Analysis system and method for testing gears

Abstract

A gear rotation testing method directed to analyzing and displaying gearset performance data, including kinematic transmission error, acquired using a gearset rotation testing machine or gearbox test fixture includes analyzing and visualizing this data in the time domain, frequency domain, and a combination thereof. The present invention further includes fundamental improvements in core signal processing, analysis and signal processing sequences that allow for more insightful exploration of the data, methods for visualizing and reporting the data and results, and a man-machine user interface paradigm with greater flexibility and usability for delivering these functions and features.

Description

[Technical field]

[0001] The present invention is directed to the processing, analysis, and display of sensor output, particularly with respect to gear testing. [Background technology]

[0002] The present invention is primarily directed to the processing, analysis, and display of various sensor outputs, particularly sensor outputs related to gearset motion transmission error (MTE), noise, and vibration phenomena that may occur during rotation testing of gearsets on a testing machine such as those described and shown in U.S. Patent Nos. 6,120,355 and 7,553,115, the disclosures of which are incorporated by reference. The present invention may also be implemented on a functional testing platform for gear rotation testing, such as a single flank or double flank testing machine, in which the relative motion between the axes of a pair of meshed gears is measured as they are rotated, for example, as shown by FIG. 1 of US 2020 / 0292305, the disclosures of which are incorporated by reference.

[0003] Sensors that produce outputs to which these methods can be applied include rotational position measuring devices such as encoders and resolvers, vibration measuring devices such as single and multi-axis accelerometers and acoustic sensors, and other motion or displacement measuring devices such as optical glass scales, magnetic scales, optical devices, laser devices, ultrasonic devices, and capacitive or inductive displacement transducers.

[0004] The sensors can be arranged in many configurations and arrangements. Rotary sensors typically monitor two spindles on which the driving and driven members of a gear set are mounted. If the device under test contains more than one set of gears (e.g., a gearbox or planetary assembly), the motion of other rotating elements can be measured by additional rotary encoders.

[0005] Linear, vibration, acoustic, and other sensors can be mounted at fixed locations on or near the testing machine, or on the linear or rotary motion elements of the testing machine (e.g., oscillating head and linear axes). For example, displacement measuring devices can be applied to a double flank gear set testing machine, whose output can also be analyzed by the system of the present invention. Vibration sensors can respond to solid borne vibrations, air borne vibrations, or a combination of both.

[0006] One or more accelerometers may also be attached to the rotating spindle to measure rotational motion, including acceleration, velocity, and position.

[0007] Rotating the installed gearset members under given speed and load conditions established by the testing machine induces vibrations and other motions in accordance with the nature and quality characteristics of the gearset being tested.

[0008] It is an object of the present invention to use said testing machine sensors to provide data and signals that can be processed and analysed to provide insight into the operational and quality characteristics of the gearset, in particular the motion error, noise and vibration characteristics.

[0009] It is a further object of the present invention to provide additional insight into the operational and quality characteristics of the gearset by processing and analysing mathematically derived data and signals, which may for example be obtained from computer simulations or may be the result of calculations of sensor data, such as accelerations analytically determined from position and time information.

[0010] The data or signals constituting the input to the system of the invention may be sampled and understood with reference to time (time sampling) or with reference to the rotational motion of one or more of the rotating gear members (rotation sampling). In the analysis of the above sensor signals related to the motion of the gear set, it is often particularly useful to represent the signals using rotation sampling. Where the invention employs rotation sampling, time information is preserved to facilitate conversion between time and rotation sampling, as required.

[0011] The present invention is directed to the analysis and display of gearset performance data including kinematic transmission error acquired using a gearset rotational test machine or gearbox test fixture, and includes analyzing and visualizing this data in the time domain, frequency domain, and a combination thereof. The present invention further includes fundamental improvements in the core signal processing, analysis and signal processing sequences that allow the data to be explored in a more insightful way, methods for visualizing and reporting the data and results, and the man-machine user interface paradigm to provide these functions and features in a more flexible and useful manner.

[0012] A salient aspect of the methodology of the present invention is the ability to extract and display dynamic behaviors that were previously hidden within data records that were treated as essentially static. Other aspects include the ability to trace or attribute data and results to individual teeth of the gearset member being tested (tooth “indexing”), and the ability for the user to interact with the display and dynamically change both analysis and visualization parameters. In addition to traditional “contract testing” (post-processing of collected data records according to strict predefined test and analysis parameters), the new flexible “always-on” paradigm for gearset rotation testers also provides these capabilities and features, whereby data collection, processing, analysis, anomaly detection, etc. are all performed autonomously and opportunistically whenever possible, without waiting for specific instructions from a human user or the initiation of a predefined cycle. In both the test and analysis methods, the human user can also further exploratively and interactively adjust parameters for analysis and display. It is to be understood that in the present invention, the terms “user” and “operator” are synonymous.

[0013] A first embodiment of the present invention is directed to a method of testing gears comprising providing a pair of gears including a first gear and a second gear, the first gear and the second gear operable to rotate in mesh with each other. The first gear is rotated on a gear tester with the second gear, the gear tester configured with one or more sensors operable to provide an output signal indicative of a rotational characteristic of the one or more gears. At least one independent signal is generated, the independent signal being at least one of a signal based on an output from one or more of the sensors or an analytically derived signal. From the at least one independent signal, at least one frame portion having a non-zero duration is selected, each of the selected frame portions being: determining a set of model basis functions based on the selected frame portion; generating model coefficients by projecting the selected frame portions onto model basis functions; determining a reconstructed model from the model coefficients and the model basis functions; obtaining a residual by subtracting the reconstructed model from the selected frame portion; The method further comprises: (a) displaying and analyzing the residuals to identify quality characteristics of at least one of the first gear and the second gear, and accepting or rejecting at least one of the first gear and the second gear based on the quality characteristics; and (b) displaying and analyzing the model coefficients or the reconstructed model to identify quality characteristics of at least one of the first gear and the second gear, and accepting or rejecting at least one of the first gear and the second gear based on the quality characteristics.

[0014] In a preferred embodiment, the model basis functions are determined from at least one of: (a) a duration of the selected frame portion; (b) a gear ratio of the first gear and the second gear; (c) a fundamental harmonic frequency generated by the first gear rotating with the second gear or a duration of a meshing period of the first gear meshing with the second gear; (d) a predetermined set of harmonics of each fundamental frequency, the set including zero; and (e) a set of non-periodic basis functions defined over the duration of the selected frame portion, the set including zero.

[0015] In another preferred embodiment, the reconstructed model and residuals are continually re-evaluated as additional information is acquired from sensors during machine operation.

[0016] In another preferred embodiment, multiple independent signals are sampled simultaneously at the same intervals to facilitate direct correlation and comparison.

[0017] In yet another preferred embodiment, at least one independent signal is collected at uniform time samples and subsequently interpolated to generate a sequence of regularly spaced samples at the position of one of the first and second gears.

[0018] In a further embodiment, the display and analysis results are retained in an electronic storage medium for recall; (a) Simultaneous, side-by-side presentation; (b) sequential presentation, where progression is directed by user interaction, and (c) The viewing and comparison of two or more previous records is accomplished by one or more of an automatic animated progression sequential presentation.

[0019] The present invention further discloses, as worthy of independent protection, a display and a method of displaying the residual, the reconstructed model, or a combination thereof, comprising: (a) subdividing the selected frame portion into a plurality of consecutive signal segments of equal duration, the duration being: 1. One or more complete meshing cycles; 2. One or more complete revolutions of any gear in the set, with a subdivision equal to one or more of the following: (b) Signal segments 1. Time, 2. The position of one of the gears in a set, 3. Frequency by Fourier transformation; and (c) Signal segment functions aligned and superimposed on the same independent axis, 1. Trace of signal segment function, 2. A trace of the statistical variation of the signal segment function, consisting of an arithmetic mean and / or variance, determined point by point.

