A　three-dimensional　mathematical　model　is　proposed　to　study　the　behavior　of　molten　pool　and　weld　bead　formation　in　variable-polarity　plasma　arc　welding　with　wire　feeding　under　flat　and　vertical-up　welding　conditions.　An　adaptive　heat　source　that　changes　with　the　keyhole　depth,　tracked　by　the　volume-of-fluid　(VOF)　method,　is　adopted　in　this　study.　As　the　energy　and　force　of　the　plasma　arc　accumulating,　a　keyhole　forms　and　increases　in　size,　and　the　temperature　and　flow　field　of　the　molten　pool　change　constantly.　Through　numerical　results,　the　study　found　that　the　keyhole　formation　could　be　divided　into　three　stages.　Three　forms　of　flow　patterns　in　the　molten　pool　were　discovered　in　the　keyhole　formation　process.　The　maximum　fluid　velocity　of　the　molten　pool　is　sharply　increased　initially,　then　moderately　increased,　and　finally　sharply　decreased　under　the　driving　force　of　plasma　flow.　The　established　model　is　experimentally　verified　by　the　geometrical　size　of　an　experimental　weld　bead.　This　study　may　enhance　the　understanding　of　the　dynamic　interaction　between　the　keyhole　and　molten　pool,　providing　theoretical　guidance　to　optimize　the　VPPAW　process　to　obtain　high-quality　welds.　(C)　2017　Elsevier　Ltd.　All　rights　reserved.