3,000 rpm up to 30,000 rpm. Typical stationary applications include spindle drives or turbo compressors. They are increasingly being used as high-speed direct drives, Science and Research 22 Tribologie + Schmierungstechnik · volume 71 · issue 1/ 2024 DOI 10.24053/ TuS-2024-0004 Introduction and motivation Brake rotors and static pressure plates, which are pressed together during the braking process, are a constructive component of a large number of common brake designs. According to the classification by S CHLECHT , B. [1], these brakes fall under the category of multi-disc brakes with axially displaceable braking surfaces. Common types include multi-disc solid brakes, permanent magnet brakes and spring-applied brakes, which cover a wide range of applications from industry to e-mobility and materials handling. Miniaturisation and cost reduction are development efforts in drive technology across all industries and thus represent an important aspect in the development of brakes. Particularly due to the increasing spread of electrically controlled drives that can also decelerate drive trains recuperatively, permanent magnet brakes and spring-applied brakes are now mainly in demand as emergency and holding brakes. Although these are necessary, they are rarely used and are therefore subject to increased cost and installation space pressure [2], [3]. The increasing number of mobile applications also promotes the demand for brakes of increasingly high power density [4]. In addition, the field of application of high-speed drives is constantly expanding due to their favourable ratio of material used to output power; they are now available in a wide power range from 0.1 kW to several MW [5]. High-speed drives have a much higher rated speed than the typical industrially used speeds, from well over Investigation of the friction and deformation behaviour of high-speed brakes Magnus Schadomsky, Johann Rauhaus, Lars Blumenthal, Detmar Zimmer, Balázs Magyar* submitted: 18.09.2023 accepted: 19.03.2024 (peer-review) Presented at the GfT Conference 2023 Spring-applied brakes are widely used components in industrial drive systems. They provide a braking torque by friction between a mostly organic friction lining and a metallic counter surface. Increasing with decreasing size, they currently achieve speeds of up to 6,000 rpm, which corresponds to a sliding speed in frictional contact of up to 35 m/ s. At the same time, there is a trend towards high-speed drives, with speeds of 10,000 rpm and above. So far, little is known about the behaviour of the friction value and torque of conventional spring-applied brakes with low-cost organic friction linings under these operating conditions. For this reason, a test rig was developed that allows testing at sliding speeds of up to 120 m/ s with different load inertias. The tests carried out at KAt so far showed that with limited friction work, the conventional spring-applied brake reaches the nominal braking torque at higher sliding speeds. In addition to thermal overload of the friction lining, plastic deformation of the friction bodies can also permanently disrupt the operating behaviour of brakes operated at high sliding speeds. The plastic deformation of the friction discs manifests itself, for example, in a saucer-like shape of the discafs, leading to a reduction in the air gap and causing unwanted changes in the friction conditions. This paper describes the relationship between friction work and friction coefficient in organic linings and the physical mechanism of the deformation process of the friction discs. Based on these possible measures to reduce deformation are explained. Keywords spring-applied brake, brakes, High speed brakes, High speed friction, saucer-shaped deformation, thermal deformation Abstract * Magnus Schadomsky, M.Sc. Johann Rauhaus, M.Sc. Lehrstuhl für Konstruktions- und Antriebstechnik (KAt), Universität Paderborn, 33098 Paderborn Lars Blumethal, M.Sc. Prof. Dr.-Ing. Detmar Zimmer, ehemals Lehrstuhl für Konstruktions- und Antriebstechnik (KAt), Universität Paderborn, 33098 Paderborn Prof. Dr.