2017 Volume 58 Issue 3 Pages 485-493
This paper presents an advanced control system for tilting-ladle-type automatic pouring machines used in the metal casting industry. In order to pour liquid from the lowest possible position, an approach for motion trajectory generation of pouring ladle is proposed in this paper. The proposed approach controls the falling position of outflow liquid and avoids collision between ladle and obstacles. This approach defined three pouring modes derived from the positional relation between ladle and obstacles. Pouring mode switching was also proposed to shift to the lowest pouring mode depending on pouring conditions and ladle posture. An analytical algorithm of the falling position control system was built. The effectiveness of the proposed control system was validated through experiments using a laboratory automatic pouring machine with a monitoring system.
This Paper was Originally Published in Japanese in J. JFS 88 (2016) 27–36.
In the casting industry, the pouring process is one of the burdensome processes for workers, since they may be exposed to high temperature and powder dust. In addition, when molten metal is poured manually, the quality of casting products often varies depending on pouring skill. Thus, in order to reduce risks and improve the accuracy of products, advances have been made in the automation of the pouring process1,2).
There are some approaches to automate pouring process, e.g., tilting-type3–9), stopper-ladle-type10–14), pressure-type15). In East Asia, the tilting-type automatic pouring approach is the main stream. The tilting-type approach has several advantages over other approaches, including the possibility of applying the skill of hand pouring and a mechanism that is easier to maintain. In the pouring process, it is important to control the outflow of molten metal from a ladle and pour into the correct position of the sprue cup in a mold. Various approaches of flow rate control have been studied, including making a reference from the teaching-play-back approach3), introducing fuzzy control theory4), using shape input of ladle motion from look-up table between tilting velocity and weight of molten metal in the ladle5), estimating fluid parameters based on computational fluid dynamics simulation and modulate the control system6), and constructing a repetitive control system to improve accuracy of filled weight7). Our group also proposed mathematical plant models of pouring process and controlled the flow rate using an inverse plant model, which is based on the balance equation of liquid volume in a ladle8). Furthermore, the falling position control approach of outflow liquid is proposed based on estimation of outflow liquid9).
It is also important to set the proper pouring height since some problems related to higher pouring are shown in previous studies, increase the amount of air entrainment16), and induce splash by impact force easily17). Thus, it is estimated that product quality and safety of production lines will be improved if the height of the pouring mouth becomes lower when molten metal is poured into a mold. However, such an approach has not been proposed for tilting-type automatic pouring machines.
Therefore, in this paper, a novel approach for motion trajectory generation is proposed, which lowers the height of the pouring mouth and derives the motion trajectory of the pouring ladle. In order to prevent damage, the proposed approach considers collision avoidance of a ladle and obstacles. The effectiveness of proposed approach is verified by some experiments using an automatic pouring machine with measurement of the falling position of outflow liquid by a camera measurement system. A trapezoidal ladle without a nozzle was used to simplify the mathematical model of outflow streamline and the propose generation approach focused on the outer shape of equipment.
An illustration of the automatic pouring machine used in the present work is shown in Fig. 1. A ladle is transferred by servo motors: Y-axis for back and forward direction and Z-axis for down and up direction. And a ladle is tilted on Θ-axis. The movable range of each motor is limited; Y-axis 0.4 m, Z-axis 0.6 m, and Θ-axis: ±90˚ (0˚ is defined as a horizontal posture of a ladle). A load cell built into a support member of the ladle, measures the total weight. Each servo system of motors receives velocity references from a Digital Signal Processor (DSP) and drives based on references. In the present work, ADSP674, a DSP manufactured by Chubu Electric Co. Ltd., was used. The sampling time of the DSP was 0.01 s, which is a sufficiently small term for the pouring process control.
Experimental equipment.
Since the position of the pouring mouth moves by a tilting motion, falling trajectory of outflow liquid varies. To stabilize the falling trajectory, the position of the pouring mouth was fixed by the synchronized control of Y and Z-axes with the tilting motion of Θ-axis18).
