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Large-size gear profile grinder is extremely important for high-accuracy machining of large-scale and high-performance gears. A lot of heat is generated during the service process, leading to thermal errors of large-size gear profile grinder. In recent years, the data-based modeling and prediction methods have been widely used in manufacturing systems to control thermal errors. However, a limited bandwidth and latency characteristic of industrial Internet has brought serious challenges to the real-time and efficient processing of a large-volume data. To solve the above problems, a digital twin system of thermal error control is proposed for large-size gear profile grinders. The theoretical-based modeling method is used to prove the memory behavior, and then the feasibility of applying gated recurrent unit (GRU) to thermal error control is demonstrated due to its strong long-term memorizing capability. Then the hyper-parameters of GRU model is optimized by an improved bat algorithm (IBA), and the self-learning IBA-GRU error model is proposed. Finally, a digital twin system of thermal error control is established based on a new haze-cloud computing architecture to improve the executing efficiency, and the self-learning IBA-GRU error control model is embedded into the digital twin system. With the implementation of the digital twin system, the reduced percentages for the maximum tooth profile tilt deviations of $$f_{H\alpha l}$$ and $$f_{H\alpha r}$$ for the left and right tooth flanks are 58.43% and 64.16%, respectively, and the reduced percentages for the maximum total tooth profile deviations of $$F_{\alpha l}$$ and $$F_{\alpha r}$$ for the left and right tooth flanks are 28.78% and 34.53%, respectively. The saved ratio of the transferred data is up to 76.30% in 5 months. The executing efficiency of the digital twin system with IBA-GRU as control model is higher than that with other models and architectures.

Heavy metal pollution in soil is a global problem with serious impacts on human health and ecological security. Phytoextraction in phytoremediation, in which plants uptake and transport heavy metals (HMs) to the tissues of aerial parts, is the most environmentally friendly method to reduce the total amount of HMs in soil and has wide application prospects. However, the molecular mechanism of phytoextraction is still under investigation. The uptake, translocation, and retention of HMs in plants are mainly mediated by a variety of transporter proteins. A better understanding of the accumulation strategy of HMs via transporters in plants is a prerequisite for the improvement of phytoextraction. In this review, the biochemical structure and functions of HM transporter families in plants are systematically summarized, with emphasis on their roles in phytoremediation. The accumulation mechanism and regulatory pathways related to hormones, regulators, and reactive oxygen species (ROS) of HMs concerning these transporters are described in detail. Scientific efforts and practices for phytoremediation carried out in recent years suggest that creation of hyperaccumulators by transgenic or gene editing techniques targeted to these transporters and their regulators is the ultimate powerful path for the phytoremediation of HM contaminated soils.

A geometrical-mechanical-thermal interaction model was proposed to predict the thermal contact resistance (TCR) between the bearing inner ring and shaft journal. By introducing the randomness of asperity distribution, the rough surface of bearing rings was characterized by the 3D Weierstrass-Mandelbrot (W-M) function and the fractal parameters were identified by the structure function method. A multiscale contact mechanics model was then proposed to compute such contact parameters as the actual contact area and contact pressure. Then the predictive model of TCRs was proposed based on the characterization method of micromorphology and the multiscale contact mechanics model to predict the TCR between the bearing inner ring and shaft journal. The results obtained by the proposed model were compared with that without introducing the surface contact coefficient and a series of experimental data. The effects of such parameters as the interference fit, the surface roughness, and the asperity top curvature radius on the TCR were investigated. The results showed good agreement, demonstrating the validity of the model. The TCR decreased with the interference fit because the actual contact area was increased. Moreover, the TCR increased with the surface roughness because the actual contact area was reduced. The results obtained by assuming that asperities had different top curvature radii was greater than that assuming that asperities had mean top curvature radii.

