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Please read 'Why We Should Use Dynamics Analysis? (Part 1)' in advance before reading this part.

3. Reasons to Use Dynamic Analysis

If defects are found in products that are already in the market, we have to spend a significant amount of money. Machine defects include yield, cracking, vibration, and noise. To prevent such problems, it would be ideal to be able to review everything before launching the product, but in reality, it is difficult to do so. Therefore, when a problem occurs, the cause is often mass or inertia when analyzing the problem.

Even if the analysis is performed before or after the problem occurs using simulation, the problem caused by mass or inertia may not be found if only the static analysis is applied. Various problems caused without considering mass and movement can be classified into the following three categories.

① “The prototype was broken during the test!”

② “Strange vibration occurs!”, “It makes strange noise!”

③ “Crack has occurred on the product in use!”

3.1 “The prototype was broken during the test!”

In this case, the stress generated on the structure exceeds the yield stress and causes permanent deformation or great damage. The cause of the problem is that a dynamic load was not considered.

STEADY STATE

The image above shows the change in reaction force until the moving structure stops. The structure stopped at T1 and there has been no change since that point. The reaction force in the static state is F1. However, as shown in the figure, a reaction force F2, which is greater than F1, occurred in the dynamic state. In some cases, the reaction force in the moving state is greater than in the static state. In this case, judging only from the results of the static analysis may lead to misjudging the wrong design as safe one.

The reason for the larger reaction force in the dynamic state (moving state) than in the static state (equilibrium state) is the mass (inertia). Of course, when using the static analysis, you can properly predict and use the reaction force caused by the mass, but it is quite difficult to predict it properly as the object vibrates while moving. However, in the dynamic analysis, the reaction force change due to the movement of the mass is automatically considered in the calculation, so users do not have to worry about the problem.

Let us take the following example. Figure 4 shows the result of the dynamic analysis of a stacker used for automation of logistics. We can notice that the reaction force in the dynamic state where the structure is moving is greater than in the static state.

3.2 “Strange vibration occurs!”, “It makes strange noise!”

Vibration is movement. However, since the static analysis is based on the premise that it does not move, it cannot be confirmed. In other words, you must use the dynamic analysis to see vibrations.

Among the dynamic analysis, this chapter explains the transient analysis. While other dynamic analysis methods solve problems by using frequency as a variable, the transient analysis does so by using time as a variable. The method of analyzing the problem with a time variable can analyze the vibration in more detail than the method using frequency. This is because frequency analysis uses only some frequencies, whereas transient analysis uses time that includes all frequencies.

When a person attempts to find the cause of strange vibrations and sounds using frequency analysis, it may be difficult to find the cause of the problem if the frequency range to be analyzed is not properly selected. This is because the natural frequency of the machine varies continuously depending on the location, speed, and contact of moving parts. However, there are no such problems in the transient analysis because the transient analysis automatically reflects it in the calculation even if the natural frequency changes as the machine moves.

In many cases, additional transient analysis is adopted as a way to prevent the recurrence of problems only after they have occurred in the product, even though vibration and noise problems have been verified by the existing modal analysis, which is the method of using frequencies. Let us check it out with the following example.

The prototype produced by company A, which produces factory automation products, made a very unpleasant noise. To solve this problem, company A measured noise and found the frequency in question. Then, the frequency was compared with the result of the modal analysis to identify the vibration mode in question and to confirm where the problem had occurred. Based on this, the problem was solved by changing the design to avoid resonance.

So far, it is a common approach for many companies. Company A did not only concentrate on solving urgent problems, but also deliberated how to prevent the recurrence of the same problems in the future.

This simulation was mentioned as a method to prevent recurrence, but as seen earlier, company A thought it was sufficient because the static analysis and the modal analysis were already in the business process. The prototypes with the problem had also passed the modal analysis. Nevertheless, the problem has arose.

Meanwhile, company A paid attention to the transient analysis that had not been adopted in-house yet. However, until now, only the static analysis and modal analysis were included in the business process, so there was no person who could perform the transient analysis. The fact that there were no people with experience with the transient analysis was also the reason why they showed interest in the transient analysis late. Since it was not possible to evaluate it in-house, company A sought an outside expert specializing in the transient analysis, which we would call company B. The first request made to company B was to recreate the problem that had already occurred. Company A first wanted to check whether the problem could be found in advance through transient analysis. The transient analysis model created by company B reproduced the problem. In this process, company A acquired the skills needed to improve the simulation accuracy of its products from company B.

