Design and Simulation of a Road Maintenance Vehicle with a Multi-working Position Manipulator and an Automatic Feeding Mechanism

Over the years, road maintenance has become more and more difficult and labor-consuming, so automation in road construction and maintenance is currently actively developing in the United States, China and other countries in the world. In order to solve the problem of high maintenance efficiency and low cost, maintenance equipment with high degree of automation and good maintenance efficiency is required [1-3].

In terms of the need to lift the onboard devices during maintenance, some scholars design a special lifting device for road maintenance vehicles, and analyzes the layout and stress of the lifting device [4]. According to the maintenance requirements in plateau areas, a multifunctional maintenance vehicle equipped with small maintenance equipment is designed [5]. Ma et al. [6] puts forward a comprehensive road maintenance vehicle with good integration and reasonable configuration, using the theory of inventive problem solving (TRIZ). Nevertheless, many of the existing road maintenance vehicles require workers to clean the target pits and cracks using onboard crusher, cutter and blower, fill the hot mix asphalt (HMA) or cold feed, and then compact the road repeatedly with the onboard compactor. There are many defects with this maintenance strategy: (1) The complicated maintenance process has many hidden safety hazards related to the frequent lifting of onboard maintenance devices; (2) The onboard maintenance devices, which cause strong vibration and heavy dust, must be operated manually, posing serious damages to workers’ health; (3) The power between onboard maintenance devices has not been fully optimized, leading to redundant power sources and resource waste [7-12].

To solve the problems, this article designs an indexable maintenance equipment that integrates multiple functions (e.g. cutting, pouring, milling and high-pressure cleaning) at the end of the manipulator. The design attempts to provide the same power source to all maintenance devices, and ensure that the indexable vehicle can switch between different working positions as per the maintenance need. In addition, the following systems were set up to treat common road diseases: HMA heating and mixing system, waste crushing and recycling system, automatic feeding mechanism and asphalt heating and insulation system. The indexable equipment, coupled with the four systems, form a novel road maintenance vehicle.

In order to accomplish the above tasks, Firstly, this article designs the functional principle of highway maintenance vehicle. Secondly, it designs and calculates the parameters of key components, determines the parameters of the end manipulator, and determines the parameters of the mixing device through fluid simulation. Finally, the overall layout design of highway maintenance vehicles is completed.

3.1 Manipulator parameters and end trajectory analysis

The manipulator parameters affect the end trajectory, which in return determines whether the manipulator can work effectively. The more rational its parameters, the wider the effective working range of the manipulator. To eliminate the motion interference, it is necessary to fully analyze the end trajectory.

Our manipulator is a six-degree-of-freedom (6DOF) mechanism of three segments, in which the third segment is telescopic. The three segments are hinged to a turntable. Figure 2 shows the kinematics model of the manipulator established by the Denavit–Hartenberg (D-H) method. In the figure, $z_0, z_1, z_3$ and $z_5$ are joints rotating about the joint axis, and $z_2, z_4$ and $z_6$ are joints moving along the joint length. The D-H parameters of each joint is listed in Table 1 [13~15].

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Figure 2. Kinematics model of the manipulator

Table 1. D-H parameters of the manipulator

According to the joint parameters (Table 1) and the kinematics model (Figure 2), the transformation matrix $A_i$ from the i-th joint to the i-1-th joint can be established as:

$A_{1}=\operatorname{Rot}\left(Z_{0}, \phi_{0}\right) \operatorname{Tr} a n s(0,0, h) \operatorname{Tr} a n s(s, 0,0) \operatorname{Rot}\left(X_{1}, 90^{\circ}\right)$

$A_{2}=\operatorname{Rot}\left(Z_{1}, \phi_{1}\right) \operatorname{Rot}\left(Y_{2},-90^{\circ}\right),$

$A_{3}=\operatorname{Tr} \operatorname{ans}\left(0,0, l_{1}\right) \operatorname{Rot}\left(Y_{3}, 90^{\circ}\right)$

$A_{4}=\operatorname{Rot}\left(Z_{3},-\phi_{2}\right) \operatorname{Rot}\left(Y_{4},-90^{\circ}\right)$

$A_{5}=\operatorname{Trans}\left(0,0, l_{2}\right) \operatorname{Rot}\left(Y_{5}, 90^{\circ}\right)$

$A_{6}=\operatorname{Rot}\left(Z_{5},-\phi_{3}\right) \operatorname{Rot}\left(Y_{6},-90^{\circ}\right) \operatorname{Tr} \operatorname{ans}\left(0,0, l_{3}\right)$

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where, $\theta_{123}=\phi_{3}+\phi_{2}-\phi_{1} ; \theta_{12}=\phi_{2}-\phi_{1}$.

