Modeling and Identification of Pouring Flow Process With Tilting-Type Ladle for an Innovative Press Casting Method Using Greensand Mold

Transcription

1 Modeling and Identification of Pouring Flow Process With Tilting-Type Ladle for an Innovative Press Casting Method Using Greensand Mold Yusuke Matsuo*, Yoshiyuki Noda*, azuhiko Terashima*, unihiro Hashimoto**, Yuji Suzuki*** * Dept. of Production Systems Engineering, Toyohashi Univ. of Technology ** Sintokogio, Ltd. *** Aisin Takaoka Co., Ltd. Abstract Recently, a new method of a press casting using greensand mold was proposed by our group as a means of ferrous casting. This method has advantages in terms of energy savings and cost because a sprue cup and runner channel are not needed. Still, it is important to pour accurately and quickly in this method. Therefore, a feedforward outflow control is presented by using a mathematical model and inverse dynamics. The outflow is measured by a loadcell under the ladle. However, the loadcell data has a large uncertainty that is caused by the tilting motion. Therefore, a compensation for the loadcell is proposed. The determination of the back-tilting time is optimized by a dichotomy method. Finally, the effectiveness of the proposed system is shown through simulation and experiment. ey words: press casting, automatic pouring, outflow volume control, batch-type pouring, modeling 210/1

2 Introduction Recently, a new innovative casting method involving a press casting using greensand mold has been proposed and studied as a ferrous casting method by our research group. This method involves a process in which molten metal in a ladle is first poured into a lower mold, and then the upper mold is pressed down on the lower mold which fills the molten metal. This method has the advantage of low cost, because a sprue cup and runner channel are not needed. The cast is produced in this method without a runner channel, which is the source of much waste in the traditional approach. As a result, the pouring temperature can be reduced. Therefore, this new casting method costs less than the traditional approach and saves energy. However, it is important when using this method to accurately and quickly pour the molten metal into the mold. Therefore, outflow control of the liquid in the automatic pouring process plays a more important role in this new casting process. On tilting-type automatic pouring machines used in industrial plants, a teaching and playback method is used. However, much time is spent on the teaching in this process, and It is difficult to achieve target outflow with accuracy because the human error. Outflow control has been largely studied by using feedback control [1],[2]. In the literature [2], the velocity curve of the ladle s tilting is switched several times during pouring by using feedback information of the molten metal. However, the appropriate velocity is determined by the trial-and-error method in the experiment. On the other hand, our group proposed a feedforward control using a fun-type ladle. A fun-type ladle is a simple shape that seems to be easy to control. A better method is required to control ladles of general shapes. In addition, our previous paper provides a method for predicting the pouring quantity that flows out after a ladle is back-tilting to cut the pouring. However, because the previous method requires real-time measuring of molten metal weight and model calculation, applying it to real Industry seems difficult. Therefore, in this paper, outflow control of the liquid in an automatic pouring process is proposed. Modeling by using the system identification method is presented, and then feedforward control using the inverse dynamics of the pouring process is achieved. The automatic pouring machine has a servo-motor to drive a ladle and a loadcell for measuring outflow. However, the outflow measured directly by the loadcell has a large level of uncertainty, because the data includes the reaction force caused by the tilting. Therefore, a compensation method [3] incorporating a mathematic model of the loadcell is being newly proposed here. Finally, the effectiveness of the proposed system is shown through simulation and experiment. It is shown that the method proposed in this 210/2

3 paper can be applied to pouring systems used in industry, and the cost of molten metal can be reduced by the proposed optimum outflow control. Automatic Pouring System The laboratory water experimental apparatus and the industry molten metal apparatus used in this paper are shown in Figs.1(a) and (b) respectively. The rotary direction of the T-axis is driven by an AC servomotor in both apparatuses. The driving force of the AC servomotor can be amplified by reducing the gear ratio. The center of the ladle s rotation shaft is placed near the ladle s center of gravity. When the ladle is rotated around the center of gravity, the tip of the ladle nozzle (or mouth) moves in a circular trajectory. It is then difficult to pour the molten metal into a mold if the pouring mouth is moved by tilting. Then, the position of the tip of the ladle nozzle is maintained during pouring by means of a synchronous control of the Y- and Z-axes for rotational motion around the T-axis of the ladle [4]. The rotation angle is measured by an encoder installed in the AC servomotor. Y-, Z- and T-axes are also driven by AC servomotors, but the driving force of each of these motors is amplified through the ball screw mechanism. Each axis can be independently moved. The weight of fluid in a ladle is measured by a loadcell located under the pouring machine. The measured values from the encoder of each axis and the loadcell are input into a computer with an A/D converter. A control input is sent to a motor driver via a D/A converter, driving the AC servomotor. In the automatic pouring machine with water used as the substance being pouring, a control instruction is carried out in the DSP through the AD/DA converter and an up/down counter. In the apparatus used industrially in plants, a control instruction is carried out in the PLC through the AD/DA converter and an up/down counter. And the apparatus used in industry is controlled by position control. So, the tilting angle obtained by the water experiment is directly applied to the industry apparatus. A Series of Models of the Total Pouring Process In this section, modeling of the pouring process is carried out using water. The kinematical viscosity of the water (293[]) and the molten metal (1673[]) are [m 2 /s] and [m 2 /s], respectively. Therefore, the fluid behavior of the water is nearly identical to that of the molten metal. Here, two models, from the input voltage u(t)[v] for the motor to the flow rate q(t) are divided into two parts. 1. A model showing the relation between the input voltage of the AC servo motor u(t) and the tilting angular velocity of the ladle ω(t) : G M 2. A model showing the relation between the tilting angular velocity of the ladle ω(t) and the flow rate into a under mold q(t) : G q 210/3

