A fast and non-destructive method for identifying the resonant frequency of a heavy-duty mechanism

Abstract

This invention proposes a rapid and non-destructive method for identifying the resonant frequency of heavy-duty mechanisms. The load-end speed curves and motor-end speed curves under closed-loop and open-loop conditions at the motor end are obtained using the speed step response method and the current step response method, respectively. By performing an FFT transform on the two speed curves, the resonance peak is obtained, allowing for rapid measurement of the structural resonant frequency and the combined resonant frequency. This method eliminates the need to purchase an additional resonance analyzer, reducing measurement costs, and avoids the damage to large, heavy-duty servo mechanisms caused by sinusoidal frequency sweep measurements. It can not only be used for rapid identification of structural resonant frequencies but also to guide the design of servo controllers.

Description

Technical Field

[0001] This invention belongs to the field of servo systems, specifically relating to a method for rapid and non-destructive identification of the resonant frequency of a heavy-duty mechanism. Background Technology

[0002] Structural resonance has a significant impact on radar servo systems, especially those with high load inertia, such as large-scale phased array radar servo systems for telemetry and control. Structural resonance is generally considered to be caused by the flexibility of the drivetrain and the load inertia. The impact of structural resonance characteristics on servo system performance is manifested in the limitation of the servo system bandwidth. Structural resonance can also couple with the electrical system, resulting in a low-frequency, low-damping-coefficient combined resonance in the servo system. This combined resonance acts on the speed loop at the radar motor end, directly affecting the dynamic performance of the speed loop. For shipborne telemetry and control radar, it also limits the effective improvement of ship roll isolation. Therefore, it is necessary to identify the characteristics of structural resonance and combined resonance to lay the foundation for the bandwidth design of each component of the servo system and the tuning of controller parameters. Summary of the Invention

[0003] To address this, this invention proposes a rapid and non-destructive method for identifying the resonant frequency of heavy-duty mechanisms. First, it establishes the theoretical relationships between motor-end speed and current, and between load-end speed and motor-end speed in an open-loop configuration. Based on this, a step response method is proposed to measure the resonant frequency. The load-end speed curves and motor-end speed curves in both closed-loop and open-loop states are obtained using the speed step response method and the current step response method, respectively. By performing an FFT transform on the two speed curves, the resonance peak is obtained, allowing for the rapid measurement of the structural resonant frequency and the overall resonant frequency. This invention eliminates the need to purchase an additional resonance analyzer, reducing measurement costs and avoiding damage to large, heavy-duty servo mechanisms caused by sinusoidal frequency sweep measurements. It can not only be used for rapid identification of structural resonant frequencies but also to guide the design of servo controllers.

[0004] The present invention provides a method for rapid and non-destructive identification of the resonant frequency of a heavy-duty mechanism, which specifically includes the following steps:

[0005] 1) Resonance generation

[0006] The stiffness of an electromechanical servo system is represented by torsional stiffness. Stiffness affects the system's dynamic performance by influencing its resonant characteristics. The structural resonant frequency ω of the electromechanical servo system is defined. l and damping ξ l Comprehensive resonant frequency ω z and damping ξ z ,but:

[0007]

[0008] In the formula, K ml For the torsional stiffness of the system, Jm and J l The moments of inertia of the motor and the load, respectively, C l is the velocity damping coefficient.

[0009] Define motor speed ω m (s) and electromagnetic torque M m (s), motor terminal speed ω m (s) and antenna terminal rotation speed ω l The transfer function relationships between (s) are expressed as follows:

[0010]

[0011] In the formula, i0 is the deceleration ratio of the system.

[0012] The response curve of a motor under a step speed is a typical unit step response curve of a second-order underdamped system. Its transient process is a damped oscillation process, and the oscillation frequency is the structural resonant frequency. The response curve under a unit electromagnetic torque step is approximately considered as a damped oscillation curve superimposed on a ramp curve, and the damped oscillation frequency is the combined resonant frequency.

[0013] 2) Rapid identification of resonant frequency

[0014] First, keep the antenna stationary and assume that it is not subject to any external load. Then, open the speed loop and close the current loop only, setting the speed command value to 0. At this time, the current loop setpoint is also 0. Based on this, give a step torque current and observe the motor speed output curve. Then, perform an FFT transformation on the motor speed output curve. The resonance peak of the amplitude-frequency characteristic is the comprehensive resonant frequency.

