proe function formula
Name: Sine curve
Establishment environment: Pro/E software, Cartesian coordinate system
x=50*t
y=10*sin(t*360)
z=0
Name: Helical curve
Establishment environment: PRO/E; cylindrical coordinates (cylindrical)
r=t
theta=10+t*(20*360)
z=t*3
02
Butterfly curve
Spherical coordinates PRO/E
Equation: rho = 8 * t
theta = 360 * t * 4
phi = -360 * t * 8
03
Rhodonea curve
Use Cartesian coordinate system
theta=t*360*4
x=25+(10-6)*cos(theta)+10*cos((10/6-1)*theta)
y=25+(10-6)*sin(theta)-6*sin((10/6-1)*theta)
*********************************
04
Spiral in circle
Column coordinate system
theta=t*360
r=10+10*sin(6*theta)
z=2*sin(6*theta)
05
Involute equation
r=1
ang=360*t
s=2*pi*r*t
x0=s*cos(ang)
y0=s*sin(ang)
x=x0+s*sin(ang)
y=y0-s*cos(ang)
z=0
06
Logarithmic curve
z=0
x = 10*t
y = log(10*t+0.0001)
07
Spherical spiral (using spherical coordinate system)
rho=4
theta=t*180
phi=t*360*20
Name: Double arc outer cycloid
Cardir coordinates
Equation: l=2.5
b=2.5
x=3*b*cos(t*360)+l*cos(3*t*360)
Y=3*b*sin(t*360)+l*sin(3*t*360)
Name: Star Line
Cardir coordinates
equation:
a=5
x=a*(cos(t*360))^3
y=a*(sin(t*360))^3
Name: Heart Line
Build environment: pro/e, cylindrical coordinates
a=10
r=a*(1+cos(theta))
theta=t*360
Name: Leaf Shaped Line
Setting up the environment: Cartesian coordinates
a=10
x=3*a*t/(1+(t^3))
y=3*a*(t^2)/(1+(t^3))
Spiral in Cartesian coordinates
x = 4 * cos (t *(5*360))
y = 4 * sin (t *(5*360))
z = 10*t
08
parabola
Cartesian coordinates
x = (4 * t)
y = (3 * t) + (5 * t ^2)
z =0
Name: Disc spring
Setting up the environment: pro/e
Cylindrical sitting
r = 5
theta = t*3600
z =(sin(3.5*theta-90))+24*t
Equation: Archimedes spiral
x = (a +f sin (t))cos(t)/a
y = (a -2f +f sin (t))sin(t)/b
Pro/e relational expressions and functions related explanatory data
Functions used in relations
Mathematical function
The following operators can be used in relations (including equations and conditional statements).
The following mathematical functions can also be included in the relationship:
cos () cosine
tan () Tangent
sin () sine
sqrt () square root
asin () arc sine
acos () arc cosine
atan () arc tangent
sinh () Hyperbolic sine
cosh () Hyperbolic cosine
tanh () Hyperbolic tangent
Note: All trigonometric functions use unit degrees.
log() base 10 logarithm
ln() natural logarithm
exp() the power of e
abs() absolute value
ceil() is the smallest integer not less than its value
floor() The largest integer that does not exceed its value
You can add an optional argument to the functions ceil and floor, and use it to specify the number of decimals to be rounded.
The syntax of these functions with rounding parameters is:
ceil(parameter_name or number, number_of_dec_places)
floor (parameter_name or number, number_of_dec_places)
Where number_of_dec_places is an optional value:
1) Can be expressed as a number or a user-defined parameter. If the parameter value is a real number, it will be truncated to an integer by the CNC WeChat public account cncdar.
2) Its maximum value is 8. If it exceeds 8, the number to be rounded (the first argument) will not be rounded, and its initial value will be used.
3) If you don't specify it, the function is the same as the previous version.
Use the ceil and floor functions that do not specify the number of decimal places. Examples are as follows:
ceil (10.2) is 11
floor (10.2) has a value of 11
Use the ceil and floor functions that specify the number of decimal places. Examples are as follows:
ceil (10.255, 2) is equal to 10.26
ceil (10.255, 0) is equal to 11 [same as ceil (10.255)]
floor (10.255, 1) is equal to 10.2
floor (10.255, 2) is equal to 10.26
09
Curve table calculation
Curve table calculation allows users to use curve table features to drive dimensions through relationships. The size can be a sketcher, part, or assembly size. The format is as follows: evalgraph("graph_name", x), where graph_name is the name of the curve table, x is the value along the x-axis of the curve table, and the y value is returned.
