Abstract : Accurate measurement of backlash width is essential for effectively eliminating backlash through control algorithms. This paper summarizes several methods for determining backlash width: indirect measurement, no-load detection, and load detection. The application of photoelectric encoders in backlash width determination is highlighted. Keywords : vehicle tracking device; backlash; photoelectric encoder CLC Number: TP273 Document Code: A [align=center]The measurement methods of backlash in Tracking Device for Vehicles Ding Jiaoteng Xu Zunlei Luo Yao ( School of Electromechanical Engineering; Xidian University; Xian 710071 )[/ align ] Introduction With the advancement of science and technology, higher performance requirements are placed on the power transmission system in vehicle-mounted tracking devices. The main factor affecting system control performance is the widespread presence of various nonlinearities in the power transmission process. Among them, backlash nonlinearity is not only an indispensable nonlinearity in mechanical transmission but also a significant factor affecting the system's dynamic performance and steady-state accuracy. If the influence of backlash is not eliminated, in addition to causing output errors, the system will experience performance degradation or even instability due to limit cycle oscillations or impacts. Simultaneously, rigid gear collisions will generate severe oscillations and noise. Therefore, in-depth research on backlash nonlinearity in mechanical transmission systems has significant theoretical and engineering application value. To analyze the characteristics of backlash nonlinear systems, it is necessary to measure the specific parameters of the backlash component to effectively eliminate backlash through control algorithms. Therefore, accurately measuring the backlash width is essential. This paper lists several methods for measuring backlash width. 2. Indirect Measurement Method The backlash of the power transmission system is indirectly measured using the hysteresis angle of the fundamental component of the output signal. Currently, it is easy to accurately measure the hysteresis angle using high-precision displacement sensors and advanced data acquisition systems. The backlash is analyzed using the describing function method, a common analysis method for nonlinear systems. In the known describing function of a nonlinear system, the sinusoidal input signal of the nonlinear element is: The output signal e(t) = Asinωt is a non-sinusoidal periodic signal function. The output of the nonlinear element is approximated by the fundamental component x[sub]1[/sub](t) of the output signal. The waveform of the fundamental component of the output signal under the action of the sinusoidal input signal is shown in Figure 1: [align=center] Figure 1 Input-output waveform[/align] According to the reference [1], the hysteresis angle is: This shows that the hysteresis angle is related to the amplitude A of the input signal and the backlash C (C=2a) of the system. If a constant excitation signal is given, the hysteresis angle can be obtained by testing, and the backlash C can be solved. Theoretically, the formula for solving the backlash C can be derived, but it is cumbersome. In actual calculation, the approximate value of the backlash can be obtained by using the number-matching method through a computer. 3. No-load detection method A method to obtain the backlash width without an output measuring element [2]. One is the measurement of the semi-static backlash width. First, run the motor in the forward direction until its speed is zero, at which point it comes to a standstill. Then, apply a small torque pulse in the reverse direction to make the motor run in the opposite direction. Since this torque pulse is very small, the motor displacement is less than the dead zone width of the backlash, so no torque is transmitted to the output shaft. The measurement is of the entire angular displacement. Gradually increase the amplitude of the torque pulse. As long as the displacement is less than 2a of the backlash width, the angular displacement will increase with the increase of the torque pulse. Finally, as the gear starts to run in the reverse direction, only when the torque pulse is just transmitted to the output shaft or the load inertia will the subsequent torque pulses be absorbed by the load inertia. This allows us to determine the width of the backlash. One method is to obtain the backlash width by dynamic measurement [3]. The step response curve of the servo motor system is measured using Composer software. When the actual system makes a step response, the speed decreases from high to low. This phenomenon can be explained as the driving wheel running in the backlash when the motor starts. When the driving and driven wheels come into contact, they collide and the motor speed decreases. Since there are multiple gear pairs in the reducer and the load, the speed decreases from high to low multiple times. Therefore, the backlash width is estimated approximately based on the multiple attenuation values ​​h of the motor speed and the time period t. Considering the complexity of the actual system and the random disturbance of the load, multiple sets of data are obtained through multiple measurements and calculations, and their average value is taken. 