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Users Manual

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Index

CMM2000 INTRODUCTION 

CS CMM2000 is an application oriented to the analysis of Radial Cams , Cylindrical Cams or GENEVA Wheels, STAR Wheels and INTERMITTENT Drum Mechanisms when is known the follower motion.

The design activity consist in the geometric definition of the Cam profile and, as immediate result, the check of the follower operation.

In order to create the Cam curve responding to the y = f(a) coinciding with the required y = f(t) it is supposed that the camshaft rotates at the fixed constant angular velocity ω = 2 π / t (in the case it is α = ω * t)

All the typology of the follower are tacken sthg. into account :

1. RADIAL Translating Follower

2. OSCILLATING Follower

Inside the two Follower typology are taken into account the following Follower types :

1. Roller Follower

2. Flat-faced Follower

3. Knife-edge Follower

It is possible to take into account the Follower constraint obtaining the cam contour either for positive drive or spring load. A part from any structural aspect inside the Cam drawing, CMM2000 gives exclusive reference to the kinematics aspect of the Cam.

The kinematics correlates the attended features of the Follower (position, velocity, acceleration) with those of the mover (Cam profile).

The analysis can follows two way :

1. When it is known the follower Motion Type the Cam profile, correlated with displacement, velocity and acceleration are immediately calculated.

2. When it is known the Cam profile (FILE of POINTS) are verified the Follower kinematics as displacement, velocity and acceleration.

It s necessary therefore to select the Follower type in order to correctly synthesize the Cam profile.

RADIAL Translating Follower

1. Roller Follower
   
   The synthesized profile correspond to the track followed by the centre of the Roller.
   The effective Cam profile can be obtained offsetting the synthesized Profile of a quantity
   corresponding to the Roller radius or directly using the “Cutter radius Offset” on the CNC.

2. Knife-edge Follower
   
   The case is analogous to the previous but the radius of the Follower is “0”

3. Flat-faced Follower
   
   The contact point between Cam profile and the flat of the Follower change position continuously in respect to the axis of the Flat-faced Follower. The synthesized profile is generated by the group of the envelope lines of the displacements.

OSCILLATING Follower

1. Roller Follower

2. Knife-edge Follower

3. Flat-faced Follower

Each condition arranges an automatic solution introducing the Cam profile correction when are known the feature of the Cam-Follower group.

CMM2000 INPUT DATA 

The INPUT data, to define the Cam Profile, can to be acquired with some different characteristic as :

1. Basic Curves definition

2. File of points

3. S.V.A. graphic : displacement, velocity and acceleration.

CMM2000 is interfaced with MECAD, a program oriented to kinematic motion analysis, consequently it is directly enabled to read its graphic Files of points S.V.A.

CMM2000 is also enabled to read files CMM of previous versions..

Load a file

With the introduction of a sequence of Data INPUT the program generates interactively a S.V.A. graphic, with no regard to the characteristics of the Follower and the type of Cam, this graphic will be used afterwards to define the Cam Profile when will be known the structure of the Follower selected and the type of Cam .

Graphic sample of a S.V.A.

CMM2000 INPUT MENU'

BASIC CURVES

Select one of the Basic Curves proposed inside the menù to insert the stage succession of the S.V.A. graphic defining mode and displacements of the follower.

When is inserted the first Basic Curve it is possible to insert the general data of the

Cam which will appears in the upper part of the Dialog Box.

The required parameters are (in mm.) :

- Radius of Base Circle for Radial Cams and Total length for Translating Cam.

- Initial Displacement ( normally is “0”)

BASIC CURVES definition

Dwell – Concentric circle to the rotation Axes

The activity generate a dwell stage on the Cam, it is required the rotation angle.

BASIC CURVE Graphic

Constant Velocity

The activity generate a displacement stage on the Cam, climb (displacement +) or slope (displacement -) following the Basic Curve with constant velocity of the follower and zero the acceleration.

Required Data :

Cam Rotation Angle or length of the stage.

Total displacement of the follower (+/-)

It is suggested to don’t use this Basic Curve for the first stage, when this is impossible it is opportune to introduce them with a Dwell–Concentric circle whose length must be longer than the calculation Step.