By the D-H method, the end posture of a member can be obtained by the transformation matrix $^{0} T_{n}=\prod_{n=0}^{n} i-1 A_{i}$, where, $^{0} T_{n}$ is the function of such variables as $\phi_{1}, \phi_{2}$ and $\phi_{3}$ and $i-1 A_{i}=\left[\begin{array}{cc}{{^i-1}R_i} & {^{i-1}P_{i}} \\ {0} & {1}\end{array}\right]$ is the transformation matrix from the i-th coordinate system to the i-1-th coordinate system ($^{(i-1)} R_{i}$ is the posture matrix; $^{i-1} P$ is the position matrix). In this way, the position of the manipulator’s end relative to the fixed coordinate system $z_0$ can be constructed as:

$\left\{\begin{aligned} X_{D}=& \cos \phi_{0}\left[s+l_{1} \cos \phi_{1}+l_{2} \cos \theta_{12}+l_{3} \cos \theta_{123}\right] \\ Y_{D}=\sin \phi_{0}\left[s+l_{1} \cos \phi_{1}+l_{2} \cos \theta_{12}+l_{3} \cos \theta_{123}\right] \\ Z_{D}=h+l_{1} \sin \phi_{1}+l_{2} \sin \theta_{12}-l_{3} \sin \theta_{123} \end{aligned}\right.$ (1)

The speed at any point in the coordinate system relative to the fixed coordinate system $z_0$ can be calculated by:

$\frac{d^{0} p}{d t}=\left(\sum_{j=1}^{i} \frac{\partial^{0} A_{i}}{\phi_{i}}\right)$ $^ip; i=1,2 \cdots, n$       (2)

Thus, the speed of the manipulator’s end relative to fixed coordinate system $z_0$ at $ϕ_0=0$ can be determined as:

$\left\{\begin{array}{l}{\dot{X}_{D}=-l_{1} \dot{\phi}_{1} \sin \phi_{1}-l_{2}\left(\dot{\phi}_{2}-\dot{\phi}_{1}\right) \sin \left(\phi_{2}-\phi_{1}\right)} \\ {\dot{z}_{D}=l_{1} \dot{\phi}_{1} \cos \phi_{1}-l_{2}\left(\dot{\phi}_{2}-\dot{\phi}_{1}\right) \cos \left(\phi_{2}-\phi_{1}\right)}\end{array}\right.$     (3)

The acceleration of any point in the coordinate system relative to the fixed coordinate system $z_0$ can be calculated by:

$\frac{d^{20} p}{d t^{2}}=\left(\sum_{j=1}^{i} \frac{\partial^{20} A_{i}}{\phi_{j}^{2}} \ddot{\phi}_{j}\right)$ $^ip; i=1,2 \cdots, n$          (4)

hence, the acceleration of the manipulator’s end relative to fixed coordinate system $z_0$ at $ϕ_0=0$ can be determined as:

$\left\{\begin{aligned} \ddot{X}_{D} &=-l_{1} \ddot{\phi}_{1} \cos \phi_{1}-l_{2}\left(\ddot{\phi}_{2}-\ddot{\phi}_{1}\right) \cos \left(\phi_{2}-\phi_{1}\right) \\ \ddot{Z}_{D} &=l_{1} \ddot{\phi}_{1} \sin \phi_{1}+l_{2}\left(\ddot{\phi}_{2}-\ddot{\phi}_{1}\right) \sin \left(\phi_{2}-\phi_{1}\right) \end{aligned}\right.$   (5)

Since the levelling device guarantees the perpendicularity of $l_3$ to the ground, the manipulator movement must satisfy the angular relationship of $ϕ_3=90+ϕ_1-ϕ_2$. The end trajectory of the manipulator in the X-Z plane is shown in Figure 3 below.

