As an important component of rotating equipment such as pumps, compressors, and reactors, the hydrodynamic mechanical seal plays a vital role in ensuring the stable operation of the main machine. The machining accuracy of the hydrodynamic groove depth is an important factor that affects its stable operation. At present, laser machining technology has been widely used in the machining of hydrodynamic grooves, but the general groove depth machining error is still approximately 1?2 μm, and a large groove depth machining error can easily cause seal instability or failure. Therefore, accurate control of the hydrodynamic groove depth is of great significance to improve the sealing performance and operating stability. However, there is still a lack of simple and effective methods and measures to accurately control the groove depth of hydrodynamic grooves, and thus further study is required. Based on the depth calculation model of hydrodynamic grooves and the groove depth machining error model of multi-inversion, this study investigated the inversion of process parameters and groove depth machining accuracy control in nanosecond laser machining of mechanical seal hydrodynamic grooves. This study is expected to provide theoretical guidance and technical support for the accurate control of groove depth in various mechanical seal hydrodynamic grooves or microgrooves in other fields.

A parameter inversion program is compiled based on the groove depth calculation model for laser machining of hydrodynamic grooves previously proposed by the research group. Combined with the definition of groove depth error and groove depth relative error, a multi-inversion groove depth machining error model is constructed. The model considered two conditions, namely, experimental groove depths smaller and greater than the target groove depth. The inversion program is used to study the single inversion of process parameters and the machining accuracy control of groove depth with multi-inversion. A SiC sealing ring is used as the experimental object, and a nanosecond fiber laser marking machine and a surface roughness profile shape measuring machine are used for experimental verification. A comparative analysis is conducted with the theoretical results. The methods and strategies for laser precision machining of mechanical seal hydrodynamic grooves are proposed based on the theoretical and experimental results.

In the single inversion study, the inversion results of 16 sets of process parameters obtained based on the inversion program are consistent with the experimental results. The maximum relative error of groove depth is less than 17.00%, and the minimum relative error is only 0.60%, while most of the groove depth relative errors are all less than 10.00%. These results show that the parameter inversion program based on the groove depth calculation model has a high calculation accuracy. In the multi-inversion study, if the experimental groove depth of the first inversion is smaller than the target groove depth, the relative error of groove depth can be controlled from 17.00% to less than 2.60% through two inversions. If the experimental groove depth of the first inversion is greater than the target groove depth, the number of markings can be reduced to make the experimental groove depth just less than the target groove depth, and the groove depth machining error can be controlled from 5.55% to less than 2.25% through two inversions, both of which satisfy the design control target requirement that the maximum relative error of the hydrodynamic groove depth does not exceed 5.00%. This means that regardless of whether the experimental groove depth of the first inversion is smaller or greater than the target groove depth, multiple inversions can effectively improve the machining accuracy of groove depth and achieve the precision machining of hydrodynamic grooves.

The inversion program compiled in this study has high inversion accuracy and can quickly predict the process parameters satisfying different target groove depths. Among 16 sets of single inversion results under different target groove depths, the maximum relative error of groove depth is less than 17.00%. Theoretically, when the relative error of groove depth is 20.00%, it can be controlled within 5.00% and 1.00% through two and three inversions, respectively. Even if the relative error of groove depth is as high as 50.00%, it can still be controlled within 5% through five inversions. Therefore, the number of inversions needed to satisfy the design control objectives of hydrodynamic grooves can be determined by the theoretical analysis. When the experimental groove depth of the first inversion is less than the target groove depth and its relative error is 17.00%, the relative error of the groove depth is controlled within 5.00% through two inversions, and the experimental results are consistent with the theoretical results. This shows that it is feasible to adopt the method of successive approximation by multi-inversion to improve the machining accuracy of hydrodynamic groove depth and provides a new idea for precise control of groove depth for laser machining of hydrodynamic grooves. The method of gradual approximation by multi-inversion proposed in this paper can effectively improve the machining accuracy of hydrodynamic groove depth through finite inversion. It has advantages such as strong controllability, high efficiency and accuracy, and simple operation. This study can provide theoretical guidance and technical support for the accurate control of groove depth in various mechanical seal hydrodynamic grooves or microgrooves in other fields.