Acta Polytechnica doi:10.14311/AP.2018.58.0017 Acta Polytechnica 58(1):17–25, 2018 © Czech Technical University in Prague, 2018 available online at http://ojs.cvut.cz/ojs/index.php/ap IMPROVEMENT OF MACHINE SAFETY DEVICES B. M. Hevkoa, R. B. Hevkob, O. M. Klendiic,∗, M. V. Buriakb, Y. V. Dzyadykevychb, R. I. Rozumb a Ternopil Ivan Pul’uj National Technical University, Ruska Str., 56, Ternopil, Ukraine b Ternopil National Economical University, Lvivska Str., 11, Ternopil, Ukraine c Separated Subdivision of National University of Life and Environmental Sciences of Ukraine, Berezhany Agrotechnical Institute, Akademichna Str., 20, Berezhany, Ukraine ∗ corresponding author: klendii_o@ukr.net Abstract. The article presents a development of new machine safety devices, which provide protection of operating elements from overload. Theoretical calculations have been made in order to determine the optimum design, kinematic and dynamic parameters of safety devices. A test bench has been developed and experimental investigations have been conducted in order to determine basic parameters of overload clutches. Keywords: safety devices; overload clutch; design and kinematic parameters; dynamic load; test bench; operating elements of machines. 1. Introduction Operating elements of the machines, which operate under a wide range of conditions with materials that have various flow characteristics, are most likely to come under influence of external loading, which is usually random and can be critical both for operating elements and their drives [1, 2, 4–12, 16–20]. Such critical loads often cause a breakdown of equipment, which requires significant material resources for its repair and a lengthy downtime, which has a negative influence on productivity and efficiency of technologi- cal machinery. That is why it is necessary to improve and develop advanced types of safety devices (over- load clutches), choose their optimum design-kinematic parameters and operating modes when operating ele- ments get overloaded, which can provide their reliable breakage protection, reduce dynamic load in the pro- cess of half coupling slipping and an automatic repair of machines after their overload is removed. 2. Materials and methods In order to formalize the process of overload protec- tion of machine operating elements, it is necessary to make calculations for determining the overload clutch parameters. This paper considers protection of oper- ating elements of machines with rotating and axial as well as with only rotating process of operation. Fig- ure 1 shows the design of a conveyer with an overload clutch. While in operation, a loose material enters a body through a hopper and gets onto a screw feeder, which conveys it in the unloading direction. When solid bodies get into the space between the surface of the screw rotation and the inner surface of a screw body, there is a seizure and the screw stops [3]. In order to resume the operation of a screw conveyer, it has been Fig. 1. Screw conveyer with an overload clutch: 1 – nut; 2 – spring element; 3 – axial bearing; 4 – driven half coupling; 5 – drive half coupling; 6 – hopper; 7 – screw body; 8 – screw feeder; 9 – pipe (screw feeder shaft); 10 – needle bearing; 11 – solid shaft; 12 – flange drive side; 13 – frame; 14 – flange non-drive side; 15 – angular contact bearing; 16 – balls; 17 – rack Fig.2. An overload clutch operation scheme When torque transmission takes place, balls contact the hollows of a drive half coupling, which provides rotation of an overload clutch and a screw element. A driven half coupling is spline- mounted on a shaft with the possibility of axial shift. Clearance  is provided between a driven half coupling and a nut; its value corresponds to prevention mode. Diametrically to the arrangement of balls and hollows, on both sides of hollows on the driven half coupling face, there are angled operational and reverse grooves; here, operational groove angle β is significantly less than reverse groove angle  . When there is overload, a driven half coupling stops and a drive one continues rotating, which causes bond failure between balls and hollows. Since balls move along an operational groove, there is a ‘soft’ axial removal of a jammed screw. When there is further rotation of a drive half coupling, balls get into hollows along a reverse groove and, thus, the initial state of a clutch is restored. In case of operating element seizure, there is major declutching of half couplings, that is to say, balls get out of hollows by value h along ab – line, which causes disengagement of the Figure 1. Screw conveyer with an overload clutch: 1 – nut; 2 – spring element; 3 – axial bearing; 4 – driven half coupling; 5 – drive half coupling; 6 – hopper; 7 – screw body; 8 – screw feeder; 9 – pipe (screw feeder shaft); 10 – needle bearing; 11 – solid shaft; 12 – flange drive side; 13 – frame; 14 – flange non-drive side; 15 – angular contact bearing; 16 – balls; 17 – rack. suggested using an overload clutch with time-spaced slipping modes and an axial shift of a screw. Figure 2 represents its concept design and a general view of the work surface of a driven half coupling. When the torque transmission takes place, balls contact the hollows of a drive half coupling, which provides the rotation of an overload clutch and a screw element. A driven half coupling is spline-mounted on a shaft with the possibility of an axial shift. A clear- ance, δ, is provided between a driven half coupling and a nut; its value corresponds to a prevention mode. Diametrically to the arrangement of balls and hollows, on both sides of hollows on the driven half coupling’s face, there are angled operational and reverse grooves; in this case, the operational groove angle β is signifi- cantly less than the