A high level of accuracy is always required when machining a work-piece. To achieve this level of accuracy, the characteristics and dynamics of the machine should be studied and analysed, the machine responds to excitations and inputs. Many papers have been published explaining and identifying the machine’s dynamic characteristics such as milling and grinding.
In part of computational modelling and simulation, Xiao et al, (1992) have used intelligent plunge control to develop Optimisation Strategies for a grinding cycle. Also, in 1980, Garcia- Gardea et al. developed a Dynamic Data System (DDS) approach which was used for estimating the dynamic characteristics of machining process. This approach work by analysing the cutting force signals, is also based on the statement that, the cutting forces signals should have all features of machine dynamics. Due to the fact that the modelling was based on real experiment data which was collected from machining operations, the DDS method can give better accuracy on dynamic characteristics estimation for the machine tool.
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Cheng et al, (2007) worked on a milling machine, they tried to explain and identify the frequency response of a spindle for the tool holder. The impact test has been used with a low- mass accelerometer in order to determinate the Frequency Response Function (FRF) of the system unit. Non- rotating mode for the spindle was used for this approach. In addition, this method can provide acceptable results and reliable predictions of the response. On the other hand, some spindles’ responses vary with their spindle rotating speed and the predictions of Frequency Response Functions (FRF) based on the non-rotating mode for spindle may not be sufficient when the spindle is rotating at a speed of about 10,000 RPM. However, another measuring method called Reacceptance Coupling Substructure Analysis was used for the system response predictions, it also was shown that the response was quite different (Movahhedy and Mosaddeh, 2006; Schmitz et al., 2004; Xiong, G.L. et al., 2003; Tian and Hutton, 2001).
The dynamics of the cylindrical grinding machine have been studied using model experimental data by Jiang et al. (2007). During the grinding process, they were trying to collect and avoid typical values of the machine-produced vibration. In this work, non-contact displacement sensors and accelerometers were used to collect readings of 25 measuring points which were set on the grinding machine. In the first experiment, the machine’s natural frequency was identified in the condition of static mode, where the impact load was used to produce the input excitation force. The critical frequencies have been identified for the wheel that was rotating with speeds of 70-700 RPM in a second experiment. The same test was performed but in a real grinding process. Also, the critical vibration frequencies during the grinding process were revealed and also analysis of the relationship between the work-piece spindle speed and surface coarseness was obtained. In addition, it concludes that when they were increasing the spindle speed, the surface roughness of the work-piece was improved. As the result of that, the work-piece should be ground at high spindle speed in order to improve the surface roughness.
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In 2005 Zhang et al. studied some ways in dynamic analysis of machining process, to improve the surface roughness of the work-piece. In order to achieve that, they worked to determine the characteristics of frequency amplitude for the machining process. The following conditions of machining process have been considered:
The grinding wheel type is Synthetic Aluminium Oxide (250 mm).
Cutting speed was between 30 to 35 m/s.
Depth of Cut 0.005 to 0.03 mm.
Grain size was about 0.4 and 0.5 mm.
The range of vibration frequency was from 0 to 120 Hz.
The range of vibration amplitude was from 0.001 to 0.002 mm.
They concluded that the developed model was only giving good results with the considered range of vibration frequency, also the machine quality behaviour was changed with the changing of frequency.
The Finite Element Method (FEM) has been used by Kang et al., (2001) for modelling a harmonic response of the milling machine. In order to identify the stability margins, analysing of modal, static and stability have been conducted. They identified the natural frequencies of their system, these frequencies and model shapes of the jigs allowed them to obtain the instability speed threshold. However, for the design of spindle bearing systems, the Computation Aided Engineering (CAE) strategies cannot present a complete solution.
Denkena et al. (2016) have done an experiment to investigate the dynamic behaviour of the integrated z-slide (the spindle unit) in a CNC-milling machine. They used an electro dynamic shaker to provide the excitation force. This shaker was fixed in vertical direction to the spindle unit. They also used a force sensor fixed to the tool side, so the applied force could be measured. The spindle was excited with a linear frequency sweep. The maximum excitation frequency they reached was 200 Hz. Moreover, their results show that the sensitivity of the strain gauges is quite stable in the range of frequency values under 100 Hz. Then, the natural frequency of the spindle unit was appearing from 100 Hz to 150Hz as shown in figure 6.1.
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Figure 6. 1: Test setup and frequency responses of the sensory spindle unit (Denkena, B. et al., 2015).
Prakosa and others (Prakosa et al. 2013) were dealing with an activity in machine tools’ performance that can improve spindle static and dynamic stiffness. They were identifying mathematical models for static stiffness, dynamic stiffness and temperature rise in the milling machine tool. Their models conformed well to the results from real experiments. To validate the dynamic model for their spindle unit, they used the Frequency Response Function (FRF) experiment using a Hammer impact and spectrum analyser. However, they validated the static stiffness model experimentally. A pneumatic actuator was used to actuate static load at the machine spindle head. Also, a dial indicator was used to measure the corresponding deflection.
6.2.1 Resonance Vibration
Modes are used as a simple and efficient means of characterizing resonance in vibration. The majority of structures can be made to resonate. Under the best experimental conditions, a structure can be made to vibrate with excessive, sustained, oscillatory motion. Resonant
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vibration is caused by an interaction between the inertial and elastic properties of the materials within a structure. Resonant vibration is often the cause of, or at least a contributing factor to, many of the vibration related problems that occur in structures and operating machinery. To better understand any structural vibration problem, the resonances of a structure need to be identified and quantified. A common way of doing this is to define the structure’s modal parameters (Guillaume, 2006).
Forced vibration can come from: External loads.
Ambient excitation. Imbalances.
Internally generated forces.
Resonant vibration occurs when one or more of the resonances or natural modes of vibration of a machine or structure is excited. Resonant vibration typically amplifies the vibration response far beyond the levels of deflection, stress, and strain caused by static loading
(Boisson et al. 2014).
Modes and resonances are intrinsic properties of a structure and shape. Resonances are determined by the material properties (mass, stiffness, and damping properties) and boundary conditions of the structure. Each mode is defined by a natural (modal or resonant) frequency, modal damping, and a mode shape. If the material properties or the boundary condition of a structure change, its modes will definitely change. For example, if mass is added to a beam structure, it will in a different way because its modes have changed.
At or near the natural frequency of a mode, the overall vibration shape (operating deflection shape) of a machine or structure will tend to be dominated by the mode shape of the resonance.
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From the works that have been done on this issue of machine system response, it is to be noted that it is not simple to identify the system’s dynamic characteristics. Also, there are no fully accurate results that come from computation methods and simulation analysis because other external factors are not considered, which can affect performance and stability of the system. However, this work gives a clear view of the system’s response.