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SAE ARP 826 Document Information:
Title
Electrical Computing Resolvers
SAE International
Publication Date:
Jan 1, 1970
Scope:
This document covers resolvers which are used to perform coordinate
transformations as well as sine
and cosine computations. It includes both the categories of
compensated and uncompensated resolvers
which perform these functions. Linear resolvers are also included
because of their similarity to
resolvers.
Definitions
Electrical Computing Resolver -
An electromagnetic device having primary and secondary windings so
oriented that the voltages on
the Secondaries are sine and cosine functions of the angular position
of the rotor with respect to
the stator, multiplied by linear functions of the voltages applied to
the primaries. The device is
used for the computation of sine and cosine functions and for
coordinate transformations.
Resistor Compensated Resolver -
A resolver which contains one or more resistors having external
termination intended for connection
to an amplifier to bring the transformation ratio or phase shift of
the resolver amplifier
combination within close limits, or internal elements which compensate
for changes in resolver
characteristics with variation in temperature or other conditions.
Winding Compensated Resolver -
A resolver which contains one or more windings magnetically coupled to
the primary, with external
terminations for providing a feedback voltage to a booster amplifier
which energizes the primary,
This design usually provides close control on transformation ratio and
phase shift, and reduces
effects of changes in temperature, frequency, applied voltage, or
impedance loading to very low
levels.
Linear Resolver -
A linear resolver converts a mechanical input, rotor position, into an
electrical output which is
a linear function of rotor position over a specified angular travel.
For purposes of this document
the linear resolver will be considered as a special resolver.
Definitions of Terms
Rotor Angle -
The rotor angle of a resolver is the angular displacement of the rotor
from the electrical zero
position. Rotation in a counter-clockwise direction facing the shaft
extension end is to be
considered a positive angular increase. When two shaft extensions
exist, the one opposite the lead
or terminal end will be used for this definition.
Windings
Primary Windings -
A primary winding is one which receives energizing power.
Secondary Winding -
A secondary winding is one from which an output is taken.
Compensator Winding -
A compensator winding is an additional winding which provides a
feedback voltage to adjust
transformation ratio, phase shift, or loading effects.
The following terminal designations shall be used:
Terminal designations or colors are such that stator and compensator
winding terminals with like
numbers have like polarity.
Phase Shift
Phase Shift -
The time phase of the voltage at the computing resolver secondary with
respect to the energizing
voltage is the phase shift. The phase shift is measured i n degrees
and minutes with the rotor at
maximum coupling.
Phase Shift Variation -
The change in numerical value of phase shift relative to ambient
temperature, input voltage level,
excitation frequency, or shaft position should be expressed as a
percentage relative to the value
of phase shift at maximum coupling under specified excitation voltage,
specified excitation
frequency, and specified temperature.
Voltage Identification
In-Phase Voltage -
An in-phase voltage is of the same time phase as the resolver output
of fundamental frequency at
maximum coupling.
Quadrature Voltage -
A quadrature voltage differs by 90 deg time phase from the resolver
output of fundamental frequency
at maximum coupling.
E (R13) is the fundamental in-phase voltage between rotor terminals R1
and R3.
E (R13) is the fundamental in-phase between stator terminals S1 and
S3.
Other voltages are similarly defined.
The sequence of the terms within the parenthesis indicate the sense of
the voltage vector.
Voltage Position
Minimum Voltage (Null) Position -
A position of the rotor at which the secondary voltage of fundamental
frequency, that is in time
phase with the secondary voltage at maximum coupling, is zero (0).
Maximum Coupling Position -
A position of the rotor at which the secondary voltage of fundamental
frequency that is in time
phase with the secondary voltage is a maximum.
Null Voltage
Fundamental Null -
Fundamental null, obtained at the minimum voltage positions; is the
fundamental component of the
residual voltage when the in-phase voltage is zero. This residual
voltage consists entirely of
quadrature voltage.
Total Null -
When the fundamental in-phase output voltage obtained at the minimum
voltage positions is zero, the
residual voltage measured with a vacuum tube voltmeter indicating the
average value of the voltage
wave in terms of the rms value of an equivalent sine wave, is termed
the total null. It includes
harmonics and fundamental quadrature voltages.
