Discussion on Mechatronic Driving Systems with Stepper Motors, Used in Micro-Mechanics
DISCUSSION ON MECHATRONIC DRIVING SYSTEMS WITH STEPPER MOTORS, USED IN MICRO-MECHANICS Stefan Vaduva, Anghel Constantin National Institute for Research and Development in Mechatronics and Measurement Technique, Sos. Pantelimon, Nr. 6-8, Sector 2, Bucharest, Romania
[email protected];
[email protected] Abstract - This paper deals with the mechatronic driving systems with stepper motors, used in micromechanics, their applications, features and the relationships between them. Also, a few types of experimental booths are discussed. Keywords: driving systems, stepper motors, inertial load, experimental booth for gears.
1. Introduction • Stepper motors are ideal interface between mechanical and electronic control applications that need precise and controlled movement. Mechatronic driving systems with stepper motors, used in micro-mechanics have the following advantages: - open-loop operation - univocity of conversion of the number of control pulses and incremental angular or linear displacement - compatibility with control - high positioning accuracy - enables starts, stops, and changes in directions of rotation without loss of steps - long lifespan and low maintenance; therefore, the are used together with gearing in integrated construction or classic applications: copiers and printers used in banking; dispensers; distributors; air conditioning equipment; applications for displacement and positioning of optical systems; 2D and 3D positioning tables, orientation and positioning equipment used in robotics; medical equipment; equipment for integrating physical quantities; devices for automotives and rolling stock bus locomotives and narrow lines); specific driving for military (guidance and positioning) applications and so on. The disadvantages of using stepper motors are: - angle step, so fixed increment of rotation for a given motor - relatively low rotational speed Parameters of driving systems for stepper motors - angle step, respectively precision angular positioning - shape, amplitude, duration and frequency of control pulses - limit torque - limit frequencies - couple (curve) frequency command parameter - load inertia
Stepper motor frequency-torque parameter
Fig. 1 The Figure 1 shows that: • possible operation with the risk of generating a very high engine noise (which may be due to vibrations of mechanical origin, aerodynamic rotor origin, due to air swirl of rotating machine products, or of magnetic origin, vibration of the magnetic circuit along the engine). • pestricted area due to resonance phenomenon manifested by loss of synchronism and steps (which is largely due to inertia of the system). • proper functioning of the starting and stopping of engine is done without loss of steps. • possible operation, with the risk of generating a very high engine noise (which may be due to vibrations of mechanical origin, aerodynamic rotor origin, due to air swirl of rotating machine products, or of magnetic origin, vibration of the magnetic circuit along the engine). • restricted area due to resonance that is manifested by loss of synchronism, thus steps (which is largely due to the inertia of the system).
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Discussion on Mechatronic Driving Systems with Stepper Motors, Used in Micro-Mechanics • Inertial load is a very important parameter of drives with stepper motors Load inertia is denoted by JL Load inertia relates to the rotor shaft, and influences not only periods of acceleration or deceleration, as well as control and optimal frequencies and resonance. Full load inertia (the moment of inertia is calculated reduced to the shaft) includes: - moment of inertia of the working device - moment of inertia of the kinematic elements (gears, levers, screws, move, etc.) - moment of inertia of the motor rotor Regarding the inertia of the system, the overall curve (characteristic) of start frequency (start) - inertia of the system, is shown in Fig.2
Fig. 2 It is noted that: - for low inertias, starting frequency is higher - an increase in inertia leads to lower starting frequencies Approximately, the starting frequency for a load with the following formula can be calculated:
(1) where: fs- the maximum starting frequency of the motor Jo - moment of inertia of the motor rotor JL - moment of inertia of workload F - starting frequency corresponding to the JL load Referring to the inertia of the system, the parameter which characterizes the driving system is the ratio of inertia:
(2) Or when using a micro-reducers, with a transmission ratio (ir) greater than one:
(3) This ratio differs depending on the type of construction of a family of stepper motors:
