Analytical prediction of part dynamics for machining stability analysis

An analytical procedure is developed to predict workpiece dynamics in a complete machining cycle in order to obtain frequency response functions (FRF) which are needed in chatter stability analyses. For this purpose, a structural modification method which is an efficient tool for updating FRFs is used. The removed mass by machining is considered as a structural modification in order to determine the FRFs at different stages of the process. The method is implemented in a computer code and demonstrated on different geometries. The predictions are compared and verified by FEA. Predicted FRFs are used in chatter stability analyses, and the effect of part dynamics on stability is studied. Different cutting strategies are compared for increased chatter free material removal rates considering part dynamics

Acetylation of BMAL1 by TIP60 controls BRD4-P-TEFb recruitment to circadian promoters.

Many physiological processes exhibit circadian rhythms driven by cellular clocks composed of interlinked activating and repressing elements. To investigate temporal regulation in this molecular oscillator, we combined mouse genetic approaches and analyses of interactions of key circadian proteins with each other and with clock gene promoters. We show that transcriptional activators control BRD4-PTEFb recruitment to E-box-containing circadian promoters. During the activating phase of the circadian cycle, the lysine acetyltransferase TIP60 acetylates the transcriptional activator BMAL1 leading to recruitment of BRD4 and the pause release factor P-TEFb, followed by productive elongation of circadian transcripts. We propose that the control of BRD4-P-TEFb recruitment is a novel temporal checkpoint in the circadian clock cycle

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

Selection of design and operational parameters in spindle-holder-tool assemblies for maximum chatter stability by using a new analytical model

In this paper, using the analytical model developed by the authors, the effects of certain system design and operational parameters on the tool point FRF, thus on the chatter stability are studied. Important conclusions are derived regarding the selection of the system parameters at the stage of machine tool design and during a practical application in order to increase chatter stability. It is demonstrated that the stability diagram for an application can be modified in a predictable manner in order to maximize the chatter-free material removal rate by selecting favorable system parameters using the analytical model developed. The predictions of the model, which are based on the methodology proposed in this study, are also experimentally verified

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

Investigating dynamics of machine tool spindles under operational conditions

Chatter is one of the major problems in machining and can be avoided by stability diagrams which are generated using frequency response functions (FRF) at the tool tip. During cutting operations, discrepancies between the stability diagrams obtained by using FRFs measured at the idle state and the actual stability of the process are frequently observed. These deviations can be attributed to the changes of machine dynamics under cutting conditions. In this paper, the effects of the cutting process on the spindle dynamics are investigated both experimentally and analytically. The variations in the spindle dynamics are attributed to the changes in the bearing parameters. FRFs under cutting conditions are obtained through the input-output relations of the cutting forces and the vibration response which are measured simultaneously. Experimentally and analytically obtained FRFs are then used in the identification of the bearing parameters under cutting conditions. Thus, bearing properties obtained at idle and cutting conditions are compared and variations in their values are obtained

On Hermite-Hadamard type inequalities for multiplicative fractional integrals

In this study, we first establish two Hermite-Hadamard type inequality for multiplicative (geometric) Riemann-Liouville fractional integrals. Then, by using some properties of multiplicative convex function, we give some new inequalities involving multiplicative fractional integrals.WOS:0005415092000062-s2.0-8508949314

New generalized midpoint type inequalities for fractional integral

Agarwal, Praveen/0000-0001-7556-8942WOS: 000504461100011Here, our first aim to establish a new identity for differentiable function involving Riemann-Liouville fractional integrals. Then, we obtain same generalized midpoint type inequalities utilizing convex and concave function

On Fejér Type Inequalities For Products Two Convex Functions

In this paper, we first obtain some new Fejér type inequalities for products of two convex mappings. Moreover, by applying these inequalities for Riemann-Liouville fractional integrals, we establish some Fejér type inequalities involving Riemann-Liouville fractional integrals. The most important feature of our work is that it contains Fejér type inequalities for both classical integrals and fractional integrals