Electrical Zero
Rotor Excited Resolvers -
That minimum voltage position of the secondary circuit S2-S4 from
which a small counter-clockwise
deflection of the rotor will induce a voltage E (S24) approximately in
phase with E (R13), when the
unit is excited with rated voltage between terminals R1 and R3, and
terminals R2 and R4 are
shorted.
Stator Excited Resolvers -
That minimum voltage position of the secondary circuit R2-R4 from
which a small counter clockwise
deflection of the rotor will induce a voltage E (R24) approximately
180 deg out of phase with E
(S13), when the unit is excited with rated voltage between terminals
S1 and S3, and terminals S2
and S4 are shorted.
Linear Resolver -
That position of the rotor for which the output windings experience
minimum coupling.
Electrical Angle
Resolver, Rotor Excited -
The electrical angle is the angle "a" displaced in a positive
direction from electrical zero which
satisfies the relative magnitudes and polarities of the secondary
voltages in accordance with the
following equations:
Where: N is the ratio between the maximum fundamental rms, voltage
between two secondary terminals
(S1 and S3 or S2 and S4), with the other two terminals open, and the
primary voltage applied
between two primary terminals (R1 and R3 or R2 and R4).
Resolver, Stator Excited -
The electrical angle is the angle "a" displaced in a positive
direction from electrical zero which
satisfies the relative magnitude and polarities of the secondary
voltages in accordance with the
following equations:
Where: N is the ratio between the maximum rms, voltage between two
secondary terminals (R1 and R3
or R2 and R4), with the other two terminals open, and the primary
voltage applied between two
primary terminals (S1 and S3 or S2 and S4).
Linear Resolver -
The electrical angle "a" is the rotor position which satisfies the
relative magnitude and
polarities of the secondary voltages of a linear resolver in
accordance with the following
equation:
Transformation Ratio
Transformation Ratio -
The ratio of the no-load maximum fundamental secondary voltage to the
fundamental supply voltage
applied to the primary.
Transformation Ratio Unbalance -
Transformation ratio unbalance is found by noting the maximum
difference in the numerical value of
transformation ratio of each output winding as each input winding is
excited. This maximum
difference expressed as a percentage of the nominal transformation
ratio will be used to express
transformation ratio unbalance.
Transformation Ratio Variation -
The change in a numerical value of any particular transformation ratio
relative to ambient
temperature, input voltage level, or excitation frequency, should be
expressed as a transformation
ratio difference relative to the value of transformation ratio under
nominal excitation voltage,
nominal excitation frequency, and a specified temperature.
Voltage Gradient -
The output voltage expressed as a function of input angle over the
specified linear range - for
example, volts per degree.
Errors
Null Spacing Errors -
Null spacing error is the deviation expressed in angular units from
180 deg between the two minimum
voltage positions of an output winding.
Interaxis Error -
Interaxis error in a resolver is the angular deviation of the null
positions for all rotor stator
winding combinations from space quadrature.
Resolver Function Error -
Function error is the difference between the actual fundamental
in-phase output voltage and the
theoretical voltage at any rotor displacement expressed as a
percentage of the actual fundamental
voltage at +90 deg from the minimum voltage position of the winding
under test. The theoretical
voltage shall coincide with the actual voltage at both the minimum
voltage position and at +90 deg
from that position.
Linear Resolver Functional Error -
The functional error of a linear resolver at any rotor position within
the specified limits, is the
difference between the in-phase component of the output of the
secondary winding and the
theoretical output voltage. It is expressed as percent linearity. The
theoretical output voltage is
a straight line passing through zero having a slope equal to the
voltage gradient.
Linearity -
The ideal in-phase output voltage will be zero at linear resolver zero
(EZ) by definition. The term
linearity as used in this document will be zero based linearity (See
Fig. 1). The tolerance on
linearity is expressed in percent of rated output voltage.
Calibration Angle -
A preselected shaft position in the positive quadrant (between 0 and
90 deg shaft rotation,
counter-clockwise facing the shaft extension end). A straight line
drawn through the calibration
angle and electrical zero, terminating at the positive and negative
rated excursion angles,
represents the ideal output voltage of the linear resolver, Because of
the tolerance on
transformation ratio, each linear resolver will not necessarily have
zero error at the calibration
angle.
Units -
Unless otherwise specified the units for angles are degrees, minutes,
and seconds, Potential is
volts rms. Impedance is ohms. Current is amperes rms.
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