Characterisation of the conveying effect of turned radial shaft seal counter-surfaces using a simplified hydrodynamic simulation model

Radial shaft seals are used for sealing the exit of rotating shafts of lubricated systems [39]. Their main task is to prevent the lubricant from leaking out of the working chamber and also the penetration of fluids and/or dirt particles into the working chamber [34]. The sealing function must be durable for a long period of time, since any damage during time of operation and the resulting cost of repair is much higher than the cost of the sealing ring itself. For the system to be tight, the sum of the flow components in the direction of the oil side must exceed the sum of the flow components in the direction of the air side [20]. Roughness elevations on the sealing edge lead to a conveying effect in the case of an asymmetrical distribution of contact pressure and seal distortion [32] (cf. Fig. 1). The fluid dragged along by rotation of the shaft is deflected in the axial direction at the roughness elevations.

The surface finish of the SCS has a considerable influence on the sealing system [3, 23, 40]. (In this context, the term surface finish includes the surface topography and hardness of the near surface region.) During the time of operation, it influences the wear and surface topography of the RSS. This in turn has an impact on the conveying value of the RSS, which is the ability to transfer the lubricant along the axial direction of the sealing contact. The structural pattern of the SCS also influences the flow of the lubricant in axial direction due to conveying effects [32]. As a consequence of the shaft manufacturing kinematics during turning, the SCS exhibits twist structures. During shaft rotation, these structures contribute to a transport of the lubricant to either the oil side or the air side of the RSS similar to the conveying action of a screw pump, based on the shaft rotation direction and the direction of the lead pattern of the structure. The total conveying effect of a sealing system is the sum of the effect imposed by the shaft surface and by the seal [6].

Generally a twist is any surface phenomenon that leads to a diversion of the fluid to be sealed [36]. A distinction is made between macro-twist and micro-twist structures [28]. Macro-twist refers to periodic, directional structures such as feed grooves. Micro-twist refers to micro-grinding structures whose main direction has a perpendicularity deviation from the shaft axis. Standardized parameters exist to describe the macro-twist [28] as shown in Fig. 2, but this is not yet the case for the micro-twist.

Stochastically occurring structures on the SCS, such as scratches caused by improper handling, are also categorized as twist, since they can lead to a conveying effect [1, 26].

A simplifying approach assuming an ideal exact circular corner radius and neglecting the minor cutting edge allows for the estimation of macro-twist parameters using geometric-kinematic relations (see Table 1) [31].

Movement of the lubricant towards either side of the RSS has impacts on the sealing system. Movement towards the oil side is considered as a tight system, since leakage is prevented. However, excessive transport of lubricant towards the oil side means starved lubrication in the region of the sealing ring contact. This leads to a local temperature rise and increased wear rate, followed by thermal damage of the RSS. Transportation of the lubricant towards the air side happens when the conveying effect is stronger than the pumping effect of RSS and leads to leakage. Thus the conveying of lubricant alongside of the RSS and SCS tribo-contact needs to be balanced. In the desired state of a sealing system, the pumping is mainly done by the RSS and the SCS remains as neutral as possible.

Manufacturing of the SCS is usually realised by pre-turning, hardening and infeed grinding [8, 24]. From an economic and environmental point of view, however, grinding has numerous disadvantages such as high investment costs, low flexibility, a high proportion of non-value-added machining time due to sparking. With the development of more efficient cutting materials, grinding is increasingly replaced by machining processes with geometrically defined cutting edges, such as hard turning [12, 13, 38] or other finishing processes [40]. The main advantages of hard turning include high flexibility, the possibility of complete and dry machining and the elimination of sparking time. The basic prerequisite for successful process substitution is the guarantee of component function, which is significantly influenced by the properties of the surface. However, hard turned and ground surfaces differ considerably from one another in terms of their topography and the physical properties of the peripheral zone [2, 15, 25]. The feed helix resulting from turning, i.e. the kinematic roughness, represents a pronounced macro-twist compared to ground surfaces. This can lead to a transport of the lubricant depending on the direction of rotation. For a long time, hard-turned SCSs were therefore mostly used only in units with a fixed or dominant direction of rotation [37, 41]. Investigations of machined shaft surfaces have shown the potential to create a tight sealing system and also reduce friction and wear if the right machining parameters are chosen [10, 38]. Experimental investigations require testing of various SCS manufactured with different process parameters, which means the number of samples to be manufactured and tested are high in number. The time involved in machining and also testing the samples is therefore quite expensive. However, the identification and definition of surface parameters relevant to sealing technology, which reflect the influence of the surface finish of SCS on the functional behaviour of the sealing system with sufficient accuracy, has proven to be extremely complex [9].

