Section4 Module7 InstructorNotes r3

8/12/2019 Section4 Module7 InstructorNotes r3

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Autodesk Simulation Workshop

Section 4: Dynamic Simulation

This section presents the theory and methods used to

perform a dynamic analysis of a mechanical system using

the Dynamic Simulation environment in AutodeskInventor

.

The Dynamic Simulation environment is part of an integrated

design and analysis system. It uses information generated

by the Assembly environment and creates data that can be

used by the Autodesk Simulation Mechanical finite element

tools. The seamless data transfer between state-of-the-art

design and analysis tools creates a highly productive design

environment that makes the engineering design process

more efficient.

Dynamic Simulation is based on multi-body dynamics

theory. In this theory the components of a mechanicalsystem are modeled as rigid bodies interconnected by joints. The constraint equations for

each joint are used in conjunction with Lagranges equation of motion to create a system of

differential-algebraic equations. The solution of these equations provides the position,

velocity, and acceleration of each part, as well as the reaction forces at each joint. Each part

is in dynamic equilibrium at each time step of the solution process. This allows the position,

velocity, acceleration, and reaction force information at a specific instance to be used as

boundary conditions for a finite element analysis.

The instruction modules provide both an introduction to the theory and hands-on examples of

how to perform an analysis using Assembly and Dynamic Simulation environment. The

Power Point slides provide a mixture of theory and practical information. The Power Point

slides for modules 1, 2, 5, and 8 are closely tied to the user interface of the Assembly andDynamic Simulation environments. The Power Point slides for Modules 3, 4, 6, and 7 are

more theoretical and contain sufficient mathematical detail to provide an understanding of the

underlying equations and numerical methods. The videos associated with all of the modules

are software oriented and provide examples that both demonstrate the theory and illustrate

how to run practical problems.

The videos associated with Modules 4 and 6 emphasize the difference between a kinematic

analysis that uses a prescribed motion as the driver, and a dynamic analysis that uses a

prescribed force or torque as the driver. Each analysis type computes similar information.

However, the results of these two types of analyses are often dramatically different and it is

important for a student to understand which type of analysis should be used for a particular

situation. A comparison of the results from these two videos shows the significant differencein the computed response.

The models used in the videos and Power Point presentations were taken from a boxer-style

engine. Two principal models are used: 1) the rotating parts assembly containing the

crankshaft, connecting rods, and pistons, and 2) a single cam and intake valve assembly.

Detailed example problems are solved using the models in Modules 5 and 8. Module 5

shows the entire process, starting with how to create an assembly in the Assembly

environment and ending with an examination of the results in Dynamic Simulation.

Modules Contained in Section 4

1. Dynamic Simulation Overview

2. DOF and Joints

3. Constraint Equations

4. Constraint Kinematics

5. Piston Example Problem

6. Lagranges Equation

7. Lagrangian Multipliers

8. Cam Example Problem


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Table of ContentsClick below to jump to the current Module:

1. Module 1: Dynamic Simulation Overview ...................................................................... 3

2. Module 2: Degrees of Freedom and Joints.................................................................... 4

3. Module 3: Constraint Equations ...................................................................................... 5

4. Module 4: Constraint Kinematics ..................................................................................... 8

5. Module 5: Piston Assembly Example ........................................................................... 10

6. Module 6: Lagranges Equation ..................................................................................... 14

7. Module 7: Lagrangian Multipliers........................................................................ 16

8. Module 8: Cam Example Problem ................................................................................ 17


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1. Module 1: Dynamic Simulation Overview

Introduct ion

This module provides an overview of the dynamic simulation capability in Autodesk Inventor.Kinematic constraints are fundamental concepts associated with the type of rigid body

simulation performed by Dynamic Simulation. Kinematic constraints must be established for

each joint. A discussion of the difference between assembly constraints and kinematic

constraints is provided. The steps used to move between the Assembly and the Dynamic

environments are also discussed.

Execut ion

1) The four basic types of assembly constraints can be seen in the Assembly

environment by selecting the Constraint icon in the top ribbon menu. The Place

Constraint box appears. The four constraint types shown under the Assembly tab

are Mate, Angle, Tangent, and Insert. These four Assembly constraints enablecomplex systems to be assembled.

2) The assembly constraints used in a particular model can be seen by clicking on the

+ symbol located beside a part in the browser. In addition to all of the operations

used to create the part, the assembly constraints are listed at the bottom.

3) The motion allowed by the assembly constraints can be seen in the Assembly

environment by selecting a movable part on the screen and dragging the mouse

while continuing to press the left mouse button. In the engine assembly, the

crankshaft can be rotated about its centerline. All of the other parts move to new

locations that satisfy the assembly constraints. Although we can move the parts in

the assembly, there is no information generated about the force or moment required

to cause the motion or the forces or moments required to enforce the constraints.

