Experimental and FE Investigation on the Influence of Impact Load on the Moment Transmission of Smooth Shaft–Hub Connections

Featured Application

Safety calculation for shaft–hub connections.

Abstract

A well-known phenomenon in machinery systems is the easing of a blocked connection of mechanical parts after an impact hit close to the connection. Such impact hits may also arise in shaft–hub connections such as gears, crankshafts, or other parts. The objective of this study is to investigate the influence of local impact loads on the transmittable torque of smooth shaft–hub connections. In a specially designed test rig, it was demonstrated that the transmittable torque of the shaft–hub connection is reduced as a consequence of the impact, resulting in a reduction in the frictional force and slippage of the hub. Increasing the impact load leads to an increase in the reduction in the frictional force as well as the slippage and reduces the transmittable torque. By carrying out a modal analysis of the relevant parts and FE simulations of the impact, two possible reasons have been identified: (i) the impact load excites a vibration mode in the connection which reduces the frictional force and the transmittable torque; and (ii) the impact causes local deformation of the shaft, which results in local slip.

1. Introduction

Many complex products are manufactured through complex joining techniques, which often exhibit functional characteristics within the assembled structure. In the field of mechanical engineering, joining by forming is a conventional method [1,2] that is frequently employed in conjunction with other techniques such as welding or brazing [3]. Press-fit connections are particularly prevalent in shaft–hub connections [4,5,6,7,8]. With the help of hydroforming [9] or shrinkage connections [10] with warmer hubs and colder connections, a frictional connection is adjusted between the two components. In typical applications, more often, several hubs are adjusted on a single shaft. This is exemplified in gear boxes and crank or rotor shafts [1,4,11]. Typically, the safety calculation for the transmittable torque of shaft–hub connections is conducted in accordance with the specifications outlined in DIN 7190 [12]. Furthermore, it is well-documented that materials exhibit disparate behaviors when subjected to varying strain rates: some display increased strength [13], some become brittle [14], and some even generate acoustic emissions during the loading process [15]. Complex assemblies may also result in the generation of complex and superimposed loads. For instance, vibrations emanating from one component can have a significant effect on the bearing [16,17,18]. This may lead to failure [17] in contact zones, but it may also overcome a disadvantage of press-fit connections: their non-destructive disassembly (in terms of not cutting both joining partners) [19]. In addition to low-frequency vibration-wave-assisted disassembly [19], it is also common practice to loosen up blocked mechanical parts caused by fretting [20,21,22] with an impact hit close to the connection. Similar effects are also described in so-called Impact Drive Mechanisms (IDMs), which deal with the frictional force and stick–slip in mechanical systems during the interactions of the surfaces and the near regions of two materials [23,24], mostly in piezoelectric materials. Furthermore, somehow, similar effects were investigated in the classical tribological research area. In several papers, other groups investigated the influence of tangential vibration at low [25], high [26,27], and very high frequencies [28]. At all frequency levels, specific values were found where the friction between both tribological partners was intensively reduced due to this transverse vibration. In [26,27], computational models were developed that were able to reproduce the effects numerically. In [29], it was also found that even very low frequencies may influence failures under cycling load in what the authors called a creep–slip phenomenon. In a review work by Plooij et al. [30], three different locking mechanisms (to avoid such reduction in the frictional forces) were introduced: mechanical locking, friction-based locking, and singularity locking. The prevention of failure in the relative bolt connections is the focus of the work of [31]. The detailed experimental and numerical work comprises giving recommendations on the design features of threaded connections with collet nuts to prevent unintentional self-unscrewing [31]. In a more recent work, the same group proposed the concept of shell dampers with a shock absorber. They used the same mechanism backwards while filler material in the damper transformed longitudinal displacements of a piston into radial deformations of the shell so that no vibrational load may reduce friction in the connection, and to prevent unintentional self-unscrewing [32].

However, understanding the influence of single impact loads without permanent vibration on the transmittable torque of shaft–hub connections is so far not investigated. The mechanism described above may help to understand the result. In any case, it is essential to investigate this phenomenon for predicting and mitigating potential failures in mechanical systems.

