Axial　and　torsional　impact　drilling　technology　is　used　to　improve　the　drilling　efficiency　of　hard　rock　formation　in　the　deep　underground.　Still,　the　corresponding　theory　is　not　mature,　and　there　are　few　correlative　research　reports　on　the　rock-breaking　mechanism　of　axial　and　torsional　coupled　impact　drilling　tools.　Considering　the　influence　of　the　impact　hammer　geometry　and　movement　on　the　dynamic　load　parameters　(i.e.,　wavelength,　amplitude,　frequency,　and　phase　difference),　a　numerical　model　that　includes　a　hard　formation　and　single　polycrystalline　diamond　compact　cutter　was　established.　The　Riedel-Hiermaier-Thoma　model,　which　considers　the　dynamic　damage　and　strength　behavior　of　rocks,　was　adopted　to　analyze　the　rock　damage　under　axial　and　torsional　impact　loads.　The　numerical　simulation　results　were　verified　by　the　experimental　results.　It　was　found　that　compared　with　conventional　drilling,　the　penetration　depths　of　axial,　torsional,　and　axial-torsional　coupled　impact　drilling　increased　by　31.3%,　5.6%,　and　34.7%,　respectively.　Increasing　the　wavelength　and　amplitude　of　the　axial　impact　stress　wave　improved　the　penetration　depth.　When　the　bit　rotation　speed　remained　unchanged,　increasing　the　frequency　in　the　axial　and　circumferential　directions　had　little　effect　on　the　penetration　depth.　However,　as　the　frequency　increased,　the　cutting　surface　became　increasingly　smooth,　which　reduced　the　occurrence　of　bit　vibration.　When　the　phase　difference　between　the　axial　and　circumferential　stress　waves　was　25%,　the　penetration　depth　significantly　increased.　In　addition,　the　bit　vibration　problem　can　be　effectively　reduced.　Finally,　the　adjustment　of　engineering　and　tool　structure　parameters　is　proposed　to　optimize　the　efficiency　of　the　axial-torsional　coupled　impact　drilling　tool.　©　2023　The　Authors