-Ing. Balázs Magyar Lehrstuhl für Konstruktions- und Antriebstechnik (KAt), Universität Paderborn, 33098 Paderborn which means that the gearbox which translates into high speed can be dispensed with. [5,6] This trend is supported by the development of high-speed asynchronous machines [6,7,8], which in relation to other types of drives are characterised by their simple design and the resulting low-cost production [9]. In the field of brake motors, high-speed drives have not yet become established. On the one hand, this is due to the often non-existent speed requirement. Furthermore, the brakes typically used are not designed for high speeds. In applications where installation space and mass are not an essential criterion, conventional brake motors will continue to be used because of the low-cost standard asynchronous motors. However, fast-running brake motors become technically relevant in applications in which high dynamics play a role and the drive itself is also moved. Furthermore, in geared motors, increasing the transmission ratio in conjunction with a faster-running motor can have a positive effect on the costs of the drive system by saving copper in the motor and brake. Given the outlined application scenarios, the development of brakes with high power density and thus high sliding speeds in frictional contact becomes relevant. This is not only a challenge from a design point of view; due to the scaling of the size with constant power, various physical problems arise. The following types of damage are described in the literature: • Hotspots: Point by point, significantly increased temperatures on the brake disc. A NDERSON , E. et al [10] describe four different types of hotspots and their consequences, e.g. structural transformation. • Hotbands: Ring-shaped areas of significantly increased temperature [11]. • Sinter carry: Increase in the coefficient of friction due to seizure of friction material and the brake disc [12]. • Fading: Collapse of the coefficient of friction due to overload and thus damage to the friction material [13]. • Melting of the friction lining in the case of organic friction materials and transfer to the pressure plate. • as well as lining detachment in the case of lining discs [14]. The aim of this paper is to investigate the potential of the currently used standard spring-applied brakes with their low-cost organic friction linings for applications in higher speed ranges. Furthermore, the deformation of the pressure plates due to high temperatures in frictional contact will be investigated. State of science and technology Spring-applied brakes The spring-applied brake is mainly mounted directly on the B-side of an electric motor. The design corresponds to the disc brake, the braking force is provided by pretensioned compression springs acting on the armature disc (Figure 1). The braking torque is generated by frictional engagement between the friction linings of the rotor, the armature disk and the B end shield of the motor, which is usually protected by a friction plate. The friction system generally consists of organic friction linings in combination with steel or cast counter surfaces [15]. The brake is released electromagnetically by energising the coil. Thus, the brake is linked (closed) in the de-energised state. This design implements the closed-circuit current principle. Figure 1 shows the two possible switching states of a conventionally designed spring-applied brake. The braking torque of a spring-applied brake is calculated according to (1). (1) Legend: T B Nominal braking torque F F Spring force r m Friction radius µ Friction coefficient z Number of friction surfaces = Science and Research 23 Tribologie + Schmierungstechnik · volume 71 · issue 1/ 2024 DOI 10.24053/ TuS-2024-0004 Figure 1: Basic construction and mode of operation of a spring-applied brake cient of friction collapses. The damage to surface elements is also the mechanism that determines wear. The decisive factor for the thermal load of a friction lining is the friction power, which in turn is influenced by other variables such as friction speed, contact pressure or inertia. It decisively determines the temperature in the friction contact and thus influences the balance between damage and regeneration of the surface elements. [18] It is known that an impermissibly high friction work during braking leads to a collapse of the friction coefficient and subsequently the braking torque. High temperatures caused by excessive friction power can also have a negative effect on the friction coefficient. [16, 18] In general, the thermal load of friction linings is determined by the following variables: - Temperature in frictional contact, - Specific friction work (2), - Specific friction power (3), whereby the respective influence depends on the load constellation. [18] (2) (3) Legend: q Specific friction work J Inertia ω Angular speed A Friction surface of a brake lining q˙ Specific friction power T B Brake torque z Number of friction surfaces Above approx. 