**4. Conclusion**

**3.2. Preliminary Experimental results**

82 Advances in Vibration Engineering and Structural Dynamics

function of spindle age.

**Figure 9.** Blank Tool (left) and Blank Tool in Spindle (middle and right).

**Figure 10.** Natural Frequency vs. Machine Hours.

The experimentally evaluated Frequency Response Function (FRF) data were collected for a machine over the period of twelve months. A 1-inch diameter blank tool with a 2-inch pro‐ trusion was used. A typical shrink fit tool holder was also used (See Figure 9). This type of holder was selected for its rigid contact surface with the tool. Therefore, any play in the whole system was going to be attributed to the spindle. The tested machine was used to pro‐ duce typical machined parts and was not restricted to one type of cut. This was done to ob‐ serve the spindle decay over time while operating under normal production conditions. The tool was placed in the spindle and the spindle was returned to its neutral position as shown in Figure 9. Acceleration transducers were placed in both the *X* and *Y* direction. The tool was struck with an impulse hammer in both the *X* and *Y* directions and corresponding bending natural frequencies were evaluated over the time. Figure 10 shows the bending nat‐ ural frequencies of the non-spinning spindle vs. machine hours. As can be seen, system nat‐ ural frequencies in both *X* and *Y* directions reduce with spindle's life, which can be attributed to bearings decay. Further reseatrch is underway to analyze more spindles and to model the system decay by establishing a relationship between bearings stiffness, *Ks*, and machine hours. This, in turn, can be used to predict the optimum machining parameters as a

The effects of spindle system's vibrational behavior on the stability lobes, and as a result on the Chatter behavior of machine tools have been established. It has been observed that the service life changes the vibrational behavior of spindles, i.e., reduced natural frequency over the time. An analytical model of a multi-segment spinning spindle, based on the Dynamic Stiffness Matrix (DSM) formulation and exact within the limits of the Euler-Bernoulli beam bending theory, was developed. The beam exhibits coupled Bending-Bending (B-B) vibra‐ tion and, as expected, its natural frequencies are found to decrease with increasing spinning speed. The bearings were included in the model using two different models; rigid, simplysupported,frictionless pins and flexible linear spring elements. The linear spring element stiffness, *Ks*, was then calibrated so that the fundamental frequency of the system matched the nominal data provided by the manufacturer. This step is vital to the next phase of the authors' ongoing research, where the bearing wear would be modeled in terms of spindle's service time/age, to investigate the consequent effects on the stability lobes and, in turn, on themachine Chatter.