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Figure 3. End trajectory of the manipulator in the X-Z plane ($l_1,l_2$ take different values)

As shown in Figure $3(a),$ when the first section length $l_{1}=1.8 m,$ second section length $l_{2}=1.5 m$ and third telescopic section length $l_{3}=2 m,$ the end trajectory of the manipulator is segment $A-B$ at $\phi_{2}=130^{\circ}$ and $\varphi_{1} \in 30^{\circ} \sim 70^{\circ},$ segment $C-D$ at $\phi_{2}=50^{\circ}$, and $\varphi_{1} \in 30^{\circ} \sim 70^{\circ},$ segment $B-C$ at $\phi_{1}=30^{\circ}$ and $\phi_{2} \in 50^{\circ} \sim 130^{\circ}$ , and segment $A-D$ at $\phi_{1}=70^{\circ}$ and $\phi_{2} \in 50^{\circ} \sim 130^{\circ}$ .

In Figure 3(a), $l_1=1.8min$ the dotted line and $l_1=1.5m$ in the solid line. It can be seen that, with the reduction in the $l_1$, the manipulator trajectory moves towards the negative direction of the Z axis and the X axis, indicating that the compaction roller is more likely to interfere in the manipulator movement at a smaller $l_1$. In Figure 3(b), $l_2=1.8m$ in the dotted line and $l_2=1.5m$ in the solid line. It can be seen that, with the reduction in the $l_2$, the manipulator trajectory moves towards positive direction of the Z axis and the X axis, indicating that a large $l_2$ promotes maintenance and suppresses interference. 

In Figure 4, the lengths of the first section, the second section and the third telescopic section are $l_1=1.8m$, $l_2=1.5m$ and $l_3=2m$, respectively, and $ϕ_2$ changes between 50° and 130°. Figure 4(a), where $30°≤ϕ_1≤70°$ in the solid line and $30°≤ϕ_1≤80°$ in the dotted line, shows that the increase in the upper bound of $ϕ_1$ does not promote the effective motion trajectory of the manipulator. Figure 4(b), where $50°≤ϕ_2≤130°$ in the solid line and $50°≤ϕ_2≤130°$ in the dotted line, shows that the increase in the lower bound of $ϕ_2$ does not promote the effective motion trajectory of the manipulator.

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Figure 4. End trajectory of the manipulator in the X-Z plane (ϕ_1,ϕ_2 take different values)

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Figure 5. End trajectory of the manipulator in the X-Y-Z plane (angle of the compaction swing rod take different values)

In Figure 5(a), the swing angle $ϕ_0$ of the rotary table changes between -30° and 30°, the lengths of the first section, the second section and the third telescopic section are $l_1=1.8m$, $l_2=1.5m$ and $l_3=2m$, respectively, the length and radius of the compaction roller are 0.78m and 0.28m, respectively, while the length and swing angle of the compaction swing rod are 1.5m and 20°, respectively. In this case, the compaction roller is retracted. In addition, the origin of the coordinate system is 1.5m above ground. It can be seen from Figure 5(a) that the lowest point of the compaction roller is greater than 0.7m from the ground, which does not hinder the normal movement.

In Figure 5(b), all the parameters are the same as in Figure 5(a), except for the swing angle of the compaction swing rod (60°). In this case, the compaction roller is at the working position for compaction. The origin of the coordinate system is still 1.5m above ground. It can be seen from Figure 5(b) that the compaction roller (Figure 4) is in contact with the target road, exerting no interference in the manipulator trajectory.

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Figure 6. End trajectory of the manipulator in the X-Y-Z plane (radius of the compaction roller takes different values)

In Figure 6(a), the swing angle ϕ_0 of the rotary table changes between -60° and 60°, the lengths of the first section, the second section and the third telescopic section are $l_1=1.8m$, $l_2=1.5m$ and $l_3=1.5m$, respectively, the length and radius of the compaction roller are 2m and 0.35m, respectively, while the length and swing angle of the compaction swing rod are 1.5m and 60°, respectively. In this case, the compaction roller is in contact with the ground. It can be seen from Figure 6(a) that the compaction roller interferes in the manipulator trajectory. Specifically, the manipulator trajectory is shifted by 0.5m to the positive direction of Z axis, due to the reduction of the length of the third telescopic section $l_3$, and expands in the Y-direction thanks to the growth in the swing angle $ϕ_0$ of the rotary table.