350 °C, the organic compounds of the friction linings decompose, which is why other materials are used for application scenarios with very high thermal loads, such as racing clutches. Sintered metal, carbon fibre or ceramic materials can withstand higher temperatures, but have a significant cost disadvantage. [17,20] A LBERS , A. et al [20] shows that there is a need for research into the systematic understanding of the performance limits of organic friction linings and has developed a test concept in which sliding speeds of up to 40 m/ s can also be considered. Saucer-shaped deformation Another effect that can become problematic with increasing power density is the saucer-shaped deformation of the pressure plate, also known as thermal shielding [21, 22]: As a result of the unilaterally converted frictional power during a braking process, the pressure plate heats up and = 2 = Science and Research 24 Tribologie + Schmierungstechnik · volume 71 · issue 1/ 2024 DOI 10.24053/ TuS-2024-0004 The spring force is applied by a variable number of compression springs and is approximately constant due to the small pitch of spring required. The average friction radius would be mathematically the average radius at the lining ring averaged over the surface. In reality, however, it has been shown that the effective friction radius wanders and so that the braking torque is also uneven [16]. The friction coefficient depends mainly on the friction partners, but it is also influenced by other parameters such as temperature, contact pressure or sliding speed. Commercially available spring-applied brakes usually have two friction surfaces. Organic friction linings In the case of organic friction linings, the carrier matrix of the friction lining consists of elastomers or synthetic resins into which fillers with various functions are introduced. These are abrasives to increase the coefficient of friction, lubricants to reduce wear and fibres to increase strength and thermal resistance. The temperature resistance of the carrier matrix and the fibres significantly limits the thermal load capacity of the friction lining. The coefficient of friction collapses under thermal overload. Organic friction linings are used in clutches and springapplied brakes, among others, in spring-applied brakes often with a high rubber content. [16,17,18] The coefficients of friction are usually given for sliding speeds up to a maximum of 20 m/ s; data for higher sliding speeds are rarely found. Friction systems with organic friction linings form a friction layer on the surface during wearing in, which significantly influences the behaviour of the friction coefficient. The generally low thermal conductivity of organic friction materials leads to a high temperature at the friction surface, especially when they run dry, i.e. are enclosed by the insulator air. Due to these short time high temperatures of locally up to 800°, the highly carbonaceous friction layer with a thickness of 0.001 - 20 µm is formed. This friction layer has a decisive influence on the behaviour of the friction value; at the same time, it serves as a thermal protective shield for the friction lining underneath. If the friction lining runs in under constant thermal load, the friction layer stabilises after a certain number of braking operations and thus also stabilises the coefficient of friction. If the thermal load changes, the behaviour of the friction layer and thus the coefficient of friction also changes. [17, 18, 19] The model according to SEVERIN, D. [18] considers the surface elements of the friction layer: Here, a surface element participates in the friction force transmission until it is damaged. Then it regenerates and after a certain period of time it starts to wear again. If damage and regeneration of surface elements are in equilibrium, the coefficient of friction remains constant. If the thermal load increases unacceptably, more surface elements are damaged than regenerated. The result is that the coeffiexpands on one side. If thermally induced stresses in the pressure plate exceed the yield point of the material, irreversible plastic deformation occurs. The decrease of the yield point at high temperatures additionally favours the plastic deformation. Figure 2 shows the resulting shape of a plate that is inclined towards the friction surface. Such a set-up entails various problems: Compared to the non-saucer-shaped state, the air gap is reduced when the brake is open. On the one hand, this can lead to unwanted dragging of the brake; on the other hand, the compensation of the reduced gap requires an increase of the actuation travel, which is by design not always possible. In the braked state, the saucer-shaped deformation leads to changed friction conditions: As a result of the change in geometry, instead of a friction surface, there is cantilevering in the outer area of the friction surface provided by the design. This causes an increase in the friction power density and can lead to thermally induced friction lining damage, breakage of friction lining due to increased surface pressure, uneven wear and noise development or metallurgical changes [10]. Due to the shift in the effective friction radius, the braking torque deviates from the brake’s design braking torque. The thermal build-up of individual