An electrical machine with a brush commutator arrangement (1) is proposed. Brushes (3) and a commutator (5) are adapted and arranged such that, upon operating the electrical machine (1), the brush (3) and the commutator (5) are displaced relative to each other in a lateral displacement direction (7) and a contact surface (9) of the brush (3) mechanically contacts a contact surface (11) of the commutator (5) along an overlapping area (13) thereby generating an electrical contact. Accordingly, an electric current is transmitted between brush (3) and commutator (5) through the overlapping area (13). An orthogonal electrical conductivity of the brush (3) and/or the commutator (5) in a direction (25) orthogonal to a respective contact surface (9, 11) locally varies along the lateral displacement direction (7). An orthogonal electrical conductivity distribution in the brush (3) and/or the commutator (5) is adapted such that, even when operating the electrical machine at maximum allowable power, for at least 90% of all spatial configurations during displacing the brush (3) and the commutator (5) relative to each other, an electrical current density through the overlapping area (13) does not exceed 130% of a rated maximal average electrical current density through the brush commutator arrangement (1). Due to the specific variation of orthogonal electrical conductivity within the brush (3) or commutator (5), sparking and resulting wear in the proposed brush commutator arrangement (1) may be reduced.