6A Sensor Design
Interface’s 6A Multi-Axis sensors enable the measurement of forces and moments in the three spatial directions (x, y, z). This article presents various designs of force/moment sensors.
Structure and Function of Force/Torque Sensors
Introduction
As with one-dimensional force or torque sensors, deformation bodies made of high-strength spring steel or high-strength aluminum are used, which are equipped with strain gages as the measuring element.
Strain Gage Technology
Strain gage technology has proven effective for force and torque sensors in converting mechanical deformation into an electrical quantity.
Metal foil strain gages are most commonly used in these applications. These metal foil strain gauges are characterized by excellent linearity and very low hysteresis. The metal foil is matched to the thermal expansion coefficient of the deformed body: the thermal expansion of the body is compensated by a corresponding – negative – temperature coefficient of the resistance. This so-called self-compensation supports the actual compensation of thermal drift through the application of a Wheatstone bridge, either full or half bridge configuration.
By using strain gage full bridges and the known compensation circuits, individual components of the three forces and moments can be selectively isolated from one another. Additionally, the strain gage full bridge offers the highest output signal and the best compensation for temperature-induced drift compared to half- or quarter-bridges.
The design of the deformation body offers further possibilities for separating the load components, e.g. by (isotropic or anisotropic) spring joints and parallel guides.
The design of the deformation body determines the measuring range of the force/torque sensor.
Solid or Hollow Cylinders
Design No. 1
By applying known strain gage circuit techniques, six strain gage full bridges are realized, each assigned to one of the six load components. The design described in [1] could be extended by switching from “simple” full bridges with opposing grids to “double full bridges” in series or parallel connection with a cylinder cover every 90 degrees around the circumference.
Tripod (Vertical)
Design No. 2
While in design no. 1 each measuring channel corresponds exactly to one load component, patent [2] describes a “tripod” with 3 vertical columns. Each column is equipped with two different measuring grids: a shear grid +45/-45° as a half-bridge on the outside, and a longitudinal grid on the inside. The shear grids provide (different) signals for torsional moment, Mz, and radial forces Fx and Fy. The longitudinal grids provide (different) signals for Fz, Mx, and My.
4-Column (Vertical)
Design No. 3
The “4-column” design from [3], [4] is used for high-precision 1A force sensors, as well as for 2A force/torque sensors, for 3A force sensors, and for 6A force/torque sensors. By equipping the 4 columns with full bridges, each measurement channel can be assigned exactly one load component.
The measuring ranges can be adjusted by choosing the cross-section of the columns, the diameter, and the length of the columns.
4-Columns (Planar)
Design No. 4
The “4-column” design can also be implemented as a planar structure [3], [4]. As in design no. 3, the columns are equipped with full bridges. This design is particularly suitable for MEMS (Micro-Electro-Mechanical Systems). In this case, the deformation body is etched from silicon, for example, and strain gages are implemented either as semiconductor strain gages by doping or as metal foil strain gages by vapor deposition or sputtering.
MEMS (Micro-Electro-Mechanical Systems) 6A Sensors
MEMS can only be implemented for very small forces and moments on the order of 1 N, 1 Nm. For manufacturing reasons, typically only one of the four surfaces of the bending elements in a MEMS is equipped with strain gauges. This results in greater crosstalk compared to fully equipped bending elements.
Hexapod (Stewart Platform)
Design No. 5
Patent [5] from 1994 describes a Stewart platform equipped with six axial force sensors. Force sensors are used instead of actuators. A disadvantage for the sensors is the joints, which can lead to undesirable play in a force/torque sensor. The idea of
Variants of the Hexapod
The hexapod is used in various configurations as a deformation body for force/moment sensors. The joints can be replaced, for example, by solid-state joints. The influence of bending moments can also be compensated for by strain gage bridge circuits. For very large measuring ranges above 100 kN, the bending moments are compensated for by additional strain gages or measuring channels.
Measuring Cube
Design No. 6
The measuring cuboid of the patent specification [7] is a series connection of three orthogonally arranged double beams, each spanning a cube surface.
