Based on the resistance characteristics, a model of theoretical digging force was proposed in this paper, taking the tangential force, the normal force, and the bending moment into account simultaneously. Utilizing the relation among the normal resistance, the resistance moment, and the tangential resistance in practical digging process, three independent unknown quantities are transformed into only one variable. Afterwards, according to different digging patterns and complete machine limiting conditions, this research derived the constraint inequalities of the limiting digging force (LDF) and established the calculation models for LDF. Then, based on the value distribution laws of the digging resistance coefficient and the resistance moment coefficient, the calculation process and corresponding method of LDF under a given digging posture were obtained. Taking the digging resistance obtained by testing for 35 t hydraulic excavator with backhoe attachment as the reference, this paper compared the calculation results of the theoretical digging force for complete machine with those of the LDF model proposed in this research. The comparative results indicate that the LDF is consistent with the fact that the theoretical digging force is larger than or at least equal to the actual digging resistance. So, the LDF can exactly show the real limiting digging ability of the excavator more accurately. In this way, it can provide basis for mechanism optimization, structural strength design, trajectory planning, and control automation of the excavator.

The theoretical digging force is the maximum digging resistance that an excavator can overcome, which is an important measure of its digging capacity. To study the matching of the digging capacity with the actual demand and the matching of the working device mechanism, a 36.5 t backhoe hydraulic excavator is used as an example to analyse the distributions of the digging resistance under two different normal digging area working conditions and the maximum digging resistance characteristics of the tool. An appropriate digging postures are selected, based on limit digging force and compound digging force models, the theoretical digging forces under the two working conditions are obtained and matched with the measured digging resistance force values and the limiting factors affecting the digging force. The results show that the average percentage of theoretical digging forces greater than the measured digging resistance under both calculation models is 84.06% rather than 100%. The results of different digging methods all indicate that small chamber locking of the boom cylinder is too often the limiting factor for the digging force, resulting in poor matching of the working device. This study provides guidance for the improvement of the theoretical digging force model and the evaluation of the matching characteristics of the working device.

To address the flow field noise problem in twin-screw air compressors, multi-physical-field coupling technology is employed to perform flow field noise calculations for the compressor. Based on the structural characteristics and noise generation principles of the twin-screw compressor, a noise reduction design method is proposed that employs a Helmholtz resonator and a three-chamber perforated muffler at the exhaust end. The muffler’s structural optimization is performed using a genetic algorithm, and the effectiveness of the noise reduction method is validated through calculations. The results indicate that the Helmholtz resonator effectively mitigates airflow pulsation at the exhaust port, stabilizing the flow and reducing low-frequency noise at the exhaust end. Additionally, the designed three-chamber perforated muffler achieves noise reduction across a broad frequency range. With this noise reduction method, the exhaust port noise of the twin-screw compressor is reduced from 100–114 dB to 37–68 dB. These findings provide valuable insights for vibration and noise reduction in twin-screw air compressors.