reverse groove angle γ. 17 http://dx.doi.org/10.14311/AP.2018.58.0017 http://ojs.cvut.cz/ojs/index.php/ap B. M. Hevko, R. B. Hevko, O. M. Klendii et al. Acta Polytechnica Fig. 1. Screw conveyer with an overload clutch: 1 – nut; 2 – spring element; 3 – axial bearing; 4 – driven half coupling; 5 – drive half coupling; 6 – hopper; 7 – screw body; 8 – screw feeder; 9 – pipe (screw feeder shaft); 10 – needle bearing; 11 – solid shaft; 12 – flange drive side; 13 – frame; 14 – flange non-drive side; 15 – angular contact bearing; 16 – balls; 17 – rack Fig.2. An overload clutch operation scheme When torque transmission takes place, balls contact the hollows of a drive half coupling, which provides rotation of an overload clutch and a screw element. A driven half coupling is spline- mounted on a shaft with the possibility of axial shift. Clearance  is provided between a driven half coupling and a nut; its value corresponds to prevention mode. Diametrically to the arrangement of balls and hollows, on both sides of hollows on the driven half coupling face, there are angled operational and reverse grooves; here, operational groove angle β is significantly less than reverse groove angle  . When there is overload, a driven half coupling stops and a drive one continues rotating, which causes bond failure between balls and hollows. Since balls move along an operational groove, there is a ‘soft’ axial removal of a jammed screw. When there is further rotation of a drive half coupling, balls get into hollows along a reverse groove and, thus, the initial state of a clutch is restored. In case of operating element seizure, there is major declutching of half couplings, that is to say, balls get out of hollows by value h along ab – line, which causes disengagement of the Figure 2. An overload clutch operation scheme. kinematic chain of a drive. Then balls move along angled operational grooves (inclination angle β) of a driven half coupling (line bс) and, thus, there is smooth ‘soft’ axial removal of a jammed screw operating element by the maximum value 2х , which significantly decreases dynamic load on a conveyer drive. As a result of further rotation of a drive half coupling, balls return to their initial state moving along angled reverse grooves (inclination angle  ) on a driven half coupling face (line de) and a screw is moved by value 3х , that is to say, there is smooth restoration of the operational condition of a screw conveyer. Having conducted kinetostatic analysis of an overload clutch operation in a screw conveyer, the pattern of torque value change depending on half couplings rotation at various stages of their actuation has been determined [14]. In order to determine optimal parameters and characteristics of an overload clutch, its dynamic model with a screw operating element drive has been developed (Fig.3). This model is described by the following set of equations  ;21111   cTJ d    ;211221 mTcJ   (1)  ;432322   cTJ m    ,43243 rTcJ   where Td – rotating torque of a drive; Tm – rotating torque at half couplings interaction; Tr – operating element shaft resistive torque; 1с - reduces torque stiffness of drive elements between an engine and a driven half coupling; 2с - reduced torque stiffness of drive elements between a driven half coupling and an operating element shaft; 1 - angle of drive shaft torque; 2 - angle of drive half coupling torque; 3 - angle of driven half coupling torque; 4 - angle of operating element shaft torque; 1J - equivalent drive moment of inertia; 21J - equivalent drive half coupling moment of inertia; 22J - equivalent driven half coupling moment of inertia; 3J - equivalent operating element shaft moment of inertia. Rotating torque of half couplings interaction Tm is determined according to many clutch parameters: geometric dimensions of a half coupling and profile of coupling elements; stiffness and initial contact spring tension; mass of axially moving part of a half coupling together with a screw and part of load; influence of friction force (however, in case of proper lubrication, it is insignificant enough to be not taken into account). Fig.3. Dynamic model of an overload clutch with a screw operating element drive Figure 3. Dynamic model of an overload clutch with a screw operating element drive. When there is an overload, the driven half coupling stops and the drive one continues to rotate, which causes a bond failure between the balls and hollows. Since the balls move along an operational groove, there is a ‘soft’ axial removal of a jammed screw. When there is a further rotation of a drive half coupling, the balls get into hollows along a reverse groove and thus the initial state of a clutch is restored. In case of operating element seizure, there is major declutching of half couplings, that is to say, balls get out of hollows by value h along ab-line, which causes disengagement of the kinematic chain of a drive. Then the balls move along the angled operational grooves (inclination angle β) of the driven half coupling (line bc) and thus there is a smooth ‘soft’ axial removal of the jammed screw operating element by the maximum value x2 , which significantly decreases dynamic load on a conveyer drive. As a result of a further rotation of a drive half coupling, the balls return to their initial state moving along angled reverse grooves (inclination angle γ) on the driven half coupling’s face (line de) and a screw is moved by value x3 , resulting in a smooth restoration of the operational condition of the screw conveyer. Having conducted a kinetostatic analysis of an overload clutch operation in a screw conveyer, the pattern of the torque value change depending on the half coupling’s rotation at various stages of their actuation has been determined [14]. In order to determine