4 G M (s) and G q (s) are respectively referred to here as the motor model and flow rate model. MOTOR MODEL : The relationship between the tilting angular velocity of the ladle and the input voltage to the motor is described in the following equation: G MT ΩT MT = = (1) U 1+ T s T, where ω (t)[rad/s] is the tilting angular velocity, u(t)[v] is the input voltage for the T-axis, MT [rad/(sv)] is the gain of the motor, and T MT [s] is the time constant of the motor. Further, the motor model of the X-, Y-, and Z-axis is described in the same form as in Eq. (1). FLOW RATE MODEL : In this paper, the ladle shown in Fig.2 is used for the pouring. Here, with regard to the fun-type ladle, controlling the tip of the ladle nozzle invariably, the surface area of the liquid in the ladle is constant while the ladle is tilted. Therefore, the pouring flow rate can be considered to be constant when a ladle is rotated at a constant angular velocity. Hence, the flow rate model can be described by a first-order transfer function as follows. G qf MT Q( s) qf = = (2) Ω 1+ T s T, where qf [m 3 /rad] and T qf [s] are the gain and the time constant of the funtype ladle s flow rate model, respectively. However, the surface area of the liquid in a practical ladle is not constant while the ladle is tilted. Therefore, the ladle s flow rate model can be expressed by varying the gain and the time constant of the fun-type ladle s flow model in correspondence with the tilting angle. The ladle s flow rate model can be described by the Linear Parameter Varying function (LPV model) as follows. qf Q( s) q ( θ ) Gq = = (3) Ω( s) 1+ T ( θ ) s, where q (θ )[m 3 /rad] and T q (θ ) are the gain and the time constant of the flow rate model, respectively. Derivation System of Feedforward Input for Outflow Control q 210/4

5 In this paper, a feedforward system is proposed as shown in Fig.3. The inverse model is used for deriving the control input. The inverse model is shown in Eqs.(4) and (5). 1 TM d u( t) = ω ref ( t) + ω ref ( t) M M dt (4) 1 Tqf ( θ ) d ω ref ( t) = qref ( t) + qref ( t) ( θ ) ( θ ) dt (5) qf In the outflow control, the flow cuts the pouring flow through ladle backtilting in order to obtain the target outflow. However, during the back-tilting, the pouring flow continues initially. Therefore, we must predict the flow quantity during back-tilting. We call this flow quantity the after-flow quantity. Thus, we must consider the after-flow quantity as we begin the back-tilting. In this paper, the optimum back-tilting timing is detected by a dichotomy method [5] that is a general numerical solution method for algebraic equations. A block diagram of the outflow control system is shown in Fig.4. In the simulation, the control input is obtained by a dichotomy method, and outflow control is realized by giving the control input to the apparatus by means of feedforward control. Flow cutting is implemented to switch from forward-tilting to back-tilting at a given time t s [s]. The outflow when the flow is cut at t s is denoted by f(t s ) [m 3 ]. Here, Eq.(6) is solved by a dichotomy method, where f ref [m 3 ] is the target outflow. qf f f ( t ) = 0 (6) ref Compensation System of Load Cell The gain q (θ ) and time constant T q (θ ) of the flow rate model as shown in Eq.(3) are obtained by experiment. The parameters are identified using the loadcell data. However, there is a problem in the loadcell data, as they are influenced by the acceleration in the ladle s up and down movement under synchronous control as shown in Fig.5. Therefore, the exact weight of the ladle cannot be measured. Therefore, in this paper a system of compensation for the loadcell system is proposed, as shown in Fig.6. The exact weight of the molten metal in a ladle is obtained by subtracting the output of the empty ladle model from that of the original loadcell. Here, the relationship between the Z-axis acceleration and the load cell output is described by the second order transfer function in the following equation. s 2 nl Fl lω Gl = = (7) 2 A s + 2ζ ω s + ω z l nl 2 nl 210/5

