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