optimal parameters and char- acteristics of an overload clutch, its dynamic model with a screw operating element drive has been devel- oped (Figure 3). This model is described by the following set of equations: J1ϕ̈1 = Td − c1(ϕ1 − ϕ2), J21ϕ̈2 = c1(ϕ1 − ϕ2) − T, J22ϕ̈3 = Tm − c2(ϕ3 − ϕ4), J3ϕ̈4 = c2(ϕ3 − ϕ4) − Tr, (1) where Td – rotating torque of a drive; Tm – rotating torque at half coupling’s interaction; Tr – operating element shaft’s resistive torque; c1 – reduced torque stiffness of drive elements between an engine and a driven half coupling; c2 – reduced torque stiffness of drive elements between a driven half coupling and an operating element shaft; ϕ1 – angle of drive shaft’s torque; ϕ2 – angle of drive half coupling’s torque; ϕ3 – angle of driven half coupling’s torque; ϕ4 – angle of operating element shaft’s torque; J1 – equivalent drive moment of inertia; J21 – equivalent drive half coupling’s moment of inertia; J22 – equivalent driven half coupling’s moment of inertia; J3 – equivalent operating element shaft’s moment of inertia. The rotating torque of half coupling’s interaction Tm is determined according to many clutch param- eters: the geometric dimensions of a half coupling and a profile of coupling elements; stiffness and initial contact spring tension; mass of axially moving part of a half coupling together with the screw and part of the load; influence of friction force (however, in case of proper lubrication, it is insignificant enough to not be taken into account). It has been defined that torque dependence is de- termined by design, mass and spring characteristics of a clutch as well as the difference in angles of con- joint rotation of half couplings and their derivatives. Based on mathematical transformations, an expres- sion for determining the rotating torque Tm has been obtained: Tm = A+B + C +M E , (2) 18 vol. 58 no. 1/2018 Improvement of Machine Safety Devices m = 8 kg; n = 60 r.p.m. m = 8 kg; n = 100 r.p.m. а b m = 8 kg; n = 140 r.p.m. m = 8 kg; n = 180 r.p.m. c d m = 14 kg; n = 100 r.p.m. m = 20 kg; n = 100 r.p.m. e f Fig.4. Torque-vs-half-coupling-rotation curves In typical overload clutches, when reaching the next hollows, balls contact them and this causes circular impact loads on drive elements [15]. This disadvantage can be avoided if angled keys 3, with a certain inclination angle β and height hk, are arranged in front of hollows 4 (Fig.5). Then, balls 2 with a drive half coupling 1, which move at rate V =  R ( – angular velocity of a moving half coupling; R – radius of location of coupling elements) in the coupling area, get additional axial movement in the direction of spring compression and, further, under its action they get back in opposite direction. Such reciprocating movement takes certain time t, the time that a moving half coupling needs to cover distance L =  Rt, which exceeds the dimensions of a hollow. This eliminates the possibility of balls getting into hollows and reduces the level of circular impact loads. Тs Тm Тn Тn Тs Тm Тs Тm Тn Тs Тm Тn Тs Тm Тn Тs Тm Тn Figure 4. Torque-vs-half-coupling-rotation curves. where components of the expression are written as A = m(D/2)2(r sin θ0 − (D/2)(ϕ2 − ϕ3))2 r2 − (r sin θ0 − (D/2)(ϕ2 − ϕ3))2 · ( c1(ϕ2 − ϕ3) J21 + c2(ϕ2 − ϕ3) J22 ) , (3) B = m(D/2)2(ϕ̇2 − ϕ̇3)2(r sin θ0 − (D/2)(ϕ2 −ϕ3)) r2 − (r sin θ0 − (D/2)(ϕ2 − ϕ3))2 , (4) C = −m(D/2)2(ϕ̇2−ϕ̇3)2(r sin θ0−(D/2)(ϕ2−ϕ3))3 (r2 − (r sin θ0 − (D/2)(ϕ2 − ϕ3))2)2 , (5) M = c(D/2) ( λ0 + h− r + √ r2 − (r sin θ0 − (D/2)(ϕ2 − ϕ3))2 ) · r sin θ0 − (D/2)(ϕ2 − ϕ3)√ r2 − (r sin θ0 − (D/2)(ϕ2 − ϕ3))2 , (6) E = 1 + m(D/2)2(r sin θ0 − (D/2)(ϕ2 −ϕ3))2 r2 − (r sin θ0 − (D/2)(ϕ2 − ϕ3))2 · J21 + J22 J21J22 , (7) where D – diameter of the balls location on half cou- plings; r – radius of the balls. Figure 4 represents the torque-vs-half-coupling- rotation curves. Tn = c1(ϕ2 − ϕ1) characterizes the rotating torque of a drive; Ts = c2ϕ3 character- izes torque in case of a jammed driven half coupling and a screw operating element. During investiga- tions, the following parameter values were set: J1 = 40 kgm2; J21 = 0.0157 kgm2; J22 = 0.00925 kgm2; c1 = c2 = 1600Nm/rad; c = 10000N/m; h = 4.6mm; r = 12mm; D = 115mm; δ0 = 15mm. The rotation frequency of a screw operating element n varied within the range of 60–180 rpm and mass m changed ranging from 8 to 20 kg. The results of the investigations show that an in- crease in rotation frequency n causes an increase of ro- tating torques of the system. If the rotation frequency changes from 60 to 180 rpm, the rotating torque Tn is increased by 52.3%, Ts is up by 59.8% and Tm is in- creased by 51.9%. In addition, it has been determined that the mass increase of moving parts m causes an increased drive load. If the mass is increased from 8 to 20 kg, the rotating torque Tn is increased by 36.7%, Ts by 15.6% and Tm by 34.5%. In order to reduce impact loads, which arise when the balls contact the hollows of the half couplings at their slipping, the following design of a ball-type over- 19 B. M. Hevko, R. B. Hevko, O. M. Klendii et al. Acta PolytechnicaRestoration of the initial state, at constant resistive torque, is possible due to the reduction of rotation frequency of a drive half coupling, which causes the decrease of distance L and reduces contact of balls and hollows, respectively. L m C V=R ВH hл h в m m m ВД 1 2 3 4 Fig.5. Roll-out process diagram of drive half coupling shift (DV) relative to a driven one (DVN) The aim of conducting a dynamic analysis is the determination of such overload clutch parameters, at which repeated contact of balls and a driven half coupling face, at constant frequency of a driven half coupling, is possible only in the area between hollows and angles keys. Let us consider the movement of a half coupling together