There are technical applications when the main element of a mechanical system is subjected to a regular vibration pattern. An example of this is drilling with tricone bits on hard material, because under normal condition the contact surface becomes lobular, imposing a longitudinal vibration on the drilling structure. It is possible to use part of this energy to resonate a hammer, that is a substructure of the system and impacts on it. The stress wave created by the impact may be useful to release the system from the stick condition of stick-slip phenomenon or to help in the crack propagation of the material being cut. Hard rock drilling is still a great challenge for oil companies. Optimum productivity is made possible by combining the advantages of rotary and percussive drilling. The task of developing an internal hammer in the drillstring that impacts on the drill bit remains an idea to be implemented. The subject of this work is the experimental investigation and the mathematical modeling of the impact force behavior in a vibro-impact system, where a hammer is mounted on a cart that imposes a prescribed displacement. By changing the hammer stiffness and the impact gap it is possible to investigate the impact force behavior under different excitation frequencies. A methodology is presented to numerically integrate the ODEs with a discontinuous right-hand side. This work also compares different models of the impact force presented in prevailing scientific literature to determine which one best fits the experimental data. This information will be used to create a mathematical model of the test rig. The experimental data will be used to validate the mathematical model. The hammer behavior is studied in more detail using a nonlinear analysis (bifurcation diagrams, Poincaré maps and Peterka map). Nonlinear analysis shows the various responses of the hammer, such as dynamical jumps, bifurcations and chaos. Finally, this work shows the field application of this vibro-impact system. A mass-spring system is mounted to an experimental drilling rig. Experimental results shows that impact forces during drilling improve the rate of penetration.