This is why a simulation model is needed, where a SCS generated by a kinematic simulation can be given as input and the interaction of the topography of the surface finish with the lubricant can be simulated to determine the functional parameters of the sealing system, like conveying action. Using such a simulation, various combinations of the surface finishes of SCS can be investigated to determine and examine the influence of certain critical machining parameters and hard turning methods. With this knowledge, a reduced number of targeted experiments can be planned, with specific critical parameters and specific hard turning methods. This saves time, effort and is more cost effective than testing all combinations of relevant machining parameters of hard turning. Simulations of the lubrication of a sealing contact usually involve a full elastohydrodynamic simulation, where the hydrodynamic action of the lubricant, but also the deformation of seal and shaft, are considered [33, 39]. For the numerical evaluation of the averaged effect a rough surface imposed on lubricant flow, patir and cheng have introduced flow factors [29, 30]. They describe the ratio of the flow between smooth surfaces compared to the flow between rough surfaces for flow driven by a pressure gradient or the shearing motion due to sliding of one or both surfaces. The evaluation of flow factors usually involves hydrodynamic lubrication simulations of the smooth and rough case. harp and salant have expanded the flow factor calculation by using a mass conserving cavitation model and applied it to radial shaft seals [17]. rocke and salant developed a method taking into account the angular distortion of the seal roughness due to shear forces [33]. An other option is to model the surface roughness using analytical functions. Most of such models take into account the seal topography and neglect the shaft roughness [22, 35], in order to prevent the need of a more time consuming and numerically less stable transient simulation. When the shaft topography shall be considered, usually the seal roughness is neglected [14, 19]. Only few researchers have implemented transient simulations considering the topography of both shaft and seal yet [11, 39]. Those simulation models however, have a high calculation cost and time and are not always numerically stable, especially in the mixed friction region [39]. This greatly reduces the ability to apply those detailed models for the prediction of the influence of the shaft surface on the conveying effect of the shaft from the manufacturing parameters in a setting outside of academia.

In this paper a simplified hydrodynamic model is described where the surface topography of the seal and deformation in general are neglected in order to investigate solely the influence of the SCS topography on the fluid conveyance. These simplifications allow for much easier application of the model, especially outside of the academic setting. To allow for the estimation of the conveying behaviour of SCS before manufacturing, SCS generated with a kinematic simulation model of the machining process are used as input. Since the focus is to study the influence of different surface finishes of SCS on the conveying value, we assume a smooth rigid surface as contact partner, instead of a rough deformable seal surface. Thus, the simulation model is reduced to the elements necessary to study only the influence of the SCS finish. The advantage of this approach is a significant reduction of calculation cost and time, while the disadvantage is the aforementioned neglection of the seal topography and deformation and thus the loss of predictive capabilities regarding friction and the overall pumping rate of the whole sealing system. In cases where the behaviour of the whole sealing system, including effects from the seal, is to be investigated in detail, those simplifications should not be used.

In order to verify and validate the simulation model, experiments with samples of the same surface finishes of the SCS that were simulated, are carried out.