with a ball after its pullout from an angled key (Fig.6), which is performed in the process of clutch actuation due to overload. Let us assume that angular velocity of a drive half coupling 0 is constant and that of a driven one is equal to zero. When calculating, the following symbols were used:  – friction angle; R – radius of location of coupling elements; hk – height of an angled key;  – angle of rotation of half couplings; С – spring stiffness. Ffr X С r X0 hk  Y V0 DVN DV m 0 Fig.6. Analytical model of disengagement mechanism of half couplings A half coupling is influenced by elastic force, Coulomb friction, in the process of its free movement, after balls loose contact with an angled key surface and till the moment of their contact with a driven half coupling face. Let us write the equation of drive half coupling motion at the moment of its separation from a key along x -axis, which is directed parallel to the axis of a drive shaft and is measured from the plane surface of a driven half coupling: 0 ( ) sgn( ) fr mx C x F x    (8) Figure 5. Roll-out process diagram of drive half coupling shift (DV) relative to a driven one (DVN). load clutch has been suggested; its bearing elements are represented in Figure 5. When there is an overload of an operating element of a machine, a driven half coupling (DVN) slows down and stops. Here, a moving drive half coupling (DV) with a mass m continues to rotate. This causes a disengagement of the coupling elements (in this case the balls get out of the hollows) and deformation of a spring with stiffness C, which axially presses a moving half coupling. In typical overload clutches, when reaching the next hollows, the balls contact them and this causes cir- cular impact loads on the drive elements [15]. This disadvantage can be avoided if angled keys 3, with a certain inclination angle β and height hk, are arranged in front of the hollows 4 (Figure 5). Then, the balls 2 with a drive half coupling 1, which moves at a rate V = ωR (ω – angular velocity of a moving half cou- pling; R – radius of a location of coupling elements) in the coupling area, get additional axial movement in the direction of the spring compression and under its action they get back in the opposite direction. Such reciprocating movement takes certain time t, the time that a moving half coupling needs to cover the distance L = ωRt, which exceeds the dimensions of a hollow. This eliminates the possibility of balls getting into hollows and reduces the level of circular impact loads. Restoration of the initial state, at a constant resis- tive torque, is possible due to the reduction of the rotation frequency of a drive half coupling, which causes the decrease of the distance L and reduces the contact between the balls and hollows. The aim of conducting a dynamic analysis is the determination of overload clutch parameters at which a repeated contact of balls and the face of the driven half coupling, at a constant frequency of a driven half coupling, is possible only in the area between the hollows and angles keys. Let us consider the movement of a half coupling together with a ball after its pullout from an angled key (Figure 6), which is performed in the process of a clutch actuation due to an overload. Let us assume that the angular velocity of a driven half coupling ω0 is constant and that of a driven one is equal to zero. When calculating, the following symbols were used: % – friction angle; R – radius of the location of Restoration of the initial state, at constant resistive torque, is possible due to the reduction of rotation frequency of a drive half coupling, which causes the decrease of distance L and reduces contact of balls and hollows, respectively. L m C V=R ВH hл h в m m m ВД 1 2 3 4 Fig.5. Roll-out process diagram of drive half coupling shift (DV) relative to a driven one (DVN) The aim of conducting a dynamic analysis is the determination of such overload clutch parameters, at which repeated contact of balls and a driven half coupling face, at constant frequency of a driven half coupling, is possible only in the area between hollows and angles keys. Let us consider the movement of a half coupling together with a ball after its pullout from an angled key (Fig.6), which is performed in the process of clutch actuation due to overload. Let us assume that angular velocity of a drive half coupling 0 is constant and that of a driven one is equal to zero. When calculating, the following symbols were used:  – friction angle; R – radius of location of coupling elements; hk – height of an angled key;  – angle of rotation of half couplings; С – spring stiffness. Ffr X С r X0 hk  Y V0 DVN DV m 0 Fig.6. Analytical model of disengagement mechanism of half couplings A half coupling is influenced by elastic force, Coulomb friction, in the process of its free movement, after balls loose contact with an angled key surface and till the moment of their contact with a driven half coupling face. Let us write the equation of drive half coupling motion at the moment of its separation from a key along x -axis, which is directed parallel to the axis of a drive shaft and is measured from the plane surface of a driven half coupling: 0 ( ) sgn( ) fr mx C x F x    (8) Figure 6. Analytical model of disengagement mecha- nism of half couplings coupling elements; hk – the height of an angled key; ϕ – the angle of rotation of half couplings; C – spring stiffness. A half coupling is influenced by an elastic force, Coulomb friction, in the process of its free movement, after the balls lose contact with an angled key surface and until the moment of their contact with the face of the driven half coupling. Let us write the equation of the drive half coupling’s motion at the moment of its separation from a key along