Behavior of outflow liquid from a ladle was measured by the image measurement system set at a lateral side of the automatic pouring machine. The measurement system extracts outer shapes of falling liquid from an image captured by a CCD camera, using the edge detection technique, and calculates a falling position of outflow liquid as the center point of the two ends of the outer shape on the measurement position15). In this paper, STC-CLC33A, a CCD camera manufactured by Sentech Co. Ltd., measured behavior of outflow liquid, and shot data ware processed by the image processing system based on LabVIEW, the measurement control software of National Instruments Corp.
The effectiveness of the proposed approach was verified by control experiments using water since a dynamic viscosity coefficient of water is similar to that of molten metal of cast iron and experiments can be executed safely. Although there may be differences in surface tension, in this work we assumed all outflows of liquid made similar trajectory of falling.
2.2 Positional relationship between ladle and moldThe trapezoidal ladle shown in Fig. 2 was used in this study. The ladle has a shape similar to that of an actual ladle projected from a lateral plane.
Geometry of trapezoidal ladle without nozzle.
Figure 3 shows a positional relationship between a ladle and a mold in the automatic pouring system, including a mold and part of the stage of the machine that must be considered obstacles during the motion control of the ladle, and which are rectangular. The parameters of obstacles were defined as follows: a distance Dm from a corner point of a mold to the center point of a sprue cup, and a level difference Hs between a surface of a mold and that of a stage. The target of falling position of outflow liquid was the center point of a sprue cup.
Positional relation between ladle and obstacles.
To achieve the flow rate control and the falling position control of outflow liquid, some process models must be constructed, namely, the motor model on Θ-axis, the flow rate model, and the free fall model of outflow liquid. This paper touches briefly on these representations because our previous studies show approaches for the flow rate control and the falling position control8,15).
3.1 Motor model on Θ-axisThe relationship between the input voltage uθ and the tilting velocity ω is represented by the following first-order lag system,
| \[\frac{{\rm d} \omega (t)}{{\rm d}t} = -\frac{1}{T_{m\theta}} \omega (t) + \frac{K_{m\theta}}{T_{m\theta}} u_\theta (t)\] | (1) |
When the outflow process is shown as in Fig. 4(a), the volume balance equation of pouring with a variation of ω becomes
| \[q(t) = -\frac{{\rm d} V_r(t)}{{\rm d}t} - \frac{\partial V_s(\theta (t))}{\partial \theta (t)} \omega (t)\] | (2) |
| \[h(t) \approx \frac{V_r(t)}{A(\theta (t))}\] | (3) |
| \[q(t) = c \int_0^{h(t)} L_f(h_a) \sqrt{2gh_b} dh_b,\quad (0 < c \le 1,\ h_a = h(t) - h_b)\] | (4) |
| \[q(t) = \frac{2}{3} cL_f \sqrt{2gh^3(t)}\quad (0 < c \le 1)\] | (5) |
| \[\frac{{\rm d}w(t)}{{\rm d}t} = \rho q(t)\] | (6) |
Illustration of pouring process, (a) Parameters in pouring process, (b) Parameters of pouring mouth.
Vs and A of eqs. (2) and (3) are geometry parameters of a ladle, which are derived based on inner geometry. When we use water at room temperature and a trapezoidal ladle, c is 0.659) and ρ is 1.00 × 103 kg･m−3.
3.3 Free-fall process model of outflow liquidFigure 5 shows the free-fall process of outflow liquid from a ladle. If it is assumed that a free-fall trajectory of liquid is represented the same as that of mass, the horizontal falling distance Sy can be derived as the product of a horizontal outflow velocity vt and a falling time Tf from a height Sz to the target point9),
| \[S_y(t) = v_t(t_0) \cdot T_f(t) = v_t(t_0) \sqrt{\frac{2}{g} S_z(t)}\] | (7) |
| \[v_t(t) = \beta_1 \frac{q(h(t))}{L_f \cdot h(t)} + \beta_0 = \frac{2}{3} c\beta_1 \sqrt{2gh(t)} + \beta_0\quad (v_t(t) \ge 0)\] | (8) |
Illustration of free-fall process of outflow liquid.
The outflow weight is measured by a load cell built into the pouring system. The dynamics of a load cell is represented by a first-order lag system8),
| \[\frac{{\rm d}w_L(t)}{{\rm d}t} = -\frac{1}{T_L} w_L(t) + \frac{1}{T_L} w(t)\] | (9) |
The model-based feedforward control system shown in Fig. 6 was constructed using the above process models. This system has two parts: flow rate control system and falling position control system.