In Figure 6(b), the swing angle ϕ_0 of the rotary table changes between -60° and 60°, the lengths of the first section, the second section and the third telescopic section are $l_1=1m$, $l_2=0.8m$ and $l_3=1.5m$, respectively, the length and radius of the compaction roller are 2m and 0.35m, respectively, while the length and swing angle of the compaction swing rod are 1.5m and 20°, respectively. In this case, the compaction roller is still in contact with the ground. It can be seen from Figure 6(b) that the compaction roller clearly interferes in the manipulator trajectory. The manipulator moves in a smaller range and its trajectory shifts towards the positive direction of the X axis, because of the shortening of the first and second sections.

Table 2. Motion parameters of the manipulator

According to the above analysis results, the swing angle and length of the compaction swing rod were determined as 20°~60° and 1.5m, respectively, and the length and radius of the compaction roller were selected as 0.78m and 0.28m, respectively. The final parameters of the manipulator are listed in Table 2.

3.2 Mathematical model for manipulator kinematics

Using the Lagrangian method, the manipulator’s dynamics equation can be expressed as:

$T_{i}=\sum_{j=1}^{n} K_{i j}(\phi) \dot{\phi}_{i j}+\sum_{j=1}^{n} \sum_{t=1}^{n} H_{i j t}(\phi) \dot{\phi}_{j} \dot{\phi}_{t}+G_{i}(\phi)$     (6)

where, $T_i$ is the driving force acting on the manipulator; $K_{ij}(ϕ)$ is the moment of inertia of the manipulator; $H_{ijt}(ϕ)$ is the centripetal force or the Coriolis force between the joints; $G_i (ϕ)$ is the gravity. After simplifying $K_{i j}, H_{i j t}$ and $G_{i}$, the above formula can be rewritten as:

$K_{i j}=\sum_{p=\max (i, j)}^{n} m_{s}\left[^{s} \delta_{i}^{T} k_{s}^{s} \delta_{j}+^{s} d_{i} g^{s} d_{i}+^{s} \gamma_{s} g\left(^{s} d_{i}^{s} \delta_{j}+^{s} d_{j}^{s} \delta_{i}\right)\right]$       (7)

where, $m_{s}$ is the mass of the manipulator s; δ is the angle between the tangential line of a point M and radius vector of the point; $k_s$ is the matrix of the cross-coupling coefficient of point M; $d_{i}\left(d_{j}\right)$ is the measured distance of $x_{i}\left(z_{j}\right)$ along $y_{i}$; $s_{Y_{\mathcal{S}}}$ are the coordinates of the manipulator’s center of mass in the coordinate system of the manipulator; g is the acceleration of gravity;

$H_{i j t}=\frac{\partial D_{i j}}{\partial \theta_{t}}-\frac{1}{2} \frac{\partial D_{j k}}{\partial \theta_{i}}$       (8)

$G_{i}=^{i-1} g \sum_{s=i}^{n} m_{s}^{i-1} \gamma_{s}$         (9)

where, $^{i-1} g=\left[-g g^{0} o_{i-1}, g g^{0} n_{i-1}, 0,0\right]$; g^0=[g,0",0,0"]; $^{i-1}\gamma_{s}$ are the coordinates of the manipulator’s center of mass in the i-1-th coordinate system.

