Transactions on Engineering Sciences vol 1, 1993 WIT Press, ISSN

Transcription

1 Contact analysis in clamping-roller free-wheel clutches K. Diirkopp, W. Jorden Laboratorium fur Konstruktionslehre, Uni-GH- Paderborn, D~4 790 Paderborn, Germany ABSTRACT Free-wheels are coupling devices which index depending on their direction of rotation. The most important types used in industry are frictionally engaged. In the design of such machine parts an exact knowledge about the tribological system is mandatory for optimizing the system behaviour. The clamping zones of roller clutches have been tested in various recent research programs considering friction and wear behaviour as a result of contact processes by the Laboratorium fur Konstruktionslehre (LKL) at the University of Paderborn. This contribution will focus on the unique tribological system in a clamping-roller free-wheel clutch. Furthermore, this paper addresses the processes in contact during torque transmission. INTRODUCTION Free-wheels are self-instructing clutches. Whether the torque is transmitted depends on the direction of rotation. In one direction, the driving part rotates the driven part. When the direction of rotation is reversed it disengages itself automatically from the driven part. Free-wheels may be employed as overrunning clutches, backstops or indexing clutches. Frictionally engaged free-wheels are mostly used in industry. In this group of clutches, the clamping-roller free-wheel is one of the more important types. A typical example of the structure of this type of clutch is shown in figure 1. It has a star-shaped inner race with six plane ramps, bearings and a flange. As shown in figure 1, a grip roller clutch is built up of several evenly spread grip zones. The functioning of the whole system depends on how each of the clamping zones involved fulfills its task. Therefore, the conditions in a single clamping zone and especially the contact mechanisms have been examined, in order to be able to describe the whole systems behaviour.

2 436 Contact Mechanics Figure 1: Clamping-roller free-wheel clutch with star- shaped inner race, clampingrollers, springs, bearings and flange. EMPIRICAL TESTS AT A CLAMPING ZONE Until recently there have been hardly any empirically valid test results concerning the specific friction and wear behaviour of free-wheels [1]. Test stands were developed at the University of Paderborn by the LKL on which the specific structure of a single clamping zone is simulated (figure 2). The test stands simulate the indexing behaviour of a roller clutch in which the torque transmission is initiated by a star-shaped inner race [2,3]. Figure 2: Design drawing of the test stand [3].

3 Contact Mechanics 437 To get Wohler fatigue curves, many experiments were made with several different parameter combinations aimed at testing the fatigue life that can be expected. The results are representable in Wohler diagrams. Mainly the following parameters have been varied: motional conditions (indexing frequency), Hertzian stress level, materials, the grade of roughness and the lubricants. The samples employed show forms of wear which are typical in free-wheels like pittings, scoring, plastic deformation and smoothing. Not only fatigue life tests were carried out, but also research on the coefficient of friction. This was especially necessary since during the fatigue life tests, and in engineering practice as well, the grip roller sometimes suddenly pops out of the clamping gap although there are not necessarily strong tokens of wear. In this cases the fricitonal forces involved are not strong enough to hold the grip roller in the clamping gap. So besides of the results from wear, low coefficient of friction is also a possible source of failure of the free-wheel. First systematic tests concerning the frictional problems have also been carried out by LKL in a test stand for a model free-wheel. During this tests the angle of inclination of the clamping ramp was widened, so that the clamping roller popped out. The normal and tangential forces were measured from which the fricitonal force can easily be determined. By continual repetition of the experiment under varying parameters it is possible to come to empirically determined results about the coefficient of friciton. Recent research at the LKL seeks to verify the fatigue life times so determined as well as the measured friction by means of comparative tests of real free-wheels. These empirical studies concerning friction and wear are supposed to lead to an approach for mathematical calculation of the tribological system of the clamping-roller free-wheel. The determined data allow deduction of the coefficients for a mathematical model. Models of calculation for friction and wear in a clamping roller free-wheel are yet only available in approaches of smaller range [2, 3, 4]. A complete description of the relations in the whole system of the clamping-roller free-wheel has not been determined, yet. A detailed analysis of processes concerning the places of contact, however, is supposed to make such an approach possible. THE CLAMPING ZONE AS A UNIQUE TRIBOLOGICAL SYSTEM Figure 3 shows the main construction elements (outer race, grip roller and ramp of clamping) and the forces which appear during the torque transmission. (The spring (see figure 1) and the forces which arise from it is not considered here since the forces are very small in comparison to those which appear during the torque transmission.)

4 438 Contact Mechanics 2a Figure 3: Structure of a single clamping zone a: inner race with ramp, b: roller, c: outer race, rj inner radius of the outer race, d%: roller diameter; F: resultant force during torque transmission, F^: normal force, Fj tangential force, a: grip angle There are only simple connections between the main interesting parameters. The tangential forces determine the transmissible torque. The torque can be calculated from: T-nr^F (1) where F^ is the tangential force, r^ the inner radius of the outer race and n the number of clamping zones. The torque can only be transmitted if the factional forces in the clamping zone given by F, = HF. (2) (where [i is the coefficient of friction and F^ the normal force) are higher than the tangential forces F = F^ tan a (3) (a is the clamping angle). We can infer from this the principal conditions for a perfect functioning which can be expressed by the condition for friction: tan a < i (4)

