Multistep Hermite collocation methods for solving Volterra Integral Equations

In this paper, we propose a new class of multistep collocation methods for solving nonlinear Volterra Integral Equations, based on Hermite interpolation. These methods furnish an approximation of the solution in each subinterval by using approximated values of the solution, as well as its first derivative, in the r previous steps and m collocation points. Convergence order of the new methods is determined and their linear stability is analyzed. Some numerical examples show efficiency of the methods.     

Stability improvement and regenerative chatter suppression in nonlinear milling process via tunable vibration absorber

In this paper, a tunable vibration absorber set (TVAs) is designed to suppress regenerative chatter in milling process (as a semi-active controller). An extended dynamic model of the peripheral milling with closed form expressions for the nonlinear cutting forces is presented. The extension part of the cutting tool is modeled as an Euler–Bernoulli beam with in plane lateral vibrations (x–y directions). Tunable vibration absorbers in x–y directions are composed of mass, spring and dashpot elements. In the presence of regenerative chatter, coupled dynamics of the system (including the beam and x–y absorbers) is described through nonlinear delay differential equations. Using an optimal algorithm, optimum values of the absorbers' position and their springs' stiffness in both x–y directions are determined such that the cutting tool vibration is minimized. Results are compared for both linear and nonlinear models. According to the results obtained, absorber set acts effectively in chatter suppression over a wide range of chatter frequencies. Stability limits are obtained and compared with two different approaches: a trial and error based algorithm and semi-discretization method. It is shown that in the case of self-excited vibrations, the optimum absorber improves the process stability. Therefore, larger values of depth of cut and consequently more material removal rate (MRR) can be achieved without moving to unstable conditions.     

Dynamics of regenerative chatter and internal resonance in milling process with structural and cutting force nonlinearities

In this paper, internal resonance and nonlinear dynamics of regenerative chatter in milling process is investigated. An extended dynamic model of the peripheral milling process including both structural and cutting force nonlinearities is presented. Closed form expressions for the nonlinear cutting forces are derived through their Fourier series components. In the presence of the large vibration amplitudes, the loss of contact effect is included in this model. Using the multiple-scales approach, analytical approximate response of the delayed nonlinear system is obtained. Considering the internal resonance dynamics (i.e. mode coupling), the energy transfer between the coupled x–y modes is studied. The results show that during regenerative chatter under specific cutting conditions, one mode can decay. Furthermore, it is possible to adjust the rate at which the x-mode (or y-mode) decays by implementation of the internal resonance. Therefore, under both internal resonance and regenerative chatter conditions, it is possible to suppress the undesirable vibration of one mode (direction) in which accurate surface finish is required. Under the steady-state motion, jump phenomenon is investigated for the process with regenerative chatter under various cutting conditions. Moreover, the effects of structural and cutting force nonlinearities on the stability lobes diagram of the process are investigated.     

Deactivation of Escherichia coli with different volumes in drinking water using cold atmospheric plasma

This experimental study aimed to evaluate the potential of cold atmospheric plasma jet to deactivate Escherichia coli from drinking water. We studied the effect of the volume of water samples on the performance of plasma jet on deactivation of E. coli of 1, 500, 1,000, 1,500, and 2,000 cubic centimetres. The results of deactivation of E. coli in 500 and 1,000 cc water samples were the same as one cc of a water sample and we observed 8-log reduction of E. coli using 50 W. In 1,500 and 2,000 cc water samples at 8 min using a power of 50 W, 4.5 and 2.9 log reduction of E. coli was achieved and while we used 20 W, 2.5 and 1.8 log reduction of E. coli bacteria was performed. This indicated that the increasing volume of water above 1,500 cc caused the reduction of the efficiency of E. coli removal. Also, increasing power caused to increase E. coli removal efficiency. In addition, we monitored changes in pH values and temperature during experiments. Using 20 W, the temperature was increased (natural temperature of the water was 22 °C) 2 °C after 8 min while applying 50 W, the temperatures were raised 5 °C. pH of the water after 8 min in the 1,000 cc water sample, with an input power of 20 W, decreased from 7.1 to 5.5; while the input power was 50 W, pH changed from 7.1 to 4.3. With an increase in plasma irradiation time, the number of E. coli had a significant decrease per min while using in samples of 1 cc. After 8 min, we observed 4-log reductions of E. coli with the input power of 20 W and 8-log reduction of bacteria with the input power of 50 W. In 1,500 and 2,000 cc of water samples using plasma radiation for 8 min, 2.5 log and 1.8 log reduction of E. coli was achieved, respectively. This means that an increasing volume of water above 1,500 cc needs more power and time to deactivate E. coli from the water.