Extracting Static and Dynamic Information From Hallpot® Angle Sensors:Linear & Sinusoidal Sensors

John R. Potts, Senior Scientist/Engineering Manager

BRIEF
Elweco Inc. (Painesville, OH) manufactures and markets rotary transducers based on the Hall Effect. Essentially, two basic types of calibrated transducers are available: (1) directly coupled Hallpot® Angle Sensors, for precise system control and/or measurements of angular displacements generally over restricted ranges (+/- 30 degrees) and (2) directly coupled Sin-Cos Hallpot® Resolvers, for precise system control and/or measurements of angular displacements generally over unrestricted ranges (+/- 360 degrees or more). This paper discusses methods for determining shaft position, calibrating sensor output over a restricted angular range, determining shaft speed, determining shaft acceleration, and an application for extracting mechanical properties of relatively soft materials, using a Hallpot® Angle Sensor. For this paper, isothermal behavior is assumed. Thermal effects are discussed in Temperature Behavior of Hallpot® Angle Sensors and Sin-COs Hallpot® Resolvers, published on this website. Techniques for extracting information from Sin-COs Hallpot® Resolvers are discussed in Extracting Static and Dynamic Information From Sin-COs Hallpot® Resolvers: The ATAN2 Function.

Third-Party Research & Development fabricates and markets diagnostic systems based on RVDT and HallPot® rotary sensors. IDRA® Ballistometer System, which is used in cosmetic claims testing, uses a HallPot® Angle sensor and dynamically assesses and is applied to monitor changes in several mechanical properties of skin and other soft materials. Third-Party R&D also provides custom hardware and software engineering development support services for HallPot® sensors.

(1) LINEAR HALLPOT® ANGLE SENSOR

CALIBRATION PROCEDURE
At constant temperature, the sensor output, over restricted angular ranges, is linear with shaft angle:

Vlin=Zero+Sensitivity*(angle) [1]

Where, Vlin is the output response of a linear angle sensor at a particular shaft position in volts, Zero is a factory adjusted offset, in volts, and Sensitivity, in volts/degree, is a slope that is factory adjusted according to user specifications. Sensitivity is positive and sensor output increases with counterclockwise shaft rotation in the lower linear angular range, whereas Sensitivity is negative and sensor output decreases with counterclockwise shaft rotation in the upper linear angular range (see Figure 1). A protractor or digital clinometer and DC meter with 4 digit readout set to read 0-10 volts, mounting plate to support the sensor, and pointer arm which can be attached to the sensor shaft to allow angular measurements, are recommended for checking and/or calibrating the Zero and Sensitivity values for a sensor. The calibration procedure simply records the sensor output at two known shaft positions within the linear range. Sensitivity is then calculated as the difference in the readings divided by the known angular difference. The Zero for a sensor is calculated using the expression Vlin-Sensitivity*(angle).

ALIGNMENT PROCEDURE
In equation [1], the measurable value of Zero offset can differ from the factory set value. It is user adjustable and can be changed by holding the shaft at a fixed position while rotating the sensor housing. Changing the value of Zero for the sensor, in this manner, allows angular control and/or measurement about an arbitrary reference position. For example, the positive Sensitivity of the sensor waveform shown in Figure 1 is 0.1667 volt/degree and the factory Zero is 0.012 volt. Holding the shaft and rotating the sensor housing until the sensor output reads 1.667 volts, sets the value of Zero in [1] to that voltage value and in effect moves the reference angle from 0.00 to 10.0 degrees. Angles calculated using [1] would indicate shaft positions ranging from -10 degrees to + 50 degrees with respect to the reference position.

DETERMINING SHAFT SPEED FOR A LINEAR HALLPOT® ANGLE SENSOR
Accurate real-time determinations of the shaft speed of a rotating angle sensor requires that the sensor output voltages are sampled at an adequate rate. Within the sampling time interval, (Vlin-Zero)/Sensitivity must be evaluated to determine an instantaneous shaft position, i.e., absolute shaft angular displacement at the particular sampling time. A change in the determined angular displacement, for successive samples, divided by the sampling time interval is a measure of the angular speed during that interval. If the sampling time interval is sufficiently small, then the angular speed calculated will be an accurate approximation of the instantaneous shaft speed.

