In this paper we design an open-loop active normal force for dry friction dampers, aiming to enhance the damping effect. The active normal force is composed of a constant term plus a time-varying term with zero mean value. The constant term is the best constant normal force that minimizes the forced response in the resonant frequency band. The time-varying force can be expressed by the Fourier Series and here we assume that it is composed of four harmonics with respect to the excitation frequency. Overall eight unknown parameters are therefore to be determined, namely the combination coefficients of the fours harmonics and phase differences between them. First, the global sensitivity of these parameters with respect to the forced response are analysed, in order to select the most significant parameters and to eliminate the unimportant ones. To do that the Fourier Amplitude Sensitivity Test (FAST) is performed based on the Lumped Parameter Model, where the forced response of is calculated by the Multi-Harmonic Balance Method (MHBM) combined with Alternating Frequency/Time domain (AFT). The arc-length continuation technique is used to improve the convergence. We found that the interaction between the amplitude and phase of the second harmonic significantly impacts the forced response around resonance frequencies. Then only these two parameters are considered to minimize the forced response in the frequency band, rather than considering all eight parameters. Results show that a further 25% reduction of the response peak can be achieved by the designed time-varying normal force in comparison with the best constant normal force. The proposed design process is applicable for any dry friction dampers if it is possible to impose an open-loop active normal force.