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2. Global parameters used in the construction of micro-reducers of driving systems with stepper motors The main feature that defines a micro-reducers is the ability to withstand a maximum torque in continuous operation for optimal lifetime. Generally, in the field of micro-mechanics, the maximum torque in steady state is of the order of tens of N ∙m, reaching a value of (5-10) N∙m depending on the workload. Each micro-reducer has a torque limit called breaking torque defined as the couple which would destroy the micro-reducer a first time. It is worth mentioning that using micro-reducers, we obtain the desired speed according to the kinematic system and increases torque and angular (or linear). resolution Also, micro-reducers, when used in combination with stepper motors, provide: - high positioning accuracy due to low resolution; - small amplitude vibrations; - low inertia at startup. • Requirements of micro-mechanics gears - maintaining constant transmission ratio and providing a coverage greater than one; - transmission ratio not affected by manufacturing inaccuracies, especially the change of distance between axles; - convenient positioning of the start and ending of engagement in order to ensure a high yield; - large radial clearance between the head and the inner circle of the wheel tooth manner; - can obtain very precise gear without great wing play, interchangeable assembly required to achieve large series of products; • Optimizing the number of stages and gear ratios of step, for obtaining a reduced minimum moment of inertia It is recommended that the first two - three steps of a module editor be the same, and small, as gears near the module influence most the total moment of inertia reduced to the motor shaft. For the next steps, will be chosen larger modules because the influence of the gears over the full moment of inertia is lower, and the resistance of teeth must be greater (transmitted momentum is increasing towards output), as well as to decrease the influence of flank clearance (by increasing the precision of execution). • Defining the transfer function and development of the mathematical model for which the transfer function has a minimum value The transfer function denoted by F defines mathematical geometric elements of a gear influence on the moment of inertia, and is denoted by F and is calculated as follows:
The Romanian Review Precision Mechanics, Optics & Mechatronics, 2014, No. 46
Discussion on Mechatronic Driving Systems with Stepper Motors, Used in Micro-Mechanics
(4) Ji = moment of inertia of the wheel 1, and; Jred= moment of inertia of the entire gear, reduced to the motor shaft (arboreal wheel). The optimum value of the transfer function is the minimum one for a transmission ratio itot; These values were obtained by deriving function F k , x compared to i1 (for two steps) and i1 and i2 (three steps), and i1, i2 and i3 (four steps) and equaling it to zero. 3. Experimental Method for Parameters of Mechatronic Systems
Determining
• Description of experimental booths Experimental booths were designed and created in two versions. Experimental booth (shown in Fig. 3) without transmission gears, with elastic clutch for
accurate transmission of angular movement from stepper motor to encoder (1000 pulses / rev), which monitors (measures) actual (real) angular movements of the stepper motor, including blocking it (without angular displacement, and called "headway" in specialized language). The booth is provided with a roll - a load through with which various resistance moments are introduced. Also, on the motor shaft can be mounted inertia masses, so can be determined the influence of the moment of inertia reduced to the motor shaft, over: Experimental booth with transmission gears shown in Fig. 4, which has a construction similar to booth 1, but with the following changes: • over each gear transmission axle, can be mounted different inertia masses which change the inertia of the mechatronic system reduced to the motor shaft; • the clutch of the stepper motor with gear transmission is mounted on the motor shaft by a pinion which is clutched with the first gear of transmission gears characteristic (curve).
Fig. 3 Experimental booth without transmission gears Both booths are connected to the electronic control unit of the stepper motor, for transmitting control pulses
with a frequency that is preset and for processing the data provided by the encoder.
Fig. 4 Experimental booth with transmission gears The Romanian Review Precision Mechanics, Optics & Mechatronics, 2014, No. 46
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Discussion on Mechatronic Driving Systems with Stepper Motors, Used in Micro-Mechanics resonance points of the mechatronic system and loss of steps.
• The software for parameters optimization runs on a PC or Notebook platform and is developed in LabVIEW and enables electronic communication function with the electronic driver, in order to establish the parameters and motor commands needed to determine the behavior in complex situations at different frequencies and eventually the detection of
• The user interface is shown in Figure 5 and is perfect for the requirements resulting from experiments made with a specific type of motor and gear transmission.