The object of this study is to examine the influence of local impact loads on the transmittable torque of smooth shaft–hub connections. To the best of the authors’ knowledge, no such study has yet been carried out. In a specially designed test rig, it was demonstrated that the transmittable static torque of the shaft–hub connection is reduced as a consequence of the impact, resulting in a reduction in the frictional force and the slippage of the hub: press fits with the same interference fit will start to rotate at a lower torque than they would withstand in a static torsion test rig without an impact load. Additionally, this study aims to identify the underlying mechanisms that contribute to the observed changes in performance through modal analysis and finite element (FE) simulations; the influence of the ball mass, impact velocity, preload, and distance between the ball and hub is systematically studied. The findings are expected to provide valuable insights into the design and maintenance of mechanical connections, enhancing the reliability and longevity of machinery systems.

2. Models and Methods

In this study, the base material of the shaft is a low-alloyed construction steel, 1.0580, according to [33]. The base material of the hub is a heat-treated medium alloy cold work tool steel, 1.3505, according to [34]. A detailed microstructural material analysis as in [35] is not performed in this paper but might be the content of future work. The hollow shaft and hub were thermally joined. There is a smooth connection between the joining parts. The interference fit of the shaft–hub connection is approximately 21 µm.

In order to investigate the possible phenomena during the impact load, a test rig was developed, which is shown in Figure 1. The torque is applied in the shaft by a bolt, which introduces a force on a lever of a defined length. The rotation forces the hub to press against a part of the frame. This leads to a preload torque of the shaft–hub connection. In order to determine the preloaded torque, the force is measured via a load cell ($5\mathrm{k}\mathrm{N}$, A. S. T. GmbH, Dresden, Germany). By multiplying the measured force with the length of the lever, the preloaded torque can be calculated. It is important to note that the preload torque must not reach the static transmittable torque of the connection. A mass is then dropped from a height at a defined position. The mass falls perpendicularly to the frame on the shaft (not the hub) to minimize any further torque load on the shaft–hub connection that may arise from the introduced impulse. Please note that the test rig also obtains a bearing frame to stabilize the shaft–hub connection and avoid effects from the bending of the shaft. A marker is placed on the shaft and hub to detect any slippage of the hub. The slippage of the hub is indicated by the markers moving in relation to each other.

The impact of the mass induces an oscillation which then leads to the stimulation of the connection at a specific frequency. As a result, the frictional force and the contact pressure in the connection is reduced locally [23,26,27,31] and the transmittable torque of the shaft–hub connection is temporarily reduced. Simulative investigations were conducted alongside the experimental tests to verify this assumption. The simulations were performed with the software Abaqus™ 2019 (Co. Simulia, Vélizy-Villacoublay, France) and the general work of [36] was taken into account. Linear hexahedral elements of type C3D8R with reduced integration were used in all simulations.

Modal analyses were conducted to determine the natural frequencies and mode shapes. As contacts are unaccountable, the shaft–hub connection is modelled as a monolithic structure in the simulation model.

Subsequently, the identified natural frequencies were employed in a frequency response analysis. In order to simulate contact pressure accurately, the shaft and the hub are defined as two distinct parts with different material properties. Depending on the stimulated eigenmodes, the radial stress between the shaft and the hub can be reduced. These radial stress reductions indicate the changing of the real contact pressure in a shaft–hub connection.

In addition to the modal analysis, the experimental test setup is numerically evaluated. The geometry and boundary conditions in the simulation are based on the test setup, which is shown in Figure 2.

The impact of the mass on the shaft can produce a slip zone in the contact, in addition to the vibration modes. This slip zone temporarily reduces the transmittable torque. To test this phenomenon, the given geometry data and parameters were used to simulate the test sequence in Abaqus™. The simulation model consists of a hollow shaft on which a hub has been mounted with an interference fit. The impact is introduced by a ball (point contact)—see Figure 3. The preloaded torque on the shaft–hub connection is defined via a virtual spring with a spring stiffness of $D=\mathrm{270,000}\mathrm{N}/\mathrm{m}\mathrm{m}$. The element nodes of the two areas, marked in red, are each linked to the virtual points RP1 and RP2. This allows the element nodes to be controlled via the aforementioned virtual points. According to DIN 7190 [8], the coefficient of friction in the contact can be assumed as $\mu =0.2$. The component’s meshing is developed according to the matching mesh strategy, in which all the contact nodes between the hub and the shaft are coincident.

In the simulation model, all translational degrees of freedom $U$ and the rotational degrees of freedom $U_R$ are constrained at RP2 of the shaft. Conversely, the translational $U_X,U_Y$ and rotational degrees of freedom $U_{RX},U_{RY}$ are restricted at the other end of the shaft—see Figure 4. The virtual spring is compressed by a defined distance $U_F$ in the $U_X$ direction, which, in turn, twists the shaft. This leads to a reaction moment in RP2. The ball drops onto the shaft at a defined speed $v$. If the hub will slip as the result of the impact of the ball, the compressed spring relaxes. Consequently, the reaction moment in RP2 decreases in a manner analogous to that observation in the experiment—see Figure 4.