4) The Dynamic Simulation is accessed by selecting the Environments tab located at

the top of the screen and then selecting the Dynamic Simulation icon located at the

far left.

5) In Dynamic Simulation the assembly constraints are replaced by kinematic

constraints. Although similar to assembly constraints, the kinematic constraints are

uniquely different. Assembly constraints can be written between any of the features

of two parts. Kinematic constraints, on the other hand, relate relative motion at joints

to the inertial degrees of freedom of the parts. The inertial properties of the part are

generally referenced to the principal axes of inertia that are fixed at the center of

mass of the part.

6) Standard types of kinematic constraints used in Dynamic Simulation include

prismatic, revolution, cylindrical, and spherical. There are other types of standardjoints in addition to those used for the engine assembly.

7) An important feature of Dynamic Simulation is its ability to automatically transform

assembly constraints into kinematic constraints. In some cases Dynamic Simulation

develops a unique set of kinematic constraints. In others, redundant kinematic

constraints are generated. Redundant kinematic constraints exist when more than

one constraint is associated with a specific degree of freedom. Redundant

constraints should be removed so that the computed joint reactions are unique.


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Additional kinematic constraints may also be added in the Dynamic Simulation

environment.

8) Additional information about kinematic constraints is provided in subsequent modules

and detailed example problems are presented in Modules 5 and 8.

2. Module 2: Degrees of Freedom and Joints

Introduct ion

This module contains information about degrees of freedom and joints and how joints affect

the mobility of a mechanism. Mobility is the number of independent degrees of freedom that

can be moved in a mechanism. Each joint in a mechanism removes degrees of freedom and

decreases the mobility. The concepts are illustrated using assembly constraints in the

Assembly environment.

Execut ion

A cylinder liner and piston from a boxer style engine are used to demonstrate the degrees of

freedom and mobility associated with different types of constraints.

1) The unconstrained cylinder liner and piston each have six degrees of freedom

three translations and three rotations. These degrees of freedom can be shown on

the screen by selecting each part and dragging it in a particular direction or rotating it

about a particular axis. The Rotate Component function is obtained by selecting a

part, right clicking and selecting Rotate Component.

2) There are a total of twelve degrees of freedom associated with the two unconstrainedparts. The mobility of the two components without constraints is 12.

3) The first constraint will be a ground constraint. The cylinder liner will be fixed by

selecting the part on the screen, right clicking and selecting Grounded. This will fix

the three translations and three rotations of the cylinder liner and prevent them from

moving. This operation has removed 6 degrees of freedom from the system and the

mobility of the two components is reduced to 6. The mobility of 6 represents the

degrees of freedom of the piston that has no constraints.

4) The next constraint will align the centerline of the cylinder liner with the centerline of

the piston. This creates a cylindrical joint that allows the piston to slide along and

rotate about a single axis. This constraint is imposed by selecting the Constrain

icon located in the top ribbon and selecting the mate icon in the box that appears.

The centerline of the cylinder liner is selected by selecting one of the cylindrical

surfaces. The centerline of the piston is also selected by selecting one of the

cylindrical outside surfaces on the piston. In both cases Inventor will display the

centerline on the graphics window. After the Constrain box is closed, the piston can

be selected and dragged using the left mouse button. Note that the piston can

translate along and rotate about the centerline of the cylinder liner. The cylindrical

joint removes four degrees of freedom and reduces the mobility of the two part

system to 2.

5) Delete the mate just imposed so that another type of joint can be imposed.


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6) The next constraint will remove the rotational degree of freedom from the cylindrical

joint. Using the same process used in step 4, a mate is added between the

centerline of the cylinder liner and the centerline of the piston. The rotational degree

of freedom is removed by also adding a mate constraint between the cylinder liners

local xy plane and the pistons local xy plane. These planes are found in the origin

folder for each part in the browser. The piston can be selected and dragged on the

screen using the left mouse button, but it cannot be rotated. This type of joint is

equivalent to the prismatic joint found in Dynamic Simulation. A prismatic joint

removes five degrees of freedom and only permits relative motion along an axis

common to both parts. The mobility of the combined system is reduced to one

degree of freedom. The ground removes six and the prismatic joint removes five,

leaving one translational degree of freedom.

7) Delete the two mates used to implement the prismatic joint so that the next joint type

can be imposed.

8) The next constraint is equivalent to a revolution joint found in Dynamic Simulation.

This joint is implemented using the insert function. Select Constrain from the top

menu. Next, select the insert icon from the Place Constraint box that pops up. The

insert icon is the last of the four types. Select the top outside edge of the piston todefine both a point and axis of rotation. Next, select the top inside edge of the

cylinder liner to define both a point and axis of rotation. The insert function makes

the two points coincident and only allows motion about the common axis. The mouse

can be used to rotate the piston inside of the cylinder liner. A revolution joint

removes five degrees of freedom. The remaining degree of freedom is the rotational

motion about the centerline axis. This reduces the mobility of the two-part system to

1.

