The thrust fluctuation of linear motors is one of the key factors affecting their motion accuracy and stability. Quantitative analysis of this problem requires the combination of multidisciplinary knowledge such as electromagnetic theory, mechanical dynamics and signal processing. Taking permanent magnet synchronous linear motors as an example, its thrust fluctuation is mainly caused by physical mechanisms such as non-sinusoidal electromagnetic excitation, slot effect, end effect and mechanical assembly error. The slot effect is a periodic force fluctuation caused by the change of magnetic permeability when the stator teeth and the permanent magnet pole face move relative to each other. The frequency is related to the pole pitch and the number of teeth; the end effect is a non-periodic force disturbance caused by the sudden change of the magnetic field boundary conditions when the mover enters and exits the effective length of the stator. In addition, factors such as asymmetric winding parameters, uneven magnetization of permanent magnets, and guide rail straightness errors will also aggravate thrust fluctuations, making the thrust present complex time domain and frequency domain characteristics.
To quantify thrust fluctuations, a multidimensional indicator system needs to be established. The peak fluctuation amplitude is the difference between the maximum and minimum thrust values, which directly reflects the absolute intensity of the fluctuation; the relative fluctuation coefficient is the ratio of the peak fluctuation amplitude to the average thrust, which is convenient for horizontal comparison under different working conditions; the spectrum characteristics analyze the frequency components through Fourier transform, and can identify the main harmonic sources such as the cogging effect; the root mean square error is used to measure the discrete degree of thrust deviation from the average value, which is suitable for random fluctuation evaluation; dynamic response indicators such as overshoot and adjustment time in step response can reflect the impact of thrust fluctuation on the dynamic performance of the system. These indicators need to be selected according to the application scenario. For example, precision machining focuses on peak fluctuation and spectrum purity, while high-speed transmission focuses on root mean square error and dynamic response speed.
Electromagnetic simulation is the basic means to quantify thrust fluctuations. By establishing a motor model through finite element analysis software (such as Ansoft Maxwell), the magnetic field distribution and electromagnetic force at different positions can be accurately calculated. The modeling process includes defining the geometric structure of the mover, stator and air gap, setting material parameters such as permanent magnet remanence and core permeability, applying sinusoidal current excitation and simulating actual operating conditions, tracking the thrust change curve during the mover movement, and finally extracting the time domain waveform and spectrum through post-processing to separate the contribution of the cogging effect and the end effect. The simulation results can intuitively reveal the main source of thrust fluctuations, such as the cogging effect is manifested as a periodic sawtooth wave, and the end effect presents an asymmetric "edge distortion", providing a theoretical basis for structural optimization.
Experimental testing is a key link in verifying theoretical modeling. Common methods include direct measurement by force sensor, that is, connecting high-precision sensors in series between the mover and the load to collect thrust signals in real time. The sampling frequency needs to be 5-10 times higher than the fluctuation frequency to avoid aliasing; the indirect derivation law of speed and acceleration measures the mover speed through a laser interferometer, and combines the inertial force formula to reverse the thrust, but it is necessary to accurately compensate for friction and guide rail resistance; frequency domain analysis uses fast Fourier transform to decompose the thrust signal spectrum, identify the main frequency components and harmonic amplitudes, such as the main frequency of the cogging effect is usually related to the speed, pole pitch and number of slots. In the experiment, variables need to be controlled to compare the fluctuation differences under different working conditions to ensure the accuracy of the simulation model.
The impact of thrust fluctuation on system performance varies depending on the application scenario. In the field of precision machining, such as lithography machines and semiconductor packaging equipment, micron-level thrust fluctuations may cause machining trajectory deviations and affect device accuracy; in high-speed transmission systems such as maglev trains and linear motors modules, low-frequency fluctuations may cause mechanical resonance and reduce running stability; in servo control systems, thrust fluctuations increase the difficulty of controller design, and if they are not effectively suppressed, they may cause system oscillation. When quantifying the impact, the "thrust fluctuation-error transmission" model can be used for analysis. For example, in the feed system, the thrust fluctuation is converted into position error through the system stiffness, and the formula is Δx=ΔF/k, so as to evaluate the specific impact on the processing accuracy.
Based on the results of quantitative analysis, the technical path to suppress thrust fluctuation can be designed in a targeted manner. In terms of structural optimization, the permanent magnet skew pole or Halbach array design can weaken the fundamental frequency component of the slot effect, the stator core adopts a slotless structure or fractional slot winding to reduce the slot harmonics, and the magnetic shielding of the mover end can reduce the magnetic field distortion caused by the end effect; the control algorithm compensation includes feedforward compensation, adaptive control and frequency domain harmonic suppression, such as pre-injecting reverse compensation signals according to the fluctuation curve measured offline, or dynamically adjusting the current using real-time data; process improvement involves high-precision magnet processing and assembly, guide rail straightness calibration, to reduce the influence of uneven magnetization, mechanical eccentricity and air gap changes.
The quantitative analysis of thrust fluctuations of linear motors will develop in the direction of multi-physics field coupling and intelligent diagnosis. Multi-physics field modeling needs to be combined with temperature field and vibration field analysis to study the impact of thermal deformation and mechanical coupling on thrust fluctuations; online monitoring technology based on sensor fusion and machine learning algorithms can achieve real-time identification and early warning of fluctuations; sensorless control indirectly predicts fluctuations through back-EMF estimation or flux observation to reduce system costs. At the same time, the emergence of new motor topologies such as transverse flux linear motors and superconducting linear motors has posed new challenges to fluctuation quantification methods and suppression technologies, requiring further integration of electromagnetic, mechanical, and control multidisciplinary theories to achieve breakthroughs. In short, accurately quantifying thrust fluctuations and achieving effective suppression is the core link in improving the performance of linear motor systems, and is of great significance to the development of precision manufacturing, high-speed transmission and other fields.
