A simulation of the NC-shape grinding process of free formed surfaces is considered. A central issue in the simulation is the numerical solution of dynamic Signorini problems. Here, space adaptive techniques for such problems are discussed. The Newmark method in time and low order finite elements in space are used for discretisation. For the global discretisation error in space, an a posteriori error estimate is derived on the basis of the semi-discrete problem in mixed form. This approach relies on an auxiliary problem, which takes the form of a variational equation. An adaptive method based on the estimate is applied to improve the finite element approximation. Numerical results illustrate the performance of the presented method.