Block diagram for falling position control system.
The flow rate controller is realized by Pf−1 and Pmθ−1, inverse model of motor model Pmθ and flow rate model Pf. By the forward models (1), (2), and (5) shown in Sec. 3, Pmθ−1 is derived as eq. (10) and Pf−1 is derived as eqs. (11) and (12)8,9),
| \[u_\theta (t) = \frac{T_{m\theta}}{K_{m\theta}} \frac{{\rm d} \omega_{\mathit{ref}}(t)}{{\rm d}t} + \frac{1}{K_{m\theta}} \omega_{\mathit{ref}}(t)\] | (10) |
| \[h_{\mathit{ref}}(t) = \left( \frac{3q_{\mathit{ref}}(t)}{2cL_f \sqrt{2g}} \right)^{\frac{2}{3}}\] | (11) |
| \[\omega_{\mathit{ref}}(t) = -\frac{\displaystyle A(\theta (t)) \frac{{\rm d}h_{\mathit{ref}}(t)}{{\rm d}t} + q_{\mathit{ref}}(t)}{\displaystyle \frac{\partial V_s(\theta (t))}{\partial \theta (t)} + \frac{\partial A(\theta (t))}{\partial \theta (t)} h_{\mathit{ref}}(t)}\] | (12) |
The estimation process of horizontal falling distances Ef and Eo is constructed based on free-fall process model Po to achieve control falling position at ro. Since the trapezoidal ladle was used, Ef is expressed as eq. (13) and Eo is expressed as eq. (14).
| \[\bar{v}_t(t) = \frac{2}{3} c\beta_1 \sqrt{2gh_{\mathit{ref}}(t)} + \beta_0\] | (13) |
| \[\bar{S}_y(t) = \bar{v}_t(t_0) \sqrt{\frac{2}{g} S_z(t)}\] | (14) |
The ladle position such that the position of the pouring mouth becomes the lowest one and also does not collide with obstacles is achieved when the boundary of the ladle attaches with that of obstacles. There were three approaches which achieves such conditions, shown in Fig. 7 if it is assumed that it took a sufficiency short time for liquid to fall from pouring mouth to the target position on the sprue cup and the ladle could move along the boundary19,20). The approaches are defined as pouring modes 1, 2, and 3, respectively. The pouring height Sz of each mode was derived from the positional relation of ladle and obstacles, and the estimated falling trajectory of outflow liquid. The definition of each Sz is described in the following paragraphs. Note that the horizontal position of pouring mouth Sy was derived after derivation of Sz.
Ladle motions for pouring from lower position, (a) Mode 1, (b) Mode 2, (c) Mode 3.
In pouring mode 1, a ladle slides along the upper surface of a mold, shown in Fig. 7(a). The height of pouring Sz1 was derived from a shape and a posture of the ladle as eq. (15),
| \[S_{z1}(t) = L_s \cos (\theta (t) + \gamma)\] | (15) |
In pouring mode 2, a ladle is attached to corner point of a mold P during a pouring process. Point Q is obtained as an intersection point between mold upper surface and perpendicular line of pouring mouth. Assuming that Dp is a distance between point P and point Q, then It had the following relationship with position of sprue cup Dm and falling distance of outflow liquid Sy2.
