Bearings can only be connected to rigid bodies (part). If you want to connect a
bearing to a flexible body, then a dummy body must be inserted in between.
Comment 2
The default value is calculated internally with respect to the units of the system.
AISI 52100 steel has been chosen as the default material.
Currently, only hydrodynamic lubrication is utilized for journal bearings. Thus,
the applied methodology is valid for eccentricity ratios up to 0.9. This means that
the maximum distance between the journal and bearing centers should be up to 90% of
the radial clearance (radial clearance=RB-RJ). An IMPACT contact element between
journal and bearing graphics is implemented to deal with numerical issues that may
arise in cases of large eccentricity, or to provide a solution for a static analysis.
However, results that are derived from both lubrication and contact should not be
regarded as realistic. Contact occurrence and/or large eccentricity may indicate
that current journal bearing characteristics should be changed.
Comment 2
The method attribute defines the methodology used to describe the lubrication
(hydrodynamic) forces and moments.
The Sommerfeld method includes negative lubricant pressures in the calculation
of the forces, while the Gumbel includes only positive. Consequently, the Gumbel
method is more accurate because lubricants cannot withstand negative pressures.
The short method should be used when the length-to-bearing diameter ratio is
smaller than 0.5. The long method is adequate when the diameter ratio is bigger
than 2. Either the short or long method can be used for ratios between 0.5
and 2. The proper choice depends on the application.
The Dynamic Gumbel method considers the continuous variation of the location
where the positive pressure exists each time step. Thus, it provides better
results in a transient state, but is computationally more expensive. For example,
in the picture below, the region of positive pressure is not aligned with the
line that connects the two centers as in the Gumbel method.
Use the lubrication_force_graphics attribute for a better understanding of the
pressure distribution along the journal bearing. The force vectors represent the
pressure that acts at the journal.
Comment 4
The requests that are received for a journal bearing are the relative displacement,
velocity, and acceleration between the journal bearing centers expressed in the
rm and the absolute displacement, velocity, and acceleration of the journal and
bearing center expressed in the output_rm. Also, the lubrication forces and moments
that act at the journal and the bearing are received. The maximum and minimum
pressure and the minimum oil film thickness, along with their radial and axial
(for misaligned) positions, are calculated to evaluate the performance of the
journal bearing. The axial position is measured with respect to the z axis of the
rm, while the radial position is the angle that is measured from the x axis of
the rm.
Comment 5
nr and na attributes can be increased if a finer force vector distribution
is wanted. Also, an increase may be required for better results of the Maximum/Minimum
Pressure and Minimum Oil Film Thickness Requests. For misaligned journal bearings,
these values may be increased for obtaining a more accurate solution. Although,
increasing nr and na leads to a reduced computational performance in most cases.
The HelicalGearSet element automatically creates
a pair of two helical gears based on user input and calculated values. However,
if the HelicalGear element is used, then some parameters
cannot be auto-calculated, such as center distance, addendum lowering, and so forth.
You must consider this when creating gear sets using individual HelicalGear elements.
Comment 2
Backlash ratio (\(j_{i}\)) is defined as the parameter that if multiplied by
the half circular pitch of the gear tooth, the circumferential backlash for each
gear is calculated.
Backlash (circumferential) or tooth thickness allowance is the slight reduction
of the theoretical tooth thickness on the pitch circle (calculated as backlash –
free state) to prevent gear jamming. The center distance is not changed by this;
the ratio only affects the gear tooth thickness.
Another way to introduce extra backlash to the gear tooth is to increase the center
distance. Profile shift parameters are also adjusted.
The total backlash (for both gears) is calculated as:
\(backlash = 0.5 (j_{1}+j_{2}) cp\)
where, \(cp\) is the circular pitch and calculated as:
\(cp = \frac{m_{n} \pi}{\cos(\beta)}\)
Comment 3
Addendum lowering is calculated from the summation of the profile shifts to ensure
that tip clearance does not change.