The SCS kinematic simulation serves as input for the hydrodynamic simulation. It is built on a dexel based model which was first introduced and described for the simulation of milling operations in [4, 5]. Since physical effects such as burr formation, chipping as well as cutting forces or temperatures are not considered it is called ’kinematic simulation’. The tool, which is represented in simplified form by its cutting edge contour, is moved through the workpiece volume according to its movement trajectory. Any intersecting volume is subtracted from the workpiece volume leaving a track of the cutting edge. The simulation is implemented by modelling both workpiece and tool in a dexel-based data model. For the current investigations the simulation principle was adjusted for turning operations. Using this model, the surfaces were simulated according to Table 2.

Variations include different values for feed, corner radius, shaft diameter and as the comparison of conventional cutting tools vs. cutting tools with special wiper geometry, which is used to produce a reduced surface roughness compared to conventional tools [7]. Variants 9 and 10 use the same machining parameters as variant 3 and 4, the only difference is the use of a wiper geometry instead of a tool with a conventional corner radius (Fig. 4). This results in significantly reduced values of roughness Rz and is expected to also influence the conveying action.

As long as the shaft diameter remains constant, the twist angle only depends on the feed (see Table 1). Therefore, variants 3.1 and 3.2 with 40 mm and 100 mm shaft diameters and consequently different twist angle as variant 3 have been investigated as well.

The variants listed in Table 2 were also manufactured in order to perform reverse pumping experiments. The amount of possible experiments was limited and did not permit investigation of further parameter sets. The alloyed case hardening steel 16MnCr5 was used for the investigations. The specimens were in case-hardened state (hardness 56 HRC, case hardness depth 0.8 mm). After pre-machining, the specimens were characterised by a diameter of 80.1 mm. For the machining experiments, cubic boron nitride (CBN) tipped indexable inserts of the type CCGW09T3 were used. The cutting material of the inserts contains approx. 65%–70% of CBN particles with an average grain size of 4 \({\upmu}\)m and TiN as binder. Furthermore, the inserts are coated with a TiAlN/TiCN layer offering a thickness of 2 \({\upmu}\)m. Standardized indexable inserts with a clearance angle of \(\alpha=7\)°, a rake angle of \(\gamma=0\)° and a tool included angle of \(\epsilon_{r}=80\)° were used. The cutting edge contains a negative chamfer with a width of 0.12 mm and a chamfer angle of 25°. In combination with the tool holder used a tool cutting edge angle of the minor cutting edge of \(\upkappa\)m\({}_{r}\)’ = 5° results. In addition to the feed rate, the corner radius (\(r_{\epsilon}\)) was varied in three equal steps in the range from 400 \(\upmu\)m to 1200 \(\upmu\)m in order to investigate the influence of different kinematical surface roughness on the hydrodynamic properties. Furthermore, standardised indexable inserts with a wiper geometry were used. They contain an arc-shaped transition from the corner radius to the minor cutting edge that is visualized in Fig. 4 in comparison to a standard geometry without modified minor cutting edge. The radius of this arc is significantly larger than the corner radius and determines the theoretical roughness. Thus, a significantly smaller surface roughness can be achieved with the same cutting parameters. An additional advantage of this wiper geometry form is that it is less sensitive to deviations from the theoretical cutting edge angle of the minor cutting edge. The machining experiments were conducted on a precision lathe of the type SPINNER PD 32. In the finish machining experiments the feed was varied as shown in Table 2. Lower feeds should lead to a decrease of the kinematical surface roughness and thus to a smaller reverse pumping value. The cutting speed and the depth of cut were kept constant at 180 m/min and 0.05 mm, respectively, since they do not change the outcome of the kinematic simulation. This last turning step was performed without any lubrication as it is usual for hard machining of steels. The geometrical properties of the machined surfaces were measured using a stylus instrument type Mahr LD 120. The stylus was characterized by a spherical radius of 2 \({\upmu}\)m and an included angle of 90°. After finish machining, the surface roughness of all specimens was measured at three positions offset by 120° in the circumferential direction with respect to the direction of the feed motion. The measuring length was 4 mm. The filtering of the profiles was done in accordance with ISO 11562 [18].

