scholarly journals Prediction of the Frequency Response Function of a Tool Holder-Tool Assembly Based on Receptance Coupling Method

2018 ◽  
Vol 8 (6) ◽  
pp. 3556-3560
Author(s):  
X. J. Xuan ◽  
Z. H. Haung ◽  
K. D. Wu ◽  
J. P. Hung
Keyword(s):  
Frequency Response ◽  
Response Function ◽  
Frequency Response Function ◽  
High Speed ◽  
Milling Process ◽  
Element Analysis ◽  
Tool Holder ◽  
Machine Performance ◽  
Receptance Coupling ◽  
Overhang Length

Regenerative chatter has a fatal influence on machine performance in high-speed milling process. Basically, machine condition without chattering can be selected from the stability lobes diagram, which is estimated from the tool point frequency response function (FRF). However, measurements of the tool point FRF would be a complicated and time-consuming task with less efficiency. Therefore prediction of the tool point FRF is of importance for further calculation of the machining stability. This study employed the receptance coupling analysis method to predict the FRF of a tool holder-tool module, which is normally composed of substructures, tool holder and cutter with different length. In this study, the angular components of FRFs of the substructures required for coupling operation were predicted by finite element analysis, apart from the translational components measured by vibration experiments. Using this method, the effects of the overhang length of the cutter on the dynamic characteristics have been proven and successfully verified by the experimental measurements. The proposed method can be an effective way to accurately predict the dynamic behavior of the spindle tool system with different tool holder-tool modules.

scholarly journals FINITE ELEMENT ANALYSIS OF CENTRELESS-LUNETTE TURNING OF HEAVY SHAFT

2017 ◽  
Vol 16 (3) ◽  
pp. 196-205
Author(s):  
Yu. V. Vasilevich ◽  
S. S. Dounar
Keyword(s):  
Frequency Response ◽  
Response Function ◽  
Frequency Response Function ◽  
Polymer Concrete ◽  
Element Analysis ◽  
Support Tool ◽  
Near Resonance ◽  
Dynamic Damping ◽  
It Support ◽  
Concrete Filling

Dynamics of huge renovated lathe is simulated. Turning scheme concerns to heavy rotor shaft finishing. Lofty parts and milling head may create dynamic problems. Static, modal and harmonic frequency response function simulations were provided. Bearing system consists of bed, support, tool, lunettes, tailstock. Headstock didn’t take part in shaft holding. Static and dynamic rigidities founded 3–4 times less for support than for shaft. Tool rigidity lessens from 186.5 to 11.9 N/µm for speeding from slow to near resonance turning. Twelve lathe eigenmodes were evaluated. Two eigenmodes are most dangerous. It is “shaft swinging on lunettes” (M1, 26.7 Hz) and “support pecking” (M3, 54.4 Hz). Bed has excessive flexibility due to through holes and lack of inner ribbing. Polymer concrete filling is moderately effective. Changing two-lunette (2L) scheme to three-lunette (3L) increases rigidity of shaft at 2.09 times at statics but gives limited action in dynamics. Resonant peaks on frequency response function are lowered only at 1.32 times for M1, M3. Effect of dynamic damping is revealed under condition of proximity middle lunette to lofty support. Support serves as tuned mass damper. Measures of machine tool reinforcement are simulated. Shaft swinging according to M1 may hardly be blocked by passive means. It would be better to bypass it. “Support pecking” resonance (M3) succumbs to only full set of measures. Small effect of partial reinforcement is predicted. Three frequency intervals are recommended for turn-milling at huge lathe: pre-resonant (<20 Hz), inter-resonant (35–45 Hz) and post-resonant (>65 Hz). The last one is more suited. Next design step is to create triangle inner ribbing system or caissons inside of bed.

