Mitsubishi Heavy Industries Technical Review Vol. 57 No. 3 (September 2020)
1Visualization of Resistive Torque Distribution andEvaluation of Rotational Axis Characteristics forImprovement of Machining Accuracy
KYOTA TOKUYAMA*1 TOMOHIRO IKAWA*1
ICHIRO AWAYA*1TOSHIYUKI SHIMOWAKI*2

NAOKI IIYAMA*2YUTA KOJIMA*3Devices that require high assembly accuracy, such as machine tools, often require
performance evaluation through actual machining after assembly is complete in order to evaluate
the soundness of the rotational axis.
By accurately estimating the resistive torque at the time when the built-in motor is rotated ata low speed, the magnitude of the rotational axis resistive torque, which depends on the angle andangular velocity, can be evaluated. Furthermore, by displaying the resistive torque distribution inthree dimensions, the uniformity of the rotational axis resistive torque can be evaluated at aglance. This inspection test can be conducted immediately after mounting the motor without actualmachining.
This report presents a technology that makes it possible to evaluate the state of a rotational
axis by visualizing the resistive torque distribution.

|1. Introduction
In order to understand the state of the rotational axis of devices that require high assembly
accuracy, such as machine tools, performance evaluation through actual machining is required, so atest after completion of assembly is required. In addition, although there are several methods offactor analysis and numerical quantification for performance evaluation, they require a separate
measuring instrument to be attached, so such methods may not lead to machining accuracy.
With such a background, Mitsubishi Heavy Industries Machine Tool Co., Ltd. developed atechnology to quantify and visualize the resistive torque around the rotational axis based on thedriving data of the built-in motor in order to understand the states of the rotational axis and use
them to improve equipment performance.
Chapter 2 of this report shows the configuration of the target machines, chapter 3 gives anexplanation of the developed algorithm and the verification results using an element test device andchapter 4 presents the results of applying this technology to a gear grinding machine.

|2. Target machine configuration and state quantity to be evaluatedFigure 1 shows the element test device that we made to simulate a target machine. The target
machine is, like the spindle of a gear grinding machine, composed of a motor that is the drive
source of the rotational axis, bearings, a seal and a load that acts as the inertia of the rotational axis.
Figure 2 schematically represents the machine shown in Figure 1. The dynamic
characteristics in the low speed region are expressed by the equation of motion (1). In this equation,is motor inertia,
is load inertia,
is motor angle,
is motor torque,is motor
internal resistive torque (cogging torque, etc.) andis load resistive torque.
=+−−(1)is cogging torque and Coulomb friction, but the Coulomb friction is small, and thecogging torque is dominant. Therefore, first, two resistive torques are calculated from the right sideof the following equation.
+=−+(2)*1

CIS Department, ICT Solution Headquarters, Mitsubishi Heavy Industries,Ltd.

*2

Engineering Headquarters, Mitsubishi Heavy Industries Machine Tool Co., Ltd.

*3

Value Chain Headquarters, Mitsubishi Heavy Industries Machine Tool Co., Ltd.

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By estimating and removing the cogging torque component
from the resistive torquewaveform,is obtained.
The machine characteristics are understood by estimating the load resistive torquebased on the equation (1). In particular, by estimating the resistive torque using the operating dataat the time when the axis is rotated at a low speed, it is possible to accurately understand thecharacteristics of the machine.

Figure 1 Construction of targetmachine (element test device)

Figure 2 Schematic diagram of machine element|3. Visualization and analysis technology of distribution of rotational
axis resistive torqueFigure 3 illustrates the visualization flow of resistive torque distribution for understanding
the state of the rotational axis. The resistive torque distribution is obtained by performing processes[1] to [4] based on the test data acquired at multiple rotation speeds. Sections 3.1 to 3.4 give thedetails of each process.

Figure 3

3.1

Visualization flow of resistive torque distribution

Estimation of resistive torque

Based on the equation of motion (1), the load resistive torquegenerated at a resistive
element of the machine is estimated as the estimated load resistive torque.
For inertias
andin the equation (1), use the design information, and for the motor
torque, the command value. By properly estimating the remaining motor internal resistive, the estimated load resistive torquetorqueand motor angular acceleration
can beaccurately obtained.
First, the motor internal resistive torqueis removed by one of the following methods.
(1) Substitute the motor torque at the time when the load element is removed, and the motor isdriven alone.
(2) Extract the measurement noise and cogging torque, which are obtained in advance, using FFT(Fast Fourier Transform) analysis and remove them from the motor torque.

Mitsubishi Heavy Industries Technical Review Vol. 57 No. 3 (September 2020)
3(3) Create the 3D table described later in section 3.3 for the motor alone and obtain the differencein the 3D table between the motor alone and the combination of the motor and the resistive
element as shown in Section 3.4.
The motor angular acceleration
is derived by numerically differentiating the measured
motor angle
without phase lag while removing noise using offline processing. The casepresented in this report uses the Savizky-golay filter(1) based on the function fitting by the methodof least squares method.
The estimated load resistive torque
was estimated by the equation (1) using the state
quantities derived as described above.

3.2

Calculation of resistive torque feature quantity

Using the estimated load resistive torqueestimated in the previous section and themeasured motor angle, the resistive torque featureand angular velocity command value
quantities for the angle and angular velocity are calculated by the following process.
(1) Estimate the estimated load resistive torque τ for each angular velocity operation preparedin advance.
(2) For each angular velocity operation, calculate the feature quantity from the estimated load
resistive torquein the angular range with equal intervals. Calculate feature quantities
using the maximum value, the p-p value, the variance, the average value, etc., according to
the purpose. Figure 4 is the calculation method using the maximum value as an example.