Subsequently, company A added a transient analysis to the simulation process and was able to reduce vibration and noise problems. This described the process of introducing the transient analysis with the example of company A. However, why could the problem not be found by the modal analysis, but found by the transient analysis?

The reason for not finding a problem in the modal analysis is that there are situations that have not been considered. As the machine system moves, the position and posture of the parts change, thus the system's natural frequency changes. If we predicted all possible situations and analyzed the modes in advance, we could have identified the problem in advance, but it is impossible to do so in practice. There are bound to be mistakes. Therefore, if the problem situation is not included in the predicted scenario, the problem may not be identified. However, the transient analysis using time not only creates a situation in which the natural frequency of the system changes as all parts intuitively move over time, but also automatically reflects changes in characteristics in the calculation, so a detailed review is possible without user intervention. Therefore, the transient analysis is likely to be reproduced as is in a normal situation or problem situation only if the necessary characteristics are properly entered.

The image below shows that the natural frequency of ball screws, which are frequently used in FA (factory automation) and motion control, depends on the nut position.

CHANGES IN THE NATURAL FREQUENCY OF THE BALL SCREW

ACCORDING TO THE CHANGE OF THE NUT POSITION

3.3 “Crack has occurred on the product in use!”

Machine damage includes static damage and fatigue damage. This chapter focuses on fatigue damage. Some people call the durability analysis to solve the problem of fatigue damage the core of a structural analysis. Although durability analysis is so difficult, it is essential.

The previous two chapters were about the cases where defects were filtered out during the design review phase or at the latest in the prototype phase, but this time, the problem occurred after the product was released. In other words, it can be regarded as more serious situations than the previous cases.

Static damage can be found by the static analysis (static strength analysis), but the durability analysis, a type of the dynamic analysis, must be performed in order to find fatigue damage. This is because the weak points identified from the stress distribution obtained by the static analysis and the damaged parts identified by the durability analysis can be different. In other words, if only the static analysis is used, the problem of fatigue damage may not be identified.

RESULTS OF DURABILITY ANALYSIS USING DYNAMIC ANALYSIS

Similar to the vibration described in the previous chapter, there are methods of using the time and frequency domains for the durability analysis. The method of using the load expressed in the frequency domain is called “vibration fatigue analysis.”

It is known that the vibration fatigue analysis is simpler than the method using the time domain because the system response is assumed to be linear. In addition, the durability analysis for random vibrations in which frequency cannot be specified can be performed using PSD (power spectrum density).

A time domain approach is generally introduced as a burden for computer processing due to the large amount of data acquired in a series of time, which also applies in theory. These days, however, computer performance has seen great improvement, so there is no burden on actual use.

The vibration fatigue analysis assumes that the system's response is linear. However, it does not make this assumption when considering the load change over time and has the advantage of performing the durability analysis in consideration of shock, contact, and other nonlinear reactions. Two images below show examples of fatigue damage of construction equipment and changes in strain over time. (This case used the dynamics software, RecurDyn.)

CASE OF FATIGUE DAMAGE OF CONSTRUCTION EQUIPMENT

CHANGE OF STRAIN OVER TIME OF WHEEL LOADER PUSH LINK

(The two images above are taken from the presentation material at the 2017 RecurDyn User Conference)

The three questions mentioned at the beginning of Chapter 3 are as follows:

① “The prototype was broken during the test!”

② “Strange vibration occurs!”, “It makes strange noise!”

③ “Crack has occurred on the product in use!”

From this article, we could see how the dynamic analysis can help with each of these problems. The benefits of using the dynamic analysis introduced in this article are as follows:

① Since the exact dynamic load is used, the safety of the product can be improved.

② Because frequency is investigated without omission, vibration problems can be pinpointed.

③ The fatigue life of the products subjected to non-linear loads such as impact can also be predicted.

[Column] Why We Should Use Dynamic Analysis? (Part 1)

Written by Taero Cha (Director of China Business Division)