3. Results and Discussion

The first experimental series were carried out to determine the transmittable torque of the connection without the influence of impulse. The interference fit of all analyzed shaft–hub connections is approximately 21 µm. A bolt is used to steadily increase the torque until it suddenly drops as the hub slips, which is shown in Figure 5. Two different hubs were tested. The maximum transmittable torque for the first hub (orange) is $170 \mathrm{N}\mathrm{m}$ and, for the second hub (blue), $150 \mathrm{N}\mathrm{m}$. After the first slip, the hubs have been further loaded. The transmittable torque after the first slippage drops for both hubs to approximately $125 \mathrm{N}\mathrm{m}$. At the end of the experiment, the lever returns to the initial position and the torque drops to zero. It can be assumed that the reduction in the frictional force and accompanied slippage cause the damage to the contact surface between the shaft and the hub [20,22] such as fretting, which can lead to a change in the coefficient of friction and the resulting transmittable torque.

Figure 6 displays the results for the second experimental series. The preload torque varies between $110 \mathrm{N}\mathrm{m}$ and $115 \mathrm{N}\mathrm{m}$, below the previously determined limit. The impact energy from the falling mass is $9 \mathrm{J}$. At the start of the experiment, the markers on the hub and the shaft lie on top of each other. The impulse forces the hub to slip, which, in turn, reduces the preloaded torque. This is reflected in the measured curve by the drop of the torque. Upon completion of the experiment, a discrepancy between the marker positions can be observed. In other studies, attempts are made to avoid this effect of unintentional “self-unscrewing” [31,32].

The diagram in Figure 7 illustrates a test in which the hub was preloaded once to $80\mathrm{N}\mathrm{m}$ and the same impulse ($m=1.6\mathrm{k}\mathrm{g}$, $v=990\mathrm{m}\mathrm{m}/\mathrm{s}$) was initiated several times on the same position of the shaft. The measured curve shows that the highest reduction in the torque, about $20\mathrm{N}\mathrm{m}$, is observed with the initial impulse. Further impulse initiation leads to a lower reduction in the torque due to the gradational reduction in the frictional force in the connection [25,26,27,28]. A saturation of the minimum transmittable torque can be seen at $35\mathrm{N}\mathrm{m}$.

The modal analysis yields natural frequencies and their corresponding mode shapes, as illustrated in Figure 8. Two specific mode shapes have been identified with their respective natural frequencies. The initial form indicates a torsional mode occurring at a frequency of 5578 Hz, which can lead to an additional torque load experienced by the shaft–hub connection. In Figure 9a, the resulting radial stress as a function of the peripheral angle is shown. The accumulation with the preloaded torque on the connection may surpass the maximum limit, leading to a hub slippage.

The second mode indicates a bending shape at a natural frequency of 8155 Hz, resulting in a decrease in the localized contact pressure and, therefore, a lower transmittable torque. Furthermore, localized slip zones can occur at the hub edge. In conjunction with a preload, the slip zones can spread throughout the entire width of the hub (see Figure 9b) and lead to a slippage and may cause the fretting phenomena. Please note that an additional preloading increases the mode-dependent natural frequencies [17]. Those natural frequencies are above those from the studies of [25,26,27] but under those from [28] and it can be proven that frictional forces and the resulting contact pressures may reduce at varying frequencies. As also mentioned in [28], we can achieve only a rough qualitative agreement of the experimental and numerical work so far.

Figure 10 shows the results of a simulation, in which a ball with a mass $m=1.6\mathrm{k}\mathrm{g}$ falls with the velocity $v=3000\mathrm{m}\mathrm{m}/\mathrm{s}$ at an angular position $\alpha =90°$ on the shaft. The upper plot shows the contact pressure before the impulse is initiated. The application of the impact leads to a deformation of the shaft which results in a change in the contact pressure for a short period of time. At the edge zone, the pressure decreases at an angle of $0°$ to $90°$ and, at the angle $90°$ to $300°$, the pressure increases. The reduction in the pressure results in a slippage of the hub. While the hub is changing in thickness, the results from [26] can be confirmed: the tangential stiffness (which is dependent on the thickness) is very important for the friction force reduction.