For mixed features, you can specify the trajectory parameter trajpar as the second argument of the function.
Note: Curve table features are usually CNC WeChat public number cncdar used to calculate the y value corresponding to the x value within the defined range on the x-axis. When out of range, the y value is calculated by extrapolation. For x values smaller than the initial value, the system calculates the extrapolated value by extending the tangent line from the initial point. Similarly, for x values greater than the end point value, the system calculates the extrapolated value by extending the tangent line outward from the end point. Add WeChat: steven52014 will send a copy of macro program tutorial
Compound curve orbit function
The orbit parameter trajpar_of_pnt of the compound curve can be used in the relationship.
The following function returns a value between 0.0 and 1.0: trajpar_of_pnt("trajname", "pointname"). Where trajname is the name of the compound curve, and pointname is the name of the reference point.
The trajectory is a parameter along the compound curve, on which the plane perpendicular to the tangent of the curve passes through the reference point. Therefore, the reference point does not have to be on the curve; the parameter value is calculated at the point closest to the reference point on the curve.
If the composite curve is used as the skeleton of the multitrack scan, trajpar_of_pnt is consistent with trajpar or 1.0-trajpar (depending on the starting point selected for the hybrid feature).
10
About relationship
Relationship (also called parameter relationship) CNC WeChat public account cncdar is an equation between user-defined symbol size and parameters. The relationship captures the design relationship between features, between parameters, or between components, thus allowing users to control the effect of model modification.
Relationships are a way to capture design knowledge and intentions. Like parameters, they are used to drive the model-changing the relationship also changes the model.
Relations can be used to control the effect of model modification, define the size values in parts and assemblies, and act as constraints for design conditions (for example, specify the position of holes related to the edges of parts).
They are used in the design process to describe the relationship between different parts of a model or component. Relations can be simple values (for example, d1=4) or complex conditional branch statements.
Relationship type
There are two types of relationships:
1) Equation-Make one parameter on the left side of the equation equal to the expression on the right side. This relationship is used to assign values to dimensions and parameters. E.g:
Simple assignment: d1 = 4.75
Complex assignment: d5 = d2*(SQRT(d7/3.0+d4))
2) Comparison-Compare the expression on the left and the expression on the right. This relationship is usually used as a constraint or in conditional statements for logical branches. E.g:
As a constraint: (d1 + d2)> (d3 + 2.5)
In the conditional statement; IF (d1 + 2.5) >= d7
Increase relationship
You can increase the relationship to:
1) The cross-section of the feature (in the sketch mode, if the cross-section is created by selecting "Sketcher"> "Relation"> "Add" at first);
2) Features (in part or assembly mode);
3) Parts (in part or assembly mode).
4) Components (in component mode).
When the relationship menu is selected for the first time, the preset is to view or change the relationship in the current model (for example, a part in part mode).
To gain access to the relationship, select "Relations" from the "Parts" or "Components" menu, and then select one of the following commands from the "Model Relations" menu: Component Relations-Use the relationship in the component.
If the component contains one or more sub-components, the "Component Relations" menu appears with the following commands:
─Current-By default, it is the top-level component.
─Name-Type the component name.
1) Skeleton relationship-use the relationship of the skeleton model in the component (applicable to components only).
2) Part relationship-use the relationship in the part.
3) Feature relationship-Use feature-specific relationship. If the feature has a cross-section, then the user can choose: get access to the relationship in the cross-section (Sketcher) in the CNC WeChat public account cncdar surface (Sketcher), or get the relationship in the feature as a whole Access.
Array Relations-Use relations specific to arrays.
Notes:
1) If you try to assign a relationship outside the cross-section to a parameter that has been driven by the cross-section relationship, the system will give an error message when regenerating the model. The same is true when trying to assign a relationship to a parameter that is already driven by a relationship outside of the cross-section. Delete one of the relationships and regenerate.
