Part #11: Analytic design & sensitivity analysis of V-type IPM motors
Summary
TLDRThis educational video delves into sensitivity analysis, a crucial step in the design optimization process. It teaches viewers how to perform sensitivity analysis in Excel, focusing on how dependent variables like motor weight change with independent variables such as aspect ratio and magnetic loading. The video uses practical examples to illustrate the impact of design variables on motor characteristics and includes a discussion on mechanical constraints. It concludes with an overview of the code behind the analysis, offering insights into the design process for electric motors.
Takeaways
- 🔍 Sensitivity analysis is a crucial step in the design optimization process, focusing on how dependent variables change with respect to independent variables.
- 📊 The sensitivity analysis sheet in Excel is used to perform this analysis, with inputs including cell references for decision variables, mean and max values, and the number of calculation points.
- 📈 An example is given where the weight of the motor's active parts is analyzed as a function of the aspect ratio, showing an increase in weight with an increase in aspect ratio.
- 📉 The video demonstrates how to conduct sensitivity analysis by adjusting the cell references and values for independent and dependent variables, and then running the analysis to generate graphs.
- 📋 Discretization during the analytic design can cause jumps in the sensitivity analysis curves, which are explained as a result of the design process.
- 🧲 The video explains why the outer diameter of the stator lamination is not sensitive to magnetic loading, contrary to initial expectations, by reviewing the motor output equation.
- 🔌 The variation of the stator board diameter with respect to magnetic loading is investigated, showing a decrease in diameter as magnetic loading increases.
- 🔥 An increase in electrical loading leads to a decrease in motor weight due to improved cooling methods, but also results in increased copper losses, as demonstrated in the sensitivity analysis.
- 🛠️ Mechanical constraints, such as the outer diameter of the stator lamination and stack length, are considered in the sensitivity analysis to ensure they fall within specified limits.
- 💻 The code behind the sensitivity analysis is discussed, including functions for sensitivity analysis and slot pole combination, which can be customized based on the design requirements.
Q & A
What is sensitivity analysis and why is it important in the design optimization process?
-Sensitivity analysis is a method used to understand how different variables affect a particular output or decision by systematically changing input variables and observing the changes in the output. It is important in the design optimization process because it helps identify which variables have the most significant impact on the design's performance, allowing for more informed decisions and more efficient optimization.
How is the sensitivity analysis sheet set up in the Excel file mentioned in the script?
-The sensitivity analysis sheet in the Excel file consists of five inputs: a cell reference for the decision variable, the mean value and maximum value of the selected decision variable, a cell reference for the objective (a dependent variable), and the number of calculation points. These inputs allow users to perform sensitivity analysis by varying the independent variables and observing the effects on the dependent variables.
What is an example of an independent variable and its corresponding cell reference in the sensitivity analysis?
-An example of an independent variable is the aspect ratio, and its corresponding cell reference is P18. This variable is used to investigate how the weight of the motor varies as a function of the aspect ratio.
What is the purpose of setting a minimum and maximum value for the independent variable in sensitivity analysis?
-Setting a minimum and maximum value for the independent variable allows the sensitivity analysis to cover a range of possible values for that variable. This range is used to generate calculation points and observe how changes within this range affect the dependent variable, providing insights into the variable's sensitivity and potential constraints.
How does the number of calculation points affect the sensitivity analysis?
-The number of calculation points determines the granularity of the sensitivity analysis. A higher number of points provides a more detailed view of how the dependent variable changes with the independent variable, but it may also increase computation time. Conversely, a lower number of points may result in a less detailed analysis but is quicker to compute.
What does the script suggest about the relationship between the weight of active parts and the aspect ratio?
-The script suggests that the weight of active parts of the motor increases as the aspect ratio increases. This relationship is visualized through a graph generated by the sensitivity analysis, which shows the variation of the weight of active parts as a function of the aspect ratio.
Why might there be jumps in the sensitivity analysis curve?
-Jumps in the sensitivity analysis curve may occur due to discretization. The script mentions two types of discretization during the analytic design: one for fixing the number of turns and another for the proper selection of wire gauge size from the SWG table. These jumps reflect the discrete changes in the design variables that can affect the output.
