interface 6A Multi-Axis Sensors Instruction Manual

interface 6A Multi-Axis Sensors

Specifications

Function

Function of the 6A Multi-Axis Sensors
The set of 6A Multi-Axis Sensors comprises six independent force sensors equipped with strain gauges. Using the six sensor signals, a calculation rule is applied to calculate the forces within three spatial axes and the three moments around them. The measurement range of the Multi-Axis sensor is determined:

• by the measurement ranges of the six independent force sensors, and
• by the geometrical arrangement of the six force sensors or via the diameter of the sensor.

The individual signals from the six force sensors cannot be directly associated with a specific force or moment by multiplying with a scaling factor. The calculation rule can be precisely described in mathematical terms by the cross product from the calibration matrix with the vector of the six sensor signals. This functional approach has the following advantages:

• Particularly high rigidity,
• Particularly effective separation of the six components (“low cross-talk”).

Calibration matrix
The calibration matrix A describes the connection between the indicated output signals U of the measurement amplifier on channels 1 to 6 (u1, u2, u3, u4, u5, u6) and components 1 to 6 (Fx, Fy, Fz, Mx, My, Mz) of the load vector L.

• The calibration matrix Aij includes 36 elements, arranged in 6 rows (i=1..6) and 6 columns (j=1..6).
• The unit of the matrix elements is N/(mV/V) in rows 1 to 3 of the matrix.
• The unit of the matrix elements is Nm/(mV/V) in rows 4 to 6 of the matrix.
• The calibration matrix depends on the properties of the sensor and that of the measurement amplifier.

It applies for the BX8 measurement amplifier and for all amplifiers, which indicate bridge output signals in mV/V. The matrix elements may be rescaled in other units by a common factor via multiplication (using a “scalar product”).

The calibration matrix calculates the moments around the origin of the underlying coordinate system. The origin of the coordinate system is located at the point where the z-axis intersects with the facing surface of the sensor.1) The origin and orientations of the axes are shown by an engraving on the facing surface of the sensor.

• The position of the origin may vary with 6A sensor types. The origin is documented in the calibration sheet. E.G the origin of 6A68 is in the center of the sensor.

Example of a calibration matrix (6A, 6ADF)

The force in the x-direction is calculated by multiplying and totalling up the matrix elements of the first row a1j with the rows of the vector of the output signals uj.

For example: on all 6 measurement channels is u1 = u2 = u3 = u4 = u5 =u6 = 1.00mV/V displayed. Then there is a force Fx of -13.7 N. The force in the z direction is calculated accordingly by multiplying and summing the third row of the matrix a3j with the vector of the indicated voltages uj:

Matrix Plus for 6A / 6ADF sensors
When using the “Matrix Plus” calibration procedure, two cross products are calculated: matrix A x U + matrix B x U *

Example of a calibration matrix “B”

The force in the x-direction is calculated by multiplying and summing the matrix elements A of the first row a1j with the rows j of the vector of the output signals uj plus matrix elements B of the first row a1j with the rows j of the vector of the mixed- quadratic output signals:

Example of Fx

Attention: The composition of the mixed quadratic terms may change depending on the sensor.

Offset of the origin
Forces which are not applied in the origin of the coordinate system are shown by an indicator in the form of Mx, My and Mz moments based on the lever arm.Generally speaking, the forces are applied at a distance z from the facing surface of the sensor. The location of the force transmission may also be shifted in x- and z- directions as required. If the forces are applied at distance x, y or z from the origin of the coordinate system, and the moments around the offset force transmission location need to be shown, the following corrections are required:

Note: The sensor is also exposed to the moments Mx, My and Mz, with moments Mx1, My1 and Mz1 displayed. The permissible moments Mx, My and Mz must not be exceeded.

Scaling of the calibration matrix

• By referring the matrix elements to the unit mV/V, the calibration matrix can be applied to all available amplifiers.
• The calibration matrix with the N/V and Nm/V matrix elements applies to the BSC8 measuring amplifier with an input sensitivity of 2 mV / V and an output signal of 5V with a 2 mV/V input signal.
• Multiplication of all matrix elements by a factor of 2/5 scales the matrix from N/(mV/V) and Nm/(mV/V) for an output of 5V at an input sensitivity of 2 mV/V (BSC8).
• By multiplying all matrix elements by a factor of 3.5/10, the Matrix is scaled from  N/(mV/V) and Nm/(mV/V) for an output signal of 10V at an input sensitivity of 3.5 mV/V (BX8)
• The unit of the factor is (mV/V)/V
• The unit of the elements of the load vector (u1, u2, u3, u4, u5, u6) are voltages in V

Example of Fx
Analog output with BX8, input sensitivity 3.5 mV / V, output signal 10V:

Matrix 6×12 for 6A sensors
With the sensors 6A150, 6A175, 6A225, 6A300 it is possible to use a 6×12 matrix instead of a 6×6 matrix for error compensation. The 6×12 matrix offers the highest accuracy and the lowest crosstalk, and is recommended for sensors from 50kN force.
In this case, the sensors have a total of 12 measuring channels and two connectors. Each connector contains an electrically independent force-torque sensor with 6 sensor signals. Each of these connectors is connected to its own measuring amplifier BX8.
Instead of using a 6×12 matrix, the sensor can also be used exclusively with connector A, or exclusively with connector B, or with both connectors for redundant measurement. In this case, a 6×6 matrix is supplied for connector A and for connector B. The 6×6 matrix is supplied as a standard.