Figure 11 displays the average contact pressure and the reaction moment at virtual point RP2 in the simulation as a function of time. The torsional preload was measured with a value of 145 Nm. As described above, the deformation of the shaft caused by the impulse results in a change in the mean pressure. It also causes a vibration in the shaft, which can be seen in the wave-shaped mean pressure curve. After the vibration has stopped, the mean pressure returns to its initial state. This brief reduction in the frictional force due to the vibration [25,26,27,28] is sufficient for the hub to slip, as evidenced by the reaction moment’s progression. The torque drops from 146 Nm to 134 Nm.

Figure 12 is showing the simulation result in which the impact ($m=1.6\mathrm{k}\mathrm{g}$, $v=3000\mathrm{m}\mathrm{m}/\mathrm{s}$, $E_{kin}=1.9\mathrm{J}$) was initiated three times at the same position during the captured time. Following the initiation of the first impulse, a significant reduction in the reaction moment is noticeable. The reaction moment drops from $144 \mathrm{N}\mathrm{m}$ to $126 \mathrm{N}\mathrm{m}$. On triggering the second impulse, the reaction moment decreases only by $1 \mathrm{N}\mathrm{m}$. No shift in the reaction moment is apparent upon initiating the third impulse.

In Figure 13, the influence of the distance between the hub and the point of impact ($h$) on the transmittable torque is shown. The results indicate that the biggest reduction in the torque ($20\mathrm{N}\mathrm{m}$) occurred at the smallest distance of $h=10\mathrm{m}\mathrm{m}$. As the distance ($h$) was increased, the effect of the impulse was diminished, with a barely noticeable drop in the reaction moment up to $h=35\mathrm{m}\mathrm{m}$. The results indicate that the closer the deformation field is to the hub due to the impulse, the greater the change in contact pressure and the associated drop in torque. In addition, the results may differ with different natural frequencies of the shaft or a different impact energy which causes different transverse vibrations and may arise in different locking mechanisms in the connection [30].

The result of the simulation with a cylinder instead of a sphere-shaped mass ($m=1.6\mathrm{k}\mathrm{g}$, $v=3000\mathrm{m}\mathrm{m}/\mathrm{s}$) is shown in Figure 14. Instead of being point-shaped, the contact during the impact is line-shaped. This results in a small decrease in the reaction moment of approximately $1\mathrm{N}\mathrm{m}$. This underlines the influence of the contact between the impact mass and the shaft. A change in the shape of the contact leads to a change in the energy transfer and a different tangential vibration between the point mass and the shaft due to the impulse. This results in a different deformation due to the reduction in the friction force of the shaft and the slip zone between the shaft and the hub which may arise from several influencing factors. Furthermore, a different vibration excitation of the shaft can occur.

Different studies on the influence of the impact velocity, the preload, the mass of the ball, and the distance between the impact and the shaft–hub connection were carried out. The results of all those factors are shown in Figure 15. The biggest decrease in the transmittable torque is obtained at the highest impact energies (big mass and high velocity), the closest distance to the hub, and with the highest preload. All of these changes can be attributed to the effects of vibration excitation of the shaft [17] and the temporary reduction in the contact pressures caused by the deformation and the reduction in the frictional force [19,26,27,28], with the associated increase in slippage [22]. The highest energies lead to the biggest decrease in the contact pressure in the connection and the decrease in the transmittable torque. The highest preload puts so much tension on the connection that even a slight reduction in the contact pressure can cause slippage. The influence of the distance may be related to damping effects in the material. Further studies may follow on this.

4. Conclusions

In this study, we investigated the influence of local impact loads on the transmittable torque of a shaft–hub connection. The experiments carried out show that, in a press fit, a reduction in the frictional force and a slippage can occur at a lower torque than a static torque test without any impact load. This study also shows that increasing the impact results in an increase in the slippage and a reduction in the transmittable torque. The modal analyses and FE simulations of the impact carried out show the following: the impact load excites a vibration mode that causes a local deformation of the shaft, resulting in a local slippage (and probably fretting) and reduces the transmittable torque due to a local reduction in the contact pressure. We have also systematically studied the influence of the shape of the mass, the impact velocity, the preload, and the distance between the impact mass and the hub, and came to the following conclusions:

-

Higher preloads result in an increase in slippage caused by the impact;

-

The increase in impact velocities or impact mass reduce the transmittable torque;

-

Reducing the distances between point of the impact and the hub reduce the transmittable torque.