3. Module 3: Constraint Equations

Introduct ion

Kinematic constraint equations are algebraic relationships that describe the relative motion

that can occur at joints in terms of the degrees of freedom of the principal axes of the

associated parts. The PowerPoint slides the constraint equations for a few of the standard

joints used in Dynamic Simulation. The equations are developed for planar mechanisms to

simplify the mathematics and make the underlying concepts easier to learn. Dynamic

Simulation implements these concepts in three-dimensional space instead of the two-

dimensional space occupied by planar mechanisms. However, the basic techniques are

similar. The video shows how to apply the same joints in Dynamic Simulation. The same

cylinder liner and piston used in Video 2 is used in this video. Demonstrating the similarity

between the assembly and kinematic constraints will provide insight into how the automatic

constraint generator used in Dynamic Simulation works.

Execut ion

At the start of the video the cylinder liner and piston are in the Assembly environment and

have no assembly constraints imposed.


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1) The Dynamic Simulation environment is entered by selecting Environments, located

at the top of the screen, and then selecting the Dynamic Simulation icon.

2) The mobility of the system can be checked using the Mechanism Status icon

located on the upper left side of the screen. The Degree of Mobility (dom) is zero.

This is because Dynamic Simulation automatically grounds all parts. Instead of the

kinematic constraints taking degrees of freedom away, they add degrees of freedom

when joints are added. Note that both parts appear in the Grounded folder in the

browser.

3) The Automatically Convert Constraints to Standard Joints option is turned off so

that joints can be added manually. This option is found by selecting the Simulation

Settings box at the top of the screen and then clicking the top box to turn the option

off. A pop-up box appears asking if we want to keep the automatically generated

joints. We dont have any automatically generated joints so we can answer either

yes or no. We select Yes in the video.

4) The first joint to be added is a cylindrical joint. This joint will allow relative translation

and rotation about the centerline axis of the cylinder liner and piston. This will

increase the Degree of Mobility from zero to two. The joint is added by selecting the

Insert Joint icon on the upper left-hand side of the screen; a joints table appears.The cylindrical joint is located under the upper left-hand icon. Another pop-up option

table will appear. Using the arrow next to the box to see the list of available joints,

select Cylindrical.

5) Two components and associated coordinate systems must be defined. The z-axis of

the first component is defined by selecting one of the cylindrical surfaces of the

cylinder liner. Note that a coordinate system is shown that has an axis with three

arrow heads directed along the length of the cylinder liner. This is the cylinder liner

joint coordinate system z-axis. Next we define the origin of the joint coordinate

system by selecting one of the circular edges located at the top of the cylinder liner.

This puts the origin of the joint coordinate system at the center of the circular edge.

6) Then we do the same thing for Component 2the piston. The z-axis of the joint

coordinate system for the piston is added by selecting a cylindrical surface on the

outside of the piston. A coordinate system with the z-axis directed along the length of

the cylinder will be shown. Next we define the origin of the piston joint coordinate

system by selecting the top circular edge of the piston. The coordinate system will be

moved to the top center of the piston. The switch direction icon next to Z axis for

Component 2 can be used to change the direction of the piston z-axis if it is directed

in a direction opposite to that for the cylinder liner. Click Ok.

7) The Degree of Mobility can be checked using the Mechanism Status icon. Note the

Degree of Mobility has been changed from zero to two.

8) The motion of the piston can be seen by selecting the piston and dragging the piston

with the left mouse button. The piston moves along and rotates about the common

axis.9) Delete the cylindrical joint so that another joint can be added. Select the Cylindrical

joint in the Standard Joints group in the browser, then right click and select Delete.

10) The next joint to be added is a prismatic joint. A prismatic joint allows translation only

along an axis that is common to two parts. Select the Insert Joint icon located at

the upper left corner of the screen. A list of joints is displayed. Select Prismatic

from the list.




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joint coordinate system z-axis. Next, we define the origin of the joint coordinate






the cylinder will be shown. Next we define the origin of the piston joint coordinate



Component 2 can be used to change the direction of the piston z-axis if it is directed

in a direction opposite to that for the cylinder liner. Click Ok.

13) Note that Standard Joints has been added to the browser. Clicking on Standard

Joints in the browser shows that the prismatic joint has been added to the list.

14) The system has one degree of mobility, which is the relative translation along the

centerline of the two parts. The mobility can be check by selecting Mechanism

Status from the Joint icons located in the upper left corner of the screen. 15) The mobility degree of freedom can be observed by selecting the piston on the

screen and, while holding the left mouse button down, dragging the piston along the

common centerline.

16) Delete the prismatic joint so that another joint can be added. Select the Prismatic

joint in the Standard Joints group in the browser, then right click and select Delete.

