	38.6
φ₁/^o	0.46	φ₂/^o	46.3

Figure 10.

The measured results of RMS_a distributed on the vibration screed’s length with optimization and without optimization.

The results in Figure 10 show that RMS_a at the measured points P₁₋₁₂ with optimisation not only are increased but also are distributed more evenly on the screed floor’s length compared to RMS_a without optimisation. Additionally, based on the statistical theory,¹⁵ the average value of RMS_a at the measurement points P₁₋₁₂ and the average deviation between the points P₁₋₁₂ has been calculated by $\sum_{j = 1}^{12} R M S_{a} (j) / 12$ and $\sum_{j = 2}^{12} | R M S_{a} (j) - R M S_{a} (j - 1) | / 11$ . Therefore, with the measured results of RMS_a at the measurement points P₁₋₁₂ with optimisation and without optimisation in the same Figure 10, the average value of RMS_a with optimisation is 6.92 and without optimisation is 6.39 m s⁻². The average value of RMS_a with optimisation is increased by 7.67% compared to without optimisation. Besides, the average deviation between the measurement points P₁₋₁₂ with optimisation is 0.68 and without optimisation is 1.04 m s⁻². The average deviation of RMS_a between the measurement points with optimisation is greatly reduced by 34.2% in comparison without optimisation. Consequently, these quantitative calculation results indicate that the working performance of the asphalt paver has been obviously ameliorated by using the optimized working parameters of the vibrational screed system of the asphalt paver.

Conclusions

With the design parameters of the asphalt paver, the measurement results show that on the vibrational screed system’s length, the acceleration at the measured points P₁₋₁₂ has been unevenly distributed. Thus, the working performance of the asphalt paver is quite low.

The vibrational screed system’s working parameters remarkably affect the asphalt paver’s working performance, particularly under angular deviations (φ₁,₂) and frequencies (f_vs, f_t). In order to ameliorate the asphalt paver’s working performance, the working parameters of 11 < f_t < 21 Hz, 22 < f_vs < 43 Hz, 0° < φ₁ < 60°, and 0° < φ₂ < 180° should be applied.

With the vibrational screed system’s working parameters optimised, RMS_a not only is increased but also is distributed more evenly on the screed floor’s length compared to RMS_a without optimisation. Especially, the average value of RMS_a with optimisation is increased by 7.67% whereas the average deviation of RMS_a between the measurement points with optimisation is greatly reduced by 34.2% in comparison without optimisation. Consequently, the working performance of the asphalt paver is remarkably improved.

Footnotes

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) received no financial support for the research, authorship, and/or publication of this article.

ORCID iD

Yundong Mei

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Experiment and optimum of the asphalt paver’s parameters to ameliorate the working performance

Abstract

Keywords

Introduction

Experiment with the working performance of asphalt paver

Experimental setup of the asphalt paver

Analysis of the measured results

Evaluating the effect of asphalt paver’s parameters on the working performance

Nonlinear dynamics model of asphalt paver

Analyzing simulation results

Effect of the vibration frequency (ft, fvs)

Effect of the angular deviation (α1, α2)

Optimum of parameters of asphalt paver

Optimisation approach

Optimised results

Conclusions

Footnotes

Declaration of conflicting interests

Funding

ORCID iD

References

Effect of the vibration frequency (f_t, f_vs)

Effect of the angular deviation (α₁, α₂)