[0020] The present invention further discloses, as worthy of independent protection, a display and a method of displaying the residual, the reconstructed model, or a combination of both, comprising: (a) subdividing the selected frame portion into a plurality of contiguous signal segments of equal duration, the duration being equal to one or more complete meshing periods; (b) for each signal segment, determining a scalar metric for the signal segment, the scalar metric being: 1. Peak-to-peak fluctuations, 2. Root mean square amplitude, 3. A time or rotation shift of the signal segment required to optimally align the signal segment with the reference, the reference being determined either as an average of at least two segments or as a subset of the reconstructed model having the same duration as the signal segment; 4. determining a measure of similarity to a reference determined as either an average of at least two segments or a subset of the reconstructed model having the same duration as the signal segment, the measure of similarity being one or more of the Pearson correlation coefficient and / or the root mean square error; (c) assigning two indexes to each segment, the first index being: 1. The number of complete revolutions of either the first gear or the second gear observed in the segment signal before the start of the segment duration, or 2. Corresponding to either the number of meshing cycles observed before the start of the segment duration, modulo the number of teeth of one of the first gear or the second gear; The second index is 3. The number of complete revolutions of the other of the first gear or the second gear observed in the segment signal before the start of the segment duration; or 4. Assigning a number of meshing periods modulo the number of teeth of the other of the first gear or the second gear, which corresponds to either the number of meshing periods observed prior to the start of the segment duration; (d) presenting the scalar metric mapped to a range of grayscale or color values ​​on a two-dimensional image, where one coordinate of the image corresponds to a first index and another coordinate of the image corresponds to a second index.

[0021] The present invention further discloses displays and methods that are independently worthy of protection, and displaying the residuals, the reconstructed models, or a combination thereof: (a) subdividing the selected frame portion into a plurality of sequentially indexed, consecutive or overlapping signal segments each having equal, predetermined duration; (b) expressing the signal segment as a spectral function by Fourier transformation; (c) From the spectral function, 1. Size, 2. Logarithmic magnitude, 3. Phase, 4. Determining one or more measures of phase drift as the difference between the actual phase and the phase predicted by advancing the phase of the preceding spectral function by the time or rotational distance between the two segments; (d) mapping the values ​​to a range of grayscale or color values ​​to present the spectral scale as a two-dimensional image, where one coordinate of the image corresponds to an index of the segment and another coordinate of the image corresponds to a frequency variable of the spectral function.

[0022] The present invention further discloses, as independently worthy of protection, displays and methods of displaying comprising tracing one or more of the residuals, the reconstructed model, or a combination thereof, on a graph, where an independent axis represents time or position of one of the first gear or the second gear of the gear set, and a dependent axis represents the amplitude of the displayed quantity.

[0023] The present invention further discloses, as independently worthy of protection, a display and a method for displaying model coefficients, the display and the method for displaying comprising: (a) A bar graph, with one bar per coefficient, and the height proportional to the magnitude of the coefficient. (b) plotting, for each coefficient, one or more of the following: one or more radar charts with a line segment emanating from the coordinate origin and having a length proportional to the magnitude of the complex number of the corresponding coefficient and an angle with respect to the horizontal axis proportional to the phase of the complex number of the corresponding coefficient.

[0024] The present invention further discloses, as independently deserving of protection, a method of testing gears comprising providing a pair of gears including a first gear and a second gear, the first gear and the second gear operable to rotate in mesh with each other. The first gear is rotated on a gear tester together with the second gear, the gear tester being configured with one or more sensors operable to provide an output signal indicative of a rotational characteristic of the one or more gears. At least one independent signal is generated, the independent signal being at least one of a signal based on an output from one or more of the sensors or an analytically derived signal. From the at least one independent signal, at least one frame portion having a non-zero duration is selected, each of the selected frame portions comprising: determining a set of model basis functions based on the selected frame portion; generating model coefficients by projecting the selected frame portions onto model basis functions; determining a reconstructed model from the model coefficients and the model basis functions; obtaining a residual by subtracting the reconstructed model from the selected frame portion; The method further comprises: (a) displaying and analyzing the residuals to identify quality characteristics of at least one of the first gear and the second gear, and accepting or rejecting at least one of the first gear and the second gear based on the quality characteristics; and (b) displaying and analyzing the model coefficients or the reconstructed model to identify quality characteristics of at least one of the first gear and the second gear, and accepting or rejecting at least one of the first gear and the second gear based on the quality characteristics; The method operates in an always-on mode where the preceding steps are repeated and run continuously as long as coordinated motion between a pair of gears is detected by one or more sensors and a new data frame can be replenished.

[0025] In a preferred embodiment, the gear ratio of the first and second gears that are rotated is not known a priori in the always-on mode, but the always-on mode determines the gear ratio based on real-time data received.

[0026] In further embodiments, a user can view information including at least one of measurements, displays, visualizations, and results whenever the always-on mode is operating, and the information is available regardless of whether other test modes are simultaneously active.

[0027] In a further embodiment, the information comprising at least one of a measurement, a display, a visualization, and a result is: (a) the amplitude and phase of one or more harmonics of a frequency associated with the meshing period; (b) Average signal shape over the duration of one meshing cycle; (c) Gear runout harmonic amplitude, (d) Average gear runout signal shape; (e) the presence and location of dental damage; (f) Average signal shape with the Pinion basis removed, and (g) average signal shape with gear basis removed.

[0028] In yet another embodiment, the method further includes interactively manipulating the display to better explore characteristics of the displayed data.

[0029] In another embodiment of the present invention, the display may be suspended to allow examination of the currently displayed data set without being replaced by a subsequent frame.

[0030] In a further embodiment of the invention, the current data set may be captured and stored for later retrieval or review and / or for comparison with current data.

[0031] Further embodiments of the present invention disclose examining and visualizing differences between current data and stored reference or master data.

[0032] In yet another embodiment of the present invention, the always-on mode further includes recognizing and locating damage to at least one tooth of the first gear and the second gear without having to separately configure test parameters or settings, the always-on mode identifying a partial rotation or tooth index that best represents the location of the recognized damage, and the always-on mode automatically notifying a user of such damage via a text message and / or a graphical display. [Brief description of the drawings]

