# Static And Dynamic Force Analysis Pdf

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*Journal of Vibroengineering, Vol. Based on the finite element analysis method, the static stress, deformation, vibration mode and transient response of the press bed are developed under preload conditions, as well as under the combination of the preload and nominal pressure conditions. Besides, the static loading experiment, the mode experiment and the pile-driving experiment are conducted to revise the simulation model.*

- Theory of Machines by
- The difference between static and dynamic analysis
- Static and Dynamic Balancing of Rigid Rotors

Consider a body of mass moving with acceleration as shown in figure 1 i. Link to this page:. The couple can be replaced by two parallel forces equal in magnitude and opposite in direction acting at G and H respectively as shown in Figure 2 ii.

## Theory of Machines by

Journal of Vibroengineering, Vol. Based on the finite element analysis method, the static stress, deformation, vibration mode and transient response of the press bed are developed under preload conditions, as well as under the combination of the preload and nominal pressure conditions.

Besides, the static loading experiment, the mode experiment and the pile-driving experiment are conducted to revise the simulation model.

Finally, the simulation model and analysis procedure are verified through the comparison of the experiment results and the simulation ones.

Keywords: high-speed press, static analysis, modal analysis, transient response analysis. High-speed press is a type of forging machine which is extensively used in the industrial manufacturing and production [1]. As usual, forging machines are designed by analogical and empirical methods. The size of the press is determined when setting a certain safety coefficient to ensure the maximum stress and deformation of the press are less than the allowable ones.

However, there are some problems about this method. Firstly, the stress and deformation is worked out under a series of hypothesis and a larger safety factor is often selected for safety sake. Therefore, the press designed with this method is quite bulky and material-wasting [2]. Secondly, the safety coefficient method is mainly applied to simple rod pieces.

However, it could lead to large difference between the stress obtained by the classical mechanics method and the actual ones. Thirdly, most failure modes of the press bed are loss of accuracy caused for suffering the impact load working conditions.

However, this kind of load is ignored when the press is designed by the safety coefficient method. First of all, according to the design scheme, make a prototype and then take relative tests on the prototype. Next adjust the design scheme according to the tests result. Then recycle repeat the procedure above. These tedious procedures make the traditional press design time-wasting and expensive. The virtual simulation analysis mainly consists of static and dynamic analysis for they build a base for optimized design and remanufacturing of high-speed press [5].

Through the static analysis, the stress and deformation of the press can be obtained and the weak parts under the static load conditions can be found; similarly, through the dynamic characteristic analysis, the vibration mode and weak parts of the press bed under the dynamical load conditions can be obtained [6].

This paper is devoted to dynamics analysis and static analysis of the J Straight Side high-speed Double-crack Precision Press bed in the following of this paper, it is called J high-speed Press for short. The remaining of this paper is organized as follows: Section 2 presents the static characteristic simulation analysis method.

Section 3 presents the dynamic characteristic simulation analysis method. Section 4 presents the experiment verification and Section 5 concludes this paper. As is shown in Fig. The two parts are contacted by four pairs of struts and fixed by four tie-bolts.

And there are four convex plates on the beam to fit the tie-bolts. Besides, there are two four in the beam to install the crankshaft. The worktable is installed on the upper surface of the base and the slider is driven by the crankshaft which is installed on the crankshaft-hole.

The finite element model of the high-speed press is obtained and it is shown in Fig. To ensure the press operate properly, the beam and the base should be contacted closely together. Therefore, preload should be applied on the four tie-bolts directly.

According to the computational analysis, the preload of tie-bolts should be 1. The surface of crankshaft-hole is subjected to loads which are perpendicular to the upper surface in point-load form when the press is working. The loads are shown in Fig. F 1 is According to Persson [9, 10], the loads follow cosine distribution when the contact gap is close to 0. To simplify the computation, the upper half of the crankshaft-hole is equally divided into 6 parts in the circumferential direction by 5 nodes, as shown in Fig.

The force decomposition on bearing hole. From Eq. So the load distribution of the 5 nodes of the upper half of bearing hole in the circumferential direction is shown in Table 1. The direction of the load applied to the worktable is acting vertically downward; the area of the worktable is 0. Table 1. Load distribution of the 5 nodes of upper half of bearing hole. The beam and the base are contacted by their struts and the struts are of the same stiffness, so the contact forms are set as surface-to-surface contact in flexible structures.

Four struts of the base are regarded as the target surface while the four struts of the beam are set as contact surface. The type of the contact elements of the target surface is set as Targe, while the contact surface as Conta The contact between the base and ground is set as fixed constraint. Firstly, apply Gravity on the beam and base, and then set the preload of the tie-bolts through the pretension element PRETS So the static characteristic of the bed and tie-bolts under preload can be developed.

Secondly, apply the nominal pressure on them. So the static characteristic of the bed and tie-bolts under the combination of preload and nominal pressure can be also solved. The tie-bolts bear tensile stress that is concentrated on the contact area with the nuts.

