1 Introduction

Forging process is an experience-oriented technology with a great know-how for many years. These processes produce the complex configuration from simple geometry with minimum waste of materials and energy. Therefore, hammer forging process and tool design were developed mainly by trial-and-error [1]. The advantages of a forging process such as higher strength to weight ratio, acceptable dimensional and superior micro structure of products are highly attractive for a lot of engineering parts [2]. Faster processing and high material output of forging technologies reduce the costs of forged parts with complex geometry [3]. A forging technique was improved to manufacture the thick-walled pipes without the use of a mandrel [4]. The results showed a reduction of time of deformation and saving energy costs to heat the workpiece [4]. The new techno-logical forging processes were designed in order to produce large special workpieces with concave faces [5]. The design, analysis and optimization of a hammer die forging process require the knowledge of material flow, friction, heat transfer as well as vibration [6]. Forging of plate with V-shaped dies was developed in order to the increase the uniformity of the strain distribution in forged part [7]. An improvement of forging process was suggested to ensure a uniform closing effect throughout the centreline of the inside forged region [8]. The influence of mechanical vibrations of a forging system can be characterized from different points of view such as product quality, energy loss, service life of the machine and environmental effects. The investigated hydraulic hammer consists of a ram, anvil, foundation, frame, spring-damper system and the hydraulic system as schematically shown in Figure 1 [9].

Fig. 1
figure 1

A schematic of mounted on spring elements hammer forging machine [9]

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The hydraulic system of a hammer forging consists of durable axial piston pumps driven through flexible couplings by special three-phase motors. The basic working principles of the hydraulic system of hammer forging simply rely on differences in fluid pressure. Increasing of fluid pressure under the piston and decreasing the fluid pressure above the piston cause the piston to rise. In the next step, a higher pressure of the fluid above the piston, than the fluid below it, moves the piston downward. A properly designed viscous-spring isolator system is generally used to reduce the shock and vibrations transmission to the foundation [10]. For the elastomers, both stiffness and damping have to be considered in an accurate control of the vibrations [11]. The vibration speed as a critical factor in the reduction of the forging force was investigated by Fulan in [12]. The optimization of ratio of foundation mass to anvil mass resulted in a more economical and reasonable design [13]. A new forging process was designed to increase the quality of large forged parts without significant reduction of the cross-sectional area [14]. The novelty of this work was the characterization of mechanical vibrations of a LASCO-forging machine in order to understand the effect of varying process parameters on the forging efficiency. The effect of initial velocity of the anvil before contact with the workpiece on the forging efficiency was theoretical and experimental investigated.

2 Theoretical analysis

The hammer forging process can be characterized as a mass-spring-damper (m-k-c) constrained mechanical vibration system. At first, the ram falls down under hydraulic force to strike the workpiece. The kinetic energy of ram causes the workpiece deformation. After the forming process, the ram returns and the free damped mechanical vibrations of the anvil occur. Figure 2 shows a simple mechanical vibration model of a hammer forging process considering the velocity changes of ram and anvil.

Fig. 2
figure 2

Schematic diagram of a simple mechanical vibration model of a hammer forging process

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Where Emech, U, U′, F, C, K, v1, v2, v1′, v2′, m1 and m2 refer to mechanical energy of ram, common velocity of ram and anvil in forming process, common return velocity of ram and anvil, force, damper coefficient, spring coefficient, initial ram velocity, initial anvil velocity, final velocity of ram, final velocity of anvil, mass of ram and mass of anvil, respectively. The impulse phenomenon based on the second Newton’s law can be written for m1 and m2 as the following:

$$ {m}_1{v}_1+{\int}_0^{t_1}\left(-F. dt\right)={m}_1U $$
(1)
$$ {m}_2{v}_2+{\int}_0^{t_1}\left(F. dt\right)={m}_2U $$
(2)

where t1 refers to the impulse time. Considering the mass ratio Q, and combining Eqs. 1 and 2, the common velocity of ram and anvil after impulse can be expressed by the following:

$$ (1),(2),Q=\frac{m_2}{m_1}\kern0.5em \Rightarrow \kern0.5em U=\frac{v_1+Q.{v}_2}{1+Q} $$
(3)

The coefficient of restitution k can be expressed as follows:

$$ k=\frac{\int_{t_1}^{t_2}\left(F. dt\right)}{\int_0^{t_1}\left(F. dt\right)} $$
(4)

Considering the final velocity of ram \( {v}_1^{\prime } \) and final velocity of anvil \( {v}_2^{\prime } \), the coefficient of restitution k can be formulated as a function of ram and anvil velocity before impulse and after impulse as follows:

$$ k=\frac{v_1^{\prime }-U}{U-{v}_1}=\kern0.5em \frac{v_2^{\prime }-U}{U-{v}_2} $$
(5)
$$ k=\frac{v_1^{\prime }-\frac{v_1+Q.{v}_2}{1+Q}}{\frac{v_1+Q.{v}_2}{1+Q}-{v}_1}=\frac{v_2^{\prime }-\frac{v_1+Q.{v}_2}{1+Q}}{\frac{v_1+Q.{v}_2}{1+Q}-{v}_2} $$
(6)