How does the script explain the insensitivity of the stator lamination's outer diameter to magnetic loading?
-The script explains that although one might expect the outer diameter of the stator lamination to decrease with increased magnetic loading, the motor output equation shows that the weight of active parts (and thus the volume) should decrease as the motor output constant increases with magnetic loading. This is because the equation includes the inner diameter (d), not the outer diameter (do), and the aspect ratio is held constant.
What is the significance of investigating the variation of the motor's electrical loading in sensitivity analysis?
-Investigating the variation of the motor's electrical loading is significant because it affects the motor's cooling method and copper losses. Higher electrical loading can lead to better cooling methods but also results in increased copper losses, as shown when the objective is set to copper losses (PCU) in the sensitivity analysis.
How does the script use sensitivity analysis to address mechanical constraints?
-The script uses sensitivity analysis to address mechanical constraints by investigating how changes in the aspect ratio affect the outer diameter of the stator lamination. By adjusting the aspect ratio and observing the changes in the outer diameter, the script demonstrates how to meet a mechanical constraint that requires the outer diameter to be within a certain limit.
What is the purpose of the code behind the sensitivity analysis module mentioned in the script?
-The code behind the sensitivity analysis module is designed to automate the process of running sensitivity analyses. It includes functions for generating the analysis and selecting the best combination of design variables like the number of stator slots and poles based on the application. The code is customizable to fit different designs and inputs, and it includes constraints for the number of samples to ensure accurate and reliable analysis.
Outlines
📊 Introduction to Sensitivity Analysis
This paragraph introduces the concept of sensitivity analysis as a crucial step in the optimization process of design. It explains that sensitivity analysis involves varying independent variables to observe the impact on dependent variables. The speaker demonstrates how to set up a sensitivity analysis in an Excel sheet, detailing the inputs required such as cell references for decision variables, mean and maximum values, objective cell reference, and the number of calculation points. An example is given where the weight of a motor's active parts is analyzed as a function of the aspect ratio, with specific cell references and values provided. The speaker also explains how to execute the analysis and interpret the resulting graph, which shows the relationship between the aspect ratio and the weight of active parts.
🔍 Analyzing the Impact of Magnetic Loading
In this segment, the focus is on examining how changes in magnetic loading affect the weight of active parts of a motor. The speaker sets specific minimum and maximum values for magnetic loading and runs the sensitivity analysis, noting a jump in the graph due to discretization during the design process. The speaker then shifts the objective to the outer diameter of the stator lamination, observing that it is not sensitive to changes in magnetic loading. This is counterintuitive, as one might expect the outer diameter to decrease with increased magnetic loading. However, the speaker clarifies this by reviewing the motor output equation, which includes a constant product, suggesting that an increase in magnetic loading leads to a decrease in the volume of active parts, thus affecting the outer diameter.
🔌 Exploring Electrical Loading and Its Effects
The speaker investigates the variation of the motor's active parts weight as a function of electrical loading. By adjusting the electrical loading values and running the sensitivity analysis, the speaker observes a continuous decrease in motor weight with increased electrical loading. This is attributed to the improved cooling method enabled by higher electrical loading, which in turn increases copper losses. The speaker then checks the copper losses by selecting the corresponding objective and confirms the expected increase in losses with higher electrical loading. The speaker encourages the audience to practice similar analyses for other independent variables.
🛠️ Mechanical Constraints and Sensitivity Analysis Code
The final paragraph discusses mechanical constraints, specifically the outer diameter and stack length of the stator lamination, and how they relate to the aspect ratio. The speaker demonstrates how to analyze these constraints using the sensitivity analysis sheet in Excel, adjusting the aspect ratio to meet the specified limits. The speaker then transitions to discussing the code behind the sensitivity analysis, showing the function written for this purpose and explaining the inputs and constraints coded within. The video concludes with a preview of the next topic, which involves selecting the optimal combination of stator slots and poles based on application needs.
