Method 1: Characteristic curve a(n) in polynomial- or hyperbola form

In the range above the limit speed, the current acceleration is optionally specified by a third-order polynomial or by a hyperbola function. In the case of both characteristics, a constant acceleration akonst is used in the range below ngrenz. This corresponds to acceleration at nominal speed. The curves apply to both the speed build-up and slow-down phases.

Method 1: Characteristic curve a(n) in polynomial- or hyperbola form 1:
Profile of acceleration based on a polynomial or hyperbole

Interpolation points on the drive curve a(n) are used to determine the coefficients of the curves. 4 or 3 interpolation points are required to determine them.

One interpolation point P1=(n1, (a(n1)) is already defined by the parameter for constant acceleration akonst and the limit speed ngrenz and the user can define the remaining 3 or 2 on the drive characteristic a(n). It is best for the abscissa values to be at a constant distance. The equations to determine the coefficients are listed below.

Method 1: Characteristic curve a(n) in polynomial- or hyperbola form 2:
Acceleration profile based on polynomial or hyperbole with interpolation points

Polynomial

Method 1: Characteristic curve a(n) in polynomial- or hyperbola form 3:
Method 1: Characteristic curve a(n) in polynomial- or hyperbola form 4:

, relative speed

Method 1: Characteristic curve a(n) in polynomial- or hyperbola form 5:
Method 1: Characteristic curve a(n) in polynomial- or hyperbola form 6:
Method 1: Characteristic curve a(n) in polynomial- or hyperbola form 7:

Method 1: Characteristic curve a(n) in polynomial- or hyperbola form 8:

Example of curve determination

Interpolation point

Acceleration a [°/s2]

Speed n [°/s]

1

16000

12000

2

8000

24000

3

4000

36000

4

2000

48000

aconst = 16000 [°/s2] to nlimit = 12000 [°/s]

The following is obtained for the coefficients:

b3 = -1.92901234E-10 [s/°2]
b2 = 2.08333333E-5 [1/°]
b1 = -0.88888888 [1/s]
b0 = akonst = 16000 [°/s2]

As from nominal speed (nlimit) the characteristic profile is as follows::

Method 1: Characteristic curve a(n) in polynomial- or hyperbola form 9:
Curve profile for nominal speed nlimit with polynomials

Hyperbola

Method 1: Characteristic curve a(n) in polynomial- or hyperbola form 10:

Method 1: Characteristic curve a(n) in polynomial- or hyperbola form 11:, normalised speed, Method 1: Characteristic curve a(n) in polynomial- or hyperbola form 12:

Method 1: Characteristic curve a(n) in polynomial- or hyperbola form 13:
Method 1: Characteristic curve a(n) in polynomial- or hyperbola form 14:

Method 1: Characteristic curve a(n) in polynomial- or hyperbola form 15:
Method 1: Characteristic curve a(n) in polynomial- or hyperbola form 16:

Method 1: Characteristic curve a(n) in polynomial- or hyperbola form 17:

Method 1: Characteristic curve a(n) in polynomial- or hyperbola form 18:

Method 1: Characteristic curve a(n) in polynomial- or hyperbola form 19:

Example of curve determination

Interpolation point

Acceleration a [°/s2]

Speed n [°/s]

1

16000

12000

2

8000

24000

3

4000

36000

4

2000

48000

A_konstkonst = 16000[degrees/s2] to nlimit = 12000 [degrees/s]

The following is obtained for the coefficients:

b2 = 4.166666E-1[]
b3 = 2.857142E-2[]
b1 = 2.285714E4[°/s2]

As from nominal speed (nlimit) the characteristic profile is as follows::

Method 1: Characteristic curve a(n) in polynomial- or hyperbola form 20:
Curve profile for nominal speed nlimit with hyperbola

Parameter

P-AXIS-00202

Type: 1 (hyperbola) or 2 (polynomial)

P-AXIS-00130

Limit speed nlimit

P-AXIS-00007

Constant acceleration aconst for n<nlimit

P-AXIS-00010

Minimum acceleration amin

P-AXIS-00026

Coefficient b1

P-AXIS-00027

Coefficient b2

P-AXIS-00028

Coefficient b3

Parameterisation examples

#
beschl_kennlinie.typ         1                 Hyperbola shape
beschl_kennlinie.a_min       1400              [°/s*s]
beschl_kennlinie.n_grenz     12000000          [10-3 °/s]
beschl_kennlinie.a_konst     16000             [°/s*s]
beschl_kennlinie.b1          2.285714E4        [°/s*s]
beschl_kennlinie.b2          4.166666E-1       []
beschl_kennlinie.b3          -2.857142E-2      []
#
#
beschl_kennlinie.typ         2                 Polynomial shape
beschl_kennlinie.a_min       2000              [°/s*s]
beschl_kennlinie.n_grenz     12000000          [10-3 °/s]
beschl_kennlinie.a_konst     16000             [°/s*s]
beschl_kennlinie.b1          -0.88888888       [1/s]
beschl_kennlinie.b2          2.08333333E-5     [1/°]
beschl_kennlinie.b3          -1.92901234E-10   [s/°²]
#