07NVC-176 Implementation of the Time Variant Discrete Fourier Transform as a Real-Time Order Tracking Method Brandon J. Dilworth and Jason R. Blough Michigan Technological University ABSTRACT The Time Variant Discrete Fourier Transform was implemented as a real-time order tracking method using developed software and commercially available hardware. The time variant discrete Fourier transform (TVDFT) with the application of the orthogonality compensation matrix allows multiple tachometers to be tracked with close and/or crossing orders to be separated in real-time. Signal generators were used to create controlled experimental data sets to simulate tachometers and response channels. Computation timing was evaluated for the data collection procedure and each of the data processing steps to determine how each part of the process affects overall performance. Many difficulties are associated with a real-time data collection and analysis tool and it becomes apparent that an understanding of each component in the system is required to determine where time consuming computation is located. INTRODUCTION Digital order tracking techniques vary in complexity and computational load, in general, covering two different types of techniques: Fourier Transform based and adaptive filtering and/or resampling methods. With the power of personal computers steadily increasing in the last ten years, many of the techniques avoided in the past are now being explored as viable options. In addition, some of the techniques used as post- processing algorithms are now being employed as real- time algorithms. Careful consideration must still be made when developing a real-time algorithm with respect to computer system performance and algorithm efficiency. With the power and speed of today’s computers there are many more options available to the noise and vibration engineer for analysis techniques. A number of different order tracking methods have been implemented in commercial software with many offering both types of techniques in an order analysis package. Almost every commercial package has a Fast Fourier Transform method available, and some also include a resampling based method as part of a base package. There are also a number of vendors that provide an additional package that includes the ability to separate close and/or crossing orders in data with multiple reference tachometer signals. These methods, however, are implemented solely as post-processing techniques. The time variant discrete Fourier transform (TVDFT) method is based upon a discrete Fourier transform which has a kernel whose frequency is not constant within the data block. The frequency of the kernel varies with the frequency of the order of interest, and is defined by a tachometer signal. The bandwidth of this technique may be either constant frequency or constant order bandwidth. The application of the orthogonality compensation matrix (OCM) to the kernel of the TVDFT allows for the accurate separation of close and/or crossing orders present in a data set. In the past, the application of the OCM has been a post-processing technique as the computational load can be demanding as the delta order spacing is reduced for conditions where the OCM is ill- conditioned. Increasing the delta order resolution is one method to improve the conditioning of the OCM, but it increases the required block size for the computation which increases the computational load of the algorithm. The implementation of the OCM as part of a real-time TVDFT algorithm makes it the only real-time order tracking algorithm currently available in industry capable of separating close and/or crossing orders. Although there are a few different definitions of the term “real-time” in industry, it is defined in this paper to be the ability to process data for a given block and present a result prior to the sampling of the next data block. ORDER TRACKING THEORY Orders are defined as rotational speed harmonics that relate the speed of a referenced rotating component to frequency. Order tracking is the estimation of the amplitude and phase of the response of a machine to a referenced rotating component that is allowed to vary in amplitude and frequency over time. Regardless of the method used for order tracking, the tachometer signal (either measured directly or generated virtually using a