DYNAMIC ANALYSIS OF DRIVE MECHANISM WITH FUNCTIONAL MODEL

DYNAMIC ANALYSIS OF DRIVE MECHANISM WITH FUNCTIONAL MODEL Yasunobu Uchino Department of Mechanical Engineering, Hosei University 3-7-2 Kajinocho, Koganei-shi, TOKYO, JAPAN Tatsuhito Aihara Department of Mechanical Engineering, Hosei University 3-7-2 Kajinocho, Koganei-shi, TOKYO, JAPAN Mitsuo Iwahara Department of Mechanical Engineering, Hosei University 3-7-2 Kajinocho, Koganei-shi, TOKYO, JAPAN Abstract The main characteristics of DC motors are large angular velocities and relatively small torques. However, in real system, relatively large torques and small angular velocities are required. Hence, it is necessary to introduce gears. In this paper, functional models are studied for DC motors and planetary gears and angular velocity fluctuation is considered. And, we designed motor bench and developed it. Simulation results were compared with experimental data to verify this functional models. Key words: Functional model, DC motor, planetary gear I. INTRODUCTION Recently, it has been required to shorten the product development period in companies. Therefore, the development method is shifting to the model-based development (MBD). However, actual models such as automobile and aircraft require new modelling method exceeding mechanical and electrical fields,which is too large to make afull modelling by the conventional method. Therefore, functional model was developed by Dr. Sumida as a new modeling method [-5].It can be visually depicts a block diagram with the use of physical function diagram imitating. And functional model is possible with an electrical and mechanical properties. This study is modeling a rotational machine systems by functional model as an example of the unification model between mechanical and electrical systems. The main characteristics of DC motors are large angular velocities and relatively small torques. However, in real system,relatively small angular velocities and large torques are required. Hence, it is necessary to introduce a gear.in this study we introduced a functional model of DC motor considering angular velocity nonuniformity with planetary gear. And, We was designed motor bench and developed it. Moreover, simulation result was compared with the experimental data to verify this modelling method. II. FUNCTIONAL MODEL A. Features of functional model Functional model is composed of the block diagram for explaining the function and the operation and for visual understanding of energy flow in the subjective system. Three kinds of physical values exist in it, namely the state values, the characteristics and the coefficients. The state values explain the states of system, and are divided into the flow value and the potential value. The product of the flow and the potential values becomes energy. Fig. shows the main symbols in the block diagram of functional model. Also characteristic in the functional model, represent the nature of the system or elements. In 5

addition, these are divided into those the consume the thing to store the energy []. Fig.2 shows example of characteristic in the functional model. conversion coefficient. When we multiply the unit of each up and down line of mechanical system and electrical system, both become energy [W]. III. FUNCTIONAL MODEL OF DC MOTOR A. DC motor modeling A mathematical model of the permanent magnet DC motor can be very often found in the literature. Here, it will be discussed briefly. Fig.4 shows DC Motor representation. A DC motor, the electrical energy supplied to the system by armature voltage V is converted into rotational energy driving a load with torque.the equation associated with such an electric circuit is given by Fig. Example of figure where is voltage applied to the armature terminals of the motor and is the resistance of the armature winding, and is a counter electro-motive detection. The motor exerts a torque, while supplied by voltage on the rotor. This torque acts on the mechanical structure, which is characterized by the rotor's moment of inertia and the viscous friction D. The toque is given by the equation. Fig. 2 Example of characteristic in the functional model B. Combination of the electric and mechanical system Electro mechanical energy conversion occurs when there is a change in magnetic flux linking a coil, associated with mechanical motion. Electric Motor, the input is electrical energy from the supply source, and the output is mechanical energy to the load. Fig.3 shows conversion of electric and mechanical system of motor for functional model. We made a combination model of the electric system and mechanic system that angular velocity ω was converted into voltage V, current I was converted into torque T in using motor fixed number which is a However, these equations don't consider torque exerted by the motor. The torque of the DC motor is varied by the rotation angle of the rotor. Therefore the generated torque values were assigned to the electrical system divided into sine component and the cosine component. Also, the size of the fluctuation amplitude led utilizing value the rotation angle of the theory and the rotor of the simple harmonic oscillation from being magnetically factors. Fig. 5 shows functional model of DC motor considering angular velocity fluctuation. B. Functional model of planetary gear We used a planetary gear that is modeled to the functional model by Dr.Sumida [2]. Fig.6 shows the 5

functional model of planetary gear. The modeled planetary gear is consisted of ring gear, a sun gear, and a carrier. In this study, Input is the sun gear, output is the carrier and the ring gear is fixed. Fig. 3 Conversion of the electric and mechanical system Electric system Mechanical system resistance resistance inductance viscous resistance moment of inertia Fig. 6 Functional model of planetary gear Source voltage Counter electromotive force Ⅵ Ⅳ Ⅲ Ⅱ Ⅰ Angular velocity Power supply DC Motor Torque τ Fig. 4 DC Motor representaion _sin A_nol T_A_c _cos Tmax_l Fig.7 Schematically illustrates experimental system R R2 /Ld Rd /Lq Mm /J Ci TABLE I PRM3 Fig. 5 Functional model of DC motor considering angular velocity fluctuation Rq PRM2 _sin PRM _sin NAME OF EXPERIMENTAL EQUIPMENT Ⅰ DC motor Ⅱ Coupling Ⅲ Shaft Ⅳ Rotary encoder(input side) Ⅴ Planetary gear Ⅵ Rotary encoder(output side) 52

