A method to design a variable flux electric ma-chine using no rare earth materials is proposed. Starting from a synchronous reluctance machine’s rotor the electromagnetic and mechanical design goals are derived. To improve torque production radially magnetized low coercive field magnets are inserted in the rotor, allowing for a control of the rotor flux. The flux guidance is improved by removing the webs required for mechanical sturdiness, which is achieved instead by mold injecting fiber reinforced polymer into the flux barriers. On the basis of a large design of experiments and using Gaussian process regression models, the relation between the rotor design parameters and output torque as well as external fields in the magnets is investigated and an optimization is performed. The resulting machine design allows an operation with high torque without involuntary demagnetization. The potential of the polymer filled flux barriers is confirmed through structural mechanical analysis.