[0033] [Figure 1] FIG. 1 shows a diagram illustrating always-on monitoring of encoder count and MTE calculation. [Diagram 2] 1 shows a preliminary analysis of streaming MTE data for selected channels. [Diagram 3] FIG. 1 shows a component diagram illustrating the stages of the harmonic decomposition process. [Figure 4] Shown is a representation of the MTE data decomposed into gear, pinion, meshing component bases, Legendre polynomial bases, and residual error used for subsequent analysis. [Diagram 5] 13 illustrates a representation of the base magnitudes of resolved gear, pinion, and meshing components of exemplary MTE data. [Figure 6]A discrete Fourier transform plot of the MTE data is shown, highlighting harmonics of the gear, pinion and mesh frequencies and de-emphasizing frequencies that are not correlated with the gear, pinion and mesh harmonics. [Figure 7] An overlay display of multiple MTE data frames at meshing period scale is shown on a common axis without model subtraction that would otherwise compensate for low frequency variations between frames. [Figure 8] The same overlay display as shown in Figure 7 is shown, but the modeled gear and pinion harmonic content has been subtracted from the signal to highlight the MTE variations that are directly attributable to individual tooth contact between the members. The average value of the overlaid frames is shown in black, and the dispersion bands are shown as shaded grey areas surrounded by dashed lines, both overlaid on the graphs of the individual frames. [Figure 9] Shown is a display of multiple gear period scale MTE data frames overlaid on a common axis; modeled pinion scale and mesh scale components have been subtracted from each frame to highlight only the portion of the MTE that is directly attributable to gear variations. The average MTE is shown overlaid in black. [Figure 10] Shown is a display of many MTE data frames in pinion period scale overlaid on a common axis, with the modelled gear scale component subtracted from each frame to highlight only the portion of the MTE attributable to pinion and individual tooth variations. The average MTE over the displayed frames is shown overlaid in black. [Figure 11] We show multiple spectral magnitude displays obtained by computing the discrete Fourier transform for each frame in a position overlay on the meshing period scale, as in Fig. 8. The average magnitude as a function of frequency, computed on the magnitude alone, across all MTE frames is shown by the black bar superimposed on the greyscale distribution of the individual spectral magnitudes. [Figure 12]It shows the same spectral magnitude overlay as shown in FIG. 12, but with the horizontal axis shifted to display a different frequency range, and the average magnitude evaluated with complex phasing. [Figure 13] Shown is a spectrogram display of the MTE data with the gear and pinion scale components subtracted. Position and frequency components are displayed in units of mesh period and fundamental mesh harmonic, respectively, with greyscale values ​​indicating the spectral magnitude at a given position and frequency bin. [Figure 14] Along with a representation of the periodogram calculated from the spectrogram shown in FIG. 13, we show the standard deviation of the spectral magnitude for each frequency, and the total RMS magnitude calculated over the bandwidth of a single meshing harmonic. [Figure 15] FIG. 1 shows a display of statistical measures calculated for successive meshing cycle frames of MTE data, where the statistical measures are mapped to individual contact cycles between specific gear teeth and pinion teeth and represented by greyscale or color values. [Figure 16] Complementing the mesh grid diagram in Figure 15, with a presentation of a specific mesh cycle frame of MTE data, a reference curve is shown as the average MTE per mesh for use in evaluating some of the mesh-by-mesh statistical measures. [Figure 17] 17 illustrates the separation of an input signal (e.g., the output of a sensor) into frames of data of a particular duration desired for subsequent display and analysis. FIG. 17 also illustrates the separation of the frames into segments desired for subsequent display and analysis. [Figure 18] 1 shows an example of multiple channels that may be employed in the present invention. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0034] The terms "invention," "the invention," and "the present invention" as used herein are intended to broadly refer to all of the subject matter of this specification and any claims that follow. Statements containing these terms should not be understood as limiting the subject matter described herein or the meaning or scope of any claims that follow. Moreover, this specification does not seek to describe or limit the subject matter covered by any claim in any particular part, paragraph, statement, or drawing of this application. The subject matter should be understood by reference to this entire specification, all drawings, and any claims that follow. The invention is capable of other configurations and of being practiced or carried out in various ways. It is also understood that the phraseology and terminology used herein are for the purpose of explanation and should not be considered as limiting.

[0035] The use of "comprises," "having," and "comprising," and variations thereof, herein is meant to encompass the items listed thereafter and their equivalents, as well as additional items. The use of letters to identify elements of a method or process is merely for identification purposes and is not meant to indicate that the elements should be performed in a particular order. In addition, terms such as "first," "second," and "third" are used herein for descriptive purposes and are not intended to denote or imply any importance or significance. As used herein, the singular forms "a," "an," and "the" are intended to include the plural forms unless the context clearly indicates otherwise. As used herein, the term "and / or" includes any and all combinations of one or more of the associated listed items and may be abbreviated as " / ."

[0036] Details of the invention will now be discussed, by way of example only, with reference to the accompanying drawings which illustrate the invention. In the drawings, like features or components are referred to by like reference numerals. Where applicable, various embodiments may include and / or exclude different aspects, features, and / or advantages. Also, where applicable, various embodiments may combine one or more aspects or features of other embodiments. Descriptions of aspects, features, and / or advantages of a particular embodiment should not be construed as limiting other embodiments or the claims.

[0037] The present invention includes analyzing any disturbances related to the rotational motion of two or more gears. Currently, the rotational motion transmission error (i.e. the difference between the actual motion of the output gear and the ideal motion according to the actual motion of the input gear), the linear displacement in a conventional double flank test, and the vibration acceleration of the test structure can be considered. The present invention may be implemented on a computer that is a component of the test machine or on a computer that is separate from the test machine. Information obtained from the analysis of the present invention may be sent directly to a gear processing machine (e.g. a cutting machine or grinding machine) via a closed loop system for continuous process correction. The obtained information may be stored for later study and analysis. It should be noted that in the present invention, either member of the gear set may be identified as the "input" gear and therefore the other member as the "output" gear. However, in practice the member with fewer teeth is usually identified as the input gear.

[0038] The method of the invention may, for example, continuously monitor mechanical sensors of the type described above to determine when two or more gears in a test rig are moving in unison. Motion may be indicated automatically by a non-zero correlation between rotary encoders on the input or output gears, or by the crossing of a predetermined threshold in vibration acceleration at a frequency predicted by the gearset configuration.

[0039] Whenever coordinated motion is detected, data is recorded for further analysis. The rotational positions of the input and output gears are measured via rotary encoders attached to the input and output spindles. The vibration acceleration is measured via one or more accelerometers attached to the test fixture. All measurements are time sampled and sensor readings are taken at regular time intervals.

[0040] The rotational positions of the input and output gears in the set, along with any additional time-sampled data, are interpolated (e.g., by local or global polynomial methods) and resampled so that all measurement samples occur at the same time and the input gear position steps through uniform intervals (referred to herein as rotational sampling). Irregularly spaced time values ​​that correspond to the specific times at which the time data was resampled are retained as additional measurements capturing information about the acceleration of the input gear. All contemporaneous measurements for a given position of the input gear represent a measurement "packet" of captured data for further analysis.

[0041] The rotational position of the output gear is converted to a kinematic transmission error measurement by subtracting from the output gear position the ideal position predicted by the gear ratio and the simultaneous position of the input gear.

[0042] From the rotationally sampled positions of the input and output gears, the effective gear ratio of the gear set is determined by linear regression of the observed motion. The effective ratio is converted to an estimate of the number of teeth of the input and output gears by assuming the set consists of two gears and converting the floating-point ratio into a rational expression where the number of teeth of the input gear is the numerator and the number of teeth of the output gear is the denominator.

[0043] Conversion of a floating point ratio to a rational expression may be accomplished by restricting the denominator to some maximum integer based on the application of the gear being tested, or by comparing the ratio to a preselected list of possible ratios to find the closest match.

[0044] A collection of samples, whether from an individual signal or as a "packet" of contemporaneous samples from multiple signals, may be accumulated as a frame (see top of FIG. 17). Each data frame represents all or a portion of the input signal, begins at a desired starting sample, and lasts for a predefined duration. Multiple frames may overlap in duration (see FIG. 17, "Overlapping Frames") or may be disjoint. Disjoint frames need not be contiguous in duration.

[0045] In traditional gearset testing, one test record or a defined set of records is collected and a separate analysis or DFT transformation is performed on each record. As a result, these analyses only provide results and conclusions about the average condition within the record and do not attempt to evaluate the variability of properties within the record.

[0046] For example, in performing a conventional test setup, a record having a duration of four gear revolutions may be selected from which time and frequency domain results are derived and displayed. The resulting measure of MTE at frequency per mesh may show a magnitude of 55 microradians, which is essentially the average of its components measured over the length of the record of four gear revolutions. Further inspection of the data may show that the magnitude for the first two gear revolutions was 65 microradians and for the last two gear revolutions was 45 microradians. Revealing this magnitude variability may provide important clues regarding quality characteristics of gear sets or test conditions not revealed by conventional analytical methods.

[0047] On the other hand, the inventive test method allows for the definition of multiple shorter frames within a given test record. Analysis of one or more signals within each frame provides information about the more local dynamic behavior of the gearset. Since frames are allowed to overlap each other and are of any duration, by defining frames whose duration corresponds to the entire test record, current conventional test results can be reproduced in addition to the dynamic analysis facilitated by the inventive approach.

