## 1 Introduction  
With the development of urban rail transit, traditional track engineering vehicles suffer from drawbacks such as low efficiency, high energy consumption, and significant pollution. Consequently, the environmentally friendly battery track engineering vehicle has gained popularity. Each subway line is equipped with a certain number of battery track engineering vehicles. Faced with the complex and ever-changing route conditions of urban subway systems, the bogie, a crucial component of battery track engineering vehicles, requires optimal suspension parameters to ensure operational safety [1, 2]. Researchers worldwide have conducted numerous studies on the optimization of the primary suspension parameters of the bogie. [PERSON] et al. [3] made a three-piece bogie wagon the subject of a study, minimized the vertical acceleration, and optimized the geometries of the inclined chief for unloaded and heavily loaded scenarios. [PERSON] et al. [4, 5] showed that the lateral frame force depends upon the relative interplay of lateral bogie stiffness and the snubbing force for the subject suspension designs. [PERSON] et al. [6] optimized vehicle body modal analysis on such basis. [PERSON] et al. [7, 8, 9] investigated the operational qualities such as stability and safety of a vehicle by establishing a rigid-flexible coupled model of a rail vehicle, and also revealed that elastic vibration cannot be neglected in vehicle dynamics. [PERSON] et al. [10] established a subway vehicle-rail coupling dynamics model and investigated the impact of different matches between the primary suspension and fastener stiffness on vehicle dynamic performance. [PERSON] et al. [11] explored the matching relation of six key suspension parameters to achieve optimal lateral dynamics. [PERSON] et al. [12; 13] established a virtual prototype Kriging model and radial basis function (RBF) model, and the genetic algorithm was used for multi-objective optimization to improve the vehicle operational performance. [PERSON] et al. [14] showed that the dynamics response of a vehicle with wear/comfort Pareto-optimized values of bogie suspension was robust against uncertainties in the design parameters. [PERSON] et al. [15] presented a method for the centralized optimization of key bogie suspension parameters based on vehicle lateral robust stability. [PERSON] et al. [16] investigated the stability/wear Pareto optimization of bogie suspension parameters for high-speed passenger trains. [PERSON] et al. [17; 18; 19] optimized the suspension parameters and selection of oscillator suspension and achieved Actuator optimal placement for high-speed trains to improve hunting stability. In conclusion, the optimization of the bogie structure for the bogies of old internal diesel locomotive cars equipped with an external axle-box bogie has been extensively studied to improve the safety performance under various conditions, such as high speed, heavy load, or large radius curves. However, as a new type of popular construction vehicle, fewer investigations have focused on the improvement of the stability of the inner axle-box bogie for a battery track engineering vehicle passing through minimum radius curves. The horizontal sizes of the external axle-box bogie are much larger than those of the inner axle-box bogie, and the horizontal spans of the first and second series of the suspensions are larger, with a significant gap between the suspension forces of each series. This has a considerable impact on the horizontal motion of train components; therefore, considering the dynamics requirements, the parameters of the first series of suspensions of the traditional external axle-box bogie are not suitable for the inner axle-box bogie. In addition, when a track engineering vehicle passes through a minimum radius curve, the unevenness of the track and centrifugal force make derailment and other dangerous occurrences likely [20]. Therefore, optimizing bogie parameters for vehicles traversing minimum radius curves is essential to enhance operational stability.