Fig. 4: Kelvin Voigt model - Linear viscoelastic behaviour The Kelvin Voigt model was applied to simulate the effects of the sinusoidal deformation on a viscoelastic material (Figure 4). Fig. 1: The ultrasonic system Fig. 2: The natural mode energy. Each halfwavelength element is deformed by contracting and expanding at each vibrational period. The accelerations produced at the tip of the sonotrode are huge (several thousand G's), giving the tool a very high potential energy. Thermomechanical coupling The parts to be assembled are placed between an anvil and the acoustical system, which will transfer the vibrational energy to the parts. Compression stress is used to maintain contact between the sonotrode and the part on top, and also between the two parts. The vibrational effect from the acoustical system causes a deformation of the materials (Figure 3). Fig. 3: The deformation The average energy dissipated within a unit of time can be expressed as follows: ε 0 Amplitude of the deformation Ep = ω µ Shear loss modulus The evolution of stiffness and viscosity during the cycle required a long characterization process to adapt the model, even more so in an anisotropic material like a composite. Interactions between the Frequency/Temperature/Stiffness parameters and the shear loss modulus are not compatible with the behavioural laws that are typical of simple thermoplastic welding. In the case of a monomaterial thermoplastic part, the drastic drop in stiffness as a function of temperature makes regulating the energy relatively simple: as you approach the Tg, the energy is transmitted less, and then not at all. Fig. 5: The energy dissipated at a given velocity under ultrasonic pressure p=p0sin(2πft) Within a static process, time becomes the variable that allows reaching the target energy level. For a continuous process, a permanent transient mode has to be integrated into the control loop (Figure 5). The loop will be directly affected by the set of process parameters. No87 March 2014 / jec composites magazine 93