[0048] The length of the frames may be selected to accommodate various interesting phenomena related to the motion of the gear set. Furthermore, a collection of frames may be accumulated as a "channel" (see FIG. 18) that characterizes a sequence of related frames. FIG. 18 shows an example of multiple channels that may be employed in the present invention for an exemplary pair of 5:19 ratio gears. The orbital channel is shown as being composed of frames having a length of one complete orbit (five gear revolutions). The gear channel is shown as being composed of a series of frames having a length of one complete gear revolution. Three types of pinion channels are shown. Type A is composed of a series of consecutive frames having a length of one complete pinion revolution, Type B is composed of a series of consecutive frames having a length of four pinion revolutions, and Type C is composed of a series of overlapping frames having a length of four pinion revolutions. Finally, a meshing channel is shown that is composed of a series of consecutive frames having a length of one meshing period.

[0049] For example, a channel may be defined as a collection of one or more frames, each having a duration equal to any of the following integers: One meshing period, the duration during which a pair of teeth between any two gears in a set is expected to maintain a dominant influence on the relative motion of the members; the duration of an ideal meshing period can be obtained mathematically by dividing the period during which any gear makes one complete revolution by the number of its teeth; One revolution of any gear in the set, or · An "orbit" (commonly called "hunting teeth") that is the least common multiple of the number of meshing periods that make up one revolution of each of any two interconnected gears in the set.

[0050] As shown in the example of Figure 18, the duration of a channel or frame may depend on the number of meshing periods (teeth) that make up one revolution of each member. If the user does not specify a gear ratio, an automatically determined estimate is used to determine the duration assuming a set of two gears. If the user specifies a gear ratio (which may involve more than two gears in a set), the channel duration is derived from the value specified by the user.

[0051] Within each channel and frame, a core model of one or more collected measurements may be derived as a sum of one or more truncated Fourier series, each in an orthogonal basis, referred to herein as a "component basis." The fundamental frequency of each series is the rotational frequency of one gear in the set, expressed per revolution of the input gear. A component basis also has a fundamental frequency corresponding to the fundamental frequency of a single meshing period, also expressed per revolution of the input gear. Gear sets containing three or more gears may have more than one fundamental meshing period, in which case each meshing period may be assigned one component basis.

[0052] If the user specifies the gear ratio and number of teeth, the fundamental frequency of each component basis is determined from the specified gear ratio and number of teeth, otherwise the frequency is determined from an automatically inferred number of teeth from the gear ratio determined by assuming a set of two gears.

[0053] The truncation of each component basis may be determined automatically, such as by an algorithm, or may be determined manually by user selection.

[0054] Within each frame, component bases with fundamental periods longer than the duration of the frame are either completely excluded from the model, or modified so that only components with periods shorter than the frame duration are represented in the model. The model for any frame may be supplemented by estimates of the longer-term excluded components determined in other channels that have frames of sufficiently long duration.

[0055] The Fourier model may be extended with one or more additional basis functions (collectively referred to herein as the "external basis") that represent periodic phenomena external to the gearset under test, or orthogonal basis functions (collectively referred to herein as the "non-periodic basis") that represent non-periodic phenomena over the duration of each frame. A preferred implementation of the invention uses a series of truncated Legendre polynomials as the non-periodic basis to model behavior on scales longer than the maximum harmonic period.

[0056] The coefficients of all Fourier bases of the model may be simultaneously found by Fast Fourier methods, such as the common Fast Fourier Transform (FFT). This is the conventional choice for finding the harmonic components in the frequency domain of such signals, and the disclosed system can provide this solution. However, applying these well-known and efficient Fast Fourier methods can lead to errors in identifying the harmonic components whenever non-periodic signal components are present. Therefore, the system of the present invention also includes alternative methods that can reduce or eliminate such errors.

[0057] One such alternative offered by the system simultaneously solves for the coefficients of all bases of the model, including nonperiodic or external bases, by a least-squares optimization that involves assigning arbitrary weights to the different bases in order to emphasize one base over the other and to resolve ambiguities due to the potential non-orthogonality of the different bases. This method is less susceptible to "spectral leakage" errors associated with nonperiodic components (e.g., when the frame being analyzed contains a non-integer number of revolutions of one or more gears), which is problematic in traditional fast Fourier analysis.

[0058] Another alternative offered by the system is to iteratively determine the model coefficients by projecting the previously determined model-subtracted data into each basis in turn in a predefined but arbitrary order. This iterative process is repeated until the coefficients of any basis do not deviate from the coefficients determined in the previous iteration by more than a predefined amount. This can be achieved, for example, by employing the well-known FFT to iteratively remove the spectral leakage from the model. It should be noted that in the general case of a completely unknown signal, the errors associated with FFT leakage are inherent and cannot be eliminated in any way. However, if certain frequencies are known to exist with certainty in advance (e.g., given gear and pinion harmonics), the iterative projection technique can be usefully employed by "seeding" it with these known periods.

[0059] After the core model is determined in each frame for one or more measurements, a residual for that frame and measurement is calculated by subtracting the model from the measurement. The residual represents the part of the measurement that cannot be explained by the model and provides a basis for further analysis of the irregular gearset behavior.

[0060] Once data is recorded for coordinated movements, predefined inferential analyses are performed on each channel, including but not limited to the following: · Instantaneous values ​​of Fourier and other basis coefficients in each frame of the channel. Instantaneous peak, root mean square amplitude, and average amplitude over the duration for each channel. The instantaneous "spread" of each Fourier basis coefficient as the ratio of the power at the corresponding frequency to the total power in a spectral band centered on that frequency and narrow enough so as not to encroach on similar bands surrounding adjacent components in the same Fourier basis.

[0061] In addition to the instantaneous values, the statistical variation of the calculated values ​​within a frame for each channel is calculated and reported.

[0062] One embodiment of the present invention comprises a measurement paradigm that includes an "always on" aspect and a "contractual" aspect. The contract function is a traditional approach known for many years and includes tests that are pre-configured and defined by the user according to various settings and parameters. The contract function defines the test conditions, analysis, and reports to be produced throughout the test. Today, gear testers with advanced measurement capabilities are expected to operate in this way. In other words, very little information is presented to the user except for information specifically requested and configured in advance by setting up a recipe (or "recap") for the test. If the position, motion, speed, load, or timing indicated by the tester does not match the inspection system's predictions (or "contract"), a warning or alarm is typically issued and the test is stopped.

[0063] In contrast, the always-on mode of operation allows the measurement system to constantly collect, analyze, and publish data. Thus, whenever the measurement system is powered and the software is running, the measurement system collects and analyzes available data and attempts to derive and display as much useful information as possible about its own current state, and the state of the gearset being tested (if any). In the present invention, the always-on and contract functions are not mutually exclusive and can be performed simultaneously. Data recorded during continuous monitoring can be accessed for subsequent contractual testing without requiring additional motion of the gearset.

[0064] An always-on system begins by continuously monitoring available sensors. The resulting measurements and data are then processed and displayed in real time in a format that is useful for the user. An always-on system intelligently derives a set of parameters, settings, and values ​​that describe its current state, and attempts to be as independent and robust as possible in reporting discrepancies rather than being invalidated or confused by them.

[0065] For example, if a gear set (e.g., bevel pinion and ring gear) with a gear ratio of 11:38 is installed and rotating on a test machine, but the software system is set to expect 9:38, the traditional measurement system will not process any information and will not detect any discrepancies until contract testing begins, at which point the measurement system will likely report a fault and / or generate erroneous measurement results due to the unexpected gear ratio.