17) The last joint to be added is a revolution joint. A revolution joint allows rotation only

about an axis that is common to two parts. Select the Insert Joint icon located at

the upper left corner of the screen. A list of joints is displayed. Select Revolution

from the list.





joint coordinate system z-axis. Next we define the origin of the joint coordinate






the cylinder will be shown. Next, we define the origin of the piston joint coordinate



Component 2 can be used to change the direction of the piston z-axis if it is directedin a direction opposite to that for the cylinder liner. Click Ok.

20) The system has one degree of mobility, which is the relative rotation about the

centerline of the two parts. The mobility can be checked by selecting Mechanism

Status from the Joint icons located in the upper left corner of the screen.

21) Note that Standard Joints has been added to the browser. Clicking on Standard

Joints in the browser shows that the revolution joint has been added.


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22) The mobility degree of freedom can be observed by selecting the piston on the

screen and, while holding the left mouse button down, dragging the piston. Note that

it will only rotate about the centerline.

4. Module 4: Constraint Kinematics

Introduct ion

The PowerPoint slides associated with this module show how the position, velocity, and

acceleration of components in a mechanism can be determined from kinematic and motion

constraints. Kinematic constraints control relative motion at joints, while motion constraints

impart relative motion to mobile degrees of freedom at joints. While kinematic constraints are

generally not time-dependent, motion constraints are explicit functions of time.

The video for this module shows how to impose a motion in Dynamic Simulation. The

problem used in the video example is an intake valve and cam assembly from a boxer style

engine. This assembly is also used in several of the other videos to demonstrate specific

methods or features of Dynamic Simulation.

Execut ion

The boxer intake cam assembly should be in the Dynamic Simulation environment. A

kinematic analysis is performed when a motion is used as the input to the mechanism. In a

kinematic analysis, the kinematic (joint) constraint equations and motion are used to compute

the position, velocity, and acceleration of the components in the mechanism. Theaccelerations are then be used along with the inertial properties of the system to compute the

force(s) or moment(s) required to impose the input motion(s) and the joint reactions. In

contrast, a dynamic analysis is performed when the input is a force or a torque. Subsequent

modules will show that the results obtained from a dynamic analysis are generally quite

different than those obtained from a kinematic analysis, and it is important that the

appropriate analysis is performed for the problem at hand.

In a kinematic analysis, the kinematic (joint) constraints only provide part of the equations

needed to determine the motion of the system. Motion constraints provide the remaining

equations. In general, a motion constraint must be specified for each degree of mobility.

1) Select Mechanism Status to see the number of degrees of mobility associated withthe assembly. There are three: 1) rotation of the cam shaft relative to the fixed cam

shaft bearing; 2) translation of the valve relative to the valve guide contained in

Welded Group 1; and 3) rotation of the valve about its centerline. The degree of

mobility associated with translation of the valve is removed by the 3D contact joint.

This joint couples the valve translation motion and the rotation of the camshaft. The

other degree of mobility associated with rotation of the valve could be set to zero

using a motion constraint that sets the angular velocity to zero. However, since there


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is nothing in the system to excite this motion, it will be omitted. A motion constraint

will be used with the camshaft rotation degree of mobility.

2) A motion constraint is added by selecting the joint that provides the degree of

mobility. Select the Revolution joint listed in the Standard Joints area of the

browser, then right click and select Properties.

3) There are two tabs in the pop-up box. One is for general properties; the other is for

properties associated with thee rotational dof. Select dof 1(R). The three icons

allow initial conditions to be specified, torques to be specified, or motions to be

specified. Select the third, or motion icon.

4) The Enable imposed motion box must be checked to activate the motion. Next

select the radial button next to Velocity. The motion can be constant or time-

dependent. The Input Grapher is used to specify time-dependent motions. This

feature will be presented in the video for Module 7. In this problem we will specify a

constant angular velocity of 21,000 degrees per second. This is equivalent to 3,400

rpm and is representative of the value that could be seen in a performance engine

having a crankshaft speed @ 7,000 rpm.

5) Before running the simulation, we must specify the duration of the simulation and the

number of time steps. Select the Simulation Player from the Manage area at thetop of the screen. The duration of the analysis is entered in the first box from the left

in the Simulation Player. Enter a value of 0.051 seconds. This is the time it takes for

three rotations of the camshaft rotating at a speed of 21,000 deg/seconds. The

second box contains the number of time steps. Enter a value of 540. This is

equivalent to a time step for every 2 degrees of camshaft rotation.

6) The simulation is started by pressing the forward arrow. Note that the motion of the

mechanism is displayed on the screen as the simulation proceeds.

7) The results of the analysis can be reviewed using the Output Grapher. Select

Output Grapher in the Results section of the top menu.

8) Open the Velocity folder associated with the Revolution:1 joint. Click on the box.