[0015] Furthermore, before identifying the resonant frequency, the motor speed signal needs to be processed. Specifically, the motor speed curve without considering the comprehensive resonance is subtracted from the motor speed curve with the comprehensive resonance considered. Then, the error curve is transformed by FFT. At this time, the amplitude-frequency characteristic only has a peak near the comprehensive resonant frequency. The low-frequency signal introduced by the ramp signal is eliminated, thereby avoiding misjudgment of the comprehensive resonant frequency.

[0016] Furthermore, when the antenna remains stationary and there is no external load, given the speed of the step motor, the speed closed-loop control system reacts quickly, enabling the motor to quickly reach and maintain the given speed. Through the action of the transmission structure, the speed of the antenna-end resolver can be obtained. Then, FFT transformation is performed on the speed of the antenna-end resolver, and the resonant peak of the amplitude-frequency characteristic is identified as the structural resonant frequency.

[0017] Since the angle at the antenna end is usually measured by a resolver, if you want to obtain the rotational speed of the resolver at the antenna end, you need to perform differential processing on the angle output curve.

[0018] The beneficial effects of this invention are as follows:

[0019] 1. Establish a theoretical model of the radar servo drive system that includes the structural resonant frequency. The structural resonant frequency and the combined resonant frequency of the drive system can be obtained by using the current and speed step response curves, respectively.

[0020] 2. By utilizing existing components of the servo control system, such as drivers, motors, and transmission systems, information such as resonant frequency can be obtained through the step response method, without the need for additional hardware.

[0021] 3. Compared with the resonant frequency measurement method using a resonant analyzer, this method simplifies the measurement system architecture and greatly reduces hardware costs because it does not require additional hardware. Attached Figure Description

[0022] Figure 1 A block diagram of electromechanical transmission considering structural torsional stiffness.

[0023] Figure 2 The graph shows the response curves for a unit electromagnetic torque step jump and a motor speed step jump.

[0024] Figure 3 This is a schematic diagram of the integrated resonant frequency test principle for a radar servo system.

[0025] Figure 4 The transfer function block diagram of the radar servo system integrated resonant frequency test system is shown.

[0026] Figure 5 This is a diagram illustrating the process of identifying the overall resonant frequency.

[0027] Figure 6 The flowchart shows the process of identifying the overall resonant frequency.

[0028] Figure 7 This is a schematic diagram of the test principle for the structural resonant frequency of a radar servo system.

[0029] Figure 8 The transfer function block diagram of the radar servo system structural resonant frequency test system is shown.

[0030] Figure 9 This is a graph showing the pitch motor speed curve when the enable is momentarily turned off.

[0031] Figure 10 The pitch antenna speed curve when a 15% step motor speed command is given.

[0032] Figure 11 The amplitude-frequency response curve of the pitch antenna speed when given a 15% step motor speed command. Detailed Implementation

[0033] The technical solutions in the embodiments of the present invention will be clearly and completely described below. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0034] The fast and non-destructive identification method for the resonant frequency of heavy-load mechanisms proposed in this invention specifically includes the following steps:

[0035] 1) Analysis of the resonance generation mechanism

[0036] For electromechanical servo systems with low resonant frequencies, such as high-inertia radar servo systems, the impact of system stiffness on the dynamic performance of the servo system cannot be ignored. The stiffness of electromechanical servo systems is usually expressed as torsional stiffness. Stiffness mainly affects the dynamic performance of the system by influencing its resonant characteristics. A block diagram of an electromechanical drive system considering torsional stiffness is attached. Figure 1 As shown in the figure, R and L are the equivalent resistance and inductance of the motor, respectively.

[0037] Among them, the structural resonant frequency ω l and damping ξ l Comprehensive resonant frequency ω z and damping ξ z It can be represented as:

[0038]

[0039] In the formula, K ml For the torsional stiffness of the system, J m and J l The moments of inertia of the motor and the load, respectively, C l is the velocity damping coefficient.

[0040] Motor speed ω m (s) and electromagnetic torque M m (s), motor terminal speed ω m (s) and antenna terminal rotation speed ω l The transfer function relationship between (s) can be expressed as follows:

[0041]

[0042] In the formula, i0 is the deceleration ratio of the system.