[0066] On the other hand, a fault-tolerant always-on system would know as early as possible that both spindles were rotating, and furthermore that a given kinematic ratio was strictly followed (hence it would infer that the gearset was rotating), that the kinematic ratio was, for example, 3.455, with 11:38 being the most likely corresponding actual gear ratio. The system would immediately start analysing and publishing typical Single Flank Test (SFT) and Solid Borne Noise (SBN) data associated with such a gearset, including meshing harmonic amplitudes, runout components, etc. By publishing the detected ratios immediately, the testing machine controller can compare the measurement system data with its own predicted parameters at a much earlier point in time and send messages to the user accordingly.

[0067] During always-on operation, the encoder output is continuously monitored according to a process illustrated using the example MTE signal in FIG. 1. For each defined channel, the method observes the encoder stream of frames for that channel. As described below, while the encoder position is originally sampled regularly with respect to time, it is often desirable for the measurements to be at regular rotational positions. Thus, after each frame is received, it may be resampled by local interpolation to keep the angular position of one of the gear set members at regular intervals. The resulting encoder data is then used to determine an estimate of the current gear ratio by linear regression. If no coordinated motion is detected, the data is discarded and the method waits for the next encoder information frame. Otherwise, the MTE is calculated from the frame. If the gear ratio differs from the prediction or appears to have changed from the previous frame, the newly detected ratio is provided to a subsequent analysis module or other interested observer. To mitigate the quantization noise of the encoder hardware, the MTE is low-pass filtered and downsampled, and the resulting signal is made available for subsequent processing.

[0068] Depending on the output of other sensors attached to the test machine, additional signals may be collected simultaneously with the MTE. For each channel, these signals are grouped together for the duration of one frame, which coincides with the frame in which the MTE is represented.

[0069] Each channel is extended with new frames as they become available, and frames collected before the given channel duration are discarded.

[0070] In a preferred implementation of always-on analysis, a gear set consisting of only a single pinion meshed with a single gear consists of a mesh channel whose frame duration is several mesh periods, a pinion channel whose frame duration is several pinion revolutions, a gear channel whose frame duration is several gear revolutions, and an orbit channel whose frame duration corresponds to one or more complete orbits of the gear and pinion.

[0071] Each channel waits for a new frame, a newly detected gear ratio, or a change in the parameters configured for harmonic decomposition (described below), and performs an automatic analysis as shown for the MTE analysis example in Figure 2. If a notification of a gear ratio change is received, all currently held MTE data is discarded, since adding MTE data for two different gear ratios does not yield a useful analysis. When new MTE data is received by a channel, it is added to the channel's record, and possibly "old" data (data outside the configured duration for that channel) is discarded. The currently held MTE frames are sent to a decomposition module that generates a model of the predictable components in the actual MTE, and the model is published to further analysis or visualization components. The decomposition is also recalculated whenever the decomposition settings for a channel are changed, either by an automated process or by user request. Although not shown, additional automatic analyses may occur within each channel.

[0072] The basis decomposition process is shown in Figure 3. The gear ratio, a set of desired harmonic content ("harmonic count"), and an optional maximum polynomial order are inputs to a basis module that finds a set of basis functions ("linear system") for the signal. The decomposition module embodies an algorithm that generates a set of basis coefficients representing the model, given a linear system and the input signal as input. The linear system and corresponding model coefficients are provided as inputs to an unfolding module that generates an unfolded model ("MTE model") of the signal. A differencing module subtracts the signal model from the input signal to produce a residual error.

[0073] The always-on system constantly checks for other problems such as tooth damage such as scratches or burrs, tooth spacing errors, evidence of part slippage or creep on the arbor, intermittent float or rattle on lightly loaded parts, or other abnormal conditions. As the always-on system develops data and conclusions about such phenomena, it publishes these results to a user interface (UI) or other system components so that appropriate measures can be taken. By doing all this without explicit and specific contracts to check for these conditions, detection is simplified, phenomena are identified sooner, users are more informed about current conditions regardless of the status of specific contractual tests, and the system operates more intelligently and autonomously.

[0074] The always-on user interface also allows for interaction and exploration. The user can navigate through screens and displays, access more detailed views of measurement aspects, and change real-time parameters and settings of data collection and analysis to understand and quantify aspects of the gearset's behavior. To support such extensive exploration, the machine side of the tester that controls the test parameters including motion, speed, and load can be placed in a "standby" state to facilitate detailed examination of the data using always-on analysis and UI features. The stand-by state may involve pausing or ignoring the flow of new signals and data, whether the gearset motion continues in a previous state or stops completely. In the stand-by state, a steady flow of new information gained by rotating the gearset at a constant speed may be employed so that the operator can view deviations from ideal gearset behavior in real time indefinitely.

[0075] The always-on mode also provides for capturing current data for a predefined duration to a database, file system, or volatile computer memory. The user can choose to retain the results captured and analyzed at specific intervals indefinitely, or to retroactively apply contractual testing to the retained measurement data.

[0076] In production mode, the test machine controller automatically initiates configuration-defined contractual tests according to predefined cycle sequences and timings, collects data, and displays results, without interfering with any always-on functions that may be active at the same time.

[0077] When processing data, e.g., kinematic transmission error data derived from rotational SFT measurements, several techniques can be incorporated. Gearset analysis typically uses “rotational” sampling, where the gear and pinion encoder signals are sampled uniformly in the rotational change of the pinion encoder (i.e. the difference between two successive samples of the pinion encoder is constant). As a result, the analysis inherently relates periodic phenomena to specific points in the rotation of the gear or pinion under test. Because sampling hardware typically uses regular time intervals when sampling, and gears may rotate at non-constant speeds, the encoder signals must be interpolated to convert the regular time sampling to regular rotational sampling. The bandwidth of the sampling hardware is typically much higher than that required for gearset analysis. Sampling is preferably performed at the highest supported frequency to achieve two main benefits. First, the interpolation responsible for converting the time sampling to rotational sampling reduces errors. Second, applying low-pass filters in the data acquisition software and downsampling the oversampled signal reduces the quantization noise present in the digitized signal.

[0078] When converting time sampled encoder signals to rotational samples, timing information inherent in the time samples is preserved in the form of timestamps associated with each sample. These timestamps provide information about the speed and acceleration of the gear set that is useful for alternative analysis or when converting back to a time sampled signal. By sampling at the highest possible rate, errors in these timestamps, and the resulting imputed speed and acceleration, are minimized.

[0079] In contrast to current measurement systems, the present invention claims a tooth indexing system that allows correlating specific time characteristics of motion transmission error with the contact period between specific gear teeth and pinion teeth. By default, the gearset test record, which begins when the gear and pinion are chucked in a rotary test machine and begin to rotate in coordinated motion, assigns gear tooth index 1 and pinion tooth index 1 to the first tooth that makes contact on the respective gearset member. As the motion continues through each subsequent theoretical tooth contact period, both the gear and pinion indexes are incremented, and each member's index wraps around to 1 whenever the incremented index exceeds the number of teeth of that member. The theoretical tooth contact period represents a simplified representation of tooth contact, where a pair of contacting teeth (the currently indexed teeth) are designated as active at any given time. The theoretical tooth contact period can be understood as the period of one revolution of a gear member divided by its number of teeth. In reality, due to both gear design and tooth deformation under load, more than one pair of meshing teeth for a given pair of gears may be in significant contact at a given time. The tooth indexing system of the present system preferably assumes this theoretical period, but it is envisioned that it can also support the designation of multiple pairs (overlapping) of teeth if sufficient information about this behavior is provided.

[0080] The control interface of the rotary tester may be extended with awareness of tooth numbering in two ways. First, the interface may present an "indicator" option that allows the operator to select the desired indexes for the gear teeth and pinion teeth and have the rotary tester independently position the desired teeth in a predefined orientation. Second, the interface may present a "teach" option that allows the desired index sequence to be recognized. The operator may manually position the gear and pinion such that the designated starting teeth (each with an index of 1) are aligned in a predefined orientation and, via the teach interface, instruct the software to record the member orientation as a reference. Until the part is later unchucked, all data records provided for analysis or visualization after the teach operation will include additional tags indicating the labeled reference positions. These reference position tags may be used as references that allow the operator to find which particular teeth were in contact at any point during the test.