To improve the simulation accuracy of the traditional transient thermal characteristics analysis model (TCAM) of the ball screw feed drive system (BSFDS), the optimization method of the thermal boundary conditions (TBCs), including the thermal loads, the convective heat transfer coefficient and the thermal contact resistance (TCR), was proposed. A multi-objective and multi-parameter optimization model was established based on the hybrid response surface (HRS) and a multi-objective genetic algorithm (MOGA) was developed to optimize the above TBCs. To simulate the thermal characteristics of the BSFDS under different working conditions, the generality of the method was extended to predict the TBCs under different feed rates. To validate the effectiveness of the method, the thermal characteristic experiments of BSFDS were conducted. The results showed that the simulation error for the temperature field was reduced from 25% to 10% and that the simulation error for the thermal elongation was reduced from 30% to 11%.

The contact stiffness of the spindle/tool holder is essential for the cutting stability of the spindle system because the elastic connection of the spindle/tool holder interface determines the dynamic characteristics of the spindle system. To predict the dynamic characteristics of the spindle system at the design stage, an analytical model of the contact stiffness of the spindle/tool holder interface was proposed based on the fractal theory and the multi-scale contact mechanics model to consider the combined effect of the cutting force and drawbar force on the contact stiffness. The fractal theory was used to characterize the micro-morphology of rough surfaces and the fractal parameters were identified by the power spectrum method. For the contact of two rough curved surfaces, the surface contact coefficient was introduced into the multi-scale contact mechanics model to correct the contact stiffness, the actual contact area and the contact stress. To verify the validity of the method, the experiments were conducted and the results showed that the modeling error of the contact stiffness was reduced from 25.13% to 4.72% by the proposed method. Finally, the effect of such factors as the cutting force, the mean roughness, the material properties, the preload and the temperature variation on the contact stiffness was discussed. The contact stiffness of spindle/tool holder interface increased with the cutting force and the drawbar force and that the contact stiffness decreased with the mean roughness. Moreover, the shear contact stiffness increased with the equivalent elastic modulus, the interference fit and the temperature. The conclusion was drawn that the model can be used to predict the contact stiffness of the spindle/tool holder interface at the design stage.

The neglection of thermal-structure interaction of high-speed spindle system may lead to the modeling error of the thermal characteristics. To improve the modeling accuracy, the thermal-structure interaction mechanism was analyzed and the closed-loop iterative modeling method of thermal characteristics was proposed to modify the heat sources and thermal boundary conditions of the spindle system in each substep. The heat generation of bearings and built-in motor, the convective coefficients and the thermal contact resistances (TCRs) of bearing joints were computed. The heat generation of bearings was calculated by the SKF bearing thermal model and the results were compared with that obtained by integral method. The heat generation of bearings was modified by considering the combined effect of the lubricant viscosity variation and thermally-induced preload of bearings. Moreover, a novel geometrical-mechanical-thermal model for TCRs was proposed by characterizing the rough surface morphology and by establishing the multi-scale contact mechanics of joint surfaces. To validate the effectiveness of the proposed method, the thermal characteristic experiments of the spindle system were conducted under different rotational speeds. The results showed that the modeling errors in the temperature field and thermal deformation are reduced significantly and that this model has the ability of thermal error compensation.

The gear profile grinder is important to ensure the geometric accuracy of tooth surfaces. However, its machining accuracy is significantly reduced by the geometric and thermal errors. So the geometric and thermal errors should be controlled simultaneously. The geometric error modeling and decoupling of the gear profile grinder are studied, and the mapping relationship between the geometric accuracy of tooth surfaces and machine errors is constructed. To establish a robust thermal error model, a physically-based model is established to prove the feasibility of using the bidirectional long short term memory network (Bi-LSTMN) to establish a self-learning error model. The high-frequency noises are filtered and singular values are reduced by the Savitzky–Golay (SG) filtering algorithm. An attention-gate-based Bi-LSTMN (AGBi-LSTMN) is proposed to reduce the time complexity. Then the mixed-variants whale optimization algorithm (MVWOA) is proposed to optimize the hyper-parameters, and SG-MVWOA-AGBi-LSTMN is proposed for the thermal error prediction. Finally, the simultaneous geometric and thermal error control is implemented. The results show that the total tooth profile precision is increased by ISO level 3, and the tooth profile tilt precision is increased by ISO level 5 with the simultaneous geometric and thermal error control.