When using a single gear, this parameter cannot be calculated and the default value
is zero. For the HelicalGearSet, this parameter
is calculated internally and provided to the created HelicalGear elements.
Comment 4
The default value is calculated internally with respect to the units of the system.
S45C (AISI 1045) steel has been chosen as the default material.
Comment 5
Two of the num_of_teeth_1, num_of_teeth_2 and gear_ratio
must be specified as inputs. The third is calculated consistently.
Comment 6
The profile shift coefficient must always be higher than a critical value to avoid
the undercut phenomenon. An error message is displayed if this value is less than
this limit.
Comment 7
When the number of teeth of the gear element parameter is negative, then an
internal helical gear is created.
Use the negative gear ratio to create an external/internal gear set with the
HelicalGearSet element.
Do not use a negative number of teeth on both gears.
Comment 8
If the hub diameter is not provided as an input, then it is calculated internally
as a function of the addendum and the dedendum of the gear. The hub diameter is
the inner diameter when creating external gears and the outer diameter when using
internal gears.
Comment 9
In the HelicalGear element, the following parameters
are defined:
The pitch diameter is defined as:
\(d = \frac{m_{n}}{\cos(\beta)} z\)
The tip diameter is defined as:
\(d^{*}_{a} = d + 2 m_{n} (x^{*} + h^{*}_{a})\)
\(d_{ac} = d^{*}_{a} + 2 km\)
\(d_{a} = max(|(d_{ac}| , |d^{*}_{a}∣)\)
The root diameter is defined as:
\(d_{f} = d − 2 m_{n} (h^{*}_{f}−x^{*})\)
\(if \ z<0 : d_{f} = |d_{f}|\)
Comment 10
In the HelicalGearSet element, the operating
center distance (\(a_{w}\)) is calculated internally from the definition of
the two reference markers of the element. This center distance might differ from
the initial one calculated as \(a_{i}=0.5 (d_{1}+d_{2})\). Ensure that the
working pressure angle and the working pitch diameters (\(d_{w1} , d_{w2}\))
comply with the calculated center distance.
Comment 11
The center distance of the planetary gear set must have specific limits to avoid
planet interference. The planet’s distance \(l\), as can be seen in the figure
of the PlanetaryGearSet, must follow the
following equation:
\(l > d_{a_{planet}}\)
where:
\(l = 2 a_{w} \sin(\pi N)\)
\(d_{a_{planet}}\): the tip diameter of planets
\(a_{w}\): working center distance
\(N\): Number of planets
Comment 12
The number of teeth of the PlanetaryGearSet
must follow specific constraints.
The \(z_{1}\) and \(z_{2}\) always need to be positive, and respectively,
the ring gear teeth (\(z_{3}\)) must be negative. Also, for the correct
meshing of the gears, the following equation for \(z_{1}\) and \(z_{3}\)
needs to be accomplished:
\(mod( (z_{1} − z_{3})/ N ) = 0\)
The modulo of the ratio between the difference of the sun and ring number of teeth
and the number of planets needs to be zero.
Another constraint for the planetary set, without affecting the input choices,
is that the operating center distance for the (sun-planet) and (planet-ring)
gearsets need to be equal. This does not mean that the reference center distance
is also the same due to the profile shift. The following equation for the working
pitch diameters of the gears is always true:
\(|d_{w1} + d_{w2}| = |d_{w2}+d_{w3}|\)
Comment 13
For a PlanetaryGearSet, the gear ratio (\(u\))
does not always define the transmission ratio for the gear system (\(i\)).
For the case that the carrier part is connected to the ground, the planets work
as idler gears so the transmission ratio (\(i\)) is the same as the gear ratio
(\(u\)):
\(i = u = \frac{\omega_{1}}{\omega_{3}}\)
In the case that the ring gear is connected to the ground, the transmission ratio
between the sun gear and the carrier is calculated as follows:
Comment Section#
Bearings#
Comment 1
Bearings can only be connected to rigid bodies (part). If you want to connect a bearing to a flexible body, then a dummy body must be inserted in between.