x-axis, which is directly parallel to the axis of a drive shaft and is measured from the plane surface of a driven half coupling: mẍ = −C(x+ δ0) − Ffr sgn ẋ. (8) Initial conditions of movement (at t = 0): x(0) = hk − r(1 − cosβ), (9) ẋ(0) = V0 tg β, (10) where V = ω0R – the linear speed of a moving half coupling and a ball relative to a stationary half cou- pling, transversely to x-axis. Since there is a sign reversal sgn ẋ in the right member of the equation of the non-linear function, it is to the point to consider a solution of the equation, which consists of two parts: movement in the direction of the axis (ẋ > 0) and movement in the opposite direction (ẋ < 0). The solution of each equation is identical, but it differs by the sign of the friction force. The first stage of the movement is described by mẍ = −C(x+ δ0) − Ffr; (11) after transformations it takes the following form: mẍ+ Cx = −Cδ0 − Ffr. (12) In order to solve this differential equation, it is neces- sary to find relevant characteristic roots or mk2 +C = 0. Solution of the quadratic equation has complex roots k1,2 = i √ C/m, (13) which indicates an oscillatory mode of the movement. 20 vol. 58 no. 1/2018 Improvement of Machine Safety Devices A complete solution of (13), taking into account the partial solution, which depends on the right member, takes the following form: x = (A sin γt+B cos γt) − λ0 − Ffr/C, (14) ẋ = γ(A cos γt−B sin γt), (15) where γ = √ m/C. Let us substitute the initial conditions and deter- mine the constants of the integration B = hk − r(1 − cosα) + δ0 + Ffr/C, (16) A = V0 tgα γ . (17) The movement along OX-axis continues until the moving half coupling stops. Let’s find the time t1 of this stage of the movement by substituting ẋ = 0 in (15): t1 = arctgA/B γ . (18) During this time, the half coupling moves in the fol- lowing position x1 = (A sin γt1 +B cos γt1) − δ0 − Ffr/C. (19) The obtained value of the movement of the half coupling at the end of the first stage of the movement automatically becomes the initial condition of the movement for the second stage, which is described by the following equation with a positive sign of the friction force mẍ+ Cx = −Cδ0 + Ffr. (20) Respectively, its solution takes the following form x = (A sin γt+B cos γt) − δ0 + Ffr/C, (21) ẋ = γ(A cos γt−B sin γt), (22) and constants of the integration are the following B = x1 + δ0 − Ffr/C, (23) A = 0. (24) At the second stage, the movement finishes at the moment, when the ball of the moving half coupling contacts the face of the stationary coupling at x = 0. Let’s substitute this value in (21) and we get a transcendent equation for calculating the time t2 stage lasts that the second: δ0 − Ffr/C = B cos γt2. (25) This can be solved with due accuracy only by applying a numerical method. In practice, in case of standard splined couplings, the following value can be taken as the first approximation: t2 = 1 γ arccos δ0 − Ffr/C B . (26) The total time of the contactless movement of the half couplings is tS = t1 + t2. (27) During this time, before its repeated contact with the driven half coupling’s face, the drive half coupling moves in the direction of rotation by the following distance, relative to a key edge: L = V0tS = ω0RtS. (28) The determined distance must be greater than the distance from an angled key to the furthest possible edge of an operating hollow, but it should not exceed the distance to the next angled key. Based on the conducted calculations, it has been determined that the increase of a moving mass of a half coupling m from 0.5 to 5 kg results in the increase of the contactless rotation of the half couplings from L = 7mm to L = 43mm. An ascending angle β of an angled key within the limits of 20° to 70° results in the linear increase of the value L from 13 to 32mm. A fur- ther increase of β for more than 70° is inappropriate because there is the phenomenon of backward sepa- ration of a half coupling that results in an increased impact load and significant axial displacement of the half coupling. In order to conduct experimental studies of over- load clutches with radial-axial displacement of half couplings in screw conveyers (Figures 1 and 2), a test stand for determining their optimum parameters and operating modes has been developed and is presented in Figure 7. It consists of a frame 20 with a screw conveyer that contains a feed tube 7, where there is a screw operating element 6. On the entry side, where material is fed, L, ts and Hmax, there is a hopper 5 and in the unloading area there is an opening with an adjustable shutter 9 and a screw shaft brake 8. Drive of the operating element is provided by an electric motor 3 through an overload clutch 4. In order to provide the motor starting and to reg- ulate its rotation frequency, a frequency converter (Altivar 71) with the software Power Suite v.2.5.0 was applied. Altivar 71 system was connected to the network and to a computer 1. The load can be set by a braking element as well as by using a sliding shutter. The results of the experimental studies of an overload clutch actuation in the form of a drive shaft rotation frequency curve, a torque curve and a power curve are shown on a computer display. In order to reduce the dynamic load in the process of the relative half coupling’s rotation when there is an overload, a low-dynamic fail-safe ball-type overload clutch has been developed and its design is shown in Figure 9. It consists of a drive half coupling 2 with balls 3, which contact the hollows 4 of a driven half coupling 5 21 B. M. Hevko, R. B. Hevko, O. M. Klendii et al. Acta Polytechnica а b Fig.7. Design concept (a) and general view (b) of a test stand for investigating overload clutches: 1 – computer; 2 – frequency converter Altivar 71; 3 – electric motor; 4 – overload clutch; 5 – hopper; 6 – screw; 7 – feed tube; 8 – screw shaft; 9 – shutter; 10 – frame In order to reduce dynamic load in the process of relative half couplings rotation when there is overload, a low-dynamic fail-safe ball-type overload clutch has been developed and its design in shown in Fig.8. 