Opposite cube faces are mechanically connected in parallel and measure the force along the same coordinate axis. The evaluation of these force pairs is used to determine the moments.
Alternative Design to the Measuring Cuboid
The design of the “measuring cube” is roughly equivalent to a parallel connection of two series-connected 3A force sensors (3A35, 3A60a) at a defined distance. The distance between the 3A sensors can be varied to scale the measuring range for measuring torques.
Connecting two 3A force sensors in parallel relieves each individual 3A force sensor of bending moments. This increases accuracy.
One (far too rarely) used technique for wind tunnel scales consists of arranging two 3A force sensors outside the wind tunnel, which are connected to a rigid element that holds the model.
Comparison of Design Variants
A comparison of the design variants reveals fundamental design principles.
- Compensation circuits with strain gages,
- Parallel connection of spring elements (parallel kinematics),
- Series connection of spring elements (serial kinematics),
By varying and combining these principles, it is possible to design the optimal force/torque sensor for the respective application.
Design No. 1 primarily uses the proven DMS compensation circuits.
Designs No. 2 to No. 5 are parallel kinematics. All spring elements are connected in parallel.
Design No. 6 is a series kinematic system for measuring the three force components. Each double beam for a force component is supplemented by another double beam in parallel to measure the moments caused by a force couple at a defined distance.
All three design principles solve the common task of separating the components [Fx, Fy, Fz, Mx, My, Mz] of a load vector.
Evaluation of the Variants
Advantages of Parallel Connection
Designs with parallel-connected spring elements generally exhibit a higher pitch than designs for a comparable load range using series connections. This also translates to higher dynamics for the parallel connection. Furthermore, errors due to positional or angular deviations can accumulate in series connections. Parallel connections typically allow for more compact designs.
Disadvantages of Parallel Connection
The mathematical models for real parallel circuits are complex, especially when, for example, multiaxial stress states arise due to missing joints or flexible support and clamping conditions for the spring elements.
Advantages of Series Connection
Each individual axis can be optimized independently of subsequent axes. Likewise, the mathematical model is easy to create. The large measuring range offers an advantage with force-compensated sensors that use an actuator to compensate for the deflection.
Disadvantages of Series Connection
Due to the series connection (of measuring springs), the spring travels add up, and the stiffness of a force/torque sensor in series is lower compared to one in parallel. The first of the six series-connected spring elements must also absorb the greatest lateral forces and moments, resulting in the greatest crosstalk at this spring element. The spring stiffness of the sensor differs in each measuring axis.
Variants with Three Spring Elements
Variants with three spring elements are used in two different designs:
- as a spatially structured tripod
- as a planar tripod.
Both variants involve a parallel connection of spring elements. Each spring element in both variants requires at least two Wheatstone bridge circuits, designed to respond sensitively to two mutually perpendicular load cases and to compensate particularly well for the other load case.
Variants with Four Spring Elements
Similar to the variants with three spring bodies, each spring body must be equipped with two Wheatstone bridge circuits.
[1] Dae-Im Kang, Hong-Ho Shin, Jong-Ho Kim and Yon-Kyu Park: “Design and Analysis of a Column Type Multi-Component Force/Moment Sensor”. Proceedings of the 17th International Conference on Force, Mass, Torque and Pressure Measurements, IMEKO TC3, 17-21 September 2001, Istanbul, Turkey
[2] Paul C. Watson, Samuel H. Drake: “Method and Apparatus for Six Degrees of Freedom Force Sensing”. US Patent No. US 4094192, 1978.
[3] D. Grinevsky, A. Formalsky, A.Schneider: “Force Control of Robotics Systems”, CRC Press LLC, 1997.
[4] Weiler. “Handbook of Force Measurement Technology”, …
[5] Karlsruhe Nuclear Research Centre GmbH: “Force-torque sensor”. Patent DE 4101732 C2, 1994.
[6] Office national d’études et de recherches aérospatiales (ONERA): “Poigneta detection de six composantes d’effort”. FR 82 11181, 1983.
[7] Technical University of Ilmenau: “Device for the simultaneous measurement of force and moment components”, Patent DE10 2011 106 894 B3, 2012.
