Parameterisation

General characteristics at segment transitions

Velocity: The segment set velocity VS changes at the segment transition from VS_in to VS_out. At the segment transition the velocity is always reduced to the lower of the two values.
Acceleration: The current path acceleration is always returned to a = 0 at segment transition.
Jerk: The jerk unit J changes according to the geometry at the segment transition. This can cause a significant step change in dynamics.
It is possible to smooth segment transitions.

NCI group parameters
Parameter	Meaning and boundary conditions
Curve velocity reduction mode	Coulomb, cosine or VELOJUMP
Minimum velocity	Path velocity which may not be less than this value (except peaks with movement reversal): V_min ≥ 0.0
Reduction method for C1 transitions	Reduction factor for C1 transitions: C1 ≥ 0.0
VELOJUMP: C0 reduction factors C0X, C0Y, C0Z	Reduction factors for C0 transitions for X, Y, Z axis: C0X ≥ 0.0, C0Y ≥ 0.0, C0Z ≥ 0.0 (axis parameters, online modification in interpreter possible).
DEVIATIONANGLE: Reduction factor C0 C0	Path reduction factor for C0 transitions: 1.0 ≥ C0 ≥ 0.0
DEVIATIONANGLE: Critical angle (low) φ_l	Angle from which a velocity reduction is applied at the segment transition: 0 ≤ φ_l < φ_h ≤ π
DEVIATIONANGLE: Critical angle (high) φ_h	Angle from which the velocity at the segment transition (v_link) is reduced to 0.0: 0 ≤ φ_l < φ_h ≤ π
Tolerance sphere radius TBR	Radius of the tolerance spheres: 1000.0 mm ≥TBR ≥ 0.1 mm
C2 reduction factor C2	Reduction factor for smoothed transitions: C2 ≥ 0.0
Global software limit positions for the path	Switches monitoring of the global software end positions for the path axes

Minimum velocity

Each NCI group has a minimum path velocity V_min ≥ 0.0. The actual velocity should always exceed this value. User-specified exceptions are: programmed stop at segment transition, path end and override requests which lead to a velocity below the minimum value. A systemic exception is a motion reversal. With the reduction method DEVIATIONANGLE the deflection angle is φ ≥ φ_h, in which case the minimum velocity is ignored. V_min must be less than the set value for the path velocity (F word) of each segment.

The minimum velocity can be set to a new value V_min ≥ 0.0 in the NC program at any time. The unit is mm/sec.

Classification of the segment transitions

In general, the transition from one segment to the next is not indefinitely smooth. Therefore, it is necessary to reduce the velocity at the transition point in order to avoid dynamic instability. For this purpose, the transitions are geometrically classified and the effective transition velocity - V_link - is determined in three categories.

Segments - as geographical objects - are defined here as curves in terms of differential geometry and are parameterized by the arc length.
A segment transition from a segment S_in to a segment S_out is classified in geometrical terms as type Ck, where k is a natural number (including 0), if each segment has k continuous arc length differentials and the k^th derivatives at the transition point correspond.

C0 transitions have a knee-point at the transition point.

C1 transitions appear smooth, but are not smooth in dynamic terms. One example is the straight line-semi circle transition in the stadium: at the transition point there is a step change in acceleration.

C2 transitions (and of course Ck transitions with k > 2) are dynamically smooth (jerk restricted).

Reduction method for C2 transitions

As at all transitions, at C2 transitions V_link is set to equal the minimum of both set segment velocities: V_link = min(V_in,V_out). There is no further reduction.

Reduction method for C1 transitions

First, V_link is set to the lower of the two segment target velocities: V_link = min(V_in,V_out). The geometrically induced absolute step change in acceleration AccJump in the segment transition is calculated depending on the geometry types G_in and G_out, and the plane selection G_in and G_out of the segments to be connected, at velocity V_link. If this is greater than C1 times the path acceleration/(absolute) deceleration AccPathReduced permissible for the geometries and planes, the velocity V_link is reduced until the resulting step change in acceleration is equal to AccPathReduced. If this value is less than V_min, then V_min takes priority.