Fig. 5 • The conduct of experiments The experiments were carried out using the two types of stepper motors (with 0.4 Nm, and respectively 0.28 Nm) characteristic of the micro-mechanics field, both clutched and non-clutched to the gear transmission and by modifying the moment of inertia reduced to the motor shaft axle by adding inertial mass so as to have an inertial load higher by 25% and 50 %. Sampling rate of control frequency of stepper motors was 300 Hz, covering the maximum frequency of 5000 Hz to 3333 Hz for the 0.4 Nm and the 0.28 Nm motors. The sampling rate was chosen according to the general maximum frequency of the stepper motor and stemmed from 1/10 up to 1/50 of the frequency. A lower rate generates a more accurate momentum-torque characteristic, experimentally determined. Standard weights of 200 gr, 100 gr and 50gr were used and which could be fixed on a plate caught with a flexible wire that connects the roll-torque. Each command frequency of stepper motor corresponds, in synchronous operation (without loss of steps), to a number of pulses provided by the encoder (jointly with the motor shaft via a flexible coupling); For example, for a frequency of 300 Hz (100 rev / min), the encoder delivers 105 pulses.
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For each command frequency, more weights than the standard set were added weights to the plate until the encoder indication differed from the value of the computed frequency amount. This was seen on the desktop display, using the communication protocol presented. In this way, we could determine the characteristic points and trace the motor torquecommand frequency. For each command frequency, were performed a set of 5 trials taking the average value of torque which for which there was no synchronism between the motor control frequency indications and the indications of the encoder. Similar tests were performed for stepper motor coupled to the transmission gear. For testing optimization, a software was developed software which ensured that the last gear in the transmission conducted a limited number of full rotations (5 rotations). 4. Examples of families of characteristic torquecommand frequencies for various moments of inertia. Determination of oscillations when beginning the stepper motor control
The Romanian Review Precision Mechanics, Optics & Mechatronics, 2014, No. 46
Discussion on Mechatronic Driving Systems with Stepper Motors, Used in Micro-Mechanics
Fig. 6 Upon receiving a command pulse, the rotor of the stepper motor oscillates around the equilibrium position corresponding to an angular step as shown in the figure:
These intermediate positions can be detected and measured together with the encoder of the rotor of the motor, having a high resolution of 5 pulses at an angular step of the rotor of the stepper motor.
Fig. 7 The following phases can be noted: • upon receiving the impulse, the rotor tends to exceed the displacement angle corresponding to the angular step; • the inertia of the system makes that the further angular displacement decreases below the angular step; • after a few oscillations around the value of the angular step, their amplitude is reduced and it reaches its nominal value. 5. Conclusions This stand and software can be used with success to characterize stepper motors and gear To improve the analysis of oscillations and vibrations can attach an acceleration sensor (electronic driver allows the analog input for this) Can develop software to automate detection of critical points 6. Bibliography [1] P. I. Corke and M. C. Good "Dynamic Effects in Visual Closed-Loop Systems", IEEE Trans. on Robotics and Automation, vol. 12, no. 5, 1996;
[2] N. Matsui and T. Kosaka "Instantaneous Torque Analysis of Hybrid Stepping Motor", IEEE Trans. on Industry Applications, vol. 32, no. 5, 1996; [3] RUSU and I. Birou "Robust Servo Controller Against Load Variation for the Hybrid Stepper Motor Drive", 3rd International Symposium on advanced Electromechanical Motion Systems, 1999; [4] T. Burg , J. Hu , D. Dawason and P. Vedagarbha A Global Exponential Position Tracking Controller For a Permanent magnet Stepper Motor via Output Feedback, 1994; [5] M. Khawatmi "Improvement Closed Loop Control of Stepping Motors For Use in High Speed Positioning", 3rd International Symposium on advanced Electromechanical Motion Systems, 1999; [6] Lab-Volt CYBOT product manual, 1991; [7] J. N. Chiasson and R. T. Novotnak "Nonlinear Speed Observer for the Pm Stepper Motor", IEEE Transactions on Automatic Control, vol. 38, no. 10, 1993; [8] M. M. El-Atar , I. F. El-Arabawy and T. F. Refaat "General Modelling of Stepper Motors Steady State and dynamic Analysis and Performance", MEPCON\'97, 1997.
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