The synchronization of the measured data can be e.g. with the help of a synchronization cable. For amplifiers with EtherCat interface a synchronization via the BUS lines is possible.The forces Fx, Fy, Fz and moments Mx, My, Mz are calculated in the software BlueDAQ. There the 12 input channels u1…u12 are multiplied by the 6×12 matrix A to get 6 output channels of the load vector L.

• The channels of connector “A” are assigned to channels 1…6 in the BlueDAQ software.. The channels of connector “B” are assigned to channels 7…12 in the BlueDAQ software.
• After loading and activating the matrix 6×12 in the BlueDAQ software, the forces and moments are displayed on channels 1 to 6.
• Channels 7…12 contain the raw data of connector B and are not relevant for further evaluation. These channels (with the designation “dummy7”) to “dummy12”) can be hidden from the display and the recording via the function “Channel”–> “Hide”.

When using the 6×12 matrix, the forces and moments are calculated exclusively by software, since it is composed of data from two separate measuring amplifiers.
Tip: When using the BlueDAQ software, the configuration and linking to the 6×12 matrix can be done by “Save Session”. and “Open Session” is pressed. so that the sensor and channel configuration only has to be carried out once.

Stiffness Matrix
The stiffness matrix is defined by:

Example of a stiffness matrix 6A130 5kN/500Nm

• When loaded with 5kN in x-direction, a shift of 5 / 93.8 mm = 0.053 mm in the x direction, and a twist of 5 kN / 3750 kN = 0.00133 rad results about the y-axis.
• When loaded with 15kN in z-direction, a shift of 15 / 387.9 mm = 0.039 mm in the z direction (and no twist).
• With Mx =500 Nm a twisting of 0,5kNm / 505,2kNm = 0.00099 rad results about the x-axis, and a shift from 0,5kNm / -3750 kN = -0,000133m = -0,133mm in the y-axis.
• When loaded with Mz 500Nm a twisting results of 0,5kNm / 343.4 kNm = 0.00146 rad about the z-axis (and no shift).

Calibration Matrix for 5AR Sensors
The sensors of the type 5AR allow the measurement of the force Fz and the moments Mx and My. The sensors 5AR may be used for displaying 3 orthogonal forces Fx, Fy, and Fz, when the measured torques are divided by the lever arm z (distance of force application Fx, Fy of the origin of the coordinate system).

The force in the z direction is calculated by multiplying and summing the matrix elements of the first row A1J with the lines of the vector of the output signals uj

• Fz = 100 N/mV/V u1 + 100 N/mV/V u2 + 100 N/mV/V u3 + 100 N/mV/V u4
• Example: on all 6 measurement channels is u1 = u2 = u3 = u4 = 1.00 mV/V displayed. Then a force Fz results of 400 N.
• The calibration matrix A of 5AR sensor has the dimensions 4 x. 4
• The vector u of the output signals of the measuring amplifier has the dimensions 4 x. 1 The result vector (Fz, Mx, My, H has the dimension of 4 x. 1
• At the outputs of ch1, ch2 and ch3 after applying the calibration matrix, the force Fz and the moments Mx and My are displayed. On the Channel 4 output H is constantly displayed 0V by the fourth line.

Commissioning of the sensor
The BlueDAQ software is used to show the measured forces and moments. The BlueDAQ software and related manuals can be downloaded from the website.

Commissioning of the 6×12 sensor

• When commissioning the 6×12 sensor, channels 1 to 6 of the measuring amplifier at connector “A” must be assigned to components 1 to 6.
• Channels 7…12 of the measuring amplifier at connector “B” are assigned to components 7 to 12.
• When using the synchronization cable, the 25-pin SUB-D female connectors (male) on the back of the amplifier are connected to the synchronization cable.
• The synchronization cable connects the ports no. 16 of the measuring amplifiers A and B with each other.
• For amplifier A port 16 is configured as output for the function as master, for amplifier B port 16 is configured as input for the function as slave.
• The settings can be found under “Device” → Advanced Setting” →Dig-IO.

Hint: The configuration of the data frequency must be done at the “Master” as well as at the “Slave”. The measuring frequency of the master should never be higher than the measuring frequency of the slave.

Screenshots
Adding a force / moment sensor

Configuration as Master / Slave

Troubleshooting

• Unexpected moment values when forces are not applied at the coordinate origin: the manual states that forces applied at distances (x, y, z) require corrected moments: Mx1 = Mx + y·Fz − z·Fy; My1 = My + z·Fx − x·Fz; Mz1 = Mz + x·Fy − y·Fx. Verify whether the displayed moments correspond to the offset force application location.
• Forces/moments exceed allowable limits: the sensor is exposed to moments Mx, My, Mz while corrected moments Mx1, My1, Mz1 may be displayed. The manual notes permissible moments Mx, My, Mz must not be exceeded—reduce the load accordingly.
• Calibration scaling mismatch between amplifier settings: calibration matrix scaling depends on output signal and input sensitivity. The manual provides scaling factors (e.g., multiply all matrix elements by 2/5 for BSC8 scaling; by 3.5/10 for BX8 scaling to 10V output at 3.5 mV/V input). If results seem off, confirm the amplifier input sensitivity/output signal and apply the matching scaling factor.
• 6×12 multi-amplifier data not aligning: during 6×12 commissioning, ensure connector A channels 1–6 map to components 1–6 and connector B channels 7–12 map to components 7–12. For synchronization, ensure port 16 is configured correctly (A=master/output, B=slave/input) and that the master measuring frequency is never higher than the slave measuring frequency.
• Using “Matrix Plus” mixed quadratic terms: mixed quadratic composition may change depending on sensor type. If “Matrix Plus” results are unexpected, ensure you are using the sensor-specific Matrix Plus configuration/files.