Magnetic springs using permanent magnets (PMs) have shown advantages in various fields. For instance, they are integrated into precision positioning actuators for passive gravity compensation, as well as into precision vibration isolators to reduce dynamic stiffness. In this article, an inverse design method of magnetic springs is proposed, which enables to customize the force–displacement relationship by shaping PMs. First, a concept of modulated magnetic spring is introduced, whose stator PMs are nonuniformly magnetized. The modulation method is developed to customize the force–displacement relationship. Second, uniformly magnetized PMs are shaped layer by layer to substitute the modulated PM. This process involves optimizing the size of each layer independently to generate a nearly equivalent force, resulting in a highly manufacturable special-shaped magnetic spring. Three design examples are presented and tested. The first two examples maintain a constant force and a constant negative stiffness, respectively, within 30 mm. The relative errors are only 3.7% and 2.3%, respectively, which are defined as the ratio between the maximum deviation and the mean value. The third example can compensate for the nonlinear force of the subsidiary structures and maintain a constant resultant force in 40 mm with a relative error of 2.9%. This method is confirmed to customize the force–displacement relationship for various applications.

Expert insights into the time-domain dynamic behavior of heavy-duty gearboxes form the foundations of design evaluation and improvement. However, in the existing lateral–torsional coupling (LTC) modeling method for gearboxes that is normally used for frequency-domain dynamic behavior, the meshing forces are modeled as spring dampers with fixed acting points on the meshing gears to simulate only the transient LTC effect, and thus the steady state characteristic in the time domain cannot be obtained due to the unrealistic distortion of positions and orientations as the gear angles increase. In this paper, a novel and generally applicable LTC modeling method for heavy-duty gearboxes, mainly planetary gear sets with floating components, is proposed by using space-fixed spring dampers with floating acting points on the meshing gears to study the time-domain dynamic response and to support the dynamic design of heavy-duty gearboxes. Based on the proposed method, a LTC model of a 2 megawatt (MW) wind turbine gearbox with floating components considering the time-varying meshing stiffness, bearing stiffness, torsional stiffness, and floating effect was established. The simulated results of representative components were in accordance with experimental results on a test rig, and dynamic behavior was calculated.

Piezoelectric actuators (PEAs) offer significant advantages in resolution, response velocity, and immunity to magnetic interference, making them crucial for high-precision applications such as nanopositioning, semiconductor manufacturing, and space exploration. However, their performance is affected by hysteresis nonlinearity. To overcome the limitations of conventional models in capturing rate-dependent hysteresis, we propose a novel model (called nBW) that incorporates rate-dependent terms into both the output and evolution equations. This model adapts to frequency changes, providing a more accurate representation of hysteresis across a wide frequency range. We introduce an efficient nonlinear least squares technique for parameter identification, which outperforms traditional methods such as genetic algorithms (GAs) and particle swarm optimization (PSO) in terms of both accuracy and efficiency. At 10, 50, and 100 Hz, the nBW's relative error norms are 0.95%, 1.21%, and 2.12%, respectively, compared with 2.28%, 4.76%, and 7.07% for the classical Bouc–Wen model. The nBW also demonstrates robust performance under composite-frequency inputs, with a 0.99% relative error. A hybrid control strategy, combining inverse model-based feedforward and PI feedback control, effectively minimizes tracking errors, enhancing PEAs’ precision under dynamic conditions. These results highlight the superior accuracy and control performance of the nBW. Future work will explore its extension to other smart materials.

The purpose of this paper is to accurately establish a model of a special vehicle driven by in-wheel motors (IWMs) and investigate its dynamic characteristics. This study proposes a novel integrated vehicle modeling strategy, focusing on the IWM and other key subsystems. Based on this strategy, the vehicle model is developed and simulated in ADAMS. The natural frequencies of the vehicle and transmission characteristics of key components are compared with MATLAB simulation results to validate the accuracy of the model. In the time-domain analysis, the vehicle system’s time-domain characteristics are obtained by using random road spectra of different road grades as excitations. Our simulation results demonstrate that vibration input can be reduced by between 97% and 99% after multi-stage vibration reduction. This work will provide relevant parameters for the design of special vehicles driven by IWMs.