[0081] Many of the analyses performed may be combined with specialized visualizations that allow exploring the rotating test machine data in new ways. However, the combination of analysis and visualization is a matter of convenience and not a requirement. In the realm of gearset testing, the analysis steps and visualization may be considered separately. The underlying analyses may be applied to always-on or contractual data without presenting a visualization. The results of these analyses may be compared to thresholds or otherwise reduced by some means (e.g. statistically) to simplify reporting or to make an automatic pass / fail decision on the gearset under test.

[0082] At least five different visualizations are possible. Model decomposition, · The magnitude of the DFT (Discrete Fourier Transform), ·overlay, Spectrogram, and · Interlocking grid.

[0083] Preferably, all five visualizations are linked by a core model and residuals that provide the foundation for all visualizations.

[0084] In the model decomposition visualization shown in Figures 4 and 5, for each selected measurement, the decomposition diagram shows the expansion of each component basis, external basis and aperiodic basis separately as a linear combination of functions of that basis weighted by the determined model coefficients on a common axis where the input gear position represents the independent variable and the measurement represents the dependent variable. The residuals of each measurement are shown with each basis expansion.

[0085] A control element in the user interface allows the operator to toggle between displaying each basis expansion or the residuals.

[0086] A control element allows the operator to select a preferred display scale as the fundamental period of any component or external basis represented in one or more models, whereby the input gear position is scaled so that one unit on the display axis represents the selected fundamental period.

[0087] Certain user interface elements ("tooltips") allow the operator to place a cursor on the graph and find the specific amplitude and input gear location of each component displayed near the cursor. An example of a tooltip is shown in Figure 8, where it should be understood that the data shown pertains only to that particular line and location on that particular graphical display.

[0088] A bar or line graph such as that shown in FIG. 5 shows, on separate axes, the magnitudes of some or all of the model coefficients, grouped by measure and basis, and labeled to allow finding specific coefficient amplitudes.

[0089] A tooltip allows the operator to place the cursor on this magnitude graph to find enough information to identify the specific component being queried, along with the specific numerical values ​​of the particular coefficients.

[0090] The decomposition analysis represents the periodic components of the motion transmission error as multiples of harmonics per gear, per pinion, or per mesh, optionally with aperiodic polynomial trends. Harmonic analysis is common in current gearset testing systems. However, the decomposition performed by the method of the present invention improves upon the conventional analysis by employing the aforementioned decomposition methodology to reduce the effects of spectral leakage and account for non-periodic behavior not represented in current systems.

[0091] For each gear in the gear set, the low order harmonic components determined by the decomposition are displayed to the user as an idealized or modeled gear response, and a number of these components (explicitly selected by the user or automatically by the program) are subtracted from the kinematic transmission error to obtain a residual error representing noise sources uncorrelated to the rotation of the gear set, and higher frequency per-mesh harmonic components that can serve as the basis for further analysis and visualization.

[0092] The DFT magnitude visualization shown in FIG. 6 shows, by means of a bar or line graph, the magnitude of the Discrete Fourier Transform (DFT) of the residuals of one or more current models as a function of the input gear rotational frequency.

[0093] A control element allows the operator to select a preferred display scale as the fundamental frequency of any component or external basis represented in one or more models, whereby the rotational frequency of the input gear is expressed in units of the selected frequency.

[0094] One control element allows the operator to enable a "virtual orbit", which zero-pads the current data record to a duration equal to the next highest integer number of orbits of any two interconnected gears in the set, resulting in a DFT-calculated rotational frequency that matches the fundamental rotational and meshing frequencies of both members.

[0095] If the magnitudes are displayed as a bar graph, the bars for each DFT frequency bin are preferably individually colored, shaded, labeled or otherwise differentiated according to their correspondence to multiples of the fundamental frequency of each component or outer basis (or lack of correspondence to such bases) to allow easy visual identification of correlations between periodic phenomena and frequencies attributed to individual members of the gear set.

[0096] Tooltips allow the operator to place a cursor on the DFT graph to find the magnitude and center rotation frequency of a particular DFT frequency bin.

[0097] In the position overlay visualizations shown in Figures 7, 8, 9, and 10, a control element allows the operator to select a preferred display scale as the fundamental period of any component or external basis represented in one or more models, whereby the residuals of the current one or more models are subdivided into "segments" consisting of either: · consecutive disjoint intervals having a duration equal to the selected fundamental period, or Overlapping intervals having a duration equal to the selected fundamental period plus an additional overlap interval, where successive segments overlap by an overlap interval selected automatically by the software or manually by the operator.

[0098] The line graph for each selected measurement shows on a common axis all subdivided residual segments of that measurement, each segment preferably differentiated by color or style depending on the rotational position of the input gear relative to its position at the start of the segment, allowing to examine variability between segments of data that does not belong to the determined model.

[0099] A tooltip allows the operator to place the cursor over one or more of the lines to identify the specific intervals at which the segments are defined, depending on the rotational position of the input gear.

[0100] A control element allows the operator to toggle the display of the average residual of all displayed segments for each selected measurement. In Figures 7, 8, 9, and 10, the average residuals are shown in black overlaid on the individual segments.

[0101] As shown in FIG. 8, a control element allows the operator to toggle the display of a line or band showing the point-by-point standard deviation, or a multiple thereof selected by user control, across all displayed segments for each selected measurement.

[0102] In the spectral overlay visualizations of Figures 11 and 12, the individual segments subdivided as described above for the position overlay plots are converted to spectral magnitudes by computing the discrete Fourier transform of each segment. The DFT magnitudes of each segment are then plotted together on a single set of axes that relate specific DFT frequency bins to the corresponding magnitudes of the individual data segments via a bar or line graph.

[0103] The selection of the duration of each spectral overlay segment may be done automatically, for example by fixing the duration to a duration selected for the position overlay display, or by specific user selection.

[0104] Tooltips allow the operator to place the cursor over one or more of the lines to identify the specific intervals within which the segments are defined, as well as detailed information regarding the frequency and magnitude that corresponds to the cursor position.

[0105] Control elements allow the operator to switch between displaying, for each selected measurement, the mean magnitude calculated as the average of the spectral magnitudes, or the complex (phased) average magnitude of the DFT coefficients, and other statistical measures for each DFT bin (e.g., the first, second, and third quartiles of the spectral magnitude).

[0106] A control element allows the operator to toggle the display of a box plot that presents visual information about the statistical variation between DFT magnitudes across segments for each selected measurement. The lower and upper limits of the box indicate the first and third quartiles, respectively, of the magnitude distribution for each DFT frequency bin, and the middle line indicates the median. The whiskers extend above and below the box by a multiple of the interquartile range (the difference between the third and first quartiles), which can be set by a user control to indicate the "typical" magnitude range. As shown in FIG. 12, for clarity, the individual magnitude indicators may be hidden for values ​​that fall within the range of the box plot.

[0107] In an "overlay" analysis, the residual error is divided into segments with duration equal to one revolution of one of the members, or the contact period between any two teeth. The resulting segments are overlaid on the same axis, allowing the comparison of relative characteristics between multiple correlated intervals across the test. Summary statistics for the overlapping windows, including mean response, sample-wise standard deviation, range, and RMS levels, provide a characterization of the results that is useful for comparing multiple gear sets and for identifying anomalous behavior within specific regions of individual gear sets. Visualization of the overlay analysis provides a way to identify the individual segments and summary statistics.

[0108] In the spectrogram visualization of FIG. 13, an image of each selected measurement, either as a two-dimensional color or grayscale map, or as a two- or three-dimensional waterfall graph, shows the magnitude of the short-time Fourier transform (STFT) of the currently determined residual of that measurement.

