Analytical modeling of spindle-tool dynamics on machine tools using Timoshenko beam model and receptance coupling for the prediction of tool point FRF

Regenerative chatter is a well-known machining problem that results in unstable cutting process, poor surface quality and reduced material removal rate. This undesired self-excited vibration problem is one of the main obstacles in utilizing the total capacity of a machine tool in production. In order to obtain a chatter-free process on a machining center, stability diagrams can be used. Numerically or analytically, constructing the stability lobe diagram for a certain spindleholdertool combination implies knowing the system dynamics at the tool tip; i.e., the point frequency response function (FRF) that relates the dynamic displacement and force at that point. This study presents an analytical method that uses Timoshenko beam theory for calculating the tool point FRF of a given combination by using the receptance coupling and structural modication methods. The objective of the study is two fold. Firstly, it is aimed to develop a reliable mathematical model to predict tool point FRF in a machining center so that chatter stability analysis can be done, and secondly to make use of this model in studying the effects of individual bearing and contact parameters on tool point FRF so that better approaches can be found in predicting contact parameters from experimental measurements. The model can also be used to study the effects of several spindle, holder and tool parameters on chatter stability. In this paper, the mathematical model, as well as the details of obtaining the system component (spindle, holder and tool) dynamics and coupling them to obtain the tool point FRF are given. The model suggested is veried by comparing the natural frequencies of an example spindleholdertool assembly obtained from the model with those obtained from a nite element software

Effect analysis of bearing and interface dynamics on tool point FRF for chatter stability in machine tools by using a new analytical model for spindle-tool assemblies

Self-excited vibration of the tool, regenerative chatter, can be predicted and eliminated if the stability lobe diagram of the spindle–holder–tool assembly is known. Regardless of the approach being used, analytically or numerically, forming the stability lobe diagram of an assembly implies knowing the point frequency response function (FRF) in receptance form at the tool tip. In this paper, it is aimed to study the effects of spindle–holder and holder–tool interface dynamics, as well as the effects of individual bearings on the tool point FRF by using an analytical model recently developed by the authors for predicting the tool point FRF of spindle–holder–tool assemblies. It is observed that bearing dynamics control the rigid body modes of the assembly, whereas, spindle–holder interface dynamics mainly affects the first elastic mode, while holder–tool interface dynamics alters the second elastic mode. Individual bearing and interface translational stiffness and damping values control the natural frequency and the peak of their relevant modes, respectively. It is also observed that variations in the values of rotational contact parameters do not affect the resulting FRF considerably, from which it is concluded that rotational contact parameters of both interfaces are not as crucial as the translational ones and therefore average values can successfully be used to represent their effects. These observations are obtained for the bearing and interface parameters taken from recent literature, and will be valid for similar assemblies. Based on the effect analysis carried out, a systematic approach is suggested for identifying bearing and interface contact parameters from experimental measurements

Integral equation for inhomogeneous condensed bosons generalizing the Gross-Pitaevskii differential equation

We give here the derivation of a Gross-Pitaevskii--type equation for inhomogeneous condensed bosons. Instead of the original Gross-Pitaevskii differential equation, we obtain an integral equation that implies less restrictive assumptions than are made in the very recent study of Pieri and Strinati [Phys. Rev. Lett. 91 (2003) 030401]. In particular, the Thomas-Fermi approximation and the restriction to small spatial variations of the order parameter invoked in their study are avoided.Comment: Phys. Rev. A (accepted

Coulomb corrections to bremsstrahlung in electric field of heavy atom at high energies

The differential and partially integrated cross sections are considered for bremsstrahlung from high-energy electrons in atomic field with the exact account of this field. The consideration exploits the quasiclassical electron Green's function and wave functions in an external electric field. It is shown that the Coulomb corrections to the differential cross section are very susceptible to screening. Nevertheless, the Coulomb corrections to the cross section summed up over the final-electron states are independent of screening in the leading approximation over a small parameter $1/mr_{scr}$ ($r_{scr}$ is a screening radius, $m$ is the electron mass, $\hbar=c=1$). Bremsstrahlung from an electron beam of the finite size on heavy nucleus is considered as well. Again, the Coulomb corrections to the differential probability are very susceptible to the beam shape, while those to the probability integrated over momentum transfer are independent of it, apart from the trivial factor, which is the electron-beam density at zero impact parameter. For the Coulomb corrections to the bremsstrahlung spectrum, the next-to-leading terms with respect to the parameters $m/\epsilon$ ($\epsilon$ is the electron energy) and $1/mr_{scr}$ are obtained.Comment: 13 pages, 4 figure

McLaren's Improved Snub Cube and Other New Spherical Designs in Three Dimensions

Evidence is presented to suggest that, in three dimensions, spherical 6-designs with N points exist for N=24, 26, >= 28; 7-designs for N=24, 30, 32, 34, >= 36; 8-designs for N=36, 40, 42, >= 44; 9-designs for N=48, 50, 52, >= 54; 10-designs for N=60, 62, >= 64; 11-designs for N=70, 72, >= 74; and 12-designs for N=84, >= 86. The existence of some of these designs is established analytically, while others are given by very accurate numerical coordinates. The 24-point 7-design was first found by McLaren in 1963, and -- although not identified as such by McLaren -- consists of the vertices of an "improved" snub cube, obtained from Archimedes' regular snub cube (which is only a 3-design) by slightly shrinking each square face and expanding each triangular face. 5-designs with 23 and 25 points are presented which, taken together with earlier work of Reznick, show that 5-designs exist for N=12, 16, 18, 20, >= 22. It is conjectured, albeit with decreasing confidence for t >= 9, that these lists of t-designs are complete and that no others exist. One of the constructions gives a sequence of putative spherical t-designs with N= 12m points (m >= 2) where N = t^2/2 (1+o(1)) as t -> infinity.Comment: 16 pages, 1 figur

Pembuatan detektor Sinar-X Isisan Gas jenis proporsional Tipe Jendela samping

Telah dibuat dan diteliti detektor proporsional tripe jendela samping dengan gas isian argon dan metana Tekanan total gas isian adalah 400 mmHg dengan perbandingan tekanan 95 : 5. Katoda terbuat clari stainless steel berdiameter 24,2 mm dengan panjang 100mm dan anoda dari tungsten berdiameter 0,08 mm. Jendela terbuat dari berilium, dengan panjang 24 mm dan lebar 12 mm. Dari pengujian detektor diperoleh bahwa tegangan ambang 2200 volt, plats 125 volt, slope 2,3%/100 volt, resolusi energi 11,66 % dan efisiensi 8,57 % terhadap sinar-X dengan somber Fels pada jarak 0 mm. A side window proportional counter has been made and observed. Argon and methane with the total pressure of 400 mmHg and the pressure ratio of 95 ; 5 are used as a filled gas. The cathode with diameter of 24,2 mm, length of 100 mm and anode with diameter of 0,08 mm made of stainless steel and tungsten respectively are used in this experiment. Beryllium with length of 24 mm and width of 12 mm is used as a window. The performance test of this detector shows that the treshold voltage , plateau, slope, energy resolution and efficiency for X-ray with Fe55 as a radiation source at 0 mm are 2200 volt, 125 volt, 2,3%/100 volt, 11,66 % and 8,57 % respectively