Comment 2
The default value is calculated internally with respect to the units of the system. AISI 52100 steel has been chosen as the default material.
Journal Bearings#
Comment 1
Currently, only hydrodynamic lubrication is utilized for journal bearings. Thus, the applied methodology is valid for eccentricity ratios up to 0.9. This means that the maximum distance between the journal and bearing centers should be up to 90% of the radial clearance (radial clearance=RB-RJ). An IMPACT contact element between journal and bearing graphics is implemented to deal with numerical issues that may arise in cases of large eccentricity, or to provide a solution for a static analysis. However, results that are derived from both lubrication and contact should not be regarded as realistic. Contact occurrence and/or large eccentricity may indicate that current journal bearing characteristics should be changed.
Comment 2
The
methodattribute defines the methodology used to describe the lubrication (hydrodynamic) forces and moments.The Sommerfeld method includes negative lubricant pressures in the calculation of the forces, while the Gumbel includes only positive. Consequently, the Gumbel method is more accurate because lubricants cannot withstand negative pressures.
The short method should be used when the length-to-bearing diameter ratio is smaller than 0.5. The long method is adequate when the diameter ratio is bigger than 2. Either the short or long method can be used for ratios between 0.5 and 2. The proper choice depends on the application.
The Dynamic Gumbel method considers the continuous variation of the location where the positive pressure exists each time step. Thus, it provides better results in a transient state, but is computationally more expensive. For example, in the picture below, the region of positive pressure is not aligned with the line that connects the two centers as in the Gumbel method.
Visualization of lubrication theories.#
Comment 3
Use the
lubrication_force_graphicsattribute for a better understanding of the pressure distribution along the journal bearing. The force vectors represent the pressure that acts at the journal.Comment 4
The requests that are received for a journal bearing are the relative displacement, velocity, and acceleration between the journal bearing centers expressed in the rm and the absolute displacement, velocity, and acceleration of the journal and bearing center expressed in the
output_rm. Also, the lubrication forces and moments that act at the journal and the bearing are received. The maximum and minimum pressure and the minimum oil film thickness, along with their radial and axial (for misaligned) positions, are calculated to evaluate the performance of the journal bearing. The axial position is measured with respect to the z axis of therm, while the radial position is the angle that is measured from the x axis of therm.Comment 5
nrandnaattributes can be increased if a finer force vector distribution is wanted. Also, an increase may be required for better results of the Maximum/Minimum Pressure and Minimum Oil Film Thickness Requests. For misaligned journal bearings, these values may be increased for obtaining a more accurate solution. Although, increasing nr and na leads to a reduced computational performance in most cases.Gears#
Comment 1
The
HelicalGearSetelement automatically creates a pair of two helical gears based on user input and calculated values. However, if theHelicalGearelement is used, then some parameters cannot be auto-calculated, such as center distance, addendum lowering, and so forth. You must consider this when creating gear sets using individual HelicalGear elements.Comment 2
Backlash ratio (\(j_{i}\)) is defined as the parameter that if multiplied by the half circular pitch of the gear tooth, the circumferential backlash for each gear is calculated.
Backlash (circumferential) or tooth thickness allowance is the slight reduction of the theoretical tooth thickness on the pitch circle (calculated as backlash – free state) to prevent gear jamming. The center distance is not changed by this; the ratio only affects the gear tooth thickness.
Another way to introduce extra backlash to the gear tooth is to increase the center distance. Profile shift parameters are also adjusted.
The total backlash (for both gears) is calculated as:
\(backlash = 0.5 (j_{1}+j_{2}) cp\)
where, \(cp\) is the circular pitch and calculated as:
\(cp = \frac{m_{n} \pi}{\cos(\beta)}\)
Comment 3
Addendum lowering is calculated from the summation of the profile shifts to ensure that tip clearance does not change.
It is calculated as:
\(km = a_{w} − a_{i} − m_{n} (x^{*}_{1} + x^{*}_{2})\)
When using a single gear, this parameter cannot be calculated and the default value is zero. For the
HelicalGearSet, this parameter is calculated internally and provided to the created HelicalGear elements.Comment 4
The default value is calculated internally with respect to the units of the system. S45C (AISI 1045) steel has been chosen as the default material.