4. Load detection method The traditional measurement method is to run the motor, observe the angle of load movement, and calculate the backlash width approximately by the transmission ratio. In this method, the backlash width value is related to the accuracy of the load change detection device. One approach is to use the laser source built into the vehicle-mounted tracking device to capture the distance the laser moves at a fixed position, and then measure the distance between the fixed position and the laser source to roughly determine the angle of load movement. However, this method is highly subjective and lacks accuracy. A backlash measurement method based on a photoelectric encoder was designed, which, after actual testing, demonstrates high measurement accuracy. The rotation direction of the photoelectric encoder is identified by the signals from input channels A_IN and B_IN, which differ by an electrical angle of 90º. The system uses an incremental photoelectric encoder, which emits 1000 pulses per revolution from channels A and B, operating at +5V with a high output pulse level of +4V. The counting of the output pulses is handled by a TI TMS320LF2407A DSP as the microprocessor. The DSP has an execution speed of 40MIPS, which can meet the real-time control requirements of the system; it has a FLASH program memory of up to 32K words, a built-in 16-channel 10-bit A/D conversion module, a serial communication interface module, two quadrature encoding circuits and several 16-bit general-purpose timers[4][5], which simplifies the peripheral hardware circuit. The interface circuit is shown in Figure 2. [align=center] Figure 2 Photoelectric encoder interface circuit[/align] First, fix the encoder and connect the encoder rotation shaft to the load so that the number of output pulses of the encoder corresponds to the rotation angle of the load. The structural model schematic diagram is shown in Figure (3). [align=center] Figure (3) Structural model schematic diagram[/align] First, let the motor slowly decelerate in the positive direction until the motor speed is zero, and then let the motor slowly move in the opposite direction. At the same time as the motor moves in the opposite direction, start the DSP to count the output pulses of the encoder. After the motor stops, the number of pulses counted is displayed through the digital tube, and the rotation angle of the load can be calculated. After the transmission ratio is converted, the difference between the rotation angle of the load and the rotation angle of the motor is the tooth gap between the motor and the load. The number of output pulses measured in the experiment is shown in Table (1). [align=center]Table (1) Measured data of output pulse count[/align] As can be seen from the table, the number of output pulses is 183 when the motor rotates 10 revolutions. Since the transmission ratio between the motor shaft and the load shaft is 100 in the experiment, the theoretical output pulses should be 200, which is 17 pulses less than the actual number. Therefore, the backlash width should be 3.06. Then, the backlash widths for the motor rotations from 20 to 80 revolutions are calculated as follows: 2.7, 1.8, 2.88, 3.6, 3.96, 3.24, and 2.34 . It can be considered that the backlash width of the system is 3.5. Conclusion The methods for measuring backlash width introduced in this paper can be selected according to experimental conditions. The backlash width measured by the photoelectric encoder is used as a parameter in the photoelectric automatic tracking algorithm. After actual verification, the tracking effect is good and the influence of backlash on the system is effectively eliminated. References [1] Yang Songfei, et al. A new method for measuring backlash in helicopter control system [J]. Measurement and Control Technology, 2006. [2]Dirk Gebler and Joachim Holtz,Fellow. Identification and Compensation of Gear Backlash without Output Position Sensor In High-Precision Servo Systems. Proceedings of the 24th Annual Conference of the IEEE Industrial Electronics Society.Vol.2,P662-6 [3]Jeffrey L.stein,Churn-Hway Wang.Estimation of Gear Backlash: Theory and Simulation,Journal of Dynamic Systems, Measurement, and control. 1998, Vol. 120 (3), P74-82 [4] Liu Heping, Wang Weijun, Jiang Yu, et al. TMS320LF240X DSP C language development and application [M]. Beijing: Beijing University of Aeronautics and Astronautics Press, 2003. [5] Texas Instruments Incorporated. TMS320LF2407A, LF2406A, 2F2403A, DSP datasheet, 2005. Author Biography: Ding Jiaoteng, male, born in 1981, Master, research direction: electromechanical control, contact address: P.O. Box 47, Xi'an University of Electronic Science and Technology, postcode 710071, telephone: 13572266220