A Study of Linear Joint and Tool Models in Spindle-Holder-Tool Receptance Coupling

2005 ◽  
Author(s):  
Timothy J. Burns ◽  
Tony L. Schmitz
Keyword(s):  
Frequency Response ◽  
High Speed ◽  
Nonlinear Least Squares ◽  
Analytical Models ◽  
Connection Matrix ◽  
Depth Of Cut ◽  
Combined System ◽  
Receptance Coupling ◽  
Overhang Length ◽  
Exponential Trend

The dynamics of a spindle-holder-tool (SHT) system during high-speed machining is sensitive to changes in tool overhang length. A well-known method for predicting the limiting depth of cut for avoidance of tool chatter requires a good estimate of the tool-point frequency response (FRF) of the combined system, which depends upon the tool length. In earlier work, a combined analytical and experimental method has been discussed, that uses receptance coupling substructure analysis (RCSA) for the rapid prediction of the combined spindle-holder-tool FRF. The basic idea of the method is to combine the measured direct displacement vs. force receptance (i.e., frequency response) at the free end of the spindle-holder (SH) system with calculated expressions for the tool receptances based on analytical models. The tool was modeled as an Euler-Bernoulli (EB) beam, the other three spindle-holder receptances were set equal to zero, and the model for the connection with the tool led to a diagonal matrix. The main conclusion of the earlier work was that there was an exponential trend in the dominant connection parameter, which enabled interpolation between tip receptance data for the longest and shortest tools in the combined SHT system. Thus, a considerable savings in time and effort could be realized for the particular SHT system. A question left open in the earlier work was: how general is this observed exponential trend? Here, to explore this question further, an analytical EB model is used for the SH system, so that all four of its end receptances are available, and the tool is again modeled as a free-free EB beam that is connected to the SH by a specified connection matrix, that includes nonzero off-diagonal terms. This serves as the “exact” solution. The approximate solution is once again formed by setting all but one SH receptance equal to zero, and the connection parameters are determined using nonlinear least squares software. Both diagonal and full connection matrices are investigated. The main result is that, for this system, in the case of a diagonal connecting matrix, there is no apparent trend in the dominant connecting spring stiffness with tool overhang length. However, in the full connecting matrix case, a general constant trend is observed, with some interesting exceptions.

RCSA-Based Method for Tool Frequency Response Function Identification Under Operational Conditions Without Using Noncontact Sensor

2017 ◽  
Vol 139 (6) ◽  
Author(s):  
Rong Yan ◽  
Xiaowei Tang ◽  
Fangyu Peng ◽  
Yuting Li ◽  
Hua Li
Keyword(s):  
Frequency Response ◽  
Response Function ◽  
Frequency Response Function ◽  
Fem Simulation ◽  
Operational Conditions ◽  
Receptance Coupling ◽  
Substructure Analysis ◽  
Cutting Experiment ◽  
Receptance Coupling Substructure Analysis ◽  
The Stability

The stability lobe diagrams predicted using the tool frequency response function (FRF) at the idle state usually have discrepancies compared with the actual stability cutting boundary. These discrepancies can be attributed to the effect of spindle rotating on the tool FRFs which are difficult to measure at the rotating state. This paper proposes a new tool FRF identification method without using noncontact sensor for the rotating state of the spindle. In this method, the FRFs with impact applied on smooth rotating tool and vibration response tested on spindle head are measured for two tools of different lengths clamped in spindle–holder assembly. Based on those FRFs, an inverse receptance coupling substructure analysis (RCSA) algorithm is developed to identify the FRFs of spindle–holder–partial tool assembly. A finite-element modeling (FEM) simulation is performed to verify the validity of inverse RCSA algorithm. The tool point FRFs at the spindle rotating state are obtained by coupling the FRFs of the spindle–holder–partial tool and the other partial tool. The effects of spindle rotational speed on tool point FRFs are investigated. The cutting experiment demonstrates that this method can accurately identify the tool point FRFs and predict cutting stability region under spindle rotating state.

Tool Point Frequency Response Prediction for Micromilling by Receptance Coupling Substructure Analysis

2017 ◽  
Vol 139 (7) ◽  
Author(s):  
Lu Xiaohong ◽  
Jia Zhenyuan ◽  
Zhang Haixing ◽  
Liu Shengqian ◽  
Feng Yixuan ◽  
...  
Keyword(s):  
Frequency Response ◽  
Response Function ◽  
Frequency Response Function ◽  
Research Work ◽  
Modal Parameters ◽  
Rotational Degree ◽  
Receptance Coupling ◽  
Milling Tool ◽  
Substructure Analysis ◽  
Receptance Coupling Substructure Analysis