Figure 4

3.3

Calculation of resistive torque feature quantity

Creation of 3D table

Based on the feature quantities calculated in the previous section, the resistive torquedistribution is shown as a 3D table in order to express the machine characteristics.
In this report, as an example of using the maximum value for the feature quantity, a table ofthe estimated load resistive torque maximum values with respective to the motor absolute angle andthe angular command is created. The table is expressed in a cylindrical coordinate system where
the logarithmic value of the angular velocity command value
is plotted in the radial direction,
the equally divided motor absolute angle is plotted in the angular direction and the maximum valueof the estimated load resistive torque calculated in the previous section is plotted in the height
direction. Figure 5 is an example of the 3D table.

Figure 5

3.4

Creation of 3D table

Figure 6 Example of resistive torquedistribution

Obtainment of difference between estimation and reference state

By plotting the 3D table created in the previous section in three dimensions, the resistive
torque distribution of the machine is obtained. Figure 6 gives an example of resistive torqueMitsubishi Heavy Industries Technical Review Vol. 57 No. 3 (September 2020)
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distribution at the time when the maximum value is used for the feature quantity. This distribution
enables collective evaluation of the frictional characteristics depending on the angular velocity foreach angle.
Obtaining the difference from the reference state using the created resistive torquedistribution allows for understanding the state of the machine. By using the resistive torquedistribution of a normal machine or the resistive torque distribution immediately after delivery as
the reference state, it is possible to evaluate the deviation from the normal state and the degree ofdevice deterioration.
To make it easier to obtain the difference from the reference state, the variation during one
rotation can be evaluated by obtaining the difference from the average value for each set rotation
speed. Figure 7 is the distribution obtained by obtaining the difference between the resistive torquedistribution acquired on a certain day and the resistive torque distribution acquired on another day,and then obtaining the difference from the average value at each angular velocity. This indicatesthe day difference of the device.

Figure 7 Variation during one rotation

3.5

Verification of effectiveness using element test device

In order to verify the effectiveness of this method, a resistive torque distribution at the time
when an abnormality was intentionally generated in the element test device shown in Figure 1 iscreated. Abnormality examples generated were (1) foreign matter in the bearing, (2) gradient on theseal sliding surface, (3) scratch on the seal sliding surface and (4) shaft eccentricity. Figure 8
presents the resistive torque distribution of these examples.
Each abnormality generated has a distinct distribution shape, so it is possible to narrow down
the cause of the abnormality to some extent.

Figure 8

Resistive torque distribution at time of various abnormalities|4. Application to gear grinding machine
The developed technology was applied to the spindle of a gear grinding machine to confirm
the effect of visualization of the resistive torque distribution.
The spindle of the gear grinding machine uses a built-in motor. In order to eliminate thecharacteristics peculiar to the motor, it is necessary to remove the cogging torque and switching
noise using FFT analysis as described in 3.1 (2). Figure 9 depicts the flow at the time when thistechnology is applied to a gear grinding machine and Figure 10 shows the removal flow of motor
internal resistive torque using FFT analysis.

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Figure 9Visualization flow of resistive torque distribution of gear grinding machine

Figure 10Removal flow of motor internal resistive torque using FFT analysis

Figure 11 compares the resistive torque distributions before and after the removal of motor
internal resistive torque based on the test data of the gear grinding machine.
As shown on the right of Figure 11, the torque related to cogging was not removed
completely, but can be suppressed to a sufficiently small level, and there was no particularly largebias. By removing the motor internal resistive torque, it is possible to extract the load resistive
torque component that occurs in resistive elements such as viscous resistance.

Figure 11 Comparison of resistive torque distributions before and after removal of motor
internal resistive torque using FFT analysis

Based on the extracted load resistive torque, the feature quantity was calculated, and theresistive torque distribution was created. Figure 12 gives an example of listing resistive torquedistribution in which the average value, the p-p value and the variance are used as the feature
quantities, and the angle division is classified into three levels from dense to rough.

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Figure 12

Resistive torque distributions of gear grinding machine

As shown in Figure 12, the resistive torque distribution is expressed from various points ofview depending on the feature quantity and the number of angle divisions used. For example, in theresistive torque distribution for which the p-p value is used as the feature quantity and the angle
division is rough, there are areas on a medium-speed range concentric circle where a variation
increases in a concentrated manner in certain angular ranges. By clarifying the relationship between
this variation and the machine state, the soundness of the machine can be evaluated. It is possible toevaluate the machine performance by selecting the feature quantity and angle division width
according to the purpose and evaluating the variation.

|5. Conclusion
This report presented a technology to quantify and visualize the resistive torquecharacteristics of the rotational axis of machine tools for which high precision is required and toevaluate the effect of the torque characteristics on machining accuracy. We verified theeffectiveness of this technology with an element test device, applied the resistive torquedistribution technology to a gear grinding machine and confirmed that the machine characteristics
can be expressed from various points of view.
In the future, we will analyze the relationship between this resistive torque distribution andmachining accuracy based on the accumulated test data and enhance machining accuracy byimproving assembly techniques. Furthermore, we will expand the use of this technology to the fieldof remote preventive maintenance technology.

References(1)

Savitzky, Abraham et al., Smoothing and differentiation of data by simplified least squares procedures,
Analytical chemistry 36.8 (1964): 1627-1639.