BASIC CURVE Graphic

In order to reduce the acceleration peak (initial and final), it is possible insert a displacement-fillet using the Advanced options.

Two options are available : Fillet with Radius, fillet with Basic Curve.

Fillet with Radius.
Select Radius and define its value to obtain the fillet; the Radius must be greater than the Radius of the roller follower.

Fillet with Basic Curve.
Select the Basic Curve to be used, define the angle Beta representing the width of the stretch of fillet.

In both cases :
1) The calculus preserves the position and the slope of the stage at Constant velocity modifying the entry and exit to insert the fillet.
2) When the previous Basic Curve lets the permission, it is applied a transposition of the complete stage, including the fillet, in order to preserve the start and exit position of the stage at Constant velocity in respect to the preceding Basic Curve.

The stage at Constant Velocity has preserved its position and slope while the fillet covered a part of the preceding Basic Curve.

The operator will decide to modify the application angle of the subsequent Basic Curve in order to compensate the part covered by the exiting fillet.

In the following sample are defined five Basic Curve as :

Stage at Dwell – Concentric circle : 60° deg.
Stage at Constant Velocity : 90° deg ; displacement 15 mm ; Beta Fillet 20° deg
Stage at Dwell – Concentric circle : 50° deg.
Stage at Cycloid : 90° deg ; displacement -15 mm
Stage at Dwell – Concentric circle : 60° deg.

The operator can to notice :

1) The initial stage at Dwell is reduced to 50° deg ; 10° deg are engaged by the fillet.
2) The stage at Constant Velocity including start and exit fillet results 20° deg greater
3) The second Dwell stage has been defined of 50° deg rather than 60° deg to make room to the exiting fillet.
4) The subsequent stages preserved their width and position.

CYCLOID

Required Data :

Cam Rotation Angle or length of the stage.

Total displacement of the follower (+/-)

BASIC CURVE Graphic

It is possible to define “Half” Basic Curve ; the division point correspond to the inflexion point of the graphic displacement.

Select the Option : No for complete Curve , Entry for entry half-curve and Exit for exiting half-curve

SIMPLE HARMONIC

This Curve has a cosine acceleration curve.
The projection of a generic radius point P , starting at point “0” moves vertically at point Q along the diameter D of the reference circle with simple harmonic motion while the circle rotate at constant ω.

Required Data :

Cam Rotation Angle or length of the stage.

Total displacement of the follower (+/-)

BASIC CURVE Graphic

It is possible to define “Half” Basic Curve ; the division point correspond to the inflexion point of the graphic displacement.

Select the Option : No for complete Curve , Entry for entry half-curve and Exit for exiting half-curve

DUBLE HARMONIC

This is an asymmetrical curve composed of two different harmonic motions, one being one-quarter of the amplitude and twice the frequency of the other.

It has the advantages of the simple harmonic curve with almost complete elimination of the high shock and vibration at the beginning of the stroke.

Required Data :

Cam Rotation Angle or length of the stage.

Total displacement of the follower (+/-)

BASIC CURVE Graphic

It is possible to define “Half” Basic Curve ; the division point correspond to the inflexion point of the graphic displacement.

Select the Option : No for complete Curve , Entry for entry half-curve and Exit for exiting half-curve

Modified Sinoid - Bestehorn

This is a modifiable sinoid using two supplementary parameters enabled to move the inflexion point of the graphic displacement and the position of the maximum acceleration value.

Required Data :

Cam Rotation Angle or length of the stage.

Total displacement of the follower (+/-)

X parameter

Lambda (l) parameter

BASIC CURVE Graphic

The following graphics show the changes in S.V.A. graphics enabled by the change of the parameters X and Lambda values.

Change for X only :

Parameters : X=0 , l=0.5

Parameters : X=0.134 , l=0.5

Parameters : X=0.41 , l=0.5

Parameters : X=0.5 , l=0.5

Change for Lambda only :

Parameters : X=0 , l=0.5

Parameters : X=0 , l=0.3

Parameters : X=0 , l=0.6

Sample with simultaneus variation of X and Lambda parameters
Parameters : X=0.5 , l=0.3

Parabolic or constant acceleration

This is a curve of polynomial family and has constant positive and negative acceleration values. The curve has the smallest maximum accelerations for all curves possible.