2) If the component attempts to assign a value to a dimension variable that has been driven by the relationship of the part or subassembly, two error messages will appear. Delete one of the relationships and regenerate.
3) Modifying the identity elements of the model can invalidate the relations because they are not scaled with the model. For more information about modifying units, please refer to the "About Metric and Non-Metric Units of Measurement" help topic.
Use parameter notation in relations
Four types of parameter symbols are used in the relationship:
1) Size symbol-The following size symbol types are supported:
─d#-Dimensions in part or assembly mode.
─d#:#-The size in component mode. The component or the process ID of the component is added as a suffix.
─rd#-The reference size in the part or top-level assembly.
─rd#:#-The reference size in the component mode (the component or the process ID of the component is added as a suffix).
─rsd#-The reference size of the (section) in the sketcher.
─kd#-Known dimensions in the sketch (section) (in the parent part or assembly).
2) Tolerance-These are the parameters related to the tolerance format. When the size changes from the number to the symbol, these symbols are listed.
─tpm#-Tolerance in addition and subtraction symmetric format; # is the number of dimensions.
─tp#-Positive tolerance in addition and subtraction format; # is the number of dimensions.
─tm#-Negative tolerance in addition and subtraction format; # is the number of dimensions.
3) Number of instances-These are integer parameters, which are the number of instances in the array direction.
─p#-where # is the number of instances.
Note: If you change the number of instances to a non-integer value, Pro/ENGINEER will cut off the decimal part. For example, 2.90 will become 2.
4) User parameters-these can be parameters defined by adding parameters or relationships.
E.g:
Volume = d0*d1*d2
Vendor = "Stockton Corp."
Notes:
─User parameter names must start with a letter (if they are to be used in relations).
─Cannot use d#, kd#, rd#, tm#, tp#, or tpm# as user parameter names, because they are reserved for use by dimensions.
─User parameter names cannot contain non-alphanumeric characters, such as !, @, #, $.
11
How to calculate the number of veneers for wood peeling
Rotary kinematics
In the peeling process, the trajectory that the cutting edge of the rotary knife traverses on the cross section of the wood section is called the peeling curve. The following two issues will be discussed here: the basis for designing the kinematics of the rotary cutting machine and the trajectory of the actual rotary cutting.
1) The basis for designing the kinematics of the rotary cutting machine
The purpose of the peeling wood section is to obtain a high-quality continuous veneer strip of uniform thickness, like a paper roll unwinding. There are currently two kinds of motion trajectories that meet the requirements: Archimedes spiral and circular involute.
The basic formula of Archimedes spiral is:
x=ɑsinφ cosφ
y=ɑφsinφ
The nominal thickness of the veneer unscrewed from the wooden section is the pitch of each section of the spiral in the J-axis direction of the curve (φ2=2π+φ1). To make △χ= constant, cosφ must be equal to 1, and φ=90°. When a φ=90°, y=aφsin90°=0, that is, the height of the blade is zero, and the blade should be on the x-axis (that is, in the horizontal plane passing through the axis of rotation of the wood section-the centerline of the chuck axis). It can also be said that no matter what the thickness of the veneer is required, the height of the blade is always zero (h=0)
The formula for the involute of a circle is:
x=acosφ1+aφ1sinφ1
y = asinφ1-aφ1cosφ1
In the formula: φ1-------the angle between the vertical line and the x-axis between the occurrence line and the coordinate center point.
The rotary knife moves in a straight line parallel to the x-axis, so the pitch of the involute sections in the x-axis direction is the nominal thickness of the veneer. S=△χ(acos(2π+φ1)+a( 2π+φ1)sin(2π+φ1)]-[acosφ1+acosφ1+ aφ1sinφ1
]
=[acosφ1+ a(2π+φ1)sinφ1] -[acosφ1+2φ1sinφ1]
=21πasinφl
If S is required to be a constant value (S=2πα), φl must be 2πn+270°, so y=a sin270°—acos270°=-a=h. In order to ensure the quality of veneer, in the peeling process, it is hoped that the clearance angle (cutting angle) of the rotary knife relative to the wood segment, or the angle (θ) between the back of the rotary knife and the vertical surface, should follow the rotary cutting diameter of the wood segment The value of h=-a=-s/2π changes according to the change of s value, so the rotation center of the rotary knife should also change accordingly at this time, so the structure of the rotary cutting machine is too complicated. For this reason, it is inappropriate to use the circular involute as the design of the movement relationship between the rotary cutter and the wood segment of the rotary cutter.
