Abstract Gear transmission error (TE) has become a promising diagnostic tool due to the fact that, compared with vibration responses, it is much less affected by the transfer path from the source to the measurement, and it can be measured conveniently using shaft encoders installed on the input and output of a gear stage. It is also the direct cause of vibration and noise in gears, and it is directly linked to deviations from the perfect involute tooth profile. In the literature, TE-based gear diagnostics has revolved around the analysis of changes in the gearmesh waveform, such as its amplitude or shape, which contains information about the tooth profile and deflection under load. However, if there is a bulk removal of material from the tooth surface due to wear, appearing as a mean effect across all teeth, this would in theory manifest itself as a DC shift in the transmission error, but it would not be observed in a conventional TE signal, even though it is essentially the most crucial measurement that describes wear severity. This is because the initial phases of the encoder signals used to obtain conventional TE measurements are arbitrary, and consequently the mean of TE signals is usually set to zero since it does not represent any physical quantity. Therefore, to be able to measure the effect of average wear depth on TE (mean TE), the TE signals recorded at different wear stages must somehow be rephased so as to align them to have the same fixed-reference starting point before they can be compared. This paper proposes a novel approach to conduct this rephasing of encoder signals (or even once-per-rev tachometer signals) to have the same reference within a hunting tooth period (HTP), defined as the fundamental period where the meshing of all different tooth pairs has been encountered. This rephasing enables the determination of the DC shift in the transmission error relative to a reference measurement, typically from an unworn gearset. In the case of multi-pulse-per-rev encoder signals, this DC component can be combined with the conventional TE to obtain the ‘absolute transmission error’, which indicates not just deviations from an involute profile, but also the average wear depth for all teeth in the gear set. The proposed technique is validated using encoder and tachometer measurements from a dry gear wear experiment and is found to be very robust in assessing the severity (average depth) of gear wear.

中文翻译：

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绝对传动误差：评估齿轮磨损的简单新工具

摘要 齿轮传动误差 (TE) 已成为一种很有前途的诊断工具，因为与振动响应相比，它受从源到测量的传递路径的影响要小得多，并且可以使用安装的轴编码器方便地进行测量。在齿轮级的输入和输出上。它也是齿轮振动和噪音的直接原因，它与完美渐开线齿形的偏差直接相关。在文献中，基于 TE 的齿轮诊断围绕着齿轮啮合波形的变化分析，例如其幅度或形状，其中包含有关齿形和负载偏转的信息。但是，如果由于磨损从牙齿表面大量去除材料，表现为对所有牙齿的平均效应，这在理论上会表现为传输误差的直流偏移，但不会在传统的 TE 信号中观察到，即使它本质上是描述磨损严重程度的最关键的测量。这是因为用于获得常规 TE 测量的编码器信号的初始相位是任意的，因此 TE 信号的平均值通常设置为零，因为它不代表任何物理量。因此，为了能够测量平均磨损深度对 TE（平均 TE）的影响，在不同磨损阶段记录的 TE 信号必须以某种方式重新定相，以便将它们对齐以具有相同的固定参考起点，然后它们才能被比较的。本文提出了一种新方法来对编码器信号（甚至每转一次的转速计信号）进行这种重新定相，以在猎齿周期 (HTP) 内具有相同的参考，该周期定义为所有不同齿啮合的基本周期偶遇到过。这种重新定相能够确定变速器误差相对于参考测量值的直流偏移，通常来自未磨损的齿轮组。在每转多脉冲编码器信号的情况下，该直流分量可以与传统的 TE 相结合以获得“绝对传输误差”，这不仅表示与渐开线轮廓的偏差，还表示平均磨损深度齿轮组中的所有齿。