  Aims. We estimate the dynamical evolution of the Globular Clusters
interaction with the Galactic centre that dynamically changed in the past.
  Methods. We simulated the orbits of 147 globular clusters over 10 Gyr
lookback time using the parallel N-body code phi-GPU. For each globular
cluster, we generated 1000 sets of initial data with random proper motions and
radial velocities based on the observed values. To distinguish globular
clusters interacting with the galactic centre, we used the criterion of a
relative distance of less than 100 pc. We used four external potentials from
the IllustrisTNG-100 database, which were selected for their similarity to the
present-day Milky Way, to simulate the structure of the Galaxy at different
times.
  Results. We obtained 3-4 globular cluster interactions per Gyr at distances
of less than 50 pc and 5-6 interactions per Gyr at distances of less than 80 pc
among the studied 147 globular clusters that had close passages near the
Galactic centre. We selected 10 of them for detailed study and found almost
100% probability of interaction with the Galactic centre for six of them.
  Conclusions. According to our results, the maximum interaction frequency of
globular clusters with the Galactic centre in the Milky Way is likely to be a
few dozens of passages per Gyr within a central zone of 100 pc. This low
frequency may not be sufficient to fully explain the relatively high mass (of
order 10^7 Msol) of the nuclear star cluster in the Milky Way, if we consider
only the periodic capture of stars from globular clusters during close
encounters. Therefore, we must also consider the possibility that some early
globular clusters were completely tidally disrupted during interactions with
the forming nuclear star cluster and the Galactic centre.