components of brakes is well known and has already been mentioned several times in the literature: B ESTLE , H. et al. [21] describes thermal distortion on armature discs and flange surfaces of spring-applied brakes and attributes this to unilateral heating, which causes unilateral expansion of the components. As a proposed solution, B ESTLE , H. et al [21] lists a radial reduction of the friction surface, which, however, appears to be practicable only to a limited extent due to the high friction power density. B REUER , B. et al [23] describe the thermal build-up of unilaterally bolted brake discs of vehicle brakes, which can be avoided by allowing radial expansion using an axially floating bearing. A UDEBERT , N. et al [24] have investigated the saucershaped deformation of clutch discs in automatic transmissions and deduced that it depends on a dimensionless geometric shape factor that can be used to predict the tendency of a saucer-shaped deformation as a function of temperature differences at the brake disc. X IONG , C. et al [22] have developed a calculation method for determining the critical temperature-related moments in the pressure plate based on the curved beam model. So far, however, the literature does not show any solution approaches with which the tendency to saucer-shaped deformation can be reduced for a given geometry and braking energy. Objectives and procedure In the state of the art section, the problems of organic friction linings and pressure plates in high-speed brakes Science and Research 25 Tribologie + Schmierungstechnik · volume 71 · issue 1/ 2024 DOI 10.24053/ TuS-2024-0004 Figure 2: Problems due to saucer-shaped deformationa brake open, b brake closed inertia to be braked can be represented by the drive, but in this configuration the maximum braking torque is limited to the motor torque multiplied by the installed gear ratio. Therefore, a flywheel mass module can be installed as an option, which can represent load inertias at large braking torques. This is followed by the brake module with the connection for the brake to be examined and the measurement technology. Alternatively, the brake can also be attached directly to the gearbox output of the drive module. The test stand data are listed in Table 1. Investigation of the friction torque development of organic friction linings at sliding speeds up to 50 m/ s The load on the friction components during braking is influenced by various parameters, such as speed/ sliding speed, braking torque, surface pressure, friction work and ambient temperature. To get an overview of the possible range of use in high-speed applications, the parameters speed from which braking takes place and friction work are varied. This also adjusts the friction power. In conjunction with the sliding speed and the specific friction work, comparability with other geometries can be established. The remaining influencing parameters are kept constant by always using the same brake in the same configuration and the laboratory environment. The brake data are listed in Table 2, the speeds to be investigated are specified in Table 3. Science and Research 26 Tribologie + Schmierungstechnik · volume 71 · issue 1/ 2024 DOI 10.24053/ TuS-2024-0004 during operation were highlighted. The aim of this paper is to investigate to what extent higher sliding speeds can also be achieved with organic friction linings and what measures can be taken to reduce the saucer-shaped deformation of pressure plates. This is done as follows: - Description of the test technique - Investigation of the friction torque development of organic friction linings on the basis of a spring-applied brake at sliding speeds of up to 50 m/ s under various loading situations. - Derivation of the physical background that leads to the build-up of pressure plates - Development of approaches to reduce the uplift - Experimental investigation of the approaches found - Conclusion Test engineering Figure 3 shows the structure of the modular brake highspeed friction test stand in the form of a schematic diagram. A synchronous servo drive is selected as the drive to provide constant and sufficient dynamics and torque over a wide speed range. In order to achieve the desired sliding speed of up to 100 m/ s in the friction contact, a gearbox is connected downstream of the servo drive; there is a choice of two gear ratios, i = 0.45 and i = 0.22. By default, any load Figure 3: Schematic diagram of brake high-speed friction test rig Drive data: Rated torque 95 Nm Rated speed 4,500 rpm Gearbox 1 Gear ratio 0.45 Output speed max. 10,080 rpm Output torque 42 Nm Gearbox 2 Gear ratio 0.22 Output speed max. 20,000 rpm Output torque 21 Nm Measurement data: Torque, speed, braking force, temperature, axial displacement measurement, current, voltage Table 1: Test