Comment 5
Two of the
num_of_teeth_1,num_of_teeth_2andgear_ratiomust be specified as inputs. The third is calculated consistently.Comment 6
The profile shift coefficient must always be higher than a critical value to avoid the undercut phenomenon. An error message is displayed if this value is less than this limit.
Comment 7
When the number of teeth of the gear element parameter is negative, then an internal helical gear is created.
Use the negative gear ratio to create an external/internal gear set with the HelicalGearSet element.
Do not use a negative number of teeth on both gears.
Comment 8
If the hub diameter is not provided as an input, then it is calculated internally as a function of the addendum and the dedendum of the gear. The hub diameter is the inner diameter when creating external gears and the outer diameter when using internal gears.
Comment 9
In the
HelicalGearelement, the following parameters are defined:The pitch diameter is defined as:
\(d = \frac{m_{n}}{\cos(\beta)} z\)
The tip diameter is defined as:
\(d^{*}_{a} = d + 2 m_{n} (x^{*} + h^{*}_{a})\)
\(d_{ac} = d^{*}_{a} + 2 km\)
\(d_{a} = max(|(d_{ac}| , |d^{*}_{a}∣)\)
The root diameter is defined as:
\(d_{f} = d − 2 m_{n} (h^{*}_{f}−x^{*})\)
\(if \ z<0 : d_{f} = |d_{f}|\)
Comment 10
In the
HelicalGearSetelement, the operating center distance (\(a_{w}\)) is calculated internally from the definition of the two reference markers of the element. This center distance might differ from the initial one calculated as \(a_{i}=0.5 (d_{1}+d_{2})\). Ensure that the working pressure angle and the working pitch diameters (\(d_{w1} , d_{w2}\)) comply with the calculated center distance.Comment 11
The center distance of the planetary gear set must have specific limits to avoid planet interference. The planet’s distance \(l\), as can be seen in the figure of the
PlanetaryGearSet, must follow the following equation:\(l > d_{a_{planet}}\)
where:
\(l = 2 a_{w} \sin(\pi N)\)
\(d_{a_{planet}}\): the tip diameter of planets
\(a_{w}\): working center distance
\(N\): Number of planets
Comment 12
The number of teeth of the
PlanetaryGearSetmust follow specific constraints. The \(z_{1}\) and \(z_{2}\) always need to be positive, and respectively, the ring gear teeth (\(z_{3}\)) must be negative. Also, for the correct meshing of the gears, the following equation for \(z_{1}\) and \(z_{3}\) needs to be accomplished:\(mod( (z_{1} − z_{3})/ N ) = 0\)
The modulo of the ratio between the difference of the sun and ring number of teeth and the number of planets needs to be zero.
Another constraint for the planetary set, without affecting the input choices, is that the operating center distance for the (sun-planet) and (planet-ring) gearsets need to be equal. This does not mean that the reference center distance is also the same due to the profile shift. The following equation for the working pitch diameters of the gears is always true:
\(|d_{w1} + d_{w2}| = |d_{w2}+d_{w3}|\)
Comment 13
For a
PlanetaryGearSet, the gear ratio (\(u\)) does not always define the transmission ratio for the gear system (\(i\)).For the case that the carrier part is connected to the ground, the planets work as idler gears so the transmission ratio (\(i\)) is the same as the gear ratio (\(u\)):
\(i = u = \frac{\omega_{1}}{\omega_{3}}\)
In the case that the ring gear is connected to the ground, the transmission ratio between the sun gear and the carrier is calculated as follows:
\(i_{1c} = (1−u) = \frac{\omega_{1}}{\omega_{c}}\)
Finally, in the case that the sun is fixed, the transmission ratio is modified as follows:
\(i_{3c} = (1−\frac{1}{u}) = \frac{\omega_{3}}{\omega_{c}}\)