| \[D_m = S_{y2}(t) + D_p(t)\] | (16) |
| \[S_{y2}(t) = v_t(t) \sqrt{\frac{2}{g} S_{z2}(t)}\] | (17) |
| \[D_p(t) = S_{z2}(t) \tan (\theta (t) + \gamma).\] | (18) |
| \[\tan (\theta (t) + \gamma) \cdot \sqrt{S_{z2}(t)}^2 + v_t(t) \sqrt{\frac{2}{g}} \cdot \sqrt{S_{z2}(t)} - D_m = 0.\] | (19) |
| \[S_{z2}(t) = \frac{\displaystyle \left( -\sqrt{v_t(t)^2 \frac{2}{g}} + \sqrt{v_t(t)^2 \frac{2}{g} + 4D_m \tan (\theta (t) + \gamma)} \right)^2}{4\tan^2 (\theta (t) + \gamma)}\] | (20) |
In this mode, the ladle slides along the upper surface of a machine stage. Thus, the pouring height of mode 3 Sz3 was derived by an approach similar to mode 1,
| \[S_{z3}(t) = L_s \cos (\theta (t) + \gamma) - H_s\] | (21) |
Equations of pouring height were derived to achieve collision avoidance and lower position of pouring mouth, and depending on each condition of pouring mode. To keep lower position of pouring mouth throughout the pouring process, pouring mode must be switched based on pouring condition such as flow rate and ladle posture. Therefore, by comparing calculated pouring heights of each mode, pouring mode was switched by applying the following condition,
| \[S_z(t) = \left\{ \begin{array}{@{}lc@{}} S_{z1}(t) & (S_{z1}(t) < S_{z2}(t)) \\ S_{z2}(t) & (S_{z1}(t) \ge S_{z2}(t),\ S_{z3}(t) < S_{z2}(t)) \\ S_{z3}(t) & (S_{z1}(t) \ge S_{z2}(t),\ S_{z3}(t) \ge S_{z2}(t)) \end{array} \right.\] | (22) |
Timing of pouring mode switching, (a) Mode 1 and 2, (b) Mode 2 and 3.
The generation process of ladle motion explained in this section is shown in Fig. 9.
Flow chart of calculation process for lower position pouring.
To verify the effectiveness of the proposed approach, control experiments were executed using an automatic pouring machine. In these experiments, the following three situations were compared: (I-1) pouring at fixed height without falling position control of outflow liquid; (I-2) pouring fixed at height with falling position control of outflow liquid (conventional); (I-3) pouring kept at lower position of pouring mouth (proposed). The target fluid was water.
The initial ladle posture θ(0) was 20˚, and the initial pouring height was 0.24 m which were derived from initial conditions using eqs. (15)–(22). The falling position of outflow liquid Sy was estimated as 0.00 m when flow rate q equals 0.00 m3･s−1, and therefore the horizontal position of pouring mouth was set directly above. The parameters of obstacles were defined as follows: Dm was 0.20 m: Hs was 0.05 m. Reference flow rate had two terms of constant value: term from 5 s to 7 s was 3.00 × 10−4 m3･s−1: term from 9 s to 11 s was 4.50 × 10−4 m3･s−1.
The results of pouring experiments are shown in Fig. 10. In this figure, (a) is reference flow rate; (b) is input voltage to motor on Θ-axis; (c) is titling angle of ladle; (d) and (e) are pouring mouth position on Y and Z-axes; (f) is weight of outflow liquid measured by load cell; (g) is falling position of outflow liquid on the global axis measured by camera measurement system; (h) is pouring mode transition of the proposed approach (I-3). The target position of outflow liquid Sy0 is 0 m in Fig. 10(g). In Fig. 10(d)–(g), a black circle is a marker of (I-1); a gray cross is a marker of (I-2); a light gray star is a marker of (I-3). Since the experiments of Fig. 10 (c) agree well with the simulations, tilting angle and tilting velocity was controlled on the desired trajectory. The experimental results of poured weight were also in good agreement with the simulation results in Fig. 10 (f). However, the result of (I-3) showed a sharp fluctuation after start of pouring. In the proposed approach, non-smooth motion trajectory of pouring ladle was generated when the pouring mode was switched based on the pouring height. Sharp acceleration and deceleration were induced by non-smooth motion trajectory in the vertical direction at switching timing of pouring mode. It induces quick acceleration on vertical direction when pouring mode was switched. Therefore, it seems that inertia forces were induced and another weight variation appeared on measurement result of the load cell. This problem is looked forward to solve by following ideas: compensation by estimation of inertia forces on vertical direction; smooth switching of pouring mode. In the measurement result of falling position in Fig. 10(g), control errors were suppressed within ±0.01 m in case (I-2) and (I-3), even when pouring flow rate changed from 5 s to 11 s. Thus, it was shown that the proposed approach can control falling position of outflow liquid within same accuracy of the conventional approach.
Experimental results of pouring motion control, (a) Reference flow rate, (b) Input voltage to motor on Θ-axis, (c) Tilting angle of ladle, (d) Pouring mouth position on Y-axis, (e) Pouring mouth position on Z-axis, (f) Weight of outflow liquid, (g) Falling position of outflow liquid, (h) Pouring mode transition (Case I-3).