3.3 Estimation of the power of the hydraulic motor

In the indexable maintenance equipment, the cutting, milling and indexing are powered by a hydraulic motor. The power needed for milling and cutting can be respectively estimated by [10, 11]:

$P_{X}=\frac{V \tau}{\cos \left(\frac{\pi}{4}-\frac{\beta}{2}-\frac{\gamma}{2}\right)} \times\left(\frac{\cos \gamma}{\sin \left(\frac{\pi}{4}-\frac{\beta}{2}+\frac{\gamma}{2}\right)}+\frac{\sin \beta}{\cos \left(\frac{\pi}{4}+\frac{\beta}{2}-\frac{\gamma}{2}\right)}\right) \times \frac{a_{0} Z f}{\pi d}$      (10)

$P_{Q}=\left[\frac{\tau}{\cos \left(\frac{\pi}{4}-\frac{\beta_{0}}{2}-\frac{\gamma_{1}}{2}\right)} \times\left(\frac{\cos \gamma_{1}}{\sin \left(\frac{\pi}{4}-\frac{\beta_{0}}{2}+\frac{\gamma_{1}}{2}\right)}+\frac{\sin \beta_{0}}{\cos \left(\frac{\pi}{4}+\frac{\beta_{0}}{2}-\frac{\gamma_{1}}{2}\right)}\right)+\frac{2 \pi R \lambda \mu k}{h}\right] \times V \times \frac{a_{p} B f}{2 \pi R} \times \frac{\cos ^{-1}\left(1-\frac{a_{p}}{R}\right)}{180^{\circ}\left(l_{s}+l_{w}\right)}$         (11)

where, τ is the shear yield strength of the road; β is the friction angle of the rake face; γ is the rake face of the tool; V is the tool speed; $a_0$ is the milling depth; Z is the number of millers; f is the feed amount; d is the diameter of the milling drum; R is the radius of the saw blade; λ is the continuous ratio of the saw blade; μ is the coefficient of friction; k is the compressive strength; h is 25 % of the diameter of the adamas particles; ap is the depth of the saw blade; B is the thickness of the saw blade; ls is the arc length of the cutter head; lw is the arc length of the sink.

The following parameter values were selected for further discussion: $\tau=7 \mathrm{MPa}, \gamma=120^{\circ}, \beta=10^{\circ}, \mu=0.4, h=0.15, \beta_{0}=5^{\circ}, k=0.02 \mathrm{MPs}$, $\lambda=0.5,$ and $y_{1}=80^{\circ}$. Then, the power of the hydraulic motor was estimated by formulas (10) and (11), respectively. The larger value was adopted and divided by the transmission efficiency, yielding the required power of the motor: 6Kw.

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Figure 13 Overall layout of the road maintenance vehicle

1. The mixing tank 2. The vertical loading mechanism 3. The pulverizing tank 4. One arm 5. Two arm 6. Three-arm hydraulic cylinder 7. Cutting face 8. Milling face 9. Seam filling face 10. The compaction roller 11. Warning light 12. The HMA transmission though 13. The air heating and pressurizing device 14. Control room 15. Hot asphalt box 16. Asphalt tank 17. Generating set 18. Storage bin 19. Hydraulic pump station 20. The waste transmission trough 21. The waste collection hopper 22. The rear HMA discharge trough 23. Hydraulic cylinder 24. Rack and pinion mechanism 25. Fixed-end toothed disc box 26. Rotating end toothed disc box body

The overall layout of our road maintenance vehicle is illustrated in Figure 13. Firstly, the cutting and milling waste is collected manually into the waste collection hopper 21, and then transmitted via the waste transmission trough 20 to the vertical loading mechanism 2. Next, the waste will be pulverized in the pulverizing tank 3, and relocated to the mixing tank 1, where it is mixed with asphalt under heating. The HMA will be transported via the HMA transmission though 12 and the rear HMA discharge trough 22 into the maintenance area. Finally, the HMA will be compacted by the compaction roller 10. In Figure 13, the item marked by 15 is a hot asphalt box that stores and keeps the temperature of hot asphalt. The box can heat up asphalt to a certain temperature. The hot asphalt in 15 can be pumped by the asphalt pump to 1 or poured into the cracks on the road. The air heating and pressurizing device 13 is connected to the high pressure air port on the pouring working face 9. This device cleans and blows dry the cracks with high pressure air. The indexable maintenance equipment has three working faces, which respectively correspond to the left side (pouring working position), lower side (milling working position) and right side (cutting working position). During the operation, the maintenance equipment can switch between the three working positions based on the actual demand.