[0109] A control element allows the operator to select the display scale as the fundamental frequency of any component or external basis represented in the model, so that the input gear rotational frequency and position are scaled in units of the selected frequency and period, respectively.

[0110] One control element allows the operator to select the duration of the STFT's sliding position window as either the absolute width or full width at half maximum of the window function.

[0111] The offset between successive STFT position windows may be determined by manual selection, or by automatic determination such that the window duration, overlap, and function satisfy, within a given tolerance, the Constant Overlap-Add condition required to ensure that the STFT is invertible.

[0112] Instead of manually selecting the duration of the STFT position window, the duration may be selected automatically along with an offset to provide position and spectral resolution at a given aspect ratio.

[0113] Certain controls allow the operator to enable frequency and position reassignment, which converts the STFT image into a two- or three-dimensional scatter plot in which the individual magnitudes of the STFT are shifted to irregular positions derived from the phase information of the STFT.

[0114] A bar or line graph shows the periodogram (FIG. 14) calculated from the currently displayed STFT as the mean and standard deviation of the frequency response over all position segments within the STFT.

[0115] A control element allows the user to select a spectral scale as the fundamental frequency of any component or external basis represented in the model whose frequency is greater than the spectral resolution of the periodogram, and the periodogram is used to define contiguous but disjoint frequency bands having widths equal to the selected frequency scale and centred at integer multiples of the frequencies of the selected scale, and over each band the root mean square amplitude of the periodogram is calculated and displayed as a bar or step graph on the same axes as the periodogram.

[0116] A short-time spectral analysis is performed on the residual error to highlight long-term variations of the meshing harmonics. Based on a selected time scale, which can be selected by the user or by the software based on the duration of the test and the user's desired spectral bandwidth, a Gabor transform (short-time Fourier transform with a Gaussian time window) is applied to the residual error and displayed as a two-dimensional spectrogram image with the spectral magnitude varying along the columns and the time slices varying along the rows. The time interval between successive columns of the short-time Fourier transform is selected based on the selected Gaussian window to avoid both loss and redundancy of time information.

[0117] The periodogram (average magnitude of the spectrum calculated over all columns in the spectrogram) shows the typical spectral response of the entire test, together with the RMS magnitude calculated over a band equal to one revolution of the gear or pinion, or one period of meshing contact. Comparing the individual magnitudes of the spectrum to the RMS level in a wider neighborhood provides a measure of the power concentration in the vicinity of the harmonic of interest. Short-time spectral analysis also provides a basis for more detailed investigation. As an example, by calculating from the spectrogram the time-varying average frequency in the vicinity of each meshing harmonic, phase drifts that artificially reduce the spectral amplitude reported by classical testing may be quantified.

[0118] In the meshing grid visualization shown in FIG. 15, by mapping the statistics of each meshing cycle to the interaction of one specific tooth index of each of the two interconnected gears in the set, the image as a two-dimensional color or grayscale map of each selected measurement shows the statistical variation over the meshing duration, with the statistics of interest being selected by user interaction.

[0119] The residuals of the current model of one or more measurements are subdivided into disjoint contiguous segments having a duration equal to one meshing period.

[0120] For each residual, a reference signal is defined as either the point-wise average of all segments or as an expansion of the meshed periodic component basis only of the model.

[0121] Tooltips allow the operator to place the cursor over individual meshing cycles on the grid to find the associated segment index, the tooth indices of the two interconnected members to which the segment cycle is mapped, and the numerical value of the selected statistic.

[0122] The separate images, each as a two-dimensional image consisting of a single row or column, or as a bar or line graph, respectively, show the value of the selected statistic as a function of tooth index of each interconnected member in the gear set, the statistic being averaged over all teeth of associated members that are in contact with a tooth of the member associated with the average representation.

[0123] One control element allows the operator to select any set of meshing periods from the meshing grid diagram for further investigation.

[0124] A detailed view (FIG. 16) may be displayed along with the meshing grid diagram that allows one or more measurements from a selected meshing cycle to be displayed as a function of input gear position relative to the start of each segment.

[0125] The detailed view displays selected mesh period measurements on the same axis as the measurements and the reference signals derived from those measurements.

[0126] In a "mesh grid" analysis, the residual error is divided into segments whose duration is always equal to one contact period between two teeth. Each segment is mapped to a specific gear tooth and pinion tooth that are in contact during that duration. A reference signal is calculated as the average of all per-tooth signals or as an ideal reconstruction of a configurable number of mesh harmonics derived from the decomposition. The following summary statistics are calculated for each mesh interval: Peak-to-peak amplitude, Interval error as a signal delay that maximizes the cross-correlation between the selected reference signal and the error; · The RMS (root mean square) error between the residual error and the selected criterion, · The Pearson correlation coefficient between the selected criterion and the residual error, or One of several measures of waveform similarity between reference and error.

[0127] The meshing grid visualization allows selected summary statistics to be displayed on a two-dimensional grid indexed by gear tooth number in one dimension and pinion tooth number in the other. Additional rows and columns provide the average values ​​of the selected statistics when the gear or pinion tooth index, respectively, is held constant. One or more intervals in the meshing grid may be selected to display a detailed view showing the corresponding actual residual error, overlaid on the same axis as the currently selected reference waveform.

[0128] All visualizations provide a mechanism for adjusting one or more of the core models being displayed. Data can be provided by previously determined analytical channels, or by "contract" channels consisting of a record of a given length of measurements collected previously or in real time.

[0129] A control element in the user interface allows the operator to select any contiguous subset (a "range") of all data records that will be used specifically to calculate the model.

[0130] Certain control elements allow the operator to downsample selected data records to speed up processing by applying a low pass filter and either decimation or local or global polynomial interpolation.

[0131] The control elements allow the operator to independently select the number of desired functions of each component, exterior, or non-periodic basis used in the model.

[0132] If measurements other than motion transmission error are available in the data record, a control element allows the operator to select a preferred measurement (or measurements) to be visualized.

[0133] From the selected range and downsampling rate, a core model and residual signal are derived for each selected measurement using a specified number of basis functions in each series.

[0134] Multiple visualizations may be grouped by the operator into linked "sessions," or each visualization may be treated as a separate, independent session.

[0135] A network communication channel allows for coordination between multiple visualizations in a single session, whereby operator settings and portions of signals are identified by the operator for closer scrutiny: when the operator adjusts a setting in one visualization or highlights a portion of a displayed signal, the corresponding setting is applied and the selection is highlighted in all other visualizations in the same session.

[0136] Although the present invention has been described with reference to preferred embodiments, it should be understood that the invention is not limited to these particular embodiments, and the present invention is intended to include modifications that would be apparent to those skilled in the art to which the subject matter pertains without departing from the spirit and scope of the appended claims.

Claims

1. 1. A method for testing a gear, the method comprising: providing a pair of gears including a first gear and a second gear, the first gear and the second gear operable to rotate in mesh with each other; rotating the first gear together with the second gear on a gear testing machine, the gear testing machine configured with one or more sensors operable to provide output signals indicative of rotational characteristics of one or more gears; generating at least one independent signal, the independent signal being at least one of a signal based on output from the one or more sensors or an analytically derived signal; and selecting at least one frame portion having a non-zero duration from the at least one independent signal, each of the selected at least one frame portion comprising: determining a set of basis functions for a signal based on the selected frame portion; generating model coefficients from the selected frame portions based on basis functions; determining a reconstructed model from the model coefficients and the basis functions; obtaining a residual by subtracting the reconstructed model from the selected frame portion; The method further comprises: (a) displaying and analyzing the residuals to identify quality characteristics of at least one of the first gear and the second gear; approving or rejecting the at least one of the first gear and the second gear based on the quality characteristic; And (b) displaying and analyzing the model coefficients or the reconstructed model to identify quality characteristics of at least one of the first gear and the second gear; and at least one of approving or rejecting the at least one of the first gear and the second gear based on the quality characteristic.