The flow simulation model was built in MATLAB based on the equations discussed in Sect. 2. The structure of the model is shown in Fig. 5. The kinematic model of the SCS is used as input for the flow simulation model.

The size, the orientation and the position of the simulation area in the kinematic model influence the results of the hydrodynamic simulation. In order to perform the numerical calculations, the simulation domain needs to be represented by a grid with a given resolution, which is limited by the computer’s computational power and memory. In our case, a regular grid with equally spaced elements is used.

Since the twist angle is extremely small, the cross section of the turning structure can not be represented with good accuracy, using a reasonable resolution. This is because of the difference in the orientation between simulation area and the twist of the surface.

If the grid is oriented along the axial (\(y\)) and circumferential (\(x\)) direction, as it usually is in similar applications [39], the minimum twist angle \(D_{\gamma}^{\text{min}}\) that could be represented by such a grid on a simulation area can be calculated as follows : with \(dy\) as distance between grid points in axial (\(y\)) direction and \(l_{x}\) as length of the simulation domain in circumferential direction. In order to satisfyingly represent the geometrical features of the twist structure, an significantly higher resolution would be necessary, which would strongly depend on the twist angle. With the grid described in Sect. 6.1 follows \(D_{\gamma}^{\text{min}}=0.0099\), which is not \(\ll D_{\gamma}\) of the investigated shafts (see Table 2).

In such a simulation domain and grid, this resolution dependence leads to a poor representation of the shaft surface geometry as can be seen by the step-like variation in height of the profile across the circumferential direction in Fig. 6.

To eliminate this problem the grid is oriented along the twist direction as shown in Fig. 6b. Thereby, the dependence of the grid resolution on the twist angle and also the poor representation of the shaft surface can be eliminated.

Based on this approach, the surface data for the planned SCS variants were simulated. The rotation of the simulation domain by angle \(D_{\gamma}\) also requires that the surface velocities in relation to the simulation grid \(u\) and \(v\) are recalculated (with \(u^{\prime}\) and \(v^{\prime}\): axial and circumferential direction in local coordinate system of the shaft, see also Fig. 13): The same must be taken into account, when analysing the flow velocities in the lubrication gap, which can be calculated from the simulation results.

In order to determine the influence of the machining parameters on the conveying action of the hard turned samples and also for comparison with simulation results, reverse pumping values of shafts finish-machined with different combinations of cutting parameters were evaluated and studied to conclude on the cutting parameter dependencies. RSS of type BAUM 5X7 80-100-10 made of the fluoro-elastomer 75 FKM 585 and a PAO lubricant with SAE viscosity grade 0W-20 (\(\eta=14.27\) mPas at 70 °C) were used for all investigations.

A simplified hydrodynamic simulation model has been set up to investigate the effect of different machining parameters on the function of shaft surfaces in sealing systems using radial shaft seals. The simplifications include the neglection of seal topography, deformation, force balance and mixed friction. The fluid conveying effect in axial direction has been investigated in shaft surfaces generated with a kinematic turning simulation model.

Using the model, it could be shown that the axial flow rate, which represents the conveying effect of the surface within a sealing system, strongly depends on the shaft roughness Rz and the conveying cross sectional area DF and also slightly on the twist angle \(D_{\gamma}\) and the feed \(f\). The investigation of additional parameter sets was not possible in the scope of the work presented in this paper but could improve and expand the findings further in future work.

A comparison to measured reverse pumping values of hard turned shaft surfaces shows that the simulative predictions for the axial flow rates fit well with the behaviour in a real sealing system. Deviations between the results of flow simulation and reverse pumping value measurement were shown to be caused by differences between the roughness of simulated and manufactured shaft surfaces.

The proposed simulation model can be applied to pre-estimate the effects of the different machining parameters on the conveying action of a shaft in sealing systems and thus allow manufacturers to pre-select promising parameter sets. The model will also be used to investigate shaft surfaces generated with special turning kinematics, which are supposed to generate a lead-free surface in our upcoming research.