Since there is only one rotational degree of freedom, only one box is shown. A graph

of the angular velocity of the camshaft is shown. Note that angular velocity has a

constant value of 21,000 deg/sec. This agrees with the specified motion and gives

assurance that the analysis is correct.

9) Open the Driving Force folder associated with the Revolution:1 joint. Click on the U-

imposed [1] box. A graph of the torque required to maintain the constant angular

velocity of the camshaft is shown. There is a large spike at the beginning of the

contact between the tappet and the cam lobe. There are also positive and negative

portions of the torque curve. A positive torque indicates that energy is being

delivered to the system to keep it from slowing down. The negative torque indicates

that energy must be taken out of the system to keep it from speeding up.


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5. Module 5: Piston Assembly Example

Introduct ion

This module provides a start-to-finish example of how to set up and perform a dynamicsimulation. There are four videos. The first shows how to create a connecting rod sub-

assembly. The second shows how to create an assembly of the engine block and rotating

assembly. The third shows the steps taken during the dynamic simulation. The fourth shows

how to examine the results using the Output Grapher.

Execut ion

Video 5A: Connect ing Rod Sub-Assemb ly

The video starts with all parts positioned on the graphics screen. The Upper Connecting Rod

has been grounded, but no other assembly constraints have been placed.

1) The first step will be to place the two Indexing Sleeves into the Upper Connecting

Rod. The Indexing Sleeves are important in the real connecting rod assembly

because they locate the position of the Lower Connecting Rod relative to the Upper

Connecting Rod. The two indexing sleeves will be placed into the bolt holes on the

bottom of the Upper Connecting Rod using the Insert constraint. Select Constrain

from the Position area on the top menu, then select the Insert icon from the Place

Constraint box. Next, select the edge of the flat surface located inside of the bolt

hole on the Upper Connecting Rod. Then select the outer edge of the flat surface on

the top of one of the Indexing Sleeves. The Indexing Sleeve will automatically be

moved to satisfy the constraint. The other indexing sleeve is placed in the same

manner.

2) Next, the Lower Connecting Rod will be positioned relative to the Upper ConnectingRod. Select Constrain from the Position area of the top menu, then select the

Insert icon from the Place Constraint box. Select the edge of one of the bolt holes

on the Upper Connecting Rod, and then select the corresponding edge on the Lower

Connecting Rod. The Lower Connecting Rod will automatically be moved to satisfy

this constraint. Follow the same procedure to place the constraint on the other bolt

hole. It may be necessary to pivot the lower connecting rod so that the hole can be

clearly seen.

3) Next, the Crank Bolts will be positioned relative to the Lower Connecting Rod using

the Insert constraint. Select Constrain from the Position area of the top menu, then

select the Insert icon from the Place Constraint box. Select the edge ofthe bolt

hole on the Lower Connecting Rod, and then select the inside edge at the base of

the bolt head. The bolt will automatically be moved to satisfy the constraint. The

other bolt is positioned in a similar manner.

4) Next, the Rod Bearings will be positioned. It takes three steps to position the

bearing. First, the center line of the bearing half is aligned with the center line of the

connecting rod. Select Constrain from the Position area of the top menu, then

select the Mate icon from the Place Constraint box. Select the inside cylindrical

surface of one of the Rod Bearings and then select the corresponding cylindrical

surface of the Upper or Lower Connecting Rod. The Rod Bearing will automatically

be moved to satisfy this constraint. At this point only the centerlines are constrained


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to be coincident and the bearing can be moved along the centerline and rotated

about it. Next, we must position the tab on the bearing in the notch on the

connecting rod. This requires that two common surfaces be constrained using the

Mate constraint as shown in the video. The other bearing half is positioned in a

similar manner.

5) Next, the Piston Pin Bearing is placed in the Upper Connecting Rod using the Insert

constraint. The outer circular edge of the hole at the small end of the Upper

Connecting Rod is selected, and then the inside circular edge at one end of the

Piston Pin Bearing is selected. It may be necessary to use the Aligned or Opposed

icons to orient the bearing correctly. The Piston Pin Bearing will automatically be

moved to satisfy this constraint.

6) The last step is to position the Piston Pin (Wrist Pin) inside of the Piston Bearing

using the Insert constraint. There is a 0.5905 inch offset, so that an equal amount of

the Piston Pin extends from both sides of the connecting rod.

Video 5B: Rotat ing Part Ass embly

The video starts with an assembled engine block and all of the rotating assembly parts

positioned on the graphics screen. The left engine block is grounded. Although the

assembled block does not move, it serves as a reference for placing components such as the

main bearings and the cylinder liners. These components are used to place the rotating

assembly parts.

1) Turn off the visibility of the right and left engine block and the four cylinder castings.

This enables the main bearings and cylinder liners to be seen. The visibility is turned

off by selecting the parts in the browser, then right clicking and selecting visibility.