2. The basis functions are (a) a gear ratio between the first gear and the second gear; (b) the fundamental harmonic frequency produced by the rotation of the first gear with the second gear, or the duration of a meshing period of the first gear meshing with the second gear; (c) a predetermined set of harmonics for each fundamental frequency, said set including zero; and (d) a set of non-periodic basis functions defined over the duration of the selected frame portion, the set including zero.

3. The method of claim 1 , wherein the reconstructed model and the residuals are continually re-evaluated as additional information is obtained from the sensors during machine operation.

4. The method of claim 1 , wherein a plurality of said independent signals are sampled simultaneously at equal intervals to facilitate direct correlation and comparison.

5. 2. The method of claim 1, wherein the at least one independent signal is collected at uniform time samples and subsequently interpolated to generate a sequence of regularly spaced samples at a position of one of the first and second gears.

6. You can display the residuals, the reconstructed model, or a combination of both. (a) subdividing the selected frame portion into a plurality of consecutive signal segments of equal duration, the duration being:

1. One or more complete meshing cycles; 2. One or more complete revolutions of any gear in the set, (b) dividing the signal segment 1. time, 2. The position of one of the gears in the set; 3. Frequency by Fourier transformation; (c) Signal segment functions aligned and superimposed on the same independent axis, 1. A trace of the signal segment function; 2. A trace of the statistical variation of the signal segment function, consisting of an arithmetic mean and / or a variance, determined pointwise.

7. You can display the residuals, the reconstructed model, or a combination of both. (a) subdividing the selected frame portion into a plurality of contiguous signal segments of equal duration, the duration being equal to one or more complete meshing periods; (b) determining, for each signal segment, a scalar metric for the signal segment, the scalar metric being:

1. Peak-to-peak fluctuations, 2. Root mean square amplitude, 3. A time or rotation shift of the signal segment required to optimally align the signal segment with a reference, the reference being determined either as an average of at least two segments or as a subset of the reconstructed model having the same duration as the signal segment; 4. Determining a measure of similarity to a reference determined as either an average of at least two segments or a subset of the reconstructed model having the same duration as the signal segment, the measure of similarity being one or more of the Pearson correlation coefficient and / or the root mean square error; (c) assigning two indexes to each segment, the first index being:

1. The number of complete revolutions of either the first gear or the second gear observed in the signal segment prior to the start of the segment duration; or 2. Corresponding to either the number of meshing periods observed prior to the start of the segment duration, modulo the number of teeth of said one of said first gear or said second gear; The second index is 3. The number of complete revolutions of the other of the first gear or the second gear observed in the signal segment prior to the start of the segment duration; or 4. Assigning a number corresponding to either the number of meshing periods observed prior to the start of the segment duration, modulo the number of teeth of the other of the first gear or the second gear; 2. The method of claim 1, comprising: (d) presenting the scalar metric mapped to a range of grayscale or color values ​​on a two-dimensional image, one coordinate of the image corresponding to the first index and another coordinate of the image corresponding to the second index.

8. You can display the residuals, the reconstructed model, or a combination of both. (a) subdividing the selected frame portion into a plurality of sequentially indexed contiguous or overlapping signal segments each having equal, predetermined duration; (b) expressing said signal segments as spectral functions by a Fourier transform; (c) from the spectral function, 1. Size, 2. Logarithmic magnitude, 3. Phase, 4. Determining one or more measures of phase drift as the difference between the actual phase and the phase predicted by advancing the phase of the preceding spectral function by the time or rotational distance between the two segments; 2. The method of claim 1, comprising: (d) mapping values ​​to a range of grayscale or color values ​​to present the spectral scale as a two-dimensional image, one coordinate of the image corresponding to the index of the segment and another coordinate of the image corresponding to a frequency variable of the spectral function.

9. To display, 7. The method of claim 6 including a trace of one or more of the residuals, the reconstructed model, or a combination thereof on a graph, the independent axis representing time or position of one of the first gear or the second gear of the gear set, and the dependent axis representing amplitude of the displayed quantity.

10. Displaying the model coefficients is (a) a bar graph with one bar per coefficient, the height of which is proportional to the magnitude of the coefficient; 2. The method of claim 1 , further comprising: (b) plotting, for each coefficient, one or more of the following: one or more radar charts with a line segment emanating from the coordinate origin and having a length proportional to the magnitude of the complex number of the corresponding coefficient and an angle with respect to the horizontal axis proportional to the phase of the complex number of the corresponding coefficient.

11. Display and analysis results are retained in electronic storage media for recall; (a) Simultaneous side-by-side presentation; (b) sequential presentation, where progression is dictated by user interaction; 10. The method of claim 1, wherein the display and comparison of two or more previous records is accomplished by one or more of: (c) sequential presentation with an automatic animated progression.

12. 1. A method for testing a gear, the method comprising: providing a pair of gears including a first gear and a second gear, the first gear and the second gear operable to rotate in mesh with each other; rotating the first gear together with the second gear on a gear testing machine, the gear testing machine configured with one or more sensors operable to provide output signals indicative of rotational characteristics of one or more gears; generating at least one independent signal, the independent signal being at least one of a signal based on output from the one or more sensors or an analytically derived signal; and selecting at least one frame portion having a non-zero duration from the at least one independent signal, each of the selected at least one frame portion comprising: determining a set of basis functions for a signal based on the selected frame portion; generating model coefficients from the selected frame portions based on basis functions; determining a reconstructed model from the model coefficients and the basis functions; obtaining a residual by subtracting the reconstructed model from the selected frame portion; The method further comprises: displaying and analyzing the residuals to identify a quality characteristic of at least one of the first gear and the second gear; approving or rejecting the at least one of the first gear and the second gear based on the quality characteristic; And displaying and analyzing the model coefficients or the reconstructed model to identify quality characteristics of at least one of the first gear and the second gear; approving or rejecting the at least one of the first gear and the second gear based on the quality characteristics; The method is performed in an always-on mode in which the preceding steps are repeated and run continuously as long as coordinated motion between the pair of gears is detected by the one or more sensors and a new data frame can be replenished.

13. 13. The method of claim 12, wherein a gear ratio of the first gear and the second gear that are rotated is not known a priori in the always-on mode, but the always-on mode determines the gear ratio based on received real-time data.

14. 13. The method of claim 12, wherein a user can view information including at least one of measurements, displays, visualizations, and results whenever the always-on mode is operating, and the information is available regardless of whether other test modes are simultaneously active.

15. The information includes at least one of a measurement, a display, a visualization, and a result. (a) the amplitude and phase of one or more harmonics of a frequency associated with the meshing period; (b) Average signal shape over the duration of one meshing period; (c) gear runout harmonic amplitude; (d) average gear runout signal shape; (e) the presence and location of dental damage; (f) Average signal shape with Pinion basis removed, and (g) gear basis removed average signal shape.

16. The method of claim 12 , further comprising interactively manipulating the display to better explore features of the displayed data.

17. 13. The method of claim 12, wherein the display can be suspended to allow examination of a currently displayed data set without being replaced by a subsequent frame.

18. 13. The method of claim 12, wherein the current data set can be captured and stored for later retrieval or review and / or for comparison with current data.

19. The method of claim 12, wherein differences between current data and stored reference or master data can be examined and visualized.

20. 13. The method of claim 12, wherein the always-on mode further includes recognizing and locating damage to a tooth of at least one of the first gear and the second gear without having to separately configure test parameters or settings, the always-on mode identifying a partial revolution or tooth index that best represents a location of the recognized damage, and the always-on mode automatically notifying a user of such damage via a text message and / or a graphical display.

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