Mindmap
Keywords
💡Sensitivity Analysis
💡Design Optimization
💡Independent Variables
💡Dependent Variables
💡Excel
💡Aspect Ratio
💡Magnetic Loading
💡Electrical Loading
💡Copper Loss
💡Mechanical Constraints
Highlights
Introduction to sensitivity analysis as a crucial step in the design optimization process.
Explanation of sensitivity analysis as the study of how dependent variables change with independent variables.
Guidance on setting up a sensitivity analysis sheet in Excel with inputs for decision variables, mean values, max values, and calculation points.
Example of investigating the weight of a motor as a function of the aspect ratio using sensitivity analysis.
Demonstration of how to run a sensitivity analysis and interpret the resulting plot in Excel.
Observation that the weight of active parts increases with the aspect ratio, as shown in the sensitivity analysis graph.
Discussion on the potential jumps in sensitivity analysis curves due to discretization during the analytic design process.
Analysis of how the outer diameter of a stator lamination is not sensitive to magnetic loading, contrary to initial expectations.
Review of the motor output equation to explain the relationship between magnetic loading and the weight of active parts.
Investigation of the stator board diameter's sensitivity to magnetic loading and its decrease with increased loading.
Exploration of the variational deviator motor's weight as a function of electrical loading, showing a continuous decrease with increased loading.
Analysis of the increase in copper losses when electrical loading is increased, as shown through sensitivity analysis.
Introduction to mechanical constraints, such as the outer diameter of the stator lamination and stack length, and their importance in design.
Procedure to investigate the variation of the outer diameter of the stator lamination as a function of the aspect ratio.
Demonstration of how to meet mechanical constraints by adjusting the aspect ratio to achieve a specific outer diameter.
Introduction to the code behind sensitivity analysis, including the function for sensitivity and the slot pole combination function.
Conclusion of the video with a prompt to continue the discussion in the next video.
Transcripts
hello and welcome to another video of
the course
in this video we are going to do
sensitivity analysis
the sensitivity analysis is one of the
important steps of the design the
optimization of design is done in this
step sensitivity analysis is
calculational variation of dependent
variables
as a function of independent variables
first of all let me explain the
sensitivity analysis sheet in the excel
file
here
there are five inputs in this sheet
as you can see here the first input
is cell reference of decision variable
and the second one and the third one
are mean value and max
value of selected decision variable
the input number four is the cell
reference
of objective the objective
is one of our dependent
variables here from this table
or here for example
the weight of active parts
and the last input in
sensitivity analysis sheet is
the number of calculation points
okay let's have an example
suppose we are going to investigate the
variation of the weight of motor
as a functional aspect ratio so
i set the cell reference of
independent variable equal to
p18 this is cell reference for
aspect ratio p18
i write here b18
and the cell reference
for objective
is
l42 the weight of active parts
and 42
and now i set the minimum value of
aspect ratio equal to
two and its maximum value equal to
five and
set the value of calculation points here
for example 50.
so now i can run sensitivity analysis
by hitting this push button
okay as you can see here in this plot
the labels of x and y-axis
will be updated automatically
the numerical values of the calculation
points of this graph
are accessible in the columns d
and e this is a variation of
aspect ratio and this
is calculated weight
of active parts this is for example one
calculation point
okay this graph in this example
shows that the weight of active parts of
the
motor increases by increasing the aspect
ratio
okay now let's do some sensitivity
analysis
and let's see how our objectives
will change when we change the value of
independent
variables start from
this column
i select the b average
the magnetic loading as decision
variable
the cell reference is b 11
and lets the objective be the same as
previous example that was the weight of
active parts
l42 i set
the minimum value equal to
0.55 and the maximum value equal to 0.65
now i run the sensitivity analysis
so this graph is variation of
weight of active parts as a function of
magnetic loading
as you can see here we have a jump
here
in all sensitivity analysis curve
you might see some jumps
these charms are because of
discretization
remember that we had two discretizations
during the analytic design
one was for fixing all the number of
tens
and the other one was for proper
selection of wire gauge size
from swg table
okay now let's change our objective
i set the cell reference so objective
for the oh
outer diameter of a state of lamination
the cell reference of do is l27
now if i run sensitivity analysis
you can see that the outer diameter of