Multiple parts in a sequence can be selected in the browser by holding down the Shift

key while the parts are selected. Multiple parts not in a sequence can be selected in

the browser by holding down the Ctrl key while the parts are selected.

2) The crankshaft will be placed first using the insert function. Select Constrain fromthe Position icons on the top menu, the select the insert icon. Next, select the edge

of the stepped surface next to the key slot in the crankshaft, then select the front

outside edge of the first main bearing. A negative 2.0 mm off set is also required.

The crankshaft is automatically positioned relative to the main bearing.

3) The rotational motion of the crankshaft can be seen by selecting one of the

counterbalance weights on the crankshaft, and, while holding the left mouse button

down, moving the mouse in a circular motion.

4) Next, the connecting rods will be connected to the journals on the crankshaft. The

connecting rod bearings rotate on the crankshaft journal and are prevented from

moving axially by contact between machined surfaces on both the connecting rods

and the crankshaft. They will be placed in the assembly using the Insert function.

Select Constrain from the Position icons located in the top menu, then select theInsert icon from the Place Constraint box. Select the outside edge of the machined

surface on the large end of the connecting rod. Next, select the edge of the raised

surface on one of the connecting rod journals. The connecting rod is automatically

moved to the correct position to enforce the constraint. The other connecting rods

are placed in a similar manner.

5) We can see that the connecting rods are properly constrained if we rotate the

connecting rod. Note that the large end moves with the connecting rod journals, but

that the piston ends are still free to move independently.


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6) Next, the pistons are connected to the connecting rod piston pins (wrist pins) and are

also constrained to move in the cylinder liners. Each piston requires two mate

constraints. Select Constrain from the Position icons on the top menu, then select

the Mate constraint from the icons in the Place Constraint box. Then select the

centerline of one of the piston pins, followed by selecting the piston pin hole on the

piston. This constrains the two centerlines to be coincident. Next, select the center

line of the piston and then the centerline of the cylinder liner. This will constrain the

two centerlines just selected to be coincident. The remaining pistons are placed in

the assembly using the same two-step process.

7) The rotating part assembly is now complete and the motion of the parts can be seen

by rotating the crank shaft. The position of each part can be determined if the

position of the crankshaft is known. Therefore this system has one degree of

mobility.

8) The visibility of the engine block parts can be turned back on to see the complete

assembly.

Video 5C: Dynamic Simulat ion Set Up and Execut ion

The video starts with the engine assembly created in the previous video in the Assembly

environment.

1) We enter the Dynamic Simulation environment by selecting the Environments tab at

the top of the screen and then selecting Dynamic Simulation.

2) Upon entering the Dynamic Simulation environment, the Assembly constraints are

automatically converted to Joint (kinematic) constraints. During this conversion the

program determines that there are redundant constraints. Redundant constraints are

encountered when more than one constraint controls a single degree of freedom.

The reaction forces computed when redundant constraints are present are not

unique and other solutions besides the one presented exist. We will remove these

redundant constraints later.3) The browser contains a list of the Grounded parts, Mobile Groups, and Standard

Joints. Multiple parts that are constrained to move as a single rigid body are called a

Welded Group. There are several Welded Groups shown in the Grounded area of

the browser. The parts in a Welded Group may be seen by clicking on the + sign

next to it in the browser.

4) The Mobile Groups contain those parts that can move. The Mobile Groups can be

more easily seen by selecting Mobile Groups, then right-clicking and selecting

Color mobile groups.

5) The Standard Joints that were automatically created when we entered the Dynamic

Simulation environment are shown next in the browser. There are two types of

standard joints used: revolution and cylindrical. Note the circled I next to the top

four Revolution joints. These joints have problems due to the redundant constraints.6) Information about the redundancies can be seen by selecting Mechanism Status in

the Joint icons located at the upper left hand corner of the screen. The top portion of

the Mechanism Status and Redundancy box provides information about the Degrees

of redundancy, Degrees of mobility, Number of bodies, and the Number of mobile

bodies.

7) Information associated with each kinematic chain is seen by selecting the two left

facing arrow heads. This expands the Mechanism Status and Redundancy box. The


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redundant constraint in the revolution joint between the connecting rod and

crankshaft is highlighted in orange.

8) Removal of the redundant constraints requires experience and insight into the

mobility of each joint. It can be time-consuming to figure out exactly how to constrain

the kinematic chains so that they can be removed.

9) In this case we need to change the type of joints that are automatically created.

Close out the Mechanism Status and Redundancies box by clicking on Ok. Next,

select the Simulation Settings icon in the Manage group located atthe top of the

screen. Click on the first box to turn off Automatically Convert Constraints to

Standard Joints. We will be asked if we want to Maintain Standard Joints

automatically created from Assembly Constraints; select Yes. Keeping the

automatically created joints will make it easier to change the type of joint later on.

