Proceedings of SerbiaTrib '13

probe, d 0 (t) – diameter of the technological hole inthe workpieces, t - time.In such condition, the momentum of frictionM fr (t) is:Mfr() tFz()[ t dt () d0()]t() t (2)3and therefore, friction coefficient at pt is:3 M fr ( t)() t pt() t , t0 t tps'Fz()[ t d() t d0()]t3.3 Contact over the probe tip and the probeside(2)The probe side (ps) of the welding tool iscylindrical or coned surface with or without thread[1]. The thread is of great significance for thewelding process, however, it makes greatdifficulties for the analysis of friction and it will beneglected in analysis.If only the probe side is in contact with theworkpieces, equilibrium between the forces,represented as the contact pressure at the probe sidep ps (t), and the torque T ps (t) is:2 ps () tdt () ht () pps()π tTps() t T2() t (3)2where: (t)= ps (t) – total coefficient of friction –coefficient of friction at ps, h(t) – height of theprobe (side) plunged into the workpieces.In such condition, the momentum of frictionM fr (t) is:Mfr2() tdt () htp () ps ()π t() t (4)2and therefore, friction coefficient at pt is:2 M fr ( t)() t ps() t , t24 t t5(5)dt () htp () ps ()π tWhen the probe tip and the probe side aresimultaneously involved in the contact, equilibriumof loads and the torque at the probe tip and theprobe side T pt+ps (t) can be expressed as:2() tdt () ht () pps()π tpt ps () 1() (6)T t T tIn such condition, the momentum of frictionM fr (t) is:2M fr () t T1() t T2()t (7)Assuming that the friction coefficients at theprobe side and the probe tip are the same (only as avalue): () t ps() t pt(),t tps't tst(8)transforming the equation (7), friction coefficientbecomes:6 M fr ( t)() t ,22 Fz()[ t d() t d0()] t 3 d() t h() t pps()πttps' t tst3.4 Contact over the probe tip, the probe sideand the shoulder tip(9)The shoulder tip (st) of the welding tool iscylindrical or coned surface with the greatest area[1, 2]. Shoulder tip is the last active surface of thewelding tool involving into the welding process.If only the shoulder tip is in contact with theworkpieces, equilibrium between the loads and thetorque at the shoulder tip T st (t) is:st() tFz()[ t Dt () dmax]Tst() t T3() t (10)3where: (t)= st (t) – total coefficient of friction –coefficient of friction at st, D(t) – diameter of the st,d max – maximal diameter of the probe.However, shoulder tip is never involved in thewelding process as the only active surfaces –shoulder tip is always involved in weldingsimultaneously with the probe tip and the probeside and in such case, equilibrium of loads and thetotal torque T tot (t) is:Ttot() t T1() t T2() t T3()t (11)In such condition, the momentum of frictionM fr (t) is:M fr () t T1() t T2() t T3()t (12)Assuming that the friction coefficients at theprobe side, the probe tip and the shoulder tip are thesame (only as a value): () t ps () t pt () t st (), t tstt t4(13)transforming the equation (12), friction coefficientis:6 M fr ( t)() t ,22 Fz() t A3 d() t h() t pps()π+2 t Fz( t)BA dt () d0(), t B Dt () dmax , tps'ttst3.5 Contact pressure at the probe side(14)Contact pressure at the probe side is mostlydelivered by the welding force F x (t). Since weldingforce is active only during the welding phase390 13 th International Conference on Tribology – Serbiatrib’13