Mitsubishi Heavy Industries Technical Review Vol. 57 No. 3 (September 2020)
1Vibration Suppression Technology of Vertical Precision
Milling Machine MVR Using MBD Analysis
HIROYUKI KANAZAWA*1

SHUNJI MISHINA*2

KAWAUCHI AKIHISA*3

TOMOHIRO AKAKI*1

KATO YOSHIKI*4

For products comprised of multiple parts such as machine tools, commercial aircraft, newtransportation systems and wind turbines, Mitsubishi Heavy Industries, Ltd. (MHI) is striving toimprove performance and robustness through the prediction of performance by applying Multibody
Dynamics (MBD) analysis to evaluate the vibration characteristics of structural components andthe load transfers in machine components. We have developed a high-precision simulation modelby combining MBD model and control system model for vertical precision milling machine, theperformance of which is affected directly by mechanical vibration. In addition, a vibration
suppression method utilizing the MBD model has been developed. This report introduces asummary thereof.

|1. Introduction
MHI is advancing the use of multibody dynamics (MBD) analysis that evaluates mechanicalcharacteristics such as the vibration and contact/friction of multibody systems in order to enhancethe development efficiency and quality of various products. MBD is, on the basis that a partcomposed of multiple machine elements and a product (system) composed of multiple parts aredefined as “multibody,” a numerical analysis technique to analyze the dynamics of aninter-connecting multibody system structure from the part to system level. When initiallyintroduced, MBD analysis targeted the behavior evaluation and interference problems inkinematics. However, thanks to recent technological advancements, MBD analysis has been able toevaluate, in addition to the elastic characteristics of structural parts and the characteristics ofmachine components, the performance and damage risk including variations using a virtual test in
the digital space, through linking with the same control model as the actual equipment.
We have developed a new technique to derive a vibration compensator using an MBD modelof a large vertical precision milling machine that was created so that mechanical vibration duringmachining can be reproduced. By using the new vibration compensator, improvement of thesurface quality of mold machining, in which minute mechanical vibration is generated during theacceleration/deceleration of the feed axis and deteriorates the machining quality, was obtained.
This report presents the new technique and the vibration compensator derived thereby.

|2. Creation of MBD model that can reproduce vibration duringmachining
2.1

Issues to be solved

Conventionally, the preliminary evaluation of the target specifications in the design phase ofa large vertical precision milling machine was limited to the evaluation of static and dynamic
rigidity against the machining reaction force and eigenvalue analysis, and the final machining
performance was evaluated by the machining test. However, since actual operation includes variousmachining paths and acceleration/deceleration patterns, unexpected vibrations may occur and themachining accuracy may not satisfy the evaluation standard depending on the conditions, so it took*1

Research Manager, Machinery Research Department, Research & Innovation Center, Mitsubishi Heavy Industries,Ltd.

*2

Engineering Manager, Machine Control Designing Section, Engineering Headquarters, Mitsubishi Heavy Industries Machine*3

Vibration Research Department, Research & Innovation Center, Research & Innovation Center, Mitsubishi Heavy*4

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

Tool Co., Ltd.
Industries,Ltd.

Mitsubishi Heavy Industries Technical Review Vol. 57 No. 3 (September 2020)
2time to make adjustments each time. In addition, reducing the feed rate and the acceleration inorder to satisfy the machining accuracy sometimes increased the machining time.
To solve these issues, a low-dimensional control system simulation model that does notconsider the vibration characteristics of structural parts and vibration analysis in the linear
frequency domain that does not consider the acceleration/deceleration pattern of machining pathcannot accurately grasp the factors causing transient vibration, so the examination of measures inconsideration of the constant speed pattern was insufficient.

2.2

Accuracy improvement by comparing MBD analysis results and actual
equipment behavior

In order to solve the aforementioned issues, we created an MBD model of the actual
equipment structure shown in Figure 1 and combined it with the control model in Figure 2 toenable vibration evaluation of the actual equipment operation pattern. This model contains
information on the vibration characteristics obtained from the structural analysis model in Figure 3,
as well as the shape, density and Young's modulus of the structural parts that make up the verticalprecision milling machine, in addition to the rigidity of mechanical components such as ball screws
that connect the parts, etc.

