# Practical Estimation of Machine Tool Spindle Dynamics for Maintenance Decision Making
## 1 Introduction
### Advanced Methods for Modal Analysis Data Collection  
The challenge of applying modal analysis techniques for machine tools is an active research problem as demonstrated by the recent review conducted by [PERSON] et al. on a series of emerging technologies aimed at the assessment of machine tool dynamics [12]. The authors found that while many new methods show promise, they suffered from being too situationally specific, requiring a complex experimental setup and, generally, being more time-consuming to perform than conventional methods. [PERSON] and [PERSON] developed a prototype spindle condition estimation device that uses a solenoid-driven mass to apply an impulse force to the housing of a machine tool spindle. Notable features of this design are the integration of two accelerometers and a force sensor into the device and a magnetic base, which allows the small device to be portable and attached to the spindle housings of different machines [14]. [PERSON] et al. used a custom-made impact hammer excitation system which used a double-not flexure actuated by an electromagnet to reliably excite frequencies up to 20 kHz in miniature ultra-high-speed spindles. The resultant vibrations from the spindle were measured using two mutually perpendicular laser Doppler vibrometers [15]. [PERSON] et al. developed a novel method to excite micromilling tools by shooting ball bearings at the tool using compressed air; then, tool deflections were measured using a contactless eddy current sensor. The limitations of this setup were that direct measurement of the impact force was not possible and the force imparted by the ball was modeled using finite element simulations based on geometry, mass, and velocity data for each ball bearing [16]. Noncontact methods that excite the spindle have also been explored, such as the electromagnetic system designed by [PERSON] et al., which applies a noncontact force to the tip of an HSK standard tool [17]. The system can apply both a static magnetic force and sinusoidal forces through pulse-width-modulated control signals in perpendicular x and y directions. While the system was successfully demonstrated to measure the FRF of static and rotating spindles, the electromagnetic shaker is large and takes up valuable table space in the ma chine tool that would have significant implications on the productivity of the operation in a continuous monitoring application. Finally, research has been conducted on instrumented machine tools that use sweep milling force excitation to estimate the FRF using cutting forces as the input excitation. [PERSON] et al. used a table-mounted dynamometer and a dynamometric tool holder to measure the cutting forces and response of the spindle with three mutually perpendicular accelerometers [18]. The FRF generated by the cutting force excitation agreed with both the hammer impact testing and shaker tests. On the one hand, this method is useful because measurements could in theory be collected during the actual cutting operation, and the resulting FRF would most accurately describe the specific cutting dynamics under consideration. On the other hand, [PERSON] notes that to solve the three-dimensional system of equations, a minimum of three independent cutting tests must be performed by modifying the cutting condition. This limitation may be in opposition to the constraints of the actual cutting operation in practice and, therefore, limits the usage of the method. Furthermore, the table-mounted dynamometer suffers from the same space limitations as previously described. On the basis of a review of the current state of the art, the common pitfalls of FRF data collection equipment making FRF tracking unsuitable for CBM are as follows:  
1. Stationary test equipment is complex and takes up valuable space on the machine table. 2. Portable test equipment requires the attention of a skilled operator, which is not scalable for repetitive data collection tasks. 3. Tests are time-consuming to perform. 4. Tests interfere with production cycles.