The forging efficiency as a function of k and Q can than be expressed as follows:

$$ \eta =\frac{\frac{1}{2}{m}_1.{v}_1^2-\left(\frac{1}{2}{m}_1.{v_1^{\prime}}^2+\frac{1}{2}{m}_2.{v_2^{\prime}}^2\right)}{\frac{1}{2}{m}_1.{v}_1^2} $$
(7)
$$ \eta =1-\frac{{\left(1-Q\bullet k\right)}^2+Q.{\left(1+k\right)}^2}{{\left(1+Q\right)}^2} $$
(8)

Figures 3 and 4 show the forging efficiency in dependence of k and Q.

Fig. 3
figure 3

The forging efficiency–restitution coefficient curve for different mass ratios

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Fig. 4
figure 4

The forging efficiency–mass ratio curve for different restitution coefficients

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For a constant mass ratio, the forging efficiency increases with a reduction of restitution coefficient. For mass ratios greater or equal than 50, curves are congruent.

It can be recognized that the forging efficiency strongly increases with mass ratio until a Q-value of 50 and stays constant for higher values. The characteristic forging efficiency–mass ratio curve for the investigated machine is shown in Fig. 5.

Fig. 5
figure 5

The forging efficiency–mass ratio curve for investigated forging LASCO machine

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The loss of energy due to the anvil free damped vibrations for the LASCO HO-U-315 is approximately 5% and thus much smaller than the loss of the ram energy in fall step. The loss of energy for a mass ratio more than 200 due to the free damped vibrations of anvil is close to 0. The effect of anvil initial velocity v2 on the forging efficiency can be shown in the following equation:

$$ \eta =0.022{\left(5.18-{v}_2\right)}^2 $$
(9)

For an initial anvil velocity about 0.2 m/s, the forging efficiency increases about 4% (Fig. 6).

Fig. 6
figure 6

Influence of anvil initial velocity on the forging efficiency for investigated LASCO machine

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The motion equation of the anvil under free damped vibrations can be expressed as follows:

$$ x(t)=\frac{U}{\omega_d}.{e}^{-\delta t}.\sin \left({\omega}_dt\right) $$
(10)
$$ \delta =\zeta .{\omega}_n $$
(11)

where x(t), U, ζ and ωd refer to the anvil displacement, anvil initial velocity, damping ratio and damped natural frequency. Subsequently, by differentiating Eq. 10, the velocity of the anvil v(t) can be derived as follows:

$$ v(t)=\frac{dX}{dt}\kern0.5em \Rightarrow \kern0.5em v(t)=\frac{U}{\omega_{\mathrm{d}}}.\left(-{\delta e}^{-\delta t}.\sin \left({\omega}_{\mathrm{d}}t\right)+{\omega}_{\mathrm{d}}{e}^{-\delta t}.\cos \left({\omega}_{\mathrm{d}}t\right)\right) $$
(12)

Using the machine data of the investigated hammer results in the following:

$$ x(t)=5.087{e}^{-7.54t}.\sin (17.27t)\mathrm{mm} $$
(13)
$$ v(t)=-38.35{e}^{-7.54t}\sin (17.27t)+87.71{e}^{-7.54t}\cos (17.27t)\kern0.5em \mathrm{mm}/\mathrm{s} $$
(14)
$$ a(t)=21.1{e}^{-7.54t}\sin (17.27t)-1322.87{e}^{-7.54t}\cos (17.27t)\ \mathrm{mm}/{\mathrm{s}}^2 $$
(15)

where a(t) refers to anvil acceleration. The corresponding graphs are illustrated in Fig. 7.

Fig. 7
figure 7

The velocity and the acceleration–time curve of anvil for investigated LASCO machine

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It can be seen that the free vibrations of the anvil are damped after approximately 0.25 s.

3 Experimental procedure

In the experimental part, hot hammer forging tests were carried out using a LASCO HO-U-315 hammer. The characteristic vibrational parameters of this specific machine are summarized in Table 1.

Table 1 Characteristic vibrational parameters of used LASCO machine
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The investigated trial parts were carrier plates made of two different steels S355 and 42CrMo4. The plate temperature before the forging process has been held constant throughout all tests at approximately 1280 °C. Multiple blows were necessary to fill the dies; thus, a variation of time between two blows is considered as a possible efficiency influence parameter. The complete test series for both materials are shown in Table 2.

Table 2 Hot forging test plane
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The investigated hot forging process is shown in Fig. 8.

Fig. 8
figure 8

Investigated hot forging process

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The velocity of ram and acceleration of anvil were measured on the hammer using a laser velocity meter type LSV-2000-45 from Polytec Waldbronn, an acceleration sensor type 8743A100 from Kistler and a Cronos PL measurement data acquisition system from imc Berlin. The setup of the measurement system is illustrated in Fig. 9.

