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TMC428_06 Datasheet, PDF (44/58 Pages) List of Unclassifed Manufacturers – Intelligent Triple Stepper Motor Controller with Serial Peripheral Interfaces
TMC428 DATASHEET (v. 2.02 / April 26th, 2006)
44
The shape parameter σ selects one of three functions fbox(φ), fcircle(φ), frhomb(φ), respectively a
superposition of two of them. The shape parameter σ = 0 selects the function fcircle(φ) which is the sine
function sin(ϕ ) as used for sine cosine microstepping. With this, one gets the unit circle (r=1.0) by
transformation to Cartesian coordinates {y = sin(ϕ ); x = cos(ϕ )} as outlined in Figure 12-1, a shape
parameter σ = +1.0 results in a box, and a shape parameter σ = -1.0 results in a rhomb. Other values
except those, result in something between box and circle respectively something between circle an
rhomb.
The data values y(i) of the look-up table range from 0 to 63 and the argument i ranges also from 0 to
63. In the following, natural angles (radians) ranging from (0 ≤ ϕ < 2π ) are used for the description.
The three functions for superposition controlled by the shape parameter σ are
fbox (ϕ )
=

π

4
⋅2
1
⋅ϕ
 2
if
if
0
≤
ϕ
<
π
4
ϕ
≥
π
4
fcircle (ϕ ) = sin(ϕ )
fr hom b (ϕ )
=
2
π
⋅ϕ
All together, these three functions are combined to form the function
 f (ϕ) + σ ⋅[ f (ϕ) − f (ϕ)]
f (ϕ)
σ
=

f

f f f 
circle
(ϕ )
circle
(ϕ ) + σ ⋅[
circle
box
circle
(ϕ ) −
(ϕ )]
circle
r hom b
for
for
for
σ >0
σ =0
σ <0
So, the shape parameter σ selects the type of function and it also provides a continuous transition
between circle and box respectively circle and rhomb. To estimate, what function would be best for a
given type of stepper motor, one can try microstepping based on different shape parameters σ by
downloading different micro step tables on-the-fly into the TMC428 during motion of a stepper motor.
For calculation of data for the micro step look-up table of the TMC428, one has to replace ϕ→ϕi
ranging from 0 to π /2 for the quarter period by
ϕi
=
π
2
⋅
i
64
with i = {0,1,2,3,...,63} .
The amplitude of the shape function fσ (φi) has to be limited to the range of 0.0 to 1.0 respectively to the
range of 0 to 63 for the on-chip RAM as described in the beginning of the microstepping section.
13 How to get Started in Running a Motor
First of all, the Stepper Motor Driver Datagram Configuration has to be written into its RAM area.
Additionally, the Microstep Look-Up-Table has to be initialized when using microstepping. The
parameter LSMD, that is part of the global parameter register, has to be initialized. After that, the
parameters v_min, v_max, and the clock pre-dividers pulse_div and ramp_div and the micro step
resolution usrs has to be set. Then, a_max together with a valid pair of pmul and pdiv has to be set.
The switch configuration ref_conf together with the ramp mode rm has to be chosen. The reference
switch inputs REF1, REF2, REF3 should be pulled down to ground or disabled by setting ref_conf.
With those settings, the TMC428 runs a motor if one writes either x_target or v_target, depending on
the choice of the ramp mode rm. An application note named "TMC428 – Getting Started" together with
C source code examples are available on www.trinamic.com
Copyright © 2004-2006, TRINAMIC Motion Control GmbH & Co. KG