DETERMINING SHAFT ACCELERATION FOR A LINEAR HALLPOT® ANGLE SENSOR
Determining shaft acceleration is similar to the problem of determining shaft speed, since it also requires adequate data sampling and an accurate estimate of shaft position. If the sampling time interval is sufficiently small, then calculation of the acceleration, i.e., the change in angular speed between two successive time intervals divided by the time interval, will be an accurate approximation of the instantaneous shaft acceleration.

(2) SINUSOIDAL HALLPOT® ANGLE SENSOR

CALIBRATION PROCEDURE
At constant temperature, the sensor output follows biased sine wave behavior:Vsin=Ebo+Vp*sin(angle) [2]where, Vsin is the output voltage response of the angle sensor at a particular shaft position , Ebo is a constant offset voltage with magnitude nominally equal to half the supply voltage (Vcc), VP is the maximum voltage change in Vsin due to shaft rotation (generally less than half the supply voltage), angle is the absolute angular displacement of the shaft in the rotational plane of the sensor system, and sin is the familiar transcendental mathematical function which describes precisely how the sensor output changes with the shaft angle.
Ebo and VP are generally known for calibrated sensors. If the offset and slope are unknown, they can be easily determined. Averaging the minimum and maximum sensor output voltages provides a reasonable estimate for Ebo. An estimate for VP is provided by dividing the difference between the respective minimum and maximum output voltages by 2. Overall, the best agreement between the observed sensor outputs and those calculated using [2] is achieved with an Ebo and VP determined from a least squares fit of Hallpot® Angle Sensor outputs to the basic defining equation [2]. The arcsine is a transcendental mathematical function which provides linear analogs of angular displacements over restricted ranges. Absolute shaft position is accurately calculated using the arcsine function, which is evaluated from sensor outputs using [3]:

ASIN ((Vsin-Ebo)/VP) [3]

ALIGNMENT PROCEDURE
The sensor housing can be rotated, with the shaft held at a fixed position in the rotational plane, to align a reference angle to that position.

DETERMINING SHAFT SPEED
Accurate real-time determinations of the shaft speed of a rotating Sinusoidal HallPot® Angle Sensor requires that output voltages are sampled at an adequate rate. Within the sampling time interval, the asin function must also be evaluated and used to calculate an instantaneous shaft position, i.e., absolute shaft angular displacement at the particular sampling time. A change in the determined angular displacement, for successive samples, divided by the sampling time interval is a measure of the angular speed during that interval. If the sampling time interval is sufficiently small, then the angular speed calculated will be an accurate approximation of the instantaneous shaft speed.

DETERMINING SHAFT ACCELERATION
Determining shaft acceleration is similar to the problem of determining shaft speed, since it also requires adequate data sampling and an accurate estimate of shaft position. If the sampling time interval is sufficiently small, then calculation of the acceleration, i.e., the change in angular speed between two successive time intervals divided by the time interval, will be an accurate approximation of the instantaneous shaft acceleration.

AN APPLICATION - IDRA® Ballistometer
IDRA (Integrated Dynamic Rebound Analyzer) is a turnkey, PC-based instrument manufactured and marketed by Third-Party Research & Development, which employs a dynamic technique for assessing the intrinsic viscoelastic properties of a material. See Figure 3, which is a block diagram of the IDRA system. For relatively soft materials, such as skin, the measurement technique involves a lightweight hammer, anchored at one end to a rotary transducer, which free-falls onto the test surface under gravitational force, recording and analysis of the resulting hammer oscillatory displacement-time data, and the determination of characteristic physical parameters. This instrument accepts either an RVDT or Hallpot® Angle Sensor, as the rotary transducer. Comparable, reliable performance is found for these types of sensors. Hallpot® sensors are recommended for client systems because they offer design simplicity and significant cost savings.

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Figure 3 - IDRA® Ballistometer System

Figure 4 shows the kind of mechanical diagnostic information extracted with IDRA® Ballistometer and a Hallpot® Angle Sensor. The parameters listed are determined for adjacent sections of successive curve peaks and valleys in a basic response curve. The IDRA HELP menu shows techniques for extracting additional, detailed information from this data.

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Figure 4 - Mechanical Diagnostic Information Provided By IDRA® System

Acknowledgment: Data shown in Figure 2 was provided by John Wereb of Elweco, Inc.
IDRA® is registered to John Potts and Third-Party Research & Development, Hallpot® Angle Sensor and.Sin-Cos Hallpot® Resolver are registered to Elweco, Inc.