One of the challenges in micromilling processing is chatter, an unstable phenomenon which has a larger impact on the microdomain compared to macro one. The minimization of tool chatter is the key to good surface quality in the micromilling process, which is also related to the milling tool and the milling structure system dynamics. Frequency response function (FRF) at micromilling tool point describes dynamic behavior of the whole micromilling machine-spindle-tool system. In this paper, based on receptance coupling substructure analysis (RCSA) and the consideration of rotational degree-of-freedom, tool point frequency response function of micromilling dynamic system is obtained by combining two functions calculated from beam theory and obtained by hammer testing. And frequency response functions solved by Timoshenko's and Euler's beam theories are compared. Finally, the frequency response function is identified as the modal parameters, and the modal parameters are transformed into equivalent structural parameters of the physical system. The research work considers the difference of theoretical modeling between the micromilling and end-milling tool and provides a base for the dynamic study of the micromilling system.

Effect of a Nonlinear Joint on the Dynamic Performance of a Machine Tool

2007 ◽  
Vol 129 (5) ◽  
pp. 943-950 ◽  
Author(s):  
Jaspreet S. Dhupia ◽  
Bartosz Powalka ◽  
A. Galip Ulsoy ◽  
Reuven Katz
Keyword(s):  
Machine Tool ◽  
Frequency Response ◽  
Response Function ◽  
Frequency Response Function ◽  
Dynamic Performance ◽  
Stability Lobe ◽  
Receptance Coupling ◽  
Nonlinear Joint ◽  
Stability Lobe Diagrams ◽  
Machine Structure

This paper presents the effect of experimentally evaluated nonlinearities in a machine joint on the overall machine tool dynamic performance using frequency response functions and stability lobe diagrams. Typical machine joints are very stiff and have weak nonlinearities. The experimental evaluation of the nonlinear joint parameters of a commercial translational guide has been discussed in Dhupia et al., 2007, J. Vibr. Control, accepted. Those results are used in the current paper to represent the connection between the column and the spindle of an idealized column-spindle machine structure. The goal is to isolate and understand the effects of such joints on the machine tool dynamic performance. The nonlinear receptance coupling approach is used to evaluate the frequency response function, which is then used to evaluate the stability lobe diagrams for an idealized machine structure. Despite the weak nonlinearities in the joint, significant shifts in the natural frequency and amplitudes at resonance can be observed at different forcing amplitudes. These changes in the structural dynamics, in turn, can lead to significant changes in the location of chatter stability lobes with respect to spindle speed. These variations in frequency response function and stability lobe diagram of machine tools due to nonlinearities in the structure are qualitatively verified by conducting impact hammer tests at different force amplitudes on a machine tool.

scholarly journals Road Roughness Estimation Based on the Vehicle Frequency Response Function

Actuators ◽  
2021 ◽  
Vol 10 (5) ◽  
pp. 89
Author(s):  
Qingxia Zhang ◽  
Jilin Hou ◽  
Zhongdong Duan ◽  
Łukasz Jankowski ◽  
Xiaoyang Hu
Keyword(s):  
Frequency Response ◽  
Response Function ◽  
Frequency Response Function ◽  
Gaussian White Noise ◽  
Estimation Method ◽  
Time Shift ◽  
Ride Quality ◽  
The Road ◽  
Road Roughness ◽  
Measured Response

Road roughness is an important factor in road network maintenance and ride quality. This paper proposes a road-roughness estimation method using the frequency response function (FRF) of a vehicle. First, based on the motion equation of the vehicle and the time shift property of the Fourier transform, the vehicle FRF with respect to the displacements of vehicle–road contact points, which describes the relationship between the measured response and road roughness, is deduced and simplified. The key to road roughness estimation is the vehicle FRF, which can be estimated directly using the measured response and the designed shape of the road based on the least-squares method. To eliminate the singular data in the estimated FRF, the shape function method was employed to improve the local curve of the FRF. Moreover, the road roughness can be estimated online by combining the estimated roughness in the overlapping time periods. Finally, a half-car model was used to numerically validate the proposed methods of road roughness estimation. Driving tests of a vehicle passing over a known-sized hump were designed to estimate the vehicle FRF, and the simulated vehicle accelerations were taken as the measured responses considering a 5% Gaussian white noise. Based on the directly estimated vehicle FRF and updated FRF, the road roughness estimation, which considers the influence of the sensors and quantity of measured data at different vehicle speeds, is discussed and compared. The results show that road roughness can be estimated using the proposed method with acceptable accuracy and robustness.

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