4 10 11 12 7 2 9 2 1 3 А 5 А 6 14 3 5 4 1 4 А-А 5 1 2 Б-Б Б Б 8 2 4 13 Fig. 8. A fail-safe ball-type overload clutch It consists of a drive half coupling 2 with balls 3, which contact the hollows 4 of a driven half coupling 5 on a hub 1. A driven half coupling is biased by a central spring 7, which contacts nuts 8. Diametrically to the arrangement of balls and hollows, there are angled keys 14 and step pins 12. End surface of step pins is displaced relative to a driven half coupling 5 to the side of a drive half coupling 2 and step pins contact a pressure disk 6 on the other side. There are adjustable limiting screws 11 arranged on step pins on the side where they contact a pressure disk 6. A pressure disk 6 is spring-biased to the side of a driven half coupling 5, the springs 10 are arranged on threaded axles 9. In order to reduce friction force between the face of a hub 1 and a drive half coupling 2, radial bearing balls 13 have been arranged. When there is overload, a hub decelerates and a driven half coupling decelerates as well. Here, a drive half coupling continues rotating and as a result, balls loose contact with hollows. Figure 7. Design concept (left) and general view (right) of a test stand for investigating overload clutches: 1 – computer; 2 – frequency converter Altivar 71; 3 – electric motor; 4 – overload clutch; 5 – hopper; 6 – screw; 7 – feed tube; 8 – screw shaft; 9 – shutter; 10 – frame. Thus, in case when torque increases over the limit, there is complete uncoupling of a kinematic chain. When reaching the next hollows, balls move along grooves, which causes additional axial shift of a driven half coupling and spring deformation, respectively. Under a certain ratio of design and kinematic parameters of a clutch and its elements, balls move over hollows and hit the end face of step pins (pattern of motion is represented in Fig.5). This provides dampening of axial impact loads. Motion trajectory of balls excludes circular loads in the process of clutch slipping and violent torque oscillation, respectively, decreases hollow wear and reduces impact loads on a machine drive in general. Restoration of the initial state of a clutch can be achieved by reducing its rotation frequency that makes balls get into hollows, since there is a decrease in the distance relative to contactless rotation of half couplings until balls contact a driven half coupling again. In order to conduct experimental research for investigating overload clutches with radial half couplings rotation, similar to the one represented in Fig.8, a test stand (Fig.9) for determining quality of their operation has been developed. 1 2 4 1 2 4 3 1 2 4 1 2 4 3 Fig.9. A test stand for investigating overload clutches It consists of a hydraulic motor 1 that provides rotation of an overload clutch 2. With the help of a chain-drive 3, a driven half coupling is connected with the take-off shaft of powder brakes 4, which provide critical loads on an overload clutch. RESULTS When investigating an overload clutch of a screw conveyer (Fig.1; 2), experiments were set up for four frequencies of operating element rotation, namely: n = 60; 100; 140 and 180 rev/m. As a result of the conducted investigations, Т = f(n) were plotted (Fig.10, 11). It has been determined that torque increases with the increase in frequency of rotation. In the variation range of п = 60…180 rev/m, Т increases for 20…25 %. In addition, there is a tendency of torque incensement Т relative to a change in the angle α of inclination of an operating element to horizon, spring stiffness с and clearance setting Δ. Based on the conducted multi-factor experiment, a regression equation of the dependence of an overload clutch torque on the influence of single factors (angle of inclination of an operating element to horizon α, frequency of operation element rotation n and time of resistive torque increase То) has been obtained 2 0 0106,091 0,019 0,142 0,012 0,062T n nT T      . (29) Figure 8. A test stand for investigating overload clutches а b Fig.7. Design concept (a) and general view (b) of a test stand for investigating overload clutches: 1 – computer; 2 – frequency converter Altivar 71; 3 – electric motor; 4 – overload clutch; 5 – hopper; 6 – screw; 7 – feed tube; 8 – screw shaft; 9 – shutter; 10 – frame In order to reduce dynamic load in the process of relative half couplings rotation when there is overload, a low-dynamic fail-safe ball-type overload clutch has been developed and its design in shown in Fig.8. 4 10 11 12 7 2 9 2 1 3 А 5 А 6 14 3 5 4 1 4 А-А 5 1 2 Б-Б Б Б 8 2 4 13 Fig. 8. A fail-safe ball-type overload clutch It consists of a drive half coupling 2 with balls 3, which contact the hollows 4 of a driven half coupling 5 on a hub 1. A driven half coupling is biased by a central spring 7, which contacts nuts 8. Diametrically to the arrangement of balls and hollows, there are angled keys 14 and step pins 12. End surface of step pins is displaced relative to a driven half coupling 5 to the side of a drive half coupling 2 and step pins contact a pressure disk 6 on the other side. There are adjustable limiting screws 11 arranged on step pins on the side where they contact a pressure disk 6. A pressure disk 6 is spring-biased to the side of a driven half coupling 5, the springs 10 are arranged on threaded axles 9. In order to reduce friction force between the face of a hub 1 and a drive half coupling 2, radial bearing balls 13 have been arranged. When there is overload, a