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The jarosite crystallization and new extractant system of extractant 7101 were used to separate iron and extract vanadium from titanium white waste liquid (TWWL). The influence factors and mechanisms of crystallization and solvent extraction were investigated and analyzed with SEM-EDS, XRD, FT-IR, solution thermodynamic theory and extraction isothermal curve. More than 97% of iron was precipitated with potassium chlorate of 15 g/L, pH value of 1.6, temperature of 95 °C and time of 90 min, in which the crystallization product was jarosite with a purity of 99.5% and the pH value of solution decreased after precipitation. The extraction efficiency of vanadium reached 88.6% with 10% Fe, 5% Al(III) and less of Mg (II), K(I) and Na(I) under the conditions of X7101 of 0.5, pH value of 2.0, time of 4 min and stirring speed of 40 r/min. The extraction of metal ions occurred in the order of V(V) > Fe(III) > Al (III) > Mg (II) > K(I). The vanadium almost existed as H2V10O284- at the pH value of 2.0, and the functional group of NH and C-N contributed to vanadium extraction using the extractant 7101. Four stages extraction and three stages reextraction were predicated by McCable-Thiele plots.

The Craig–Bampton method is frequently applied in most commercial multibody dynamic software. Nevertheless, the Craig–Bampton modes only represent the free-free modes in flexible multibody systems. However, the free-free modes are incapable of all engineering applications. Hence, a rational set of reference conditions must be correctly chosen to define a unique displacement field. Firstly, a simple 2D beam with two revolute joints is taken as an example to prove that the free-free modes are not suitable for all engineering applications, and the results are validated by ANSYS and the analytical solution. Secondly, the Craig–Bampton method is improved by two different methods: (i) the reference conditions are added to the original Craig–Bampton matrix and (ii) the reference conditions are applied to the shape functions to redefine the mass and stiffness matrices before constructing the original Craig–Bampton matrix. This implementation illustrates that the improved Craig–Bampton matrix can not only generate the free-free modes but is also suitable for the non-free-free modes. Finally, two discrepant reference conditions are imposed to obtain the dynamic response of the flexible connecting rod based on the improved Craig–Bampton method, which is validated using the normal mode approach. Simulations show that the improved Craig–Bampton method can be used as a general-purpose method in durability analysis.