Estimation of the Frequency Response Function of the Rotational Degree of Freedom

One of the factors that influence the dynamic characteristics of machining systems is the cutting tool. Cutting tools are very diverse, and receptance coupling substructure analysis (RCSA) is essential for analyzing the dynamic characteristics of each tool. For RCSA, a full receptance matrix of the equipment and tools is essential. In this study, rotational degree-of-freedom receptance was estimated and analyzed using translational receptance. Displacement/moment receptance was analyzed according to the distance of the response point using the first-and second-order finite difference methods. The rotation/moment receptance was estimated according to the distance of the response point. Rotation/moment receptance was analyzed using Schmitz’s method and compensation strategies. The limitations of these strategies were analyzed, and the rotation/moment receptance for the beam under free-free boundary conditions was predicted using the second compensation strategy.

Multi-point substructure coupling method to compensate multi-accelerometer masses in measuring rotation-related FRFs

Tool-tip Frequency Response Functions (FRFs) are often required in milling vibration analysis. Receptance coupling substructures analysis (RCSA) affords an efficient analytical way for different tool-tip FRFs prediction with only one modal test. The coupling theory includes both translational and rotational degrees of freedom, so rotation-related FRFs are essential to know in the test. The finite-differential technique is generally used to measure these special FRFs due to the avoidance of specialist equipment. The technique uses several translational accelerometers spatially placed close to each other to approximate the rotational vibration. However, the added sensor masses lead to the frequency shift of the test structure, and the phenomenon would aggravate as the sensors increase. The polluted measurement data would subsequently decrease the tool-tip FRFs prediction accuracy. Addressing this problem, this paper introduces a multi-point substructure coupling method to simultaneously compensate the multi-accelerometer masses in a single experimental setup. The proposed method considers the installed accelerators as multiple point masses and then uses inverse coupling calculation to isolate their effect. The compensation procedure is first effectively validated in simulation and experiment, and then it is integrated into an RCSA-based application of predicting different tool-tip dynamics. Experimental results show that the compensated FRF data can improve prediction accuracy, especially when predicting tools shorter than the tested tool.

Optimization and Tuning of Passive Tuned Mass Damper Embedded in Milling Tool for Chatter Mitigation

Milling tools with a large length–diameter ratio are widely applied in machining structural features with deep depth. However, their high dynamic flexibility gives rise to chatter vibrations, which results in poor surface finish, reduced productivity, and even tool damage. With a passive tuned mass damper (TMD) embedded inside the arbor, a large length–diameter ratio milling tool with chatter-resistance ability was developed. By modeling the milling tool as a continuous beam, the tool-tip frequency response function (FRF) of the milling tool with TMD was derived using receptance coupling substructure analysis (RCSA), and the gyroscopic effect of the rotating tool was incorporated. The TMD parameters were optimized numerically with the consideration of mounting position based on the maximum cutting stability criterion, followed by the simulation of the effectiveness of the optimized and detuned TMD. With the tool-tip FRF obtained, the chatter stability of the milling process was predicted. Tap tests showed that the TMD was able to increase the minimum real part of the FRF by 79.3%. The stability lobe diagram (SLD) was predicted, and the minimum critical depth of cut in milling operations was enhanced from 0.10 to 0.46 mm.

Design of Chatter-Resistant Damped Boring Bars Using a Receptance Coupling Approach

Deep hole boring using slender bars that have tuned mass dampers integrated within them make the boring process chatter vibration resistant. Dampers are usually designed using classical analytical solutions that presume the (un)damped boring bar which can be approximated by a single degree of freedom system, and the damper is placed at the free end. Since the free end is also the cutting end, analytical models may result in infeasible design solutions. To place optimally tuned dampers within boring bars, but away from the free end, this paper presents a receptance coupling approach in which the substructural receptances of the boring bar modelled as a cantilevered Euler–Bernoulli beam are combined with the substructural receptances of a damper modelled as a rigid mass integrated anywhere within the bar. The assembled and damped system response thus obtained is used to predict the chatter-free machining stability limit. Maximization of this limit is treated as the objective function to find the optimal mass, stiffness and damping of the absorber. Proposed solutions are first verified against other classical solutions for assumed placement of the absorber at the free end. Verified models then guide prototyping of a boring bar integrated with a damper placed away from its free end. Experiments demonstrate a ~100-fold improvement in chatter vibration free machining capability. The generalized methods presented herein can be easily extended to design and develop other damped and chatter-resistant tooling systems.

A Robust RCSA-Based Method for the In Situ Measurement of Rotating Tool-Tip Frequency Response Functions

Measuring rotating tool-tip frequency response functions (FRFs) is difficult because of the fluted tip geometry. The methods based on receptance coupling substructure analysis (RCSA) can obtain rotating tool-tip FRFs with a few tests. Existing RCSA-based methods require at least one smooth rod for measurement and then mathematically calculate the desired rotating tool-tip FRFs. However, involving the inverse of the experimentally obtained FRFs matrix, these methods are susceptible to the measurement noise in the rotating structure. In addition, the inconsistency between the holder–tool and holder–rod connections is another uncertainty which impacts accuracy. This paper presents a robust RCSA-based method to obtain rotating tool-tip FRFs. It is found that tool-tip FRFs can be calculated from another point FRFs on the same assembly. Then, one point on the smooth cylindrical shank of the tool is selected for measurement. The measured FRFs, along with those from the theoretical tool model, calculate the rotating tool-tip FRFs. Compared with the previous methods, the proposed one does not require inverting the measured FRFs matrix, inherently avoiding amplification of measurement noise. Since the tool replacement is no longer required, in situ measurement is achieved to ensure the same holder–tool connection throughout the procedure. The proposed method is first validated in a numerical case and then verified experimentally by a commercial hammer and laser vibrometer. Both results show that the method is insensitive to the measurement noise and can obtain rotating tool-tip FRFs with considerable accuracy.

A receptance-based method for frequency assignment via coupling of subsystems

This paper presents a theoretical study of the frequency assignment problem of a coupled system via structural modification of one of its subsystems. It deals with the issue in which the available modifications are not simple; for example, they are not point masses, grounded springs, or spring-mass oscillators. The proposed technique is derived based on receptance coupling technique and formulated as an optimization problem. Only a few receptances at the connection ends of each subsystem are required in the structural modification process. The applicability of the technique is demonstrated on a simulated rotor system. The results show that both bending natural frequencies and torsional natural frequencies can be assigned using a modifiable joint, either separately or simultaneously. In addition, an extension is made on a previously proposed torsional receptance measurement technique to estimate the rotational receptance in bending. Numerical simulations suggest that the extended technique is able to produce accurate estimations and thus is appropriate for this frequency assignment problem of concern.

Implementation of an Algorithm to Prevent Chatter Vibration in a CNC System

Machining of shafts characterized by a high compliance is difficult due to the occurrence of self-excited chatter vibrations. It is possible to limit their occurrence through the appropriate selection of technological parameters. For a proper selection of these parameters it is necessary to know the dynamic properties of the machine–tool–workpiece. This study proposes an approach through which these properties can be determined as a result of the synthesis of the dynamic properties of the system, using the receptance coupling method. Knowledge of these properties allows us to select the technological parameters of the lathe using the assistance system integrated into the CNC (Computerized Numerical Control). The final section of this work presents the experimental validation of the assistant and proposed procedures.