bench data The definition of the friction work is based on the definition of VDI guideline 2241-1 [25]. This defines the permissible friction work Q zul for switchable, externally actuated friction clutches and brakes at which thermal overload does not occur. Q zul depends on the switching frequency and the permissible friction work for a single switching Q E . This value depends on the size of the brake; for the spring-applied brake used, Q E is 24,000 J. For each speed, braking is carried out at 5, 12.5 and 50 percent of Q E . This is set via the simulated inertia. Before the start of the tests, the brake was broken in in order to establish a two-dimensional contact between the friction partners and to enable the formation of the friction layer [19]. Figure 4 shows the torque and speed curves of a representative braking from 1,500 rpm and 10,000 rpm each at 12.5 % (lower graph) and 50 % Q E (upper graph). It can be seen that for the braking at 12.5 % Q E , the braking torques at 1,500 rpm (blue) and 10,000 rpm (red) are very similar at about 37.5 Nm. The high Science and Research 27 Tribologie + Schmierungstechnik · volume 71 · issue 1/ 2024 DOI 10.24053/ TuS-2024-0004 Nominal braking torque 32 Nm mean friction radius 46.25 mm max. mean sliding speed 48.4 m/ s Friction surface of one lining ring 6,527 mm² Q E 24,000 J Table 2: Brake data Braking speed in rpm Average sliding speed in m/ s Maximum specific nominal friction power in W/ mm² Specific friction work in J/ mm² for 5% Q E / 12,5% Q E / 50% Q E 100 0.5 0.03 0.09 / 0.23 / 0.92 Ordinary braking torque mean speed 1,500 7.3 0.39 Usual operating speed 3,000 14.5 0.77 Usual operating speed 6,700 32.5 1.73 High-speed braking 10,000 48.4 2.58 High-speed braking Figure 4: Torque and speed curve for braking from 1,500 rpm (blue) and 10,000 rpm (red) with 12.5 % (bottom) and 50 % QE (top) respectively Table 3: Examined speeds/ sliding velocities for organic friction linings an initial sliding speed of 32 m/ s. However, it becomes clear that there are areas where the commercial brake works well even at high sliding speeds. In addition to the torque drop, friction lining adhesions were visible on the counter friction surfaces during braking from high speeds with high energies. This indicates that the friction lining or at least its components were briefly thermally overloaded. In addition, a slight saucershaped deformation of the armature disk and brake flange were observed. No other mechanical damages to the rotor or friction lining due to e.g. centrifugal force were observed. Physical background of the saucer-shaped deformation During the braking process, the pressure plate is heated on one side of the circular friction surface. At high friction power, a lot of energy is applied in a very short time, resulting in a high temperature gradient between the friction surface and the surrounding material (Figure 6 a and b). This causes the material in the area of the friction surface to expand much more than the surrounding material. The pressure plate gets a saucer shape with the convex surface on the friction side. The obstruction of the expansion causes compressive stresses in the heated area and tensile stresses in the surrounding area. If the compressive stresses exceed the yield point of the material, which is reduced due to the high temperature, plastic Science and Research 28 Tribologie + Schmierungstechnik · volume 71 · issue 1/ 2024 DOI 10.24053/ TuS-2024-0004 friction power is apparently well tolerable for small inertias, i.e. for short friction times and the associated low friction work. When braking with 50 % Q E , the braking torque of 10,000 rpm is lower from the start (33 Nm) and drops even further to about 28 Nm at the beginning of braking. Only when the speed drops significantly towards the end of braking does the braking torque rise to about 35 Nm, which is close to the average value for all braking operations. Due to the high inertia, the friction power is at a high level for a longer time period, which seems to have caused the temperature to become too high, at least in the first half of the braking process. This probably damaged the friction layer, which leads to a drop in the friction coefficient and thus the braking torque. However, according to Severin [18], the torque increase at the end of braking suggests a “regeneration of the friction layer”. Figure 5 shows the determined characteristic diagram of the tested brake, in which the friction torque is plotted against sliding speed and friction work. The diagram represents the mean value of five braking operations per operating point. It depicts that at 5 % and 12.5 % QE the braking torques are at the same level across speeds. For braking at 50 % Q E , the braking torque of the high-speed braking drops significantly, especially