10) Next, select the Mechanism Status icon. We see that a new column has been

added to the lower portion of the box. This last column will enable us to quickly

change the type of joint and observe the mechanism status information displayed in

the top of the box.

11) Select the bottom box marked Cylindrical which is associated with the cylindrical

joint between the piston and welded group containing the cylinder liner. Using thedown arrow head, select the joint type Prismatic. This actually increases the

degree of redundancy since the prismatic constraint eliminates the rotational degree

of freedom from the cylindrical joint.

12) Next, change the cylindrical joint between the piston assembly and connecting rod to

a spherical joint. This adds a mobile degree of freedom and lowers the degree of

redundancy by one.

13) Next, change the first Revolution joint between the connecting rod and crankshaft to

a cylindrical joint. This removes another degree of freedom. Repeating steps 11

through 13 for each of the kinematic chains will remove all redundant constraints.

14) The prismatic joint added in step 11 allows the piston to slide back and forth but

prevents it from rotating. The combination of the spherical joint and cylindrical joint in

steps 12 and 13 allows the connecting rod to rotate about the crankshaft journal, but

the longitudinal motion is constrained by the spherical joint at the other end.

15) A kinematic analysis will be performed by specifying a motion to the revolution joint

between the crankshaft and the main bearing. Select the last revolution joint in the

browser list, then right click and select Properties. Select the Edit imposed

motions icon located on the right top ofthe box. Then define a constant velocity of

6,000 degrees per second. This is equivalent to 1,000 rpm.

16) Next we will add friction to the prismatic joints. Select a prismatic joint in the browser,

then right click and select Properties. Select the Edit joint force icon (2nd

of 3

across the top of the box). Click on the Enable Joint Force box, and then add a

coefficient of friction of 0.2. This must be done for each of the four prismatic joints.

17) We are now ready to submit the analysis using the Simulation Player. Well set thesimulation duration to 0.375 seconds and the number of time steps to 375. Click on

the forward arrow head to start the simulation. The position of each of the mobile

parts can be seen on the screen while the simulation is executing.

18) The analysis results can be analyzed using the Output Grapher or they can be used

to perform a finite element analysis of a part at a specific instant in time.


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Video 5D: Resul ts Examinat ion using the Output Grapher

In this video the results of the simulation performed in Video 5C will be examined using the

Output Grapher.

1) Select the Output Grapher icon from the Results area at the top of the screen.

2) It may be necessary to expand the contents of the browser by selecting the + signnext to the top folder.

3) The browser contains a folder for Standard Joints. The position, velocity, and

acceleration for each mobile degree of freedom of a joint can be plotted as a function

of time. The reaction force for each constrained degree of freedom of a joint can also

be plotted as a function of time. The reaction force is the force exerted on one part

by the other to enforce the kinematic constraint.

4) First, we will examine the revolution joint used to drive the motion of the system. If

we look in the Velocities folder, we will see one velocity associated with the rotation

degree of freedom. Checking this box causes the rotational degree of freedom to be

plotted. Note that we have a constant velocity of 6,000 deg/sec. This is the value we

imposed and we gain confidence in our analysis results by seeing an expected result.

5) Next, we can plot the torque required to cause the system to rotate at 6,000 deg/sec

by plotting the item contained in this folder. Note that the torque oscillates between

positive and negative values. A positive torque indicates that energy is being put into

the system to maintain the required rotation rate. A negative torque indicates that

energy is being removed from the system to maintain the required rotation rate. This

type of behavior is common to kinematic analyses. They are, however, difficult to

realize, since an electrical motor would have extreme difficulty changing the torque in

this manner.

6) Other quantities such as the position of the piston or the wrist pin force between the

piston and connecting rod can be plotted in a similar manner.

6. Module 6: Lagranges Equation

Introduct ion

The PowerPoint slides associated with this module derives Lagranges equation of motion

from the Principle of Least Action. Lagranges equation when combined with the Lagrangian

multiplier technique contained in the next module provides a systematic approach for

developing the equations of motion of mechanical systems whose interaction between the

parts are defined by constraints. This systematic approach is particularly important because

it lends itself to computer implementation.

In this video a dynamic analysis of the cam assembly will b e performed. Lagranges equation

of motion provides the theoretical basis for the analysis. This analysis is a dynamic analysis

because we will be applying a torque to the camshaft along with initial conditions. We will be

able to see the transient response of the system. This analysis is in contrast to that

performed in Module 4, where a rotational motion was imposed on the crankshaft. We will


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5) Use the arrows on the top right side of the data entry area to select the left-most

sector. In the data entry area, set the Starting point X1 or time value to 0, and then

set the Y1 or force value to 0 N. Set the Ending point X2 or time to 0.01 seconds,

and the set the Y2 or force value to 2,000 N.

6) Use the arrows on the top right side of the data entry area to select the right sector.

