Step 18:0: Introduction to the Maths-FB

<< Click to Display Table of Contents >>

Navigation:  Getting Started Tutorials - MechDesigner > Tutorial 18: Maths FB >

Step 18:0: Introduction to the Maths-FB

The Maths FB

IMPORTANT NOTES:

Equations

You must enter the equations correctly with the correct syntax. The Maths FB will check the syntax, but not the equation itself. If you enter an incorrect equation, the output will be incorrect.
For example, if you enter the equation  ((u*t) + (0.5*a*t))to find the final velocity of a point that has constant acceleration then the result will be incorrect. The correct equation is ((u*t) + (0.5*a*t*t)).

You MUST press the Enter key on your keyboard immediately after you enter or edit an equation.

Motion Derivatives

YOU must add the symbolic equation of each motion derivative.

If your application needs position, velocity and acceleration, then you must enter the three equations separately.

If you do not add the motion derivatives (velocity and acceleration), their values remain at zero.

Units

Use the Output Data Type in the Maths FB dialog-box drop-down box to select the units at the output-connector.

The units inside the Maths FB are S.I. units. For example,

50mm at the input connector becomes 0.05m and applied to an equation.

50° at the input-connector becomes (50*2*pi/360) rads. and applied to an equation.

What can you do with a Maths FB?

The Maths FB can use data that is available at the output-connectors of other FBs.

You can use the Maths FB to do:

Simple Algebra

For example: 2+3. The output will be 5, of course.

Parametric Constants

For example, connect the output of a Motion-Dimension FB of a Crank and the output of a Force-Data FB of the same Joint. You can use the Maths FB to multiply the Torque(Nm) and the Velocity(rad/sec) values to give the Power(kW) as the output.

Top-Tip: Connect a Gearing FB to the input of a Maths FB. You can edit the Gearing FB, so that it becomes a parametric-constant of an equation in the Maths FB, for example Friction Coefficient.

Change the Units of a Variable

For example, change the units at the input-connector of a Maths FB - for example: mm or degrees - to different units at the output-connector of the Maths FB - for example: Newtons.

To Add a Maths FB and open the Maths FB dialog-box

ModellingFBtoolbar-Maths

Add a Maths FB:

1.Click modeling-FB toolbar > Maths FB

2.Click the graphic-area

The Maths FB is now in the graphic-area


Open a Maths FB dialog-box

1.Double-click the Maths FB.

or

See How to edit an Elements.

Math FB dialog-box - Basic Navigation and Example

Dialog-FB-Maths

Add Connectors; Edit Output Data Type  

Add Input buttonRed-14-1b - to add input-connectors to the Maths FB.

A new input-connector shows at its left each time you click Add Input. You need one input-connector for each variable or parameter in you equation.

Add Output buttonRed-14-2 - to add output-connectors to the Maths FB.

Each output-connector (and wire) has three data-channels, and

Click the drop-down box to select the Data-Type for all of the output-connectors

Update buttonRed-14-3 - click this button to update ANY change in the dialog.

It is easy to use the Add Input and Add Output buttons add input and output-connectors.

It is also easy to connect wires to the input and output-connectors.

However, to be able to use the Maths FB you MUST understand Wire-Numbers/Input-Connectors and Data-Channels

Three wires connected to the input of a Math FB

Three wires connected to the input of a Math FB

 

Wire Numbers  and Data-Channels

The image above shows three Wires connected to three input-connectors.

Each Wire has a three Data-Channels.

We need to explain more....

Wire-Numbers - refer to the image above.

IMPORTANT : Wire Numbers start at 0

Input-Connector 1 = Wire Number 0 - connected to the TOP input-connector

Input-Connector 1 = Wire Number 1 - connected to the next input-connector, one down from the top.

Input-Connector 1 = Wire Number 2 - connected to the next input-connector down, again

Input-Connector 1 = ...

Data-Channel

Each wire has 3(three) data-channels.

Each data-channel has a letter - p, v, and a

p = Data-Channel 1

v = Data-Channel 2

a = Data-Channel 3

The letters for the Data-Channels are ALWAYS p, v, a EVEN if the wire is not from a motion Function-Block. For example, from a Force-Data FB

Each variable in an equation is identified by its:

Data-Channel(Wire-Number)


Example Entries in an Equation:

p(0) : the p refers to Data-channel 1, and (0) refers to input-connector 1

a(2) : the a refers to Data-channel 3,  and (2) refers to input-connector 3

v(1) : the v refers to Data-channel 2,  and (1) refers to input-connector 2


How many input and output-connectors?

By way of an example, to calculate Power from Torque × Angular Velocity

P =  Ʈ . ω

Torque(N.m.) × Angular Velocity (rad/sec)

Torque data and Angular-Velocity data are the inputs and Power is the output.

Thus, you need two input-connectors and one output-connector.

To get Torque data: we must add a Force-Data FBRed-14-1b to the model.

To get Angular-Velocity data: the output from the Motion-Dimension FBRed-14-2 is in the model.

There is one output-connector when we add the Maths FB to the model.

Maths-FB-ForceTorque

Prepare the model:

1.Add a Rocker - see Tutorial 1

2.Edit the CAD-Line of the Rocker, to open the CAD-Line dialog-box.

In CAD-Line dialog-box | Mass Properties tab > User Mass Properties .
Enter a value for the Mass

In CAD-Line dialog-box | Mass Properties tab > User Mass Properties .
Enter X and Y values to move the Mass from the start-Point of the CAD-Line.