in comparison to braking at usual speeds and also in comparison to braking with less inertia. The braking torque drops even more significantly at an initial sliding speed of 48 m/ s than at Figure 5: Braking torques shown as a function of sliding speed and friction work compression occurs in the area of the friction surface. In the surrounding area, plastic strain occurs to a lesser extent due to the lower temperature. After cooling, a saucer-shaped deformation remains with the concave surface on the friction side, because the plastically compressed material contracts more than the uncompressed or stretched material in the surrounding area (Figure 6 c). Tensile stresses remain in the compressed area and compressive stresses in the surrounding area. Theoretically, the saucer-shaped deformation should not increase significantly after the first braking, because the thermal expansion from the second braking on initially only reduces the pre-tension in the pressure plate and would secondly compensate for the compression. Only beyond this point does an excess of expansion occur again. However, in a real friction system, a constant homogeneous energy input to the friction surface cannot be assumed, thus changes can still be expected after the first braking. Development of approaches to reduce the saucer-shaped deformation The high stresses resulting from thermal expansion are the main cause for the plastic saucer-shaped deformation. In principle, there are three measures that can, given an unchanged friction lining geometry, reduce the plastic saucer-shaped deformation: - Reducing the thermal expansion - Reducing the stresses caused by expansion - Increasing the stresses tolerable without plastic deformation. In the following, based a reference pressure plate, geometric and material-technical approaches are discussed by which these measures can be implemented. Reference pressure plate The full-surface geometry shown in Figure 7 is used as the reference pressure plate. There are guide noses on the outer diameter to accommodate it in the brake housing. Table 4 summarises the properties of the reference pressure plate. The standard steel S355 with medium strength was selected in order to obtain a cost-effective reference pressure plate. The frequently used cast iron lamellar graphite has an even lower saucer-shaped deformation resistance (see table 5) and was therefore not used as a reference. This means that S355 achieves a good compromise between low saucer-shaped deformation resistance and low costs. Science and Research 29 Tribologie + Schmierungstechnik · volume 71 · issue 1/ 2024 DOI 10.24053/ TuS-2024-0004 Figure 6: Phases of the saucer-shaped deformation process - a during heating, b after heating, c after cooling In the following considerations, the reference pressure plate is compared to the modified pressure plate shown in Figure 8. This has 16 radial slots, each of which is inclined 15° in the direction of rotation of the rotor in order to reduce shearing of the friction lining at the edges. Investigation of material engineering approaches The choice of a suitable material can also assist in implementing the measures for lowering plastic deformation. The identification of suitable materials is aided by an analogy with thermal fatigue strength, which has been documented in the literature, for example, by B ÜRGEL , R. et al [27] in the context of high-temperature materials. There, the considerations of the three measures mentioned are combined in a common consideration. B ÜRGEL , R. et al [27] understand the temporary and locally limited introduction of a high thermal energy into a component, which leads to a high temperature gradient within the component, as a so-called thermal shock. The different local temperatures within the component result in high stresses in the component, which can lead to thermal fatigue damage if the thermal stress is repeated cyclically. To evaluate materials with respect to their thermal shock sensitivity, [27] introduces the thermal stress index χ (4). Science and Research 30 Tribologie + Schmierungstechnik · volume 71 · issue 1/ 2024 DOI 10.24053/ TuS-2024-0004 Investigation of geometric approaches The first measure, reducing thermal expansion, can, from a geometric point of view, be achieved by stiffening the structure. Such stiffening can be accomplished by increasing the pressure plate thickness as well as reducing the inner diameter or increasing the outer diameter. It should be noted that such geometry adjustments lead to additional strain restraint and to larger temperature gradients during heating and may therefore prove counterproductive. Lowering of strain-induced stresses can be obtained by reducing the pressure plate thickness and the radial installation space, as proposed for example by Z AGRODSKI [26] for plates of a clutch. However, both measures contradict the objective of reducing thermal expansion and can therefore also have negative consequences for thermal expansion. Due to the opposing influence of different effects, such adjustments of the pressure plate are only recommended after extensive investigations. Another way to reduce strain-induced stresses is to allow an unhindered thermal expansion. In the case of the present disc geometry, thermal expansion leads in particular to high tangential stresses. The tangential stresses can be reduced by radial slotting from the inside diameter of the friction surface to the outside diameter of the pressure plate. Dimension Value Outer diameter 140 mm Inner diameter 72 mm Thickness 5 mm Outer friction diameter 139 mm Inner friction diameter 90 mm Mean friction radius 57,25 mm Material Structural steel S355 Table 4: Properties of the reference pressure plate Figure 7: Reference pressure plate made of S355 Figure 8: 16-slotted pressure plate made of S355 (4) Legend: χ Thermal stress index R m Tensile Strength λ Thermal conductivity α Coefficient of thermal expansion E E-modulus A material is particularly sensitive to thermal shock if there is a high temperature gradient in the material due to a low thermal conductivity λ. A high coefficient of thermal expansion αcauses large strains which, with a large E-modulus, result in high stresses within the component. This behavior must be considered in relation to the tensile strength of the material R m to determine if the thermally induced stress is critical in terms of potential damage. In the case of thermal saucer-shaped deformation of static compression plates, the thermal conductivity λ, the coefficient of thermal expansion α, and the E-modulus lead analogously to high stresses in the component and thus to severe saucer-shaped deformation. However, since the cause of thermal saucer-shaped deformation is plastic deformation, the yield strength RP must be used as material reference. From this, the saucer-shaped deformation resistance A (5) can be derived according [28]: (5) Legend: A saucer-shaped deformation resistance R p Yield strength λ Thermal conductivity α Coefficient of thermal expansion E E-modulus = R m E A = R p E Table 5 gives an overview of the saucer-shaped deformation resistance A for exemplary materials. According to this, E360AR structural steel is particularly sensitive to thermal saucer-shaped deformation, while little thermal saucer-shaped deformation is to be expected with copper. In reality, however, the choice of a suitable material usually involves compromises regarding function and cost. In the experimental investigations documented below, four pressure plates are compared: • Reference pressure plate made of S355 steel • Slotted pressure plate made of S355 steel • Slotted pressure plate made of 42CrMo4 steel • Slotted pressure plate made of CW004 copper Experiment In order to verify the above approaches, five successive brake applications per pressure plate were performed according to the specification shown in Table 6. After a short low-energy braking-in, five successive braking operations were conducted, each starting at a speed of 14.000 rpm. The plates were subjected to the energy and frictional power specified in Table 3. The cooling phase between the brakings was selected so that the temperature of the pressure plate fell below 70 °C. The saucer-shaped deformation of the pressure plates was measured after the second, fourth and fifth braking operation. The distance to the inner radius of the friction surface and the outer radius of the friction surface were measured at three points of the friction surface at the flat-lying pressure plate using a laser triangulation sensor. The difference between the two distance values is the saucer-shaped deformation at this point. For the over- Science and Research 31 Tribologie + Schmierungstechnik · volume 71 · issue 1/ 2024 DOI 10.24053/ TuS-2024-0004 g y g Parameter Value Friction energy per friction surface 55.5 kJ Maximum friction power per friction surface 43 kW Braking torque per friction surface 30 Nm Speed 14,000 rpm Mass moment of inertia to be braked per friction surface 51,750 kgmm² Table 6: Data of a braking cycle to investigate the saucer-shaped deformation Material group Material saucer-shaped deformation resistance A Source Cast iron lamellar graphite EN-GJL-200 6.8 [29a, 30] Cast iron nodular graphite EN-GJS-700-2 6.2 [29b] Cast steel G10MnMoV6-3 10.3 [31a] Structural steel S355JR 8.4 [32] E360AR 3.4 [31b] Case-hardening steel 16MnCr5 9.1 [31c] Heat-treatable steel 42CrMo4 10.0 [31d, 33] Copper (99.9%) CW004A 21.4 [34] Table 5: saucer-shaped deformation resistance of exemplary materials Figure 10 shows the slotted pressure plate made of CW004A lying next