Aiming　at　solving　the　lightweight　design　problems　for　bi-disc　systems　with　consideration　of　the　stiffness　and　strength　simultaneously,　a　two　stage　topology　optimization　framework　based　on　independent　continuous　and　mapping　(ICM)　method　is　developed.　First,　topology　optimization　formulations　are　established　to　guarantee　the　optimized　design　satisfying　the　key　nodal　displacement　and　stress　constraints.　Second,　an　information　function　is　introduced　to　realize　the　transformation　of　the　material　properties　between　elements　and　components.　Composite　exponential　filter　functions　are　selected　to　establish　the　relationship　between　the　properties　of　elements　and　corresponding　topology　design　variables.　Third,　approximate　explicit　quadratic　programming　model　is　obtained　by　the　sensitivity　analysis　and　Taylor　expansion.　In　the　process　of　solving,　the　duality　theory　is　used　to　establish　the　approximate　dual　model　with　less　design　variables.　Finally,　a　series　of　topology　optimization　design　problems　for　bi-disc　systems　are　presented　and　discussed　to　illustrate　the　robustness　and　feasibility　of　the　method.　This　study　finds　some　new　torsional　bi-disc　designs　and　can　also　provide　some　theoretical　references　for　the　lightweight　topology　optimization　of　a　multicomponent　system.