1. Introduction
Recently, the vibration reliability tests for mechanical systems have been increased to improve their performances and to ensure their stabilities under the repeatable loads and sudden shocks. For these tests, the fixing jigs for mounting the systems on a vibration reliability tester are required. Before the tests, the dynamic stabilities of the fixing jigs should be verified. This paper proposes an analytical technology for ensuring the dynamic structural stability for the test setup including the jig.
A jig was damaged during evaluating the vibration reliability of a rubber hose at the vibration durability research center in Changwon National University. The finite element (FE) analysis is performed for investigating the cause of the jig’s damage.
Another jig is newly devised on the basis of the investigated results for the damaged jig. And the FE model for the new jig is simulated to check its stability. Finally, the vibration reliability test for the rubber hose with the new revised jig is successfully conducted without any problem.
2. A broken jig during reliability test for a rubber hose
2.1 The description of reliability test
Figure 1 shows the test setup conducting the vibration reliability test for a hydraulic rubber hose with maintaining the inner pressure of 42MPa. The test fails if the leakage or pressure reduction is found during the test period. The jig for mounting the test specimen shall, of course, remain structurally stable during the test period. This is because the reliability of the durability assessment of the test specimen could be ensured if the stability of the jig is ensured
The jig used for the reliability test of the rubber hose is a series of gas hole, valve, and pressure gauge on only one part, considering the convenience of refueling, pressurization, and gauge reading during test, and is empirically produced by the company without the jig’s dynamic stability verification.
Figure 2 shows the long stroke vibration test equipment (J260/IMV, Japan) used for this reliability test for the rubber hose at the vibration durability research center in Changwon National University. Many vibration reliability tests and shock tests for parts and sub-assemblies of electric machines, transportation machineries, machine tools, and so on can be conducted with the test equipment under the specification as shown in Table 1.
The failure was found in 13 hours after the test which began under the test conditions as shown in Table 2.
A part of the jig as shown in Fig. 3 was broken during the vibration durability test. The crack was occurred in the lower pipe of the jig and propagated vertically.
2.2 Finite element analyses for the model of damaged jig
A three dimensional(3D) model using CATIA with the drawings provided from the company is constructed shown in Fig. 4. And then a FE analysis model with importing the CATIA 3D model using ANSYS is completed for investigating the cause of the jig’s damage.
First, mode analysis for this model is performed to check the resonance. The degrees of freedom of the nodes at the bottom of fixture are restricted as the boundary conditions for the mode analysis. Figure 5 shows the 1st mode shape, one of the mode analysis results. Since the calculated natural frequencies are listed in Table 3 are higher than the exciting frequency of 25Hz as shown in Table 2, no dangerousness due to the resonance exists. This leads that the cause of the jig damage may not be the resonance and that the other analyses for the damage are necessary.
Next, ANSYS harmonic analysis is continued to investigate the cause of jig damage. For the harmonic analysis, the 7g peak to peak acceleration with the frequency of 25 Hz was applied to the entire test model in the same way as the actual test conditions.[5]
Figure 6 shows von-Mises stress distribution, one of the harmonic analysis results. It can be seen that the equivalent stress of about 310 MPa was calculated at the actual damage spot as shown in Fig. 7. Since the stress at the damage spot exceeds the yield strength of 250 MPa for SS400, which is the material of the jig, fatigue due to repeated loads may be estimated as the cause of damage.
So a fatigue analysis is finally performed under applying Goodman failure line and fully reversed load with average stress of 0 and no average stress modification.
Figure 8 shows the calculated life distribution which is one of the fatigue analysis results, and the minimum repeatable number of the jig of 1.1507 million. The minimum life is about 13 hours at 25Hz which is much lower than the durability test time of 100 hours. This is the explicit evidence of the damage of jig. Therefore a new jig should be revised for the safe test.
3. Analyses and test for a new revised jig
3.1 The device of new jig
As the results of the harmonics and fatigue analysis show that the damaged area is weaker than the shape of the other straight support, the damaged area is modified to a straight line form, such as the shape of the other part. Figure 9 shows the CATIA 3D model for the new revised jig.
3.2 Finite element analyses for the model of revised jig
A FE analysis model with importing the CATIA 3D model for the new revised jig using ANSYS is completed for investigating the safety for the resonance and the structural stability.
First, mode analysis for this model is conducted to check the resonance. The degrees of freedom of the nodes at the bottom of fixture are restricted as the boundary conditions for the mode analysis. Figure 10 shows the 1st mode shape for the new revised jig.
Since the calculated natural frequencies are listed in Table 4 are much higher than the exciting frequency of 25Hz as shown in Table 1, the revised jig may be safe for resonance.
Next, ANSYS harmonic analysis for the revised jig is continued to investigate the structural stability. For the harmonic analysis, the 7g peak to peak acceleration with the frequency of 25 Hz is applied to the entire test model in the same way as the actual test conditions.[3] Figure 11 shows von-Mises stress distribution, one of the harmonic analysis results. Although it can be seen that the maximum von-Mises equivalent stress still exists at the damaged spot, the calculated equivalent stress of about 115MPa as shown in Fig. 12 is less than the yield strength of 250MPa for SS400, which is the material of the revised jig. This means that the structural stability for the revised jig may be ensured.
Finally a fatigue analysis for the revised jig is performed under applying Goodman failure line and fully reversed load with average stress of 0 and no average stress modification, as the same condition of damaged jig.
Figure 13 shows the calculated life distribution for the revised jig and the minimum repeatable number of the jig of 25 million. The minimum life is about 277 hours at 25Hz which is much higher than the durability test time of 100 hours. This leads that the jig can be reliability test of rubber hose with the revised jig.
3.3 Reliability test of the rubber hose with new revised jig
An improved jig is manufactured based on the analysis results. Figure 14 shows the actual reliability test setup under the test condition in Table 2. The test is successfully performed without any failure during test durable time of 100hrs. Therefore the rationality of the analytical method for securing the stability of the jig proposed in this paper has been confirmed.
4. Conclusion
A jig was damaged during the test for evaluating the vibration reliability of a rubber hose. In this paper, the FE analyses, including mode analysis, harmonic analysis and fatigue analysis, are performed for investigating the cause of the jig’s damage. It could be estimated that the damage was caused by the fatigue due to the repeated load on the jig by the FE analyses results.
A new jig was designed with the damaged part which is designed as the shape of the other side. It is also designed to be structurally robust by placing the test hydraulic hoses and the filling hole -valve -pressure gauge in parallel and connecting the two poles each other. The FE analyses for the revised jig model were conducted with the same manner as the broken jig model. The results showed that the jig model could be safe for resonance and be enough to its fatigue life. Finally, the reliability test of rubber hose with the revised jig was successfully performed without any failure during test durable time of 100hrs.
Therefore, this concludes that the dynamic stabilities of test setup including the jigs should be ensured before the vibration reliability tests and that the jig’s design technology proposed in this paper may be useful for other items as well.