hub decelerates and a driven half coupling decelerates as well. Here, a drive half coupling continues rotating and as a result, balls loose contact with hollows. Figure 9. A fail-safe ball-type overload clutch. on a hub 1. The driven half coupling is biased by a central spring 7, which contacts nuts 8. Diametrically to the arrangement of the balls and hollows, there are angled keys 14 and step pins 12. The end surface of step pins is displaced relative to the driven half coupling 5 and to the side of the drive half coupling 2 and step pins contact a pressure disk 6 on the other side. There are adjustable limiting screws 11 arranged on the step pins on the side where they contact the pressure disk 6. A pressure disk 6 is spring-biased to the side of the driven half coupling 5, the springs 10 are arranged on threaded axles 9. In order to reduce the friction force between the face of the hub 1 and the drive half coupling 2, radial bearing balls 13 have been arranged. When there is an overload, a hub decelerates and a driven half coupling decelerates as well. Here, the drive half coupling continues rotating and as a result, the balls loose contact with the hollows. Thus, in case when the torque increases over the limit, there is a complete uncoupling of the kinematic chain. When reaching the next hollows, balls move along grooves, which causes an additional axial shift of the driven half coupling and a spring deformation, respectively. Under a certain ratio of design and kinematic param- eters of a clutch and its elements, the balls move over the hollows and hit the end face of the step pins (the pattern of motion is represented in Figure 5). This provides a dampening of the axial impact loads. Motion trajectory of the balls excludes circular loads in the process of the clutch slipping and violent torque oscillation and decreases the hollow wear and reduces impact loads on a machine drive in general. Restoration of the initial state of a clutch can be achieved by reducing its rotation frequency that makes the balls get into hollows, since there is a decrease in the distance relative to the contactless rotation of the half couplings until the balls contact the driven half coupling again. In order to conduct the experimental research for in- vestigating overload clutches with radial half couplings rotation, similar to the one represented in Figure 9, a test stand (Figure 8) for determining the quality of their operation has been developed. 22 vol. 58 no. 1/2018 Improvement of Machine Safety DevicesWhen conducting the investigation, a factorial field was determined by the following range of parameter variation: 0 о ≤ α ≤ 40 0 ; 60 ≤ n ≤ 150 r.p.m.; 0,2 ≤ То ≤ 0,7 s. 65 80 95 110 125 60 100 140 180, град Т, Nm n, r.p.m. 2 1 3 4 60 72,5 85 97,5 110 60 100 140 180, град Т, Nm n, r.p.m. 2 1 3 4 а b Fig.10. Т-п relation at different angles  of inclination (а) of an operating element to horizon: (1 - α= 0 о , 2 - α= – 10 о , 3 - α= 20 о , 4 - α= – 30 о ) and spring stiffness (b): (с: 1 -:6,5 N/mm; 2- с = 17,5 N/mm; 3- с = 18,5 N/mm; 4- с = 19,5 N/mm). 70 77,5 85 92,5 100 60 100 140 180, град Т, Nm n, r.p.m 2 1 3 4 65 80 95 110 125 60 100 140 180, град Т, Nm n, r.p.m 2 1 3 4 а b Fig.11. Т-п relation at different clearance settings (а)  : (1- 1  mm; 2 - 1,5  mm; 3 - 2  mm) and at various materials (b): 1 - sand, 2 - wheat, 3 - corn, 4 - keramzit Fig. 12 represents response surfaces of torque Т relative to simultaneous change in two parameters: ),( nT ; ),( 0TT  ; ),( 0TnT . 122 116 110 104 98 92 40 30 20 10 0 150 120 T, Nm α, grad n, r.p.m. 60 100 90 116 112 108 104 100 96 0.30 0.20 T, Nm To, s 0 10 20 30 40 α, grad 0.50 0.70 114 106 110 112 104 T, Nm To, s 60 90 120 150 n, r.p.m 0.50 0.70 108 0.30 0.20 а b c Fig. 12. Response surfaces of torque Т relative to simultaneous change in two parameters: а – Т = f (n, α); b - Т = f (α, То); c - Т = f (n, То) Figure 10. T–n relation at different angles α of inclination (a) of an operating element to horizon: 1 – α = 0°, 2 – α = 10°, 3 – α = 20°, 4 – α = 30°; and spring stiffness (b): 1 – c = 6.5N/mm, 2 – c = 17.5N/mm, 3 – c = 18.5N/mm, 4 – c = 19.5N/mm. When conducting the investigation, a factorial field was determined by the following range of parameter variation: 0 о ≤ α ≤ 40 0 ; 60 ≤ n ≤ 150 r.p.m.; 0,2 ≤ То ≤ 0,7 s. 65 80 95 110 125 60 100 140 180, град Т, Nm n, r.p.m. 2 1 3 4 60 72,5 85 97,5 110 60 100 140 180, град Т, Nm n, r.p.m. 2 1 3 4 а b Fig.10. Т-п relation at different angles  of inclination (а) of an operating element to horizon: (1 - α= 0 о , 2 - α= – 10 о , 3 - α= 20 о , 4 - α= – 30 о ) and spring stiffness (b): (с: 1 -:6,5 N/mm; 2- с = 17,5 N/mm; 3- с = 18,5 N/mm; 4- с = 19,5 N/mm). 70 77,5 85 92,5 100 60 100 140 180, град Т, Nm n, r.p.m 2 1 3 4 65 80 95 110 125 60 100 140 180, град Т, Nm n, r.p.m 2 1 3 4 а b Fig.11. Т-п relation at different clearance settings (а)  : (1- 1  mm; 2 - 1,5  mm; 3 - 2  mm) and at various materials (b): 1 - sand, 2 - wheat, 3 - corn, 4 - keramzit Fig. 12 represents response surfaces of torque Т relative to simultaneous change in two parameters: ),( nT ; ),( 0TT  ; ),( 0TnT . 122 116 110 104 98 92 40 30 20 10 0 150 120 T, Nm α, grad n, r.p.m. 60 100 90 116 112 108 104 100 96 0.30 0.20 T, Nm To, s 0 10 20 30 40 α, grad 0.50 0.70 114 106 110 112 104 T, Nm To, s 60 90 120 150 n, r.p.m 0.50 0.70 108 0.30 0.20 а b c Fig. 12. Response surfaces of torque Т relative to simultaneous change in two parameters: а – Т = f (n, α); b - Т = f (α, То); c - Т = f (n, То) Figure 11. T–n relation at different clearance settings (a): 1 – ∆ = 1mm, 2 – ∆ = 1.5mm, 3 – ∆ = 2mm; and at various materials (b): 1 – sand, 2 – wheat, 3 – corn, 4 – keramzit. It consists of a hydraulic motor 1 that provides the rotation of an overload clutch 2. With the help of a chain-drive 3, a driven half coupling is connected with the take-off shaft of powder brakes 4, which provide critical loads on an overload clutch. 