Notice When changing the dynamic parameters, the permissible path acceleration for the geometries and planes and thereby the reaction of the reduction changes automatically.

Interface: XAE and interpreter

Reduction modes for C0 transitions

Several reduction methods are available for C0 transitions. The reduction method VELOJUMP reduces the velocity after permitted step changes in velocity for each axis. The reduction method DEVIATIONANGLE reduces the velocity depending on the deflection angle φ (angle between the normalized end tangent T_in of the incoming segment S_in and the normalized start tangent T_out of the outgoing segment S_out). The cosine reduction method is a purely geometrical method (see curve velocity reduction method).

The VELOJUMP method is recommended for mechanically independent axes, while for mechanically coupled axes (the Y axis is attached to the X axis, for example) the DEVIATIONANGLE method is usually recommended.

Reduction method for C0 transitions: VELOJUMP

If V_link = min(V_in,V_out), and for each axis V_jump[i] = C0[i] * min(A+[i],-A-[i]) * T is the permitted absolute step change in velocity for the axis [i], wherein C0[i] is the reduction factor and A+[i], A-[i] are the acceleration/deceleration limits for the axis [i], and T is the cycle time. The VELOJUMP reduction method ensures that the path velocity is reduced at the segment transition V_link until the absolute step change in the set axis velocity of axis [i] is at most V_jump[i]. V_min nevertheless has priority: if V_link is less than V_min, V_link is set to V_min. In the case of movement reversal with no programmed stop, there will be a jump in axis velocity.

Notice When changing the dynamic parameters, the maximum permissible step changes in axis velocity automatically change at the same time.

Reduction method for C0 transitions: DEVIATIONANGLE

Notice When changing the dynamic parameters, the reduction factors do not automatically change at the same time.

Changing the parameters for C0 transitions: DEVIATIONANGLE

Parameter
Parameter	Meaning and boundary conditions
DEVIATIONANGLE: Reduction factor C0C0	Path reduction factor for C0 transitions: 1.0 ≥ C0 ≥ 0.0
DEVIATIONANGLE: Critical angle (low) φ_l	Angle from which reduction takes effect: 0 ≤ φ_l < φ_h ≤ π
DEVIATIONANGLE: Critical angle (high) φ_h	Angle from which reduction to v_link = 0.0 takes effect: 0 ≤ φ_l < φ_h ≤ π

Interface: Interpreter

Tolerance sphere radius and C2 reduction factor

These parameters are described under the heading Smoothing of segment transitions.

Global software limit positions for the path

The 'Global software limit position monitoring for the path' offers two different ways of software position limit monitoring.

Limit position monitoring by the SAF task

This type of end position monitoring is always active if the limit position for the axis has been switched to active (axis parameter). The monitoring is carried out component for component by the SAF task. This means that if the end position is exceeded, the path velocity is instantly set to 0, and the entire interpolation group has an error.

This type of monitoring is activated through the axes parameters, and not by means of the group parameters described here.

Software limit positions on the path

To prevent the path velocity being set to 0 immediately when a violation of the software end positions is encountered, the function 'Global software end position monitoring of the path' must be enabled. If this is active, the movement stops at the NC block in which the end positions were violated. The velocity is reduced via a ramp.

So that the monitoring is only executed for the desired path axes, the software limit positions for the axis components must be selected (axis parameters).
The monitoring is carried out for the standard geometry segments. These include
Straight line
Circle
Helix
Curves with splines are not monitored. The set values associated with the splines are always within the tolerance sphere. Otherwise the limit position monitoring will make use of the SAF task.
Because meaningful and generally applicable monitoring of the end positions can only be carried out at the NC program's run-time (before lookahead) it is possible that the path axes will move as far as (but not including) the NC block in which the limit positions are exceeded.
If for some reason the axes are located outside the software limit positions it is possible to move back into the correct region in a straight line.

Parameterization:

XAE: Group parameters