# Practical Estimation of Machine Tool Spindle Dynamics for Maintenance Decision Making
## 1 Introduction  
### Background  
Condition-based maintenance (CBM), the practice of driving maintenance decisions using condition monitoring data, has been proposed as an advanced maintenance strategy enabled by Industry 4.0 initiatives to reduce the overall costs of equipment ownership and improve the productivity of manufacturing enterprises [1]. However, reports from McKinsey & Company indicate that many CBM initiatives fall short of these promised goals and report little measurable impact [2]. Unsuccessful advanced maintenance programs tend to place too much emphasis on the technology, rather than the high-impact root-cause problems of the machine [3].  
In the context of CNC milling operations, the roles of the machine tool spindle unit are to (1) facilitate the precision rotation of the tool at the commanded speed and (2) to transmit the required forces and energy to the cutting zone for metal removal [4]. The ability of a spindle to accomplish these tasks is fundamentally governed by the dynamic characteristics of the spindle's modes, that is, the mass, stiffness, and damping properties of the system. Experimental modal analysis provides a means to directly measure these dynamic characteristics by describing how a system vibrates in response to an input excitation force.  
Industry-standard spindle monitoring procedures do not outline methods for the modal characterization of machine tool spindle units. For example, the standard ISO 10816, which describes methods for evaluating the mechanical vibrations of rotating machines, considers only the vibration magnitude root mean square level [5]. Similarly, standard ISO/TR 17243, which is specifically tailored to the monitoring of machine tool spindle vibration, also onlyconsiders the average magnitude and neglects the frequency domain analysis, tracking of dynamic characteristics, or machining performance metrics for maintenance decision making [6]. This is despite the existence of established techniques for the modal analysis of machine tool spindle units. The pioneering works concerned with the modal analysis of machine tools for metal cutting were established by [PERSON] and [PERSON] [7] and [PERSON] and [PERSON] [8] in the 1950s. Another study established the groundwork for the powerful prediction of machine tool performance such as chatter stability in metal cutting processes [9]. Modal analysis has found additional usage outside of chatter prediction, such as by [PERSON] and [PERSON], who used the technique to model and predict the behavior of a machine tool spindles unit and optimize spindle design for maximum dynamic stiffness [10]. Given that the connection between modal analysis and spindle performance has been established for decades, why has the field of machine condition monitoring and CBM not capitalized on this knowledge to drive impactful maintenance decisions?  
[PERSON] et al. established that successful CBM is predicated on the ability to acquire machine condition data at regular intervals for processing and maintenance decision making [11]. Before using modal analysis for CBM applications, the problem of frequency response function (FRF) data collection must be overcome. When compared to conventional vibration monitoring practices currently used by CBM programs, the collection of FRF data is more difficult as it requires collection of both the input excitation forces and the vibration response [12]. Conventional methods for experimental modal analysis include the use of either an impact hammer or a shaker to excite the mechanical system with an impulse, a transient sine-sweep, or a random excitation [13]. However, both of these devices require specialized equipment and a skilled operator to perform the test, which presents a challenge when trying to implement this type of data collection in a wide scale CBM operation. New methods of FRF data collection are needed if CBM is to be enhanced by the tracking of modal characteristics.