4.2. Sensitivity Analysis
For each key component, sensitivity coefficients of all design parameters to the component mean life were calculated by using Equation (4), based on the reliability simulation results. For purposes of comparison, these sensitivity coefficients were ranked in
Table 8, in which the positive and negative signs represent the effect played in positive and negative ways, respectively. A detailed discussion on the sensitivities of different parameters for each key component is given as follows:
In the fuel booster pump, failure of the sealing bolt will cause a sealing failure between the volute and pump cover, which increases the risk of fuel leakage. From the aspect of sensitivity levels, the nominal diameter
d, fatigue strength index
b1, and preload
F had the greatest impacts on the mean fatigue life of the sealing bolt. Among these three parameters,
b1 acted as a negative exponential factor in the Basquin model. Therefore, a small increase in
b1 would lead to an obvious decrease in the predicted fatigue life. The parameters
d and
F belong to the geometrical parameters and operational loads, respectively. They exhibited strong sensitivities to the sealing bolt fatigue life because they play significant roles in calculating von Mises strains in the finite element simulations. This agrees with the observations in the literature [
36,
42], which also claim that the nominal diameter and the preload have a great influence on the fatigue lives of the bolts.
In addition, the fatigue strength coefficient σf1′, height of nut m, and inner circle diameter of nut s also exhibited moderate sensitivities to the mean fatigue life of the sealing bolt. It can also be seen that the impact of the pre-exponential factor (i.e., σf1′ on the predicted fatigue lives was much less than that of exponential factor b), according to the characteristics of exponential law. m and s are both geometric parameters associated with the nuts. Small fluctuations in them will not cause great changes in the calculation of the maximum von Mises strains of sealing bolts as well as their fatigue lives.
Finally, the modulus of elasticity E1 has very limited influence on the mean fatigue life of the sealing bolt. This is because E1 influences the fatigue reliability from two completely opposite directions. On one hand, it has a negative effect on the maximum von Mises strain calculated from the finite element simulation and therefore is positive in improving the fatigue life predicted from the Basquin model. On the other hand, E1 is the pre-exponential factor in the Basquin model and plays a negative role in increasing the fatigue life. While they counteract each other, the modulus of elasticity has a very limited influence on fatigue reliability.
According to the sensitivity analysis results, a design guide for improving the sealing bolt fatigue life can be proposed by paying more careful attention to parameters such as nominal diameter d and preload F. For instance, under a certain technological level, the bolt fatigue life might be sufficiently increased by using thick bolts or by appropriately reducing the preload applied on the bolts. Nevertheless, reduction in the preload must be controlled within a reasonable level to avoid other failures such as loose bolts and wear in practice.
- (2)
Spline shaft
Failure of the spline shaft will affect the power transmission efficiency, thus reducing the fuel supply capacity. Most importantly, minor and major diameters
D2 and
D1 of the small spline had the strongest influence on the life of the spline shaft. The decrease in
D2 would lead to an obvious reduction in the shaft section area, whereas the increase in
D1 will increase the number of the teeth. Both actions will result in significantly higher stress/strain levels to reduce the life of the spline shaft, regardless of whether it is driven by either shaft fatigue or tooth wear. In [
43], a similar argument was also drawn by claiming that the increase in the number of teeth plays an important role to enhance the strength of the spline shaft. Therefore, appropriate treatments on the parameters
D2 and
D1 will be the key issues to ensuring a long service life for the spline shaft.
Meanwhile, the fatigue strength coefficient σf3′ was also sort of sensitive to the spline shaft life, but not as strong as the D2 and D1 parameters. In contrast, the elastic modulus E2 of the spline shaft, oxidation wear coefficient ky, and chamfer R were significantly less sensitive to the life of the spline shaft.
- (3)
Graphite ring
Similar to the sealing bolt, failure of the graphite ring will also reduce the sealing ability of the fuel booster pump and lead to a high risk of fuel leakage. For the graphite ring, the dominant parameter for sensitivity analysis on the life of the graphite ring is inside diameter d2. Since the graphite ring is closely attached to the moving ring, a slight increase in d2 would produce a rapid increase in the contact stress between the graphite ring and the moving ring, which would significantly accelerate the abrasive wear failure. Moreover, the abrasive wear coefficient kn and spring pressure p had a moderate sensitivity to the life of the graphite ring, probably in the following ways. The wear coefficient kn is related to the lubrication state of the contact surface, the hardness of the grinding material, and other material properties. The spring pressure p provides the driving force of wear. The sensitivities of other parameters including the Brinell hardness H, thickness h2, and elastic modulus E3 were much lower and could be ignored.
Therefore, it is necessary to ensure that the inside diameter d2 is well under control in the wear life design of the graphite ring. In addition, it is also recommended that the r wear coefficient kn is reduced by controlling the lubrication, temperature, heat dissipation and viscosity of the seal, and paying attention to the selection of the spring to ensure that the spring pressure p is within a stable pressure range.
- (4)
Inducer
Failure of the inducer will cause a low fuel pressurization, which will reduce the fuel supply capacity. The fuel pressure on the front of blade
P1 exhibited the strongest sensitivity to the fatigue life of the inducer due to the fact that it is the most critical parameter in the calculation of the maximum von Mises strain, as also indicated in the literature [
44]. Next, the blade thickness
W0, fatigue strength coefficient
σf4′, fuel pressure at the back of blade
P2, and fatigue strength index
b4 exhibited middle-level sensitivity to the inducer’s fatigue life. An appropriate increase in the blade thickness
W0 is helpful to strengthen the blade structure of the inducer and reduce the maximum von Mises strain at the blade root. Finally, the least influential parameter is the elastic modulus
E4, which barely affected the inducer fatigue life.
As a result, during the operational process of the fuel booster pump, the fuel pressure on the back of the blade should be in a reasonable bound, that is, the incoming fuel should maintain a stable and small pressure. In addition, sufficient blade thickness must be guaranteed to prevent the rupture of the inducer.