The maximum value is Strain diagram of the base along the Z axis. As to the deformation under the preload, we only concern on the deformation of the worktable for that the machining precision of the press is mainly determined by the worktable.

The deformation of the worktable is homogeneous and the value is 3. Therefore, it meets the stiffness requirement. The stress and deformation of the press bed under the combination of preload and nominal pressure are solved by ANSYS.

Comparison of the maximum stress and deformation of different parts under two loading conditions preload only, as well as combination of preload and nominal pressure are shown in Table 2. The results of the analysis can be summarized as follows. When the beam bears both the preload and nominal pressure, it also bears compressive stress. The stress of the four tie-bolts decreases while the stress of the middle part of the beam increases.

The position of the maximum stress changes from the convex plate to the upper part of the crankshaft-hole. The position where the base distorts seriously changes from the contact areas between the base and the beam to the convex plate. Corresponding to the previous section, we also only concern on the stress of the tie-bots and the deformation of the worktable along the Z axis.

The maximum stress of the tie-bolts is The deformation of the middle part of the worktable is larger than the one of the two ends, and the maximum deformation is —0. The permissive deformation of the worktable is 0. Table 2. The maximum stress and deformation of different parts under two loading conditions.

The motion equation of the system was established firstly when performing modal analysis. The press bed is an elastomer with its mass distributing evenly, so it can be taken as a multiple-degree-of-freedom system which consists of several lumped masses. And its motion equation can be expressed by the following equation:. Vibration mode represents the natural dynamic features of the press system, and each vibration mode has a specific natural frequency, damping ratio and modal shape.

In this study, the vibration modes are named the first order, the second order, and so on from small to large of the specific natural frequency. The press vibrates when the order natural frequency of the vibration mode is close to the working frequency of the press. Therefore, the press has low machining accuracy, large noise and even failure when the press system works close to the natural frequency. The resonance of the press occurs when the working frequency is equal to the natural frequency.

The frequency range of the outer impulse generated by the crankshaft rotation is from 2. And the punching frequency is quite low, so only the top-ranked vibration mode needs to be considered while performing modal analysis [11]. The first ten orders natural frequencies were obtained through virtual simulation as shown in Fig. All of the first ten orders natural frequencies are higher than the working frequency, so the design of the press structure meets the requirements.

To better understand the present pattern of the vibration modes, the first three order vibration modes of the press are illustrated as shown in Fig. Generally speaking, when the punch press reaches one third of the thickness of the sheet metal, the blanking force reaches the maximum value and then decreases rapidly.

When the punch reaches the 0. The change law of the load over time is shown in Fig. According to the working principle of the press, the load under the typical processing conditions can be obtained and the results are shown in Table 3.

Table 3. The load and time distribution under the typical processing condition. In this paper, we adopt complete analysis method to perform the transient response analysis [13]. The simulation parameters are set according to Table 3. In order to obtain the law of deformation and stress of the press bed, deformation nephogram and stress nephogram along the Z axis of the bed at some selected time in a loading cycle are extracted.

They are 0. And their deformation and stress diagrams along the Z axis are shown in Fig. From Fig. In the pile-driving experiment section later, we will take these three positions as key points to analyze. Z axis deformation diagram of the bed at the selected time.

## The difference between static and dynamic analysis

Bucknor, N. September 1, September ; 3 : — A quasi-static model has been developed for a silent inverted-tooth chain drive incorporating a rocker-pin-jointed chain and involute-toothed sprockets. In some cases, this variation is found to be less than that for equivalent pin-jointed chain drives. Additionally, the center distances corresponding to the maximum and minimum torque variation are not fixed, as in the case of a pin-joined chain.

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Birades, Michel. This paper presents two three-dimensional 3D mathematical models to predict the directional behavior of bottomhole assemblies BHA's. The first model describes BHA dynamic, stepwise, transient behavior. Displacements and lateral forces, computed for each step, account for friction against the borehole wall. The second model computes a static BHA equilibrium whereby simplified friction forces are assumed. The static lateral forces are found to be an average of the highly varying ones computed by the dynamic model, but the static computer run is much faster.

## Static and Dynamic Balancing of Rigid Rotors

Crank effort: Force is exerted on the crank pin as a result of the force on the piston. Crank effort is the net effort force applied at the crank pin perpendicular to the crank which gives the required turning moment on the crank shaft. In the figure given below, when is the absolute velocity of end B of the coupler equal to the absolute velocity of the end A of the coupler?

*Unbalance is the most common source of vibration in machines with rotating parts. It is a very important factor to be considered in modern machine design, especially where high speed and reliability are significant considerations. Balancing of rotors prevents excessive loading of bearings and avoids fatigue failure, thus increasing the useful life of machinery.*

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When I was doing my first civil engineering design I hardly thought about dynamics. And to some degree, it might have been even justified back then. Now, when I understand a bit more, I would like to take you on a trip! We will learn about the differences between statics and dynamics! The main difference between static and dynamic analysis is TIME! But of course, there is implicit and explicit, and all the exciting stuff!

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