[0043] The response curves for a unit electromagnetic torque step and a unit motor speed step are shown in the attached figure. Figure 2As shown in the figure, the response curve under a unit motor speed step is a typical unit step response curve of a second-order underdamped system. Its transient process is a damped oscillation process, and the oscillation frequency is the structural resonant frequency. The response curve under a unit electromagnetic torque step can be approximated as a damped oscillation curve superimposed on a ramp curve, and the damped oscillation frequency is the combined resonant frequency.

[0044] 2) Rapid identification method for resonant frequency

[0045] Velocity step response and electromagnetic torque step response are among the most commonly used methods for testing the dynamic performance of servo systems, and are often used to evaluate the system's bandwidth, stability, and accuracy. (Appendix) Figure 3 The diagram illustrates the test principle for integrated resonance identification within the control framework of an existing radar servo system. The test principle involves first keeping the antenna stationary and assuming it is not subject to external load. Then, the speed loop is opened, while only the current loop is closed, with the rotational speed command set to 0. At this point, the current loop setpoint is also 0. Based on this, a step torque current is applied (to prevent excessive current from causing uncontrollable acceleration of the antenna, the current value is typically 5%-10% of the rated value). Since the current loop's response is much faster than the speed response, it can be assumed that the step electromagnetic torque has already been applied before the antenna begins to rotate. (See attached diagram.) Figure 3 Establish the transfer function of the test system, as shown in the appendix. Figure 4 As shown, observe the motor speed output curve; theoretically, it should be consistent with the attached curve. Figure 2 The step electromagnetic torque response curve is similar. Then, performing an FFT transform on the motor speed output curve and identifying the resonance peak of the amplitude-frequency characteristic yields the comprehensive resonant frequency.

[0046] Because the motor speed output curve includes an approximate ramp output, performing an FFT on the ramp signal reveals a significant low-frequency component that may mask the resonant peak. Therefore, before identifying the resonant frequency, the motor speed signal needs to be processed as shown in the attached diagram. Figure 5 As shown. The principle is to subtract the motor speed curve without considering the comprehensive resonance from the motor speed curve with the comprehensive resonance in mind, and then perform an FFT transformation on the error curve. At this time, the amplitude-frequency characteristic only has a peak near the comprehensive resonance frequency, and the low-frequency signal introduced by the ramp signal is eliminated, thereby avoiding misjudgment of the comprehensive resonance frequency.

[0047] The flowchart of the integrated resonant frequency identification process is attached. Figure 6 As shown, the above process can be used to identify the overall resonant frequency.

[0048] The transfer function from the motor speed to the load antenna speed is a typical transfer function of a second-order underdamped system. (See attached image.) Figure 2As shown, when the step motor speed is given, the antenna speed will exhibit damped oscillations, and the oscillation frequency is the structural resonant frequency. Therefore, a structure as shown in the attached figure can be constructed. Figure 7 The structural resonant frequency testing system shown operates on the following principle: when the antenna remains stationary and there is no external load, a given step motor speed is applied. The speed closed-loop control system reacts rapidly, causing the motor to quickly reach and maintain the given speed. Through the transmission structure, the rotational speed of the antenna end resolver can be obtained. Since the antenna angle is usually measured through the resolver, differential processing of the angle output curve is required to obtain the antenna rotational speed. Then, an FFT transformation is performed on the antenna rotational speed, and the resonant peak of the amplitude-frequency characteristic is identified as the structural resonant frequency.

[0049] In step motor speed testing, the conventional step response test procedure can be referenced, with the given step speed being approximately 10-15% of the rated value. Simultaneously, to excite the structural resonant frequency, the speed loop bandwidth must be sufficiently large, greater than 0.7 times the structural resonant frequency. However, to ensure high steady-state accuracy of the motor speed, the speed loop bandwidth cannot be excessively large. Since the motor's inertia is smaller than the load's inertia, after designing appropriate speed controller parameters, the motor speed response can be considered sufficiently fast compared to the load speed, quickly reaching the given speed and stabilizing it with high precision. At this point, the antenna speed is almost zero. Similarly, from the attached... Figure 7 Establish the transfer function of the test system, as shown in the appendix. Figure 8 As shown, observe the load speed output curve; theoretically, it should be consistent with the attached curve. Figure 2 The speed response curve of the step motor is similar.

[0050] To verify the effectiveness of the proposed testing method, an experimental study was conducted on the pitch axis of a radar. The moment of inertia of the motor on the pitch axis is J. m =0.07kgm 2 The moment of inertia of the load referred to the motor is J. l =0.32kgm 2 If the resonant frequency of the structure is ω l =3Hz, the overall resonant frequency is ω z = Around 7Hz.