to the S355 reference pressure plate on a measuring plate. On the copper pressure plate, there is hardly any visible saucer-shaped deformation, while in the case of the reference pressure plate made of S355 it is clearly visible to the naked eye. Conclusion and outlook In principle, it can be said that the commercially available friction system investigated can deliver the nominal braking torque even at high sliding speeds, as long as the friction work does not become too great. Thus, the spring-applied brake offers the potential to be used in the application scenarios outlined at the beginning without necessarily having to resort to higher-quality, more expensive friction materials. However, if the permissible scope of application is to be expanded, it is necessary to determine the definition of the permissible friction work as a function of sliding speed, because this takes the frictional power that causes temperature peaks at the onset of braking into account. Science and Research 32 Tribologie + Schmierungstechnik · volume 71 · issue 1/ 2024 DOI 10.24053/ TuS-2024-0004 all assessment, the mean of the three measured values was calculated. The measured values were validated with a feeler gauge measurement. The test results are shown in Figure 9. Qualitatively, they confirm the preliminary considerations. Also, as expected, a large part of the saucer-shaped deformation occurs after only a few braking operations. At 0.42 mm, the reference pressure plate made of S355 exhibits the highest saucer-shaped deformation after five braking operations. The second-highest saucer-shaped deformation is exhibited by the slotted S355 pressure plate with 0.23 mm. Consequently, the saucer-shaped deformation was almost halved by the slotted geometry. The change in material to the higher-strength steel 42CrMo4 again cut the saucer-shaped deformation in half, with a buildup of 0.1 mm. As expected, the copper pressure plate showed the least deformation with 0.04 mm. The small amount of saucer-shaped deformation indicates that the yield stress of the material is not reached over a large area in this pressure plate. The slight deformation is presumably due to local hotspots, through which the yield stress is exceeded selectively. Figure 10: Slotted pressure plate made of CW004 (left) and reference pressure plate made of S355 (right) lying on a measuring plate Figure 9: Test results of the saucer-shaped deformation The experimental investigation has confirmed that the solutions presented to reduce thermal deformation are effective. By introducing radial slots, it was possible to halve the buildup for identical material. Further reductions in the saucer-shaped deformation could be achieved by selectively adjusting the material on the basis of the saucer-shaped deformation index. It was also shown that the deformations can be further reduced with an increasing saucer-shaped deformation index, meaning there is a qualitative relationship between the saucer-shaped deformation index and deformation. In addition to the approaches presented here for reducing plastic deformation, more advanced approaches are also conceivable: For example, by training the pressure plates prior to the initial braking process, a stress state could be specifically set that compensates for the resulting stresses causative for the deformation. Pressure plates whose initial geometry is opposite to the resulting saucer-shaped deformation (tapered friction surface) could be deformed by the saucer-shaped deformation in such a way that their friction surfaces are approximately flat. Both approaches require precise knowledge of the expected load and saucer-shaped deformation and can therefore require adequate elaborate preliminary investigations prior to implementation. In summary, it can be stated that the saucer-shaped deformation of pressure plates that are subjected to a high energy input on one side can be significantly reduced by introducing radial slots. The effect of the slots is that thermal expansion due to the high energy input is possible, thus reducing stresses. This should be the first measure to be applied in practice. Further reductions in saucer-shaped deformation can be achieved by an adapted material selection. Since steel materials are predominantly used in practice, the recommendation is to select a material with higher strength while maintaining good thermal conductivity. Literature [1] Schlecht, B.: Maschinenelemente 1 - Festigkeit, Wellen, Verbindungen, Federn, Kupplungen, München: Pearson Studium, 2005 [2] Eitel, L.: (2016) „Trends in clutzches and brakes leverage software and customization. MOTION CONTROL TIPS“, https: / / www.motioncontroltips.com/ trendsclutchesbrakes-leverage-software-customization, 2016, Zugriff am 02. 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