6 , where l [kg s 2 /m], ω nl [rad/s] and ζ l [-] are the gain, angular velocity and dumping rate of load cell model, respectively. The parameters are identified using a simplex method [6]. The evaluation function is described in Eq.(8). J = t 2 ( f l0 ( τ ) fl ( τ )) dτ (8) 0, where f l0 (t)[m 3 ] represents the experimental data of the loadcell when the empty ladle is moved. On the other hand, where f l (t)[m 3 ] represents the output if the empty ladle mold calculated in Eq.(7), F l (s)=l[f l (t)] and L[-] denotes the operator of the Laplace transformation. Good compensation results were obtained, and they are shown in Fig.7. Flow Model Parameter Identification The flow model parameter is identified by using the proposed loadcell compensation system. The parameter identification sequence is as follows; [Procedure of parameter identification]: 1. The ladle is tilted from the given angle of the ladle to 3[deg]. 2. The outflow is measured by using a loadcell when Step 1 is effectuated. 3. The obtained data in Step 2 are approximated in the first order system. 4. The gain and time constant of the first order system are same as the gain and time constant of the LPV model in the initial tilting angle. 5. The steps from Step 1 to Step 4 are repeated at every 1[deg] interval for the operable angle (from 20 to 42 [deg] in this paper). The identification results obtained by the above sequence are shown in Fig.8. Experimental Results and Discussion In this section, the experimental results of the outflow control are shown. The simulation and experimental results of the outflow control with water, using the water experimental apparatus, are shown in Fig.9. The designed flow rate reference is shown in Fig.9. Here, as the experimental condition, the initial angle, target outflow and back-tilting motion are 26[deg], 0.783[kg] and 3[deg] for 1.5 [s], respectively. As a result, the actual outflow is 0.758[kg] for reference 0.783[kg]. The pouring error is 3.2[%]. The control input used in the water experiment is straightforwardly given to the molten metal apparatus in industry. The experimental results obtained by using the molten metal are shown in Fig.10. As the experimental condition, the initial angle, target outflow and back tilting motion are 26[deg], 5.48[kg] and 3[deg] for 1.5[s], respectively. As a result, the actual outflow is 5.74[kg] for reference 5.48[kg]. The pouring error is 4.7[%]. 210/6

7 Both the results in laboratory and industrial results are considered to be good, because the pouring error is 5[%]. This means that scrap loss is less than 5[%], and then the yield rate is 95[%]. In the traditional casting process using greensand molding, the yield rate is below 50[%]. Hence, the proposed innovative process is very effective. Conclusion This study presented a series of outflow control systems for automatic pouring machine used in an industrial plant setting. The obtained results are summarized as follows. (1) The untrue loadcell data for Z-axis motion could be compensated for by the proposed loadcell compensation system. (2) The pouring machine could pour the target outflow with an error rate of about 5[%]. (3) The system proposed in this research involves sensorless feedforward control, which can be easily applied to the existing automatic pouring machine currently used in industry. References 1. azuhiko Terashima and en ichi Yano: Supervisory Control of Pouring Proscess, 66 th World Foundry Congress, Istanbul, Turkey, 6-9 Sept, Jiro Satoh, enichi Yoshida: Automatic pouring equipment for casting "Mel Pore system, Industrial Heating, 1992, vol.29, No.4, pp19-27 in Japanese 3. Janxin Sun, Yoshihiro Fujioka, Toshiro Ono, Takeyoshi Nagao and Toru ohashi: On the Fast and High Accurate Mass Measurement under the Conditions of Floor Vibration, Journal of The Japan Society for Precision Engineering, 1998, vol. 64, No.4, pp in Japanese 4. azuhiko Terashima, en ichi Yano, Yu Sugimoto and Mitsuaki Watanabe: Position Control of Ladle Tip And Sloshing Suppression During Tilting Motion in Automatic Pouring Machine, 10 th IFAC Symposium Automation in Mining Mineral and Metal Processing (MMM2001), Japan, Tokyo, 4-6 Sept, 2001, pp Brice Carnahan, H. A. Luther, James O. Wilkes: Applied Numerical Methods, John Wiley & Sons, Inc., L. Collatz, W. Wetterling: Optimization Problem, Spring-Verlag New York, /7

8 Table Table1 Model parameter Parameter Symbol Value Motor gain (T-axis) MT [rad/(sv)] Motor gain (Y-axis) MY [m/(sv)] Motor gain (Z-axis) MZ [m/(sv)] Time constant (T-axis) T MT [s] Time constant (Y-axis) T MY [s] Time constant (Z-axis) T MZ [s] Loadcell gain l [kg s 2 /m] Loadcell angular velocity ω nl [rad/s] Loadcell dumping rate ζ l 0.28 Figures X Z T Ladle AC servo motor and encoder Ladle Z T Y Loadcell Y (a) Laboratory Automatic Pouring Machine by Using Water AC servo motor and encoder (b) Industry Automatic Pouring Machine by Using Molten Metal Fig.1 Automatic Pouring Machine Outline Nozzl Dam Fig.2 Ladle Outline Fig.3 Structure of Pouring System and Inverse System 210/8

9 Fig.4 Schematic Diagram of Outflow Control Fig.5 Effect of Synchronous Control of Ladle on the Loadcell Sensor Fig.6 Compensation System of Loadcell Fig.7 Experimental Results by Compensation System of Loadcell 210/9

10 Fig.8 Flow Model Parameter Fig.9 Experimental Results by Using Water Fig.10 Experimental Results by Using Molten Metal 210/10