Part #11: Analytic design & sensitivity analysis of V-type IPM motors

Summary

This 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

00:00

📊 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.

05:01

🔍 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.

10:03

🔌 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.

15:05

🛠️ 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.

Keywords

💡Sensitivity Analysis

Sensitivity analysis is a method used to determine how different variables affect a particular outcome in a system. In the context of the video, it is an important step in the design optimization process. It involves calculating the variation of dependent variables, such as the weight of active parts, as a function of independent variables like aspect ratio or magnetic loading. The video demonstrates how to perform sensitivity analysis using an Excel sheet with inputs for decision variables, mean values, maximum values, and calculation points, which are then used to generate plots showing the relationship between the variables.

💡Design Optimization

Design optimization refers to the process of improving a design by systematically choosing the best design variables to meet specific goals. The video focuses on sensitivity analysis as a critical step in this process, where the goal is to understand how changes in independent variables impact the dependent variables, thereby guiding the optimization of the design. For instance, the video shows how varying the aspect ratio or magnetic loading can affect the weight of active parts in a motor design.

💡Independent Variables

Independent variables are those that can be manipulated or changed in an experiment or analysis without being affected by other variables in the system. In the video, examples of independent variables include the aspect ratio (p18) and magnetic loading (b11). These variables are used in the sensitivity analysis to see how changes in them affect the dependent variables, which are outcomes of the design.

💡Dependent Variables

Dependent variables are outcomes that are affected by changes in independent variables. In the video, the weight of active parts (l42) and the outer diameter of the stator lamination (l27) are dependent variables. The sensitivity analysis investigates how these variables change in response to alterations in independent variables, which is crucial for optimizing the design.

💡Excel

Excel is a spreadsheet program used for data analysis and visualization. The video demonstrates how to use Excel to perform sensitivity analysis. It shows the setup of an Excel sheet with specific cells for inputting decision variables, mean values, maximum values, and calculation points. The results of the analysis are visualized through plots and numerical values in the spreadsheet.

💡Aspect Ratio

The aspect ratio is a dimensionless quantity used in the video as an independent variable to analyze its impact on the weight of active parts in a motor. It is defined as the ratio of the motor's height to its diameter. The video shows how increasing the aspect ratio can affect the motor's design, particularly its weight, through sensitivity analysis.

💡Magnetic Loading

Magnetic loading is a term used in the video to describe an independent variable that influences the design of an electric motor. It is defined as the amount of magnetism per unit area and is crucial for determining the motor's performance. The video demonstrates how changes in magnetic loading can affect the weight of active parts and other design parameters through sensitivity analysis.

💡Electrical Loading

Electrical loading, also mentioned in the video, is another independent variable that affects the design, particularly in terms of cooling methods and copper loss. It is defined as the current per unit area in a conductor. The video shows that increasing electrical loading can lead to a decrease in motor weight but an increase in copper losses, illustrating the trade-offs in design optimization.

💡Copper Loss

Copper loss refers to the energy lost in the form of heat due to the resistance of copper windings in an electric motor. In the video, copper loss is a dependent variable that increases with higher electrical loading. The sensitivity analysis is used to understand this relationship and its implications for motor design.

💡Mechanical Constraints

Mechanical constraints are limitations on the design imposed by physical or mechanical requirements. In the video, constraints such as the outer diameter of the stator lamination and stack length are discussed. The sensitivity analysis helps to ensure that these constraints are met while optimizing other aspects of the design.

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