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@@ -28,7 +28,7 @@ Causes:
**Types of error motion** **Types of error motion**
A distinction is made between (see Figure <fig:wardle15_synchronous_asynchronous_schematic>): A distinction is made between (see [Figure 1](#figure--fig:wardle15-synchronous-asynchronous-schematic)):
- motion errors that are harmonic of the basic rotor speed: _synchronous_ motion error - motion errors that are harmonic of the basic rotor speed: _synchronous_ motion error
- those that are node: _asynchronous_ motion errors - those that are node: _asynchronous_ motion errors
@@ -42,19 +42,19 @@ A distinction is made between (see Figure <fig:wardle15_synchronous_asynchronous
A capacitive sensor is typically used, and the measurement is performed over a time period corresponding to several (typically five) revolutions of the bearing. A capacitive sensor is typically used, and the measurement is performed over a time period corresponding to several (typically five) revolutions of the bearing.
It is displayed as a polar plot of motion error amplitude versus angle of rotation (Figure <fig:wardle15_typical_error_plot>). It is displayed as a polar plot of motion error amplitude versus angle of rotation ([Figure 2](#figure--fig:wardle15-typical-error-plot)).
<a id="figure--fig:wardle15-typical-error-plot"></a> <a id="figure--fig:wardle15-typical-error-plot"></a>
{{< figure src="/ox-hugo/wardle15_typical_error_plot.png" caption="<span class='figure-number'>Figure 2: </span>Total error motion" >}} {{< figure src="/ox-hugo/wardle15_typical_error_plot.png" caption="<span class='figure-number'>Figure 2: </span>Total error motion" >}}
The Synchronous error motion (i.e. error that are harmonics of the rotational speed) can be extracted (Figure <fig:wardle15_synchronous_error_example>). The Synchronous error motion (i.e. error that are harmonics of the rotational speed) can be extracted ([Figure 3](#figure--fig:wardle15-synchronous-error-example)).
<a id="figure--fig:wardle15-synchronous-error-example"></a> <a id="figure--fig:wardle15-synchronous-error-example"></a>
{{< figure src="/ox-hugo/wardle15_synchronous_error_example.png" caption="<span class='figure-number'>Figure 3: </span>Synchronous motion error" >}} {{< figure src="/ox-hugo/wardle15_synchronous_error_example.png" caption="<span class='figure-number'>Figure 3: </span>Synchronous motion error" >}}
It can then be separated into a "_fundamental error motion_" and a "_residual error motion_" (Figure <fig:wardle15_fundamental_and_residual_errors>). It can then be separated into a "_fundamental error motion_" and a "_residual error motion_" ([Figure 4](#figure--fig:wardle15-fundamental-and-residual-errors)).
The fundamental error motion contains only one frequency corresponding to the speed of the rotation of the bearing. The fundamental error motion contains only one frequency corresponding to the speed of the rotation of the bearing.
For radial measurements, it corresponds to the eccentricity, and is not always significant. For radial measurements, it corresponds to the eccentricity, and is not always significant.
@@ -62,7 +62,7 @@ For radial measurements, it corresponds to the eccentricity, and is not always s
{{< figure src="/ox-hugo/wardle15_fundamental_and_residual_errors.png" caption="<span class='figure-number'>Figure 4: </span>(a) Fundamental error motion; and (b) residual synchronous error motion" >}} {{< figure src="/ox-hugo/wardle15_fundamental_and_residual_errors.png" caption="<span class='figure-number'>Figure 4: </span>(a) Fundamental error motion; and (b) residual synchronous error motion" >}}
The Asynchronous error motion (Figure <fig:wardle15_asynchronous_error_motion_example>) contains all other motion error frequencies. The Asynchronous error motion ([Figure 5](#figure--fig:wardle15-asynchronous-error-motion-example)) contains all other motion error frequencies.
<a id="figure--fig:wardle15-asynchronous-error-motion-example"></a> <a id="figure--fig:wardle15-asynchronous-error-motion-example"></a>
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@@ -106,7 +106,7 @@ h\_{rad} = \epsilon\_1 \sigma (T\_1^2 + T\_2^2)(T\_1 + T\_2)
### Emissivity {#emissivity} ### Emissivity {#emissivity}
The emissivity of materials highly depend on the surface finish (the more polished, the lower the emissivity). The emissivity of materials highly depend on the surface finish (the more polished, the lower the emissivity).
Some examples are given in <tab:emissivity_examples>. Some examples are given in [Table 1](#table--tab:emissivity-examples).
Gold coating gives also a very low emissivity and is typically used in cryogenic applications. Gold coating gives also a very low emissivity and is typically used in cryogenic applications.
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@@ -23,7 +23,7 @@ The system is represented in [Figure 1](#figure--fig:siso-identification-schemat
The goal of system identification is to compute the transfer function \\(G\\) from known excitation signal \\(u\\) and from a measure of \\(y\_m\\). The goal of system identification is to compute the transfer function \\(G\\) from known excitation signal \\(u\\) and from a measure of \\(y\_m\\).
There are different ways of obtaining a model \\(G\\) of the system summarized in Table <tab:system_identification_model_types>. There are different ways of obtaining a model \\(G\\) of the system summarized in Table [Table 1](#table--tab:system-identification-model-types).
For mechatronics systems, _frequency domain identification_ is the norm. For mechatronics systems, _frequency domain identification_ is the norm.
<a id="table--tab:system-identification-model-types"></a> <a id="table--tab:system-identification-model-types"></a>