In the data entry area, we see that the starting point is correctly set to the ending

point of the previous sector. Set the Ending point X2 value to 0.02 seconds and the

Y2 value to 0.0 N. The impulse is shown on the screen.

7) Next we must define what happens if the analysis runs longer than the duration of the

impulse. Use the arrow keys to move one more sector to the right. We will select a

constant value based on the last value encountered. In our case this will be a force

of zero.

8) We are now ready to start the analysis. Press the forward button in the Simulation

Player.

9) After the analysis is complete, we can use the Output Grapher to review the results.

We will first plot the external force. We note that the impulse is shown as entered in

the Input Grapher. It is good practice to always verify that the external forces are

those you intended to apply.10) Other items can be plotted as desired.

8. Module 8: Cam Example Problem

Introduct ion

This last module shows how to add force and contact joints to the cam problem used in

previous modules. A spring is added between the upper and lower plates and 3D contact isadded between the tappet top surface and the cam lobe and dwell surfaces. There are two

videos. The first Video (8A) shows how to add the spring and 3D contact joints. The second

Video (8B) shows how to use the Output Grapher to examine the results.

Execut ion

Video 8AForce Joints

The video starts with the intake valve assembly shown in the Assembly Environment.

1) The spring shown in the assembly will be replaced with a spring joint in Dynamic

Simulation. Select the spring and then right click to obtain a list of options. SelectSuppress from this list. A suppressed part will be carried into the Dynamic

Simulation environment, but will be grounded, which effectively removes it from the

analysis.

2) Next, we will move to the Dynamic Simulation environment. Select Environments

and then Dynamic Simulation.

3) The items listed in the browser include Grounded items, Mobile Groups, Standard

Joints, and External Joints. The Standard Joints include a revolution joint between


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the camshaft and camshaft bearing, and a cylindrical joint between the valve and the

valve stem guide.

4) Next, we will add the spring by selecting Standard Joints in the browser, then right

clicking and selecting Add a Joint. A box is displayed that shows the different kinds

of joints that are available for use. A list is obtained by clicking on the down arrow.

Select Spring/Damper/Jack from the list.

5) We must identify points on two components that define the end points and centerline

axis of the spring. The point on Component 1 is defined by selecting the circular

edge associated with the surface on the lower retaining plate that the spring rests on.

The point is the center point of the circle defined by the edge. The point on

Component 2 is defined by selecting the circular edge on the upper retaining plate

that the spring contacts. It may be necessary to rotate the assembly so that the

upper retaining plate is more visible. Again the point is the center point of the circle

defined by the edge.

6) A spring is displayed in the assembly when the Insert Joint box is closed. This spring

does not look like the one that was suppressed in the Assembly Environment and

must have its properties edited.

7) A Force Joints area has been created in the browser that contains the newly addedspring. Select Spring/Damper/Jack in the browser, then right click and select

Properties.

8) Set the Stiffness to 15.0 N/mm, the Free Length to 40 mm, the Radius to 14 mm, and

the Wire Radius to 2 mm. The geometry of the spring is updated as this information

is added. Note that the spring looks a lot closer to the one previously suppressed.

9) Next, we will define the relationship between the top surface of the tappet and the

cam contact surfaces. First, we select Standard Joints in the browser, right click

and select Add a Joint. Using the down arrow in the pop-up menu, we display the

list of joints and select 3D Contact.

10) In the pop-up menu we see that we must define the two components that will have

contact. We select the top surface of the tappet for Component 1, and select the

dwell or lobe contact surface of the cam for Component 2. When contact occurs, a

very stiff spring is added between the two surfaces if the contact is compressive. If

separation occurs the spring is removed. Contact can only generate compressive

forces.

11) Friction is now added between the valve guide and the valve stem. Select the

Cylindrical Joint in the Standard Joints area of the browser, then right click and

select Properties. The friction is associated with the sliding of the valve stem as it

moves up and down in the valve guide. Therefore, we select the translation d.o.f. tab

at the top of the properties box.

12) Next, select the Edit Joint Force icon, click on the Enable joint force box, and set

the coefficient of friction to 0.2. Close the box by clicking on Ok.

13) The input motion that will drive the mechanism is defined next. A rotational velocity isentered for the cam shaft. Select the Revolution joint in the browser, then right click

and select Properties. Select the Edit joint motion icon and enter a constant

angular velocity of 21,000 degree/second. This is equivalent to a cam shaft speed of

3,400 rpm.

14) We are now ready to set the simulation duration and the number of time steps in the

Simulation Player. Set the duration to 0.051 seconds. This is the time required for

three rotations of the cam shaft. Set the number of time steps to 540 or one time for

every two degrees of rotation of the cam shaft.


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Section4 Module7 InstructorNotes r3

Documents

Transcript of Section4 Module7 InstructorNotes r3