Required Data :

Cam Rotation Angle or length of the stage.

Total displacement of the follower (+/-)

BASIC CURVE Graphic

Modified Trapezoidal

This is a curve composed of a parabolic motion combined with the cycloidal curve.

Required Data :

Cam Rotation Angle or length of the stage.

Total displacement of the follower (+/-)

BASIC CURVE Graphic

The “Advanced” option enable the possibility to define the width of elementary stages. The default values define a symmetric trapezoidal curve but it is possible to obtain various configurations changing the parameters “Delta” defining the seven percentage width of the elementary stages; instead of “Percentage width” the operator can use directly the elementary stage amplitude in deg. In the first case the sum of the elementary Percentage width must be 1.00 , in the second case the sum of the elementary width must be equal to the total Cam Rotation Angle.

Some samples obtained using different values for the parameter “Delta” :

Cubic no. 1 Curve

This is a curve of polynomial family and has a triangular acceleration curve. It is a modification of the parabolic curve, eliminating the abrupt change in acceleration at the beginning and the end of the stroke. However it does have an acceleration discontinuity at the midpoint.

Required Data :

Cam Rotation Angle or length of the stage.

Total displacement of the follower (+/-)

BASIC CURVE Graphic

Cubic no. 2 Curve

This curve is similar to the Constant Acceleration and the Cubic n.1. It differs from these, however, in that there is no
discontinuity in acceleration in the transition point and also in that its acceleration is a continuous curve for the complete rise.

Required Data :

Cam Rotation Angle or length of the stage.

Total displacement of the follower (+/-)

BASIC CURVE Graphic

Points Sequence .

This curve suppose that the operator has a sequence of points defining the Cam profile.
The activity requires the operator to introduce a sequence of coordinates of points, in the canonic format, defining the profile he will use.
See also the command of the Menù “Points”

BASIC CURVE Graphic

Polynomials .

This solution enable the operator to select one of the available solution.

Required Data :

Cam Rotation Angle or length of the stage.

Total displacement of the follower (+/-)

It is now necessary to gain access in “Advanced” to select the Polynomial Type required.

It is possible to define “Half” Basic Curve ; the division point correspond to the inflexion point of the graphic displacement.

Select the Option : No for complete Curve , Entry for entry half-curve and Exit for exiting half-curve

Fixed Modified Sinoid

The Fixed Modified Sinoid curve is a combination of two quarter of cycloidal curve and a complete sinoid curve.
This curve is a good choice in moving large masses. The modified sine curve, for lower torque and power demand, is one of the best choice of curves.

 

BASIC CURVE Graphic

It is possible to define “Half” Basic Curve ; the division point correspond to the inflexion point of the graphic displacement.

Select the Option : No for complete Curve , Entry for entry half-curve and Exit for exiting half-curve

IMPORT from CMM

This function enables the program to import a File generated with a previous version of CMM

Select the file to be imported inside the Dialog Box appearing on the monitor.

When , in the sequence, is requested a File of Point appears a message requiring the conversion.
In this case use the command “Convert from CMM” in the menù Points and repeat the operation.

IMPORT from FILE 2D

This function enables the program to obtain the Follower motion characteristics from any profile saved in DXF or MI format.
The file CAD must contain only the geometric informations of the profile completed with a point defining the start point of the profile.
( the files C:\cam-soft\cmm2000\cad\dxf \Rettangolo.dxf and C:\cam-soft\cmm2000\cad\mi \Policentrica.mi are useful examples).
Click the option “Graphic displacement” when the drawing MI or DXF already expresses the displacement trend of the follower and not the shape of the Cam (see the file C:\cam-soft\cmm2000\cad\mi \Alzate.mi ).

Insert the required data specifying the chordal tolerance to be used to convert all the circle arcs in a segmentation, the max distance from two adjacent points and the direction to follow the profile.
Using the graphic obtained for V.S.A. it is now possible to define the shape of the Cam when are known the complete characteristics of the follower.