Fig. 9
figure 9

The investigated laser measurement system on the LASCO hammer forging machine

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The laser velocity meter was positioned at a distance of 1.5 m from the hammer ram. The acceleration sensor was attached to the press table. Both measured values, ram velocity and anvil acceleration were recorded with the Cronos PL measurement system. The measurement frequency was 50 kHz.

4 Results and discussion

The experimentally measured ram velocity and anvil acceleration for standard test S355 are exemplary illustrated in Fig. 10.

Fig. 10
figure 10

Experimentally measured ram velocity and anvil acceleration for standard test S355

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It is noticeable that the ram’s velocity decreases shortly before die-part contact. This effect has been observed for all measured blows and thus must be a part of the hammer characteristics. A possible reason could be a limitation in the hydraulic pressure system or an early opening of a valve in the hydraulic circuit. The energy loss before contact of roughly 10% was experimentally determined for all tests. Figure 11 shows the fall efficiency for all experiments.

Fig. 11
figure 11

The experimentally measured fall efficiency for all tests

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All relevant time steps in the forging process were determined for each test. The average values of this time steps are summarized in Table 3.

Table 3 Experimentally measured relevant times to the forging process
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The results showed that a variation of the delay between blows has no significant effect on the relevant times in the forging process. The free damped anvil vibrations start after approximately 0.21 s, and for the next blow, the ram reaches the anvil after 0.65 s. At this time, the experimental results showed that the free damped vibrations of the anvil are already close to zero and the acceleration–time curve progression was the same for all tests. Figure 12 shows a comparison of the acceleration–time curve progression for different tests after contact.

Fig. 12
figure 12

Comparison of acceleration–time curve progression of anvil for standard/delay 0.1 s S355 tests after the contact

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A comparison of the acceleration–time curve progression for different tests before contact are illustrated in Fig. 13.

Fig. 13
figure 13

Comparison of acceleration–time curve progression of anvil for standard/delay 0.1 s S355 before contact

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The curves clearly demonstrate that the delay has no influence on the progression of acceleration–time curves before and after contact. Figure 13 shows a low-frequency oscillation and superimposed high-frequency “noise.” The low-frequency oscillation corresponds to a natural structural frequency of the forging machine. This frequency is always stimulating when the hammer is activated to perform any movement (acceleration, deceleration, impact). A further evidence that this oscillation corresponds to a natural frequency of the structure of the ram is given by the fact that it is also partially visible in the speed signal. The high-frequency noise is related to the selection of the acceleration sensor. A piezoelectric acceleration sensor with a very large measuring range (± 50,000g), as very high acceleration amplitudes, can occur in the event of a bounce. The noise is correspondingly high, here approx. ± 100g, which corresponds to 0.2% of the measuring range which is typical for such devices. The integral of the anvil acceleration after the contact was determined for each impulse and every tests using Matlab® Software. The velocity of the anvil can be used to determine the restitution coefficient k. The coefficient of restitution k was determined for all experimental tests using Eq. 5. The obtained results in Fig. 14 show that the change of restitution coefficient k for S355 due to delay is about 15% in compassion with standard test and subsequently approximately ±5% for 42Mno4.

Fig. 14
figure 14

Comparison of restitution coefficient k for all experimental tests

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The restitution coefficient k depends mainly on plastic behaviour, impulse behaviour, temperature, initial velocity before impulse and surface condition of materials. These influencing factors are not similar for investigated materials (S355, 42CrMo4). Therefore, results show a different value of k for each material and test. Considering Eq. 5, the restitution k depends on the relative velocity of ram and anvil. Therefore, the restitution k can be decreased or increased due to the value and direction of ram and anvil velocity. The results in Fig. 14 show that the average value of restitution coefficient k is about 0.6 for all tests. Replacing the mass ratio of investigated LASCO machine (Q = 50.46) in Eq. 8 results in the following:

$$ \eta (k)=1-\frac{50.46{k}^2+1}{51.46} $$
(16)

According Eq. 16, the forging efficiency η for different values of k can be observed in Fig. 15.

Fig. 15
figure 15

Influence of restriction coefficient k on the forging efficiency for all experimental tests

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The results show an increasing of forging efficiency about 12% and 5% for S355 and for 42CrMo4 due to delay.

5 Conclusion

The mechanical vibrations of a LASCO HO-U-315 hammer were investigated in order to understand the influence of different control parameters on the forging efficiency. It was shown that for a constant value of mass ratio, the forging efficiency increases with a reduction of the restitution coefficient. The forging efficiency is independent of the mass ratio after exceeding a value of 50. The effect of the initial velocity of the anvil before contact between die and part on the forging efficiency was theoretically investigated. The forging efficiency increases about 4% for an initial velocity of the anvil of about 0.2 m/s. The free damped mechanical vibrations of the anvil are found to be depended on the machine mass, the machine rigidity and the damping coefficient only. The average value of the restitution coefficient k was obtained about 0.6 for all tests. The experimental results showed that the time setting or delay between two blows increases the forging efficiency up to 12%. The energy loss during the (hammer) fall was determined to be approximately 10%.