Abstract: Rapid change of the magnetic field of the dipole and quadrupole magnets on a rapid-cycling synchrotron may induce serious eddy-current effect in the conventional vacuum chambers. In response to this issue, numerous new type vacuum chamber designs for these magnets have been proposed. These include ceramic chambers, thin-walled stainless steel chambers strengthened with transverse ribs, and ceramic rings-lined thin-walled stainless steel chambers. Recently, the HIAF engineering team at The Institute of Modern Physics, Chinese Academy of Sciences, suggested 3D-printed titanium alloy lining as an alternative to the ceramic ring lining. A vacuum chamber lined with 3D-printed titanium alloy linings offers several advantages over other designs. These include higher structural strength, smaller aperture, lower outgassing rate, and relatively lower cost. However, titanium alloy linings in vacuum chambers could become significant sources of coupling impedance on BRing, the circular main accelerator of the HIAF Facility. The influence of this impedance on beam instability, as well as the impact of potential impedance mitigation designs, still requires evaluation. This paper employs two distinct methods in the CST Studio Suite software to simulate the coupling impedance introduced by all types of titanium alloy linings-lined vacuum chambers of quadrupole magnets. The results from both methods closely agree with each other. Based on these works, we calculated the transverse dipolar impedance of the entire ring. Furthermore, using the Vlasov solver, we calculated the mode shift of ⁷⁸Kr¹⁹⁺ bunch on BRing under varying beam intensity conditions.The results indicate that, before the implementation of impedance mitigation on the titanium alloy linings-lined vacuum chambers of the dipolar and quadrupole magnets, the beam intensity threshold of ⁷⁸Kr¹⁹⁺ bunch on BRing, as given by transverse mode coupling instability, was 2.7×10¹¹ ppp. This is below the designed beam intensity for ⁷⁸Kr¹⁹⁺ bunch on BRing (3×10¹¹ ppp). However, after the application of impedance mitigation design, this beam intensity threshold will shift to 4.4×10¹¹ ppp. This suggests that the impedance mitigation on the titanium alloy linings-lined vacuum chambers of the dipolar and quadrupole magnets is effective. From the perspective of only the transverse broadband coupling impedance, it is viable to substitute the ceramic rings-lined thin-walled stainless steel vacuum chambers with the titanium alloy linings-lined thin-walled stainless steel vacuum chambers for dipolar and quadrupole magnets on BRing.