We show the existence of a subcritical Hopf bifurcation in the delay-differential
equation model of the so-called regenerative machine tool vibration. The calculation
is based on the reduction of the infinite-dimensional problem to a two-dimensional
center manifold. Due to the special algebraic structure of the delayed terms in the
nonlinear part of the equation, the computation results in simple analytical formulas.
Numerical simulations gave excellent agreement with the results.