Example : Cam obtained from the file Rettangolo.dxf.

FILE of POINTS

Using the command Create/Modify inside the menù Points is gained the access to the windows enabled to operate on Files of Points.

It is possible to Edit an existing File or create a new using the command “NEW” or “Y=FUN(X)”

Operations on File of Points

Y=FUN(X)

Enable the Operator to insert a mathematics function to generate the point of the file.

Example : Y=SIN(X).

Y=f(X)

Are required : The value of Radius of Base , the value of starting assigned to the independent variable and the value final assigned to the independent variable.

When a File is loaded or created as new, the coordinates are graphically presented, it is possible to modify the values acting on the commands appearing at the left of the window.

 

CMM2000 MENU' MODIFY

MENU’ BASIC CURVES (Top bar)
This Menù enables the command consenting to modify or change the defined Basic Curves.

 Any change in a Basic Curve is reflected on the subsequent Basic Curve.

Available Options :

DELETE BASIC CURVE
The command delete the Basic Curve selected with a click on the S.V.A graphic included into the application stage.

INSERT A BASIC CURVE
Click on the S.V.A graphic included into the application stage before which insert the new Basic Curve.
Select the type of the new Basic Curve and insert the required data.

MODIFY THE BASIC CURVE
Click on the S.V.A graphic included into the application stage of the Basic Curve to be modified, select a new Basic Curve or change the parameters of the current Basic Curve.

To modify the general data of the Cam click on the graphic S.V.A. of the first Basic Curve; in this case it is possible to modify the Base Radius and the Ramp (Total displacement).

INSERT POINT

This Menù enable the possibility to insert one or more point on the graphics S.V.A.

It is required the angular position of the new point, immediately the point is inserted on the graphic of displacement, velocity and acceleration.
When in the required position already exist a point the command is ignored.

If after the insertion of some new point, one or more Basic Curve are modified, the program automatically calculates the new correspondences on the modified S.V.A. graphics.
Also in this case when one recalculating correspondence coincide with an existing angular position coming from the change of the Basic Curve the command is ignored.

To cancel the inserted points use the command Delete Point of the same Menù.

GRAPHIC MODIFY

It possible to modify the graphics S.V.A. intervening graphically only on the displayed curve of the displacement. Selecting the command will appear a pull-down menù where may be selected the option :

· Select the Basic Curve to be used into the interval of the modification, are only available Double Harmonic and Cycloid

· May be enabled the selection of the middle point of the interval as pilot-point of the modification

· Select which other curve must be visible (velocity, acceleration) during the modification of the displacement

Confirm the section pressing the key OK, indicate the two extreme point including the modification plus the internal point that will control the interactive modification.

If no error is contained in the data it possible to drag the curves included into the selected interval, all the curves will be moved as congruent rubber-line following the position of the mouse.
It is possible to interrupt the procedure, in any moment, using the key , to confirm the change
press the left button of the mouse if the displacement must coincide with the current position of the mouse pointer OR the right button of the mouse if it is requested a precise value of the displacement, in this case will appear a DialogBox in which write the precise value of the displacement, press OK to confirm.

Note : Redefining the Basic Curve interested by an interactive modification, the modification will be lost. Instead it is possible to intervene on the previous and following Basic Curve.

CMM2000 WINDOW PROFILES

Window Profiles

Inside sub-menù are present the following Options :

RADIAL CAM / TRANSLATING CAM / CYLINDRICAL CAM

Starting from the Data INPUT the Profiles of a Radial Cam, Translating Cam, Cylindrical Cam are respectively calculated.
Select the structure of the follower and insert the required Data.

Ex. Radial Cam with OSCILLATING Follower and balancing frame.

CONJUGATE CAM / MISALIGNED FOLLOWER

For a Radial Cam, and where admitted, it is possible to calculate the Conjugate Cam profile and/or the Cam profile using a misaligned follower :

RADIAL Translating Follower :

OSCILLATING Follower :

The length of the Roking must be Negative when the point selected for the definition of the motion characteristics is in an opposite position to the Roller in respect to the Pivot Point.