[0051] First, a comprehensive resonant frequency test experiment was conducted. The test method here differs from previous ones: first, the motor speed was controlled at a constant speed, then the motor was momentarily turned off and on again. This is equivalent to applying a step load torque, similar to applying a step electromagnetic torque. Therefore, according to the above analysis, the motor speed curve is also a ramp curve superimposed with a damped oscillation curve, and the oscillation frequency is the comprehensive resonant frequency. The motor speed curve was obtained using the above method, as shown in the attached figure. Figure 9As shown, the oscillation period is approximately 0.164s, from which the overall resonant frequency of the pitch axis can be calculated to be approximately 6.1Hz.

[0052] When a 15% step motor speed is given, the antenna speed curve can be obtained similarly as shown in the attached figure. Figure 10 As shown, under the step motor speed, the antenna speed output curve is a damped oscillation curve with an oscillation period of approximately 0.33s. Performing an FFT transform on the antenna speed curve yields the amplitude-frequency response curve, as shown in the attached figure. Figure 11 As shown in the figure, the amplitude-frequency response curve shows a resonance peak near 3Hz, which indicates that this frequency is the structural resonant frequency.

[0053] This invention is not limited to the specific embodiments described above, and various modifications and variations are possible. Any modifications, equivalent substitutions, or improvements made to the above embodiments based on the technical essence of this invention should be included within the scope of protection of this invention.

Claims

1. A method for rapid and non-destructive identification of the resonant frequency of a heavy-duty mechanism, characterized in that: Specifically, the following steps are included: 1) Resonance generation The stiffness of an electromechanical servo system is represented by torsional stiffness. Stiffness affects the system's dynamic performance by influencing its resonant characteristics. The structural resonant frequency ω of the electromechanical servo system is defined. l and damping ξ l Comprehensive resonant frequency ω z and damping ξ z ,but: In the formula, K ml For the torsional stiffness of the system, J m and J l The moments of inertia of the motor and the load, respectively, C l This is the velocity damping coefficient; Define motor speed ω m (s) and electromagnetic torque M m (s), motor terminal speed ω m (s) and antenna terminal rotation speed ω l The transfer function relationships between (s) are expressed as follows: In the formula, i0 is the deceleration ratio of the system; The response curve of a motor under a step speed is a typical unit step response curve of a second-order underdamped system. Its transient process is a damped oscillation process, and the oscillation frequency is the structural resonant frequency. The response curve under a unit electromagnetic torque step is approximately considered as a damped oscillation curve superimposed on a ramp curve, and the damped oscillation frequency is the comprehensive resonant frequency. 2) Rapid identification of resonant frequency First, keep the antenna stationary and assume that it is not subject to any external load. Then, open the speed loop and close the current loop only, setting the speed command value to 0. At this time, the current loop setpoint is also 0. Based on this, give a step torque current and observe the motor speed output curve. Then, perform an FFT transformation on the motor speed output curve. The resonance peak of the amplitude-frequency characteristic is the comprehensive resonant frequency.

2. The method for rapid and non-destructive identification of the resonant frequency of a heavy-duty mechanism according to claim 1, characterized in that: Before identifying the resonant frequency, the motor speed signal needs to be processed. Specifically, the motor speed curve without considering the comprehensive resonance is subtracted from the motor speed curve with the comprehensive resonance considered. Then, the error curve is transformed by FFT. At this time, the amplitude-frequency characteristic only has a peak near the comprehensive resonant frequency. The low-frequency signal introduced by the ramp signal is eliminated, thus avoiding misjudgment of the comprehensive resonant frequency.

3. The method for rapid and non-destructive identification of the resonant frequency of a heavy-duty mechanism according to claim 1, characterized in that: When the antenna remains stationary and there is no external load, given a step motor speed, the speed closed-loop control system reacts quickly, enabling the motor to quickly reach and maintain the given speed. Through the action of the transmission structure, the speed of the antenna resolver can be obtained. Then, FFT transformation is performed on the speed of the antenna resolver, and the resonant peak of the amplitude-frequency characteristic is identified as the structural resonant frequency.

4. The method for rapid and non-destructive identification of the resonant frequency of a heavy-duty mechanism according to claim 3, characterized in that: Since the angle at the antenna end is usually measured by a resolver, if you want to obtain the rotational speed of the resolver at the antenna end, you need to perform differential processing on the angle output curve.

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