Gear　driving　devices　are　commonly　used　in　mechanical　transmission　systems.　Due　to　the　inevitable　random　errors　in　manufacturing,　installation,　and　operation,　the　dynamics　of　a　gear　transmission　system　will　fluctuate　randomly.　To　reveal　the　dynamic　characteristics,　an　interval　parameters　dynamic　model　of　a　single-stage　spur　gear　pair　is　established,　in　which　the　uncertainties　of　displacement　excitation,　load　excitation,　and　stiffness　excitation　are　included,　and　their　formulations　are　derived　in　detail　by　using　interval　mathematics.　The　established　interval　parameters　dynamic　model　is　solved　by　combining　the　Chebyshev　inclusion　function　method　and　the　Runge–Kutta　method.　Finally,　the　influence　of　the　random　interval　parameters　of　meshing　stiffness,　input　torque,　and　transmission　error　as　well　as　backlash　on　the　vibration　velocity　interval　and　transmission　reliability　of　the　gear　transmission　system　are　studied.　The　analysis　results　show　that　the　three　types　of　excitations　have　different　effects　on　the　dynamic　characteristics.　To　be　specific,　the　effects　of　uncertain　parameters　on　the　dynamic　characteristics　can　be　ordered　as　meshing　stiffness,　input　torque,　backlash,　and　transmission　error　in　sequence　from　the　strongest　to　the　weakest.　The　present　study　may　serve　as　a　sound　theoretical　basis　and　can　provide　references　for　the　design　and　vibration　control　of　spur　gear　transmission　systems.　©　The　Author(s)　2020.