FLAT FACED Follower :

Selecting one of the Option : Cam Profile Internal / External it is possible to obtain the Solid Models as represented in the
following images.
Internal External

Coordinating the Type of Cam (Internal / External) with the structure of the frame defining the Conjugate Cam, it is possible to obtain all the types of Desmodromic Cams (external track / internal track, etc.)

“Desmodromic”Cam defined with Radial Cam Internal and Conjugate Radial Cam External.

Inside the Dialog Box defining the CYLINDRICAL CAM it is possible to define the Diameter of the Tool and enable / disable the option to use or not the Cutter Radius Offset on the CNC.
These conditions are used for Data calculation of the the Tool Path in order to work the Cam on a CNC machine.

Notes :
For the case only of Cylindrical Cam with RADIAL Translating Follower, worked with a tool having the same diameter of the Roller it is possible to use the 2D Profile exportable from the window Profiles.
In all the other cases there are necessary further specific informations as follows :

Case 1.
The operator gives : Roller Diameter = 0 and Tool Diameter = 0
It is a limit case, it is generated only a Cam Profile representing the track of the centre of any Roll for any tool diameter. Inside the window Data are presented the informations regarding the tool centre, used for the CNC in the format : Angle, X, Y, Z
The Option : Use the “Cutter Radius Offset” has no effect.

Case 2.
The operator gives : Roller Diameter ≠ 0 and Tool Diameter = Roller Diameter
Inside the window Profiles will appear two Profiles representing the Upper Cam Profile and the Lower Cam Profile. Inside the window Data are presented the informations regarding the tool centre, used for the CNC in the format : Angle, X, Y, Z

IMPORTANT : It is impossible to mill the Cam Profile with a tool having a different Diameter in respect to the Roller Diameter previously defined.
The Option : Use the “Cutter Radius Offset” has no effect.

Case 3.
The operator gives : Roller Diameter ≠ 0 and Tool Diameter defined as follows :
Roller Diameter > Tool Diameter > Roller Diameter / 2
The Option : Use the “Cutter Radius Offset” is Disabled
Inside the window Profiles will appear two Profiles representing the Upper Cam Profile and the
Lower Cam Profile.
Inside the window Data are presented the informations regarding two tracks for the tool centre,
used for the CNC in the format :
Angle, X, Y, Z regarding the milling of the lower track of the Cam Profile.
Angle, X, Y, Z regarding the milling of the upper track of the Cam Profile.

IMPORTANT : It is impossible to mill the Cam Profile with a tool having a different Diameter in
respect to the Tool Diameter previously defined.

The Option : Use the “Cutter Radius Offset” is Enabled
Inside the window Profiles will appear two Profiles representing the Upper Cam Profile and the Lower Cam Profile.
Inside the window Data are presented the informations regarding two tracks on the Cam Profile, used for the CNC in the format :

Angle, X, Y, P, Q, Z regarding the milling of the lower track of the Cam Profile.
Angle, X, Y, P, Q, Z regarding the milling of the upper track of the Cam Profile.

Note : Since the Data are regarding the nominal Track surface of the Cam Profile, it is possible to use any tool diameter < Roller Diameter.

It is also important :
a ) The CNC must be enabled to use the function G41, G40, G42 (Enabling Cutter Radius Offset) jointly the use of a Rotating Axe; in this case use Data in the format Angle, X, Y, Z .
b ) The CNC must be enabled to use, in parametric mode, the values assigned to P and Q indicating the parametric corrections for X and Y ; in this case use Data in the format Angle, X, Y, P, Q, Z

CYLINDRICAL CAM, AXIAL Translating Follower, Rib Cam Profile

PRESSURE ANGLE and CAM Curvature

This function display the Graphics of the Pressure Angle and Cam curvature of the calculated Cam Profiles.

Graphic : PRESSURE ANGLE and CAM CURVATURE

THICKEN

The function generates the thicken of the active Cam Profile inserting new points belonging on the same spline.

The thicken has no effect on the graphics S.V.A. To obtain more points on these graphics use the variable defining the Angular Step calculation inside the file INI.