On the contrary, the Archimedes spiral is ideal. Regardless of the change in the nominal thickness of the veneer, the A value is always zero, and the rotary centerline of the rotary knife does not need to be changed. Therefore, it is currently used as the theoretical basis for designing the kinematic relationship between the rotary cutter and the wood segment of the rotary cutter. The actual movement trajectory during rotary cutting is in production, and the installation height (h) of the rotary knife blade is not necessarily in the same horizontal plane as the line connecting the center line of the clamping shaft. This is due to the wood species of the peeling wood section, the peeling conditions, the thickness of the peeling veneer, the structure and accuracy of the peeling machine, and other reasons. In order to obtain a high-quality veneer, h≠0 when installing the knife, which can be positive or negative, and even the center of the rotary knife can be slightly higher than the two ends of the rotary knife.
When the rotary knife blade installation position is different (h value is different), the rotary cutting curve will be:
h>0 At this time, the peeling curve is similar to the Archimedes spiral;
h=0 is the Archimedes spiral;
0>h>-a is an elongated involute
h=-a is the involute;
h<-a is the shortened involute.
Mathematical formula
UFO
Spherical coordinates
rho=20*t^2
theta=60*log(30)*t
phi=7200*t
"rho=200*t"
"theta=900*t"
"phi=t*90*10"
basket
Cylindrical coordinates
r=5+0.3*sin(t*180)+t
theta=t*360*30
z=t*5
Sine curve
Cartesian coordinate system
x=50*t
y=10*sin(t*360)
z=0
Helical curve
Cylindrical coordinates
r=t
theta=10+t*(20*360)
z=t*3
Butterfly curve
Spherical coordinates
rho = 8 * t
theta = 360 * t * 4
phi = -360 * t * 8
Rhodonea curve
Use Cartesian coordinate system
theta=t*360*4
x=25+(10-6)*cos(theta)+10*cos((10/6-1)*theta)
y=25+(10-6)*sin(theta)-6*sin((10/6-1)*theta)
Spiral in circle
Column coordinate system
theta=t*360
r=10+10*sin(6*theta)
z=2*sin(6*theta)
Involute equation
r=1
ang=360*t 90*t
s=2*pi*r*t pi*r.t/2
x0=s*cos(ang)
y0=s*sin(ang)
x=x0+s*sin(ang)
y=y0-s*cos(ang)
z=0
Logarithmic curve
z=0
x = 10*t
y = log(10*t+0.0001)
Spherical spiral
Spherical coordinate system
rho=4
theta=t*180
phi=t*360*20
Double arc cycloid
Cardir coordinates
l=2.5
b=2.5
x=3*b*cos(t*360)+l*cos(3*t*360)
Y=3*b*sin(t*360)+l*sin(3*t*360)
Star line
Cardir coordinates
a=5
x=a*(cos(t*360))^3
y=a*(sin(t*360))^3
Heart line
Cylindrical coordinates
a=10
r=a*(1+cos(theta))
theta=t*360
Leaf shape
Cartesian coordinates
a=10
x=3*a*t/(1+(t^3))
y=3*a*(t^2)/(1+(t^3))
Spiral in Cartesian coordinates
x = 4 * cos (t *(5*360))
y = 4 * sin (t *(5*360))
z = 10*t
parabola
Cartesian coordinates
x = (4 * t)
y = (3 * t) + (5 * t ^2)
z =0
Disc spring
Cylindrical coordinates
r = 5
theta = t*3600
z =(sin(3.5*theta-90))+24*t
30 degree taper hole machining
G90G54G00X0Y0M03S2500:
G43Z50.H01M08:
Z2.
#1=0.05
WHILE[#1LE5.]DO1
#2=TAN[15.]*#1
#3=5.-#2
G01Z-#1F50
X-#3F500
G02I#3
G01X0
#1=#1+0.05
END1
G0Z50.M05
G91G28Z0Y0M09