Figure 1 Structure of large vertical precision
milling machine MVR

Figure 2

Figure 3

Structural analysis model

Control model

It was confirmed that the vibration mode, which affects the quality of the machined surface,
could be indicated as illustrated in Figure 4, and that a transient response with a vibration
amplitude in the order of 10 µm to the actual machine operation pattern could be indicated as
depicted in Figure 5. In this way, MBD analysis can indicate the transient response that occurs
during actual equipment operation in addition to the vibration characteristics obtained byconventional FEM analysis. By using simulation results of this model during the design anddevelopment of actual equipment, a structure and operation pattern that realizes more accurate
machining can be created.

Mitsubishi Heavy Industries Technical Review Vol. 57 No. 3 (September 2020)
3Figure 4 Example of vibration mode prediction
results

Figure 5 Vibration comparison between
actual equipment and MBD|3. Derivation of vibration compensator using MBD model
3.1

Issues with conventional vibration compensators

In an actual machining path of a large vertical precision milling machine, transient vibrationthat causes the deterioration of the machining quality occurs when the acceleration becomes
discontinuous, such as during a change from horizontal movement to vertical movement. To
suppress this transient vibration, a compensator is used. Conventional compensator design uses aphysical model based on the mass and moment of inertia of the main components and the rigidityof parts as shown in equation (1) to indicate the vibration characteristics of the target structure.
However, a design using a physical model cannot take non-linearity into account due to the posture,
friction, backlash, etc. As a result, an error occurs during verification with the actual equipment, soa vibration suppression effect cannot be fully incorporated in the design phase.

=×××××××

Equation (1)θ : Machine tip position
θL : Linear scale position
JL : Load inertiaJC : Column inertia
DL : Load viscosity
KC : Column rigidity
CC : Column damping

3.2

Proposal of derivation technique of new vibration compensator

The new compensator is derived from the transfer function obtained from the frequency
characteristics of the target mechanism structure for which the vibration is to be suppressed, using
the MBD model that has been verified to be able to indicate the actual equipment behavior.
Specifically, the characteristic points are extracted by fitting the frequency characteristics obtainedby MBD simulation result given in Figure 6, and applied to the quadratic transfer function inequation (2) is directly derived using them. Then the new compensator is derived using the results.
２ｍ=ｓ ＋

２ｓ ＋＋Equation (2)＋

ω1 : Frequency at gain characteristic point ①
ζ1 : Attenuation factor at gain characteristic point ①
ω2 : Frequency at gain characteristic point ②
ζ2 : Attenuation factor at gain characteristic point ②

Mitsubishi Heavy Industries Technical Review Vol. 57 No. 3 (September 2020)
4Figure 6

3.3

Estimation and derivation of quadratic transfer function

Effect verification results of developed technique

We conducted effect verification of the aforementioned vibration compensator derived basedon the MBD model in actual die milling. As shown in Figure 7 and Figure 8, it was verified thatthe new vibration compensator had a vibration suppressing effect and that the quality of themachined surface was improved compared with that obtained with a conventional compensator.

Figure 7 Comparison of vibration accelerations in actual machining

Figure 8 Frequency analysis results of column mechanical vibration acceleration in actualmachining

Mitsubishi Heavy Industries Technical Review Vol. 57 No. 3 (September 2020)5|4. Conclusion
This report demonstrated that combining MBD analysis model and the actual equipment
control model of a large vertical precision milling machine realizes simulation of the overallsystem, and that it is possible to derive a vibration compensator that will improve the performanceand value of the actual equipment therefrom.
By enabling model-based examinations as shown in this report, improvement studies ofmachine structure and the optimization of the overall system including control can be carried out
quickly and accurately.
We will continue to utilize this technique to shorten the product development period andimprove product performance and robustness in the design phase.

References(1)(2)

K, Kura et.al., Latest Technologies of MVR-Eχ 5-face Machining Center for Realizing High-precision
Cutting, Mitsubishi Heavy Industries Technical Review Vol. 52 No. 1 (2015)
H, Kanazawa et.al., High-accuracy Motion Prediction Using Large-scale Multibody Dynamics (MBD)
Mitsubishi Heavy Industries Technical Review Vol. 52 No. 4 (2015)