5 Contact Mechanics 439 If this condition is not fulfilled, the roller cannot hold itself in the clamping gap. Then either the forces are not built up in the beginning of the indexing period or the roller pops out of the clamping gap, which is possible if the clamping angle is too wide (which can happen under load). The functioning of the free-wheel is thus, on the one hand, dependent on the geometrical conditions (tan a) and, on the other hand, on the frictional conditions ( i) in the clamping gap. Considering in addition the speed and force curves (figure 4) during an indexing period, it becomes apparent that the clamping zone in a free-wheel roller clutch has to be looked at as a special tribological system [4]. While free-wheeling, the grip roller is moved away from the clamping gap (period I). The frictional forces involved rotate the roller. At the beginning of the indexing period (II), the clamping roller is first braked and then increases its speed in the reversed direction when it rolls into the clamping gap (Ha). Each coupling operation requires the penetration of the lubricant film by the grip rollers. At the places of contact of the roller various tribological states can be distinguished: Several states are involved, running from perfect lubrication to different partial states to dry friction. free-wheeling blocking Figure 4: Speed- and force curves during the indexing period at the clamping zone I: free running period, II: indexing period, IIj increasing force, 11^: block, 11^: decreasing force, 0)%: circumferential of the grip roller, F: forces on roller

6 440 Contact Mechanics Obviously the functioning of the clamping process depends on specific tribological conditions, which are different from those of other machine elements. Thus the well documented test results of wear and friction conditions in, for example, roller bearings and the mathematical approaches concerning these can hardly be used for our purpose. To provide the basis for the development of a complete model which fits for the description of the free-wheel, detailed analysis of the special relations at the places of contact in the free-wheel clamping zone is carried out. NUMERICAL APPROACHES The forces which occur during the torque transmission (while dry friction predominates) evoke elastic deformations and pressings, which influence the basic conditions of functioning (equation (4)). This concerns the change of the geometry of clamping on the one hand (tan a), the conditions for the coefficient of friction on the other ( i). It is promising to analyse the system free-wheel as a whole as well as the special places of contact of the clamping gap in detail by means of the finite element method. To give an overview of the complete system's behaviour, a simple modelling of a clamping-roller free-wheel was chosen (figure 5). First results about the influence of the macro-geometric proportions can be won by help of this modelling. Figure 5: FEM model of a roller clutch Figure 6: Net structure of a clamping roller To get more insights in the circumstances at the free-wheel clamping zones, in a further step of specification the relevant engaged geometries in the places of contact are to be modelled in greater detail. For the verification of the modelling and the calibration of the results, referential data are to be considered. The Hertzian stress theorie can be taken for comparison. With the example of a clamping roller (figure 6), further proceeding can be illustrated.

7 Contact Mechanics Q!O \0 2.0 Normalized contact length Figure 7: Iterative calculation of the value of the trace of contact In the beginning of the analysis, the value of the trace of contact, the displacements, as well as the spreading of the pressings are unknown. When the values for load working on a clamping roller and a trace of contact are presupposed arbitrarily, the remaining displacements can be calculated. From the results of the finite element calculations it can be deduced whether the estimated trace of contact is too big or too small. Figure 7 shows a sample-calculation. It becomes evident that outside of the estimated trace of contact displacements were calculated which go beyond the level of the plane, which has to be regarded as fixed. This would be a penetration which does not correspond to reality. So the presupposed trace is too small, a bigger one has to be taken as basis. The value of the total deformation energy provides hints, too, whether the calculated trace of contact was estimated correctly. In case of the correct value, the total deformation energy reaches a minimum (figure 8). * 30- CD CD C o " 83 2QH Fn=4000N o!o 0\ Normalized contact length Figure 8: Deformation energy

8 442 Contact Mechanics In this way it is possible to iteratively approach the real place of contact. The finally determined results can be compared with the calculations by Hertz (figures 9 and 10) and therefore the net built up from finite elements can be calibrated. -VOO Normalized contact length Figure 9: Hertzian stress Normalized contact length Figure 10: Pressings with FEM When these basic values for the numerical calculation have been found, the places of contact in our model can be stressed with a load as in real free-wheels and be analysed. At the place of contact, not only high normal forces but also high tangential forces arise (figure 3). Changes in the clamping geometry under load can be deduced from the finite element calculations. By well-aimed analysis of the places of contact, the elementary conditions for the relations of friction can be derived. So modelling a single place of contact in a clamping zone provides insight in the working of a free-wheel roller-clutch as a whole. Empirical results as well as analysis by FEM contribute to completing our knowledge about the tribological system of aroller clutch. The expected test results can help to avoid overdimensioning as well as to realize higher loads and longer fatigue lives parallel to smaller sizes. REFERENCES l.jorden, W.: Gebrauchsdauer von Klemmfreilaufkupplungen. Konstruktion Vol. 12, pp , Schlattmann, J.: Lebensdauerermittlung von Klemmrollenfreildufen aufgrund von Werkstoffverformung, -ermildung und Wdlzverschleifi. Fortschr.-Br. VDI Reihe 5 Nr. 100, Diisseldorf, Bohnke, H.-J.: Untersuchungen zum Schmierstoffeinflufi auf die Lebensdauer eines Klemmrollenfreilaufes im Schaltbetrieb. Diss., Universitat-GH-Paderborn Tonsmann, A.: Der Einflufi des Schaltverschleifies auf die Schaltgenauigkeit von Klemmrollenfreildufen. Diss., Universitat-GH-Paderborn 1989