stator lamination is not sensitive to
magnetic loading do you know
why at the first glance you may
say that no this is wrong because when
we increase the magnetic loading
according to definition of magnetic
loading the
outer diameter of a stator lamination
should decrease
but let's review the motor output
equation
the motor output equation
is here
the output power is equal output
constant
times rotal volume times rps
and as you know in this equation
this is a fixed independent variable and
this is a fixed independent variable
and we have this constant product
so when we increase the magnetic loading
the value of motor output constant
increases
and consequently the weight of
active parts the volume of active parts
should decrease but
consider that in this equation we have d
not d o d is
the state or board diameter in a
diameter of
a state or lamination
so if you consider a constant value for
aspect ratio
we have this equation the output power
is equal g times
if you consider constant value for
aspect ratio
how he was by
the
divided by number of poles
so if you
this is town here if you replace
this explosion
inside taupe and
inserts
the calculated expression for e
and insert the calculated expression for
l in this equation we have
an equation like this g
times constant i named
it c one times
d q times
rps
so this is constant and when we increase
the magnetic loading
we expect that the inner diameter of a
stator lamination
should decrease now let's
select the cell reference of
objective value
equal to g 18
ball diameter
g 18 now
if i run sensitivity analysis
as you can see here the
stator board diameter decrease
by increasing the magnetic
loading okay now
let's investigate the variational
deviator motor as a functional
electrical loading so i select
the cell reference of design variable
for addictive record loading b12
and the objective function
for the weight of active parts l42
l42 and i
changed the value of electrical loading
from 25 kilo ampere per meter
to 45 kilo ampere per meter
and i run sensitivity analysis
and as you can see here the
weight of motor decrease
continuously when we increase the
electrical loading
again we have some jumps
here in this curve okay
but what happened when we increased the
electrical loading
remember that the electrical loading was
a functional cooling method of the motor
if we are going to use a good cooling
method we can
select a high value for electrical
loading
so why we should use good cooling method
when we want to
increase the value of electrical loading
this is because when we increase the
electrical loading
the copper loss increases let's check
i select the objective
equal to pcu the copper last
l 36
now if i run the sensitivity analysis
you can see here the copper losses
will increase when we increase the
electrical loading
okay you can do the same procedure for
the rest of independent variables
and i leave doing
those for you for practice
okay now let's talk about the next topic
of this video
let's come back to our objectives
here
we had two mechanical constraints
one for outer diameter oscillator
lamination and
the another one was for
a stack length the outer diameter of a
stator lamination should be within
15 centimeters so what i need to do
is to investigate the variation of
do as a function of the aspect
ratio so
in sensitivity analysis sheet i
select the design variable
sets the cell reference of design
variable equal to
p18 p18
and the cell reference of
our objective equal to l27
l27 and i change the aspect ratio from
two
to five
[Music]
okay let's run this
sensitivity analysis
okay as you can see here in this
figure when we increase the aspect ratio
the outer diameter of a state or
lamination decreases
this is trivial again we have two
jumps one jump here and another jump
here
so our mechanical constraint is this
and as you can see here
if i select
the value of aspect ratio
equal to 3.3
okay the outer diameter of stator
lamination
could be equal to 150 millimeters
now if i set this value here
in the main dimension sheet if i set the
value of aspect ratio equal to 3.3
you can see here that the outer
diameter of a stator lamination is 150.
now let's check the another mechanical
constraint the stack length the stack
length is equal
135 millimeters that is within
our limits
okay for the last topic of this video
i am going to show you the code behind
the
sensitivity analysis so
open developer tab
and open the code
sensitivity analysis module
as you can see here i wrote this
function
for sensitivity and
this is our design
i wrote comments in this code and you
can
edit the code if you want
based on your design our inputs
are here
and for example
in this part of the code i consider it a
constraint for the number of
samples okay the number of samples
should be a number between
10 and 200.
there is another function here in this
module that is named as a slot pole
combination
that is used for selection of best
combination
of the number of stator slots and the
number of
poles for our design based on the
application this is topical the
next video okay i think it's enough for
this video and let's continue later
thanks for watching
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