We will not enter a value for the Inertia or Radius of Gyration. This makes the mass a Point Mass - as if the mass of the Rocker is reduced to a particle.

3.Add a Force-Data FB, open the Force-Data FB dialog-box, select the Pin-Joint, and select the Point in the Base-Part to find the Torque that acts-on the Base-Part.


Edit the Maths FB

Set the Output Data Type to Power.

Click UPDATE after we select the Output Data Type and before we add equations.

The Maths FB uses SI units for all data at its input-connectors

Dialog-FB-Maths-PowerCalc-Ex-01B

The equation in the Maths FB is:

p(0)*v(1)

OR

Wire-Number 0 (top), Channel 1 (p = Torque)

×

Wire-Number 1 (bottom wire), Channel 2 (v = Angular Velocity)

SYNTAX and VALID Equations:

Click the Update after you edit the equation to find if its syntax is correct or not correct.

For example, the syntax is not correct if it does not have the correct number of parentheses. The reason is given as a message in the Feedback-Area.

The OK-tiny-11-15 at the left of each equation shows whether its syntax is correct.

More Information on Equation inside the Maths FB

FB-Maths-InputChannels

Data-Channels and Input-Connectors

When you click the Add Input button, you do not change anything inside the dialog-box. You only add a new input-connector.

Each wire you connect to the input-connector has three(3) data-channels (typically, three motion-derivatives)

The input and the data-channel of an input is identified with a letter and a number.

The letter gives the data-channel on each input. The letters are always:

p = Channel 1 ; v = Channel 2 ; a = Channel 3

We identify each input-connector with a number:

The input-connector is in parentheses in an equation.

(0), (1), (2)... for input-connectors 1, 2 and 3 respectively.

FB-Maths-Outputs

Thus, examples might be:

p(0) = Data-channel 1, with input-connector 1

a(2) = Data-channel 3, with input-connector 3

v(1) = Data-channel 2, with input-connector 2

Data at Output-Connectors

The data at each output-connector are given in sets of three.

The image has two sets of three: Output-connector 0 and 1, with Data-Channels 0–2 and 3–5, respectively.

FB-Maths-OutputCoordiantes

Output Data Type: Units (S.I. Units 'inside the Maths FB)

Output Data-Type drop-down box specifies the units for all of the output-connectors.

If you change the Output Data Type, you should click the 'Update' button at the bottom of the dialog-box.

The units that are used within each equation are the SI unit of the 'Output Data Type' : kilogram, metres, seconds, radians


WARNING:

An input of 18° becomes (2*π*18/360) = 0.314 radians within the Maths FB, and then back to 18° again when the Output Data Type is set to Rotary Coordinates.

An input of 18° becomes (2*π*18/360) = 0.314 radians within the Maths FB, BUT the data is converted to 314mm from 0.314radians at the output-connector, when the Output Data Type is set to Linear Coordinates.

To look at the values at the output-connector of a Maths FB, plot the values at the output-connector of a Maths FB with a Graph FB.

Valid Equations

The tick ,or a cross at the start of each equation identifies whether the equation is valid.

You must make it valid. An invalid equation might be where the number of parentheses is incorrect. Read the message in the Feedback Area.


Input-Wires, Output Wires: Channels and Units

Each wire has three channels.

...wire from...

Channel 1

Label & Units

Channel 2

Label : Units

Channel 3

Label & Units

Data Type / Notes

Linear Motion FB

Machine Angle

 

Deg

Machine Angular Velocity :

Deg/sec

Machine Angular Acceleration :

Deg/sec/sec

Note: Velocity: is a function of Machine Speed in Machine Settings dialog-box.

Gearing FB

Dis

Input Unit

Vel

Unit/s

Acc

Unit/s/s

Output Data is a function of input data type - Linear or Rotary

Motion

Dis

mm or deg

Vel

mm/s or deg/s

Acc

mm/s/s or deg/s/s

Output Data: motion-values, Linear or Rotary

Change the Output Data Type to the match input Units

Motion-Dimension

Dis.

mm or deg

Vel. or Ang. Vel.

mm/s or rad/s

Acc

mm/s/s or rad/s/s

If Slider, Data-Type is Linear,

If Rocker, Data-Type is Rotary

Measurement

Dis

mm or deg

Vel

mm or deg

Acceleration

If Data-Type is Linear or Rotary, and depends on the Measurement.

Point FB

Displacement

Velocity

Acceleration

Data Type is Linear.

Cam-Data FB

Pressure Angle

 

deg

Contact Pressure Angel 1

deg

Contact Pressure Angle 2

deg

Radians

 

Radius-of-Curvature Cam 1

Radius-of-Curvature Cam 2

----

Linear Units

 

Contact Force Total

Contact Force, X component

Contact Force, Y component

Units as set in Machine Settings dialog-box.

 

Shear Stress Cam 1

Shear Stress Cam 2


Units as set in Machine Settings dialog-box.

Force Data FB

Joint Total Force

Force, X Component

Y Component

Units as set in Machine Settings dialog-box.

 

Cam Contact Force

X Component

Y Component

Units as set in Machine Settings dialog-box.

 

Spring Force

X Component

Y Component

Units as set in Machine Settings dialog-box.

Maths FB

A 'special' :

Any Unit

As per equation

As per equation

You connect a wire to it and convert its units to a different Data Type. Beware of units.