Proceedings of 2nd International Conference on Mechanical and Production Engineering IV. EXPERIMENT AND SIMULATION A. Experimental and Simulation system Fig.7 schematically illustrates the motor bench with planetary gear system. Table Ⅰ shows name of experimental equipment. The actuator is the Mabuchi RS54-SH-6527 permanent magnet brush DC motor. It should be noted using a direct current stabilized power supply. On output shaft of the motor, a coupling was mounted. and fixed to the rotor shaft. This planetary gear is a Matex Inc. planetary gear LGU35-S-5SRS. This incremental encoder is a Sumtak ink.irs-32-2, with resolution of 2 pulses per revolution. It was measured that signal emitted from a rotary encoder in PXI of the measuring equipment and was handled it using LabVIEW. It was carried out simulation using a value of Table 2 and Table 3 in each DC motor and planetary gear physical characteristic. TABLE Ⅱ SPECIFICATION OF THE MOTOR Symbol Unit Value E V 2.5 R bat Ω L H R m Ω M N/m/A TABLE Ⅲ CHARACTERISTIC VALUES OF THE SIMULATION Symbol Unit Value - 325 32 35 3.2.4.6.8 2 Fig. 8 Experimental Steady-state angular velocity (input side).9.8.7.6.3. Fig. FFT analysis of experimental Steady-state Angular velocity (input side) 35 34 33 32 2 3 4 5 3 3.2.4.6.8 2 Fig. 2 Experimental Steady-state angular velocity (output side) B. Comparison between experiment and simulation Fig.8 shows experimental steady-state angular velocity (input side). Fig.9 shows simulation steady- 53

Angular velocity amplitude(rad/s) Angular velocity amplitude(rad/s) Proceedings of 2nd International Conference on Mechanical and Production Engineering state angular velocity (input side). Experimental the average of the angular velocity was 38.29(rad/s),which agree well with simulation result 37.92(rad/s). 325 32 35 3.2.4.6.8 2 Fig. 9 Simulation Steady-state angular velocity (input side).9.8.7.6.3. 2 3 4 5 Fig. FFT analysis of simulation Steady-state Angular velocity (input side) 35 34 33 32 3 3.2.4.6.8 2 Fig. 3 Simulation Steady-state angular velocity (output side) Fig.2 shows experimental steady-state angular velocity (output side).fig.3 shows simulation steadystate angular velocity (output side).here also, experimental the average of the angular velocity was 32.22(rad/s),which agree well with simulation result 3.96(rad/s).However In the experimental value, the angular velocity variation was observed large. Fig. shows FFT analysis of experimental steadystate angular velocity (input side). Fig. shows FFT analysis of simulation steady-state angular velocity (input side). Than FFT analysis result, angular velocity amplitude of the about six times as rotation frequency, which is a main component in the calculation and experimental values were in good agreement. Cause of rotation -5 order component occurring in the experiment is not clear, but presumed to be geometric factors such as the experimental apparatus. Fig.4 shows FFT analysis of experimental Steadystate Angular velocity (output side). Fig.5 shows FFT analysis of simulation Steady-state Angular velocity (output side). Actual Like the input side much difference was observed fluctuations of the angular velocity, about six times as rotation frequency is no longer seen in the simulation..9.8.7.6.3. 2 3 4 5 Fig. 4 FFT analysis of experimental Steady-state Angular velocity (output side).9.8.7.6.3. 2 3 4 5 Fig. 5 FFT analysis of simulation steady-state Angular velocity (output side) 54

V. CONCLUSION () Functional model of DC motor considering angular velocity fluctuation was developed (2) It was developed that functional model of drive system comprised of a motor and planetary gear (3) The experiment corresponding to the model was performed and it was compared and effectiveness of the development model was shown REFERENCES [] S Sumida, S., et al., A New Approach on Modeling for ProductDevelopment : Nonlinear System Basic Element, Transactions of thejapan Society of Mechanical Engineers Series C, Vol.65, No.632(998), pp.43-4 (in [2] Sumida, S., et al., Modeling for Functional Expression of RotaryApparatus : 2nd Report, Planetary Gear Train, Transactions of the Japan Society of Mechanical Engineers Series C, Vol.65, No.638 (999),pp.3926-3933 (in [3] Sumida, S., et al., Hierarchical Functional Model for AutomobileDevelopment : st Functional Deployment of Power Train, Transactions of the Japan Society of Mechanical Engineers Series C, Vol.68, No.67(22), pp.274-28 (in [4] Sumida, S., et al., Hierarchical Functional Model for AutomobileDevelopment : 2nd Functional and Mechanical Models of Engine,Transactions of the Japan Society of Mechanical Engineers Series C,Vol.68, No.67 (22), pp.282-289 (in [5] Sumida, S., et al., Hierarchical Functional Model for AutomobileDevelopment : 3rd Functional Model of Drivetrain, Transactions of thejapan Society of Mechanical Engineers Series C, Vol.68, No.67(22), pp.29-297 (in 55