## 4 Results and Discussion
### Influence of Different Loads on Blade Stress and Strain
The strength verification formula is  
\[\sigma_{\text{max}}\leq\frac{\sigma_{s}}{k}=[\sigma] \tag{7}\]  
In Equation (7), \(\sigma_{\text{max}}\) represents the maximum stress that the blade can withstand (MPa), \(\sigma_{s}\) denotes the material's yield strength (MPa), and k is the safety factor. For specialized dynamic machinery such as impellers, due to their unique operational conditions under static loading, a safety factor of k = 1.2 was selected in this study. As per the preceding context, it is apparent that the material composition of the blades was TC4, distinguished by its exceptional ductility, with a yield strength of 825 MPa. With a safety factor of k = 1.2 applied, the allowable stress for the material was established at 687.5 MPa. At the rated rotational speed of 17,188.7 rpm, the maximum equivalent stress experienced by the blades was recorded at 299.93 MPa. Notably, this stress magnitude remained below the allowable stress threshold of 687.5 MPa for the material, thereby ensuring compliance with the strength criteria for the blades at 17,188.7 rpm. For a clearer understanding of the influence patterns of different loads on the maximum deformation and maximum stress of the blades, this study contrasted the effects at 90%, 80%, and 70% of the design rotational speed. From Figure 12(a), it is observed that under various design rotational speeds, the deformation solely induced by aerodynamic loads slightly exceeded that caused solely by centrifugal loads. Moreover, the deformation resulting from the combined action of centrifugal and aerodynamic loads surpassed that induced by either force acting alone. Figure 12(b) reveals that the maximum equivalent stress induced solely by aerodynamic loads was significantly lower than that induced solely by centrifugal loads or by the combined action of centrifugal and aerodynamic loads. Figure 14 presents the variation of blades' maximum deformation and maximum stress with mass flow at different rotational speeds. Figure 13(a) shows that the blades' maximum deformation under different rotational speeds exhibited a trend of initially increasing and subsequently decreasing with the increasing mass flow, with a peak value present throughout the entire operational range. It is evident that with the continuous increase in rotational speed, the maximum deformation of the blade progressively increased. Notably, at each rotational speed, the maximum deformation under near-stall conditions exceeded that at the near-choke point, with the deformation trend of the blades intensifying as the rotational speed increased. Variations in rotational speed induced variations in blade deformation characteristics. From Figure 13(b), it can be observed that the variation trend of maximum blade stress under different rotational speeds was relatively smooth, with  
Figure 13: Deformation and stress of blades at different rotational speeds under load. minimal impact from variations in mass flow. As rotational speed increased, the variation in maximum blade stress did not exhibit a singular increasing trend; rather, it increased from 70% to 80% speed, decreased from 80% to 90% speed, and then increased again from 90% to 100% speed. Overall, the maximum stress exhibited a variation process of initial increase, subsequent decrease, and subsequent increase with the increase in rotational speed. Hence, selecting an appropriate rotational speed can effectively mitigate the blades' maximum deformation and stress.