Insert the value defining the max distance between two adjacent points belonging on the Cam Profile.
All the elements, having length grater than that defined, are splitted in two or more parts.

SPECIAL PROFILES (Intermittent Working)

This menù includes all the commands allowing the definition of Intermittent workings mechanisms.

These mechanisms don’t uses for the follower Cam basic curves, therefore during the definition no graphic S.V.A. is represented.


GENEVA WHEELS

For the definition the required Data are :

Number of Turnover station
Distance between centres of mover and Geneva Wheel
Pin diameter
R.P.M. of the Mover.

The available Output are similar to these of the Cam.

STAR WHEELS

The working operation is like the Geneva Wheels it is added a couple of gears.

For the definition the required Data are :

Number of Turnover station
Pin diameter
Module m₀
Number of Teeth for Z₁
Number of Teeth for Z₂
R.P.M. of the Mover

All the profiles necessary to the mechanism construction are completely defined.

The movements can be simulated in the window 3D.

Inside the window Basic Curves it is possible to export the 2D drawing in the format .DXF or .MI

The available Output are similar to these of the Cam.

INTERMITTENT Drum Mechanisms

CMM2000 OPTIONS MENU'

The following Options are available :

REMARKABLE POINTS

Enable / Disable the presentation of Remarkable points (vertex of elements).

CUSTOMIZE :

Enable the configuration of the parameters inside File INI in order to customize the program running.

As Maximum Angular Step in calculation and Max Step Millimeter in calculation, important parameters in definition Cam Profile.

Maximum Angular Step

Variable inside the configuration file CMM2000.INI defining the Max calculation angular Step along the Cam Profile.

Step Millimeter

Variable inside the configuration file CMM2000.INI defining the Max calculation distance [mm] between two adjacent point, it change the max angular Step when it results greater than the distance.

CMM2000 3D WINDOW SIMULATION

It operates the 3D visualization of processed Cam and simulates the Cam movement in respect to the defined Follower frame. Use the command to start / stop rotation , step to step rotation , return to start point and select, with standard command, the desired view.

In order to select the part to be exported as file IGES 3D click on the single part or in a group keeping pressed the key SHIFT.

CMM2000 OUTPUT

Some Option are available for the output :

PRINT

(window BASIC CURVES) Print the graphic S.V.A. in the current scale.

(window Cam PROFILES ) Print the drawing of the Cam Profile in the current scale.

(Menù Points – Top Bar) Print the drawing of the, just loaded, File of Points in the current scale.

EXPORT 2D

(window BASIC CURVES) export the graphic S.V.A. in the available format MI and DXF.

(window Cam PROFILES) export the drawing of the Cam Profile in the available format MI and DXF, or create a new file of point reusable in CMM2000.

MACRO ME10

(window Cam PROFILES) saves a file Macro for CAD HP ME10 containing the B-SPLINE

The Macro Output can be directly made from the Menù File in ME10 or keystroking cmmn corresponding to the macro
loaded during the start-up of the program.

DEFINE Cmmn

LOCAL NAMEFILE

{This file '/CAM-SOFT/CMM2000/TMP/LAST' is automatically written by CMM2000 in manner to load the last Cam Profile generated}

OPEN_INFILE 1 '/CAM-SOFT/CMM2000/TMP/LAST'

READ_FILE 1 NAMEFILE

CLOSE_FILE 1

INPUT NAMEFILE

END_DEFINE

INPUT macro CMMN in ME10

Conversion BSPLINE in Circle-Arcs+Lines or Lines inside ME10

EXPORT 3D

(window 3D) save the object selected in the IGES 3D format.
In order to select the part to be saved as file IGES 3D click on the single part or in a group keeping pressed the key SHIFT.

WINDOW DATA

Gaining access to the window DATA, after generation of Cam Profile, it is possible to visualize the summarizing data of the project.

It is possible to optimize the HTML Report in order to store this file all together the other useful files.

Inside Menù File (Top Bar) it is possible to select the command enabled to export Data in EXCEL format.

CMM2000 BIBLIOGRAPHY