Figures 11(a)–(c) show the positional relationships between ladle and mold during pouring control of (I-1), (I-2) and (I-3). The black dotted lines mean trajectories of tilting center position and pouring mouth. The outer shapes of ladle are drawn based on tilting angle and positions of Y- and Z-axes. The ladle drawings are based on the tilting center position and ladle posture at 0 s, 8 s, 10 s and 16 s, which focus on the times to begin and finish to pour, and of constant flow rate. In Case (I-1) and (I-2), Fig. 11(a) and (b), the space between ladle and mold became wide in the course of the pouring process since the height of pouring mouth was kept by the former falling position control. On the other hand, the proposed approach (I-3) achieved a ladle movement that remained attached with mold surface. The ladle did not intrude into the mold region, and therefore did not collide with obstacles.
Ladle motions during pouring process, (a) Pouring mouth fixed (without control), (b) Falling position control (constant pouring height), (c) Lower position pouring.
In this section, the results are shown that take into consideration an actual batch process of pouring in two cases: (II-1) falling position control holding the height of pouring mouth (conventional approach); (II-2) falling position control considering lower position of ladle (proposed approach).
In these experiments, the shape of obstacles were defined as Dm = 0.20 m and Hs = 0.05 m, and initial ladle posture θ(0) of 15˚ was assumed. The reference flow rate was repeated same pattern three times, shown in Fig. 12(a): first batch was from 3 s to 13 s; second batch was from 15 s to 25 s; third batch was from 27 s to 37 s. In one batch process, rise and fall times of flow rate were given as 3 s and constant flow rate was kept for 2 s. The flow rate of flat parts was 2.5 × 10−4 m3･s−1. Note that forward and backward tilting motions before and after pouring did not include control motion to prevent the effect of sloshing on liquid behavior. The same as in the previous section, for each cases (II-1) and (II-2), the initial height of pouring mouth was determined as the lowest position using the proposed approach with the conditions: q = 0.00 m3･s−1; θ(0) = 15˚. In this paper, the initial height of pouring mouth Sz(0) was 0.25 m. After the first batch, starting height of the next batch was determined by finished position of the previous batch, which can start to pour immediately.
Reference and experimental results of repeated pouring, (a) Reference flow rate, (b) Weight of outflow liquid, (c) Pouring mouth position on Y-axis, (d) Pouring mouth position on Z-axis, (e) Falling position of outflow liquid, (f) Pouring mode transition (Case II-2).
Figure 12 shows a comparison of experimental results: (b) is weight of outflow liquid measured by load cell; (c) and (d) are pouring mouth position on Y and Z-axes; (e) is falling position of outflow liquid on the global axis measured by camera measurement system; (f) is pouring mode transition of the proposed approach (II-2). Also, in Fig. 12(b)–(e), a black circle is a marker of (II-1); a light gray cross is a marker of (II-2). Figure 12(e) shows that falling position control was achieved for each batch process by both approaches. Additionally, control errors were minimized to less than ±0.015 m when flow rate became constant.
Figures 13 and 14 show positional relationships between ladle and obstacles. In case (II-1), the conventional approach, the space between ladle and obstacles became wide in the course of the pouring process since the pouring mouth was kept at the initial height. If an adjustment ladle motion were introduced, the space may be minimized but cycle time of the pouring process may become longer. On the other hand, in the proposed approach (II-2) shown in Fig. 14, the height of pouring mouth was kept the lowest position of ladle during the pouring process. There were no collisions in the batch processes.
Ladle motion in repeated pouring (Case II-1), (a) 1st motion, (b) 2nd motion, (c) 3rd motion.
Ladle motion in repeated pouring (Case II-2), (a) 1st motion, (b) 2nd motion, (c) 3rd motion.
This paper shows a novel approach of motion trajectory generation of pouring ladle that achieves falling position control of outflow liquid with lower position of pouring mouth. In this approach, ladle motion equations were derived for three situation based on positional relationships between ladle and obstacles, and falling trajectory of outflow liquid. In addition, the switching condition was defined to switch among three pouring modes and keep the lowest position of ladle. Finally, the effectiveness of the proposed approach was verified by pouring experiments using water. It was confirmed that the proposed approach achieved falling position control of outflow liquid with high precision.