3. Results For investigating an overload clutch of a screw con- veyer (Figures 1 and 2), experiments were set up for four frequencies of the operating element rotation, namely n = 60, 100, 140and180 rpm. As a result of the conducted investigations, T = f(n) were plotted (Figures 10 and 11). It has been determined that the torque increases with the increase in frequency of the rotation. In the variation range of n = 60–180 rpm, T increases for 20–25%. In addition, there is a tendency of a torque incensement T relative to the change in the angle α of an inclination of an operating element to horizon, spring stiffness c and clearance setting ∆. Based on the conducted multi-factor experiment, a regression equation of the dependence of an overload clutch torque on the influence of single factors (the angle of inclination of an operating element to horizon α, the frequency of operation element’s rotation n and the time of resistive torque increase To) has been obtained: T = 106.091 − 0.019α+ 0.142αn− 0.012nT0 + 0.062T 2 0 . (29) When conducting the investigation, a factorial field was determined by the following range of parameter variation: α = 0–40°; n = 60–150 rpm; To = 0.2–0.7 s. Figure 12 represents response surfaces of torque T relative to simultaneous change in two parameters: T (n, α); T (α, T0); T (n, T0). Their analysis shows that the dominating factor, which influences the value of T , is the frequency of operating element’s rotation n, then, it is the angle of its inclination to horizon α and the least influential factor is the time of the resistive torque increase To. Based on the results of the investigation of a clutch with a radial half coupling rotation (Figure 9), which have been conducted using a test stand (Figure 8), re- gression equations have been obtained for determining a circular distance L of the contactless half coupling’s rotation after the coupling elements lose contact and until their repeated contact. L = −2.92 + 2.09ω + 3.34m− 1.7C. (30) It has been determined that at the increase of C from 5000 to 10000N/m, the distance L decreases by 12mm (∆L = −12mm); at the change in ω from 13 to 27 rad/s: ∆L = +19mm; at the increase of m from 2 to 4.5 kg: ∆L = +6mm; at the change in β from 10 to 20°: ∆L = +3.5mm. The quality coefficient of the clutch actuation (a loss in the torque value of the clutch actuation at the repeated uncoupling of half couplings) is about 23 B. M. Hevko, R. B. Hevko, O. M. Klendii et al. Acta Polytechnica When conducting the investigation, a factorial field was determined by the following range of parameter variation: 0 о ≤ α ≤ 40 0 ; 60 ≤ n ≤ 150 r.p.m.; 0,2 ≤ То ≤ 0,7 s. 65 80 95 110 125 60 100 140 180, град Т, Nm n, r.p.m. 2 1 3 4 60 72,5 85 97,5 110 60 100 140 180, град Т, Nm n, r.p.m. 2 1 3 4 а b Fig.10. Т-п relation at different angles  of inclination (а) of an operating element to horizon: (1 - α= 0 о , 2 - α= – 10 о , 3 - α= 20 о , 4 - α= – 30 о ) and spring stiffness (b): (с: 1 -:6,5 N/mm; 2- с = 17,5 N/mm; 3- с = 18,5 N/mm; 4- с = 19,5 N/mm). 70 77,5 85 92,5 100 60 100 140 180, град Т, Nm n, r.p.m 2 1 3 4 65 80 95 110 125 60 100 140 180, град Т, Nm n, r.p.m 2 1 3 4 а b Fig.11. Т-п relation at different clearance settings (а)  : (1- 1  mm; 2 - 1,5  mm; 3 - 2  mm) and at various materials (b): 1 - sand, 2 - wheat, 3 - corn, 4 - keramzit Fig. 12 represents response surfaces of torque Т relative to simultaneous change in two parameters: ),( nT ; ),( 0TT  ; ),( 0TnT . 122 116 110 104 98 92 40 30 20 10 0 150 120 T, Nm α, grad n, r.p.m. 60 100 90 116 112 108 104 100 96 0.30 0.20 T, Nm To, s 0 10 20 30 40 α, grad 0.50 0.70 114 106 110 112 104 T, Nm To, s 60 90 120 150 n, r.p.m 0.50 0.70 108 0.30 0.20 а b c Fig. 12. Response surfaces of torque Т relative to simultaneous change in two parameters: а – Т = f (n, α); b - Т = f (α, То); c - Т = f (n, То) Figure 12. Response surfaces of torque T relative to simultaneous change in two parameters: (a) T = f(n, α); (b) T = f(α, To); (c) T = f(n, To). γm ≈ 1.25. The stability factor of a clutch (the torque value of the clutch actuation after a certain time of its operation in relation to the initial one) is 0.945 at the integrated time of slipping being 600 s and torque rating 155–200Nm. 4. Conclusions The article presents theoretical and experimental in- vestigations of two types of new designs of ball-type overload clutches: with a radial half coupling rota- tion and axial shift of a jammed screw in order to remove it from an overloaded area, and also a fail-safe ball-type overload clutch, which is to be mounted into the drives of technological machines, with reduced dynamic impact loads in the mode of a half coupling slipping. Based on power, kinetostatic and dynamic analysis of the clutches, the pattern and the value of the torque change, at all stages of the relative rotation of half couplings, have been considered. The influence of the main parameters on the clutch actuation dynamics in case of the operating element’s overload has been determined. The developed research prototypes of the ball-type overload clutches and test equipment, involving the frequency converter Altivar 71 and software Power Suite v.2.5.0, made it possible to conduct complex experimental investigations. In case of an overload clutch of a screw conveyer, at an angle α varying from 0 to 30°, the torque T increases by 39.7 (32.5%); if the spring stiffness c is increased from 16.5 to 19.5N/mm, T increases by 30.3 (32.45%); at a clearance value ∆ increase from 1 to 2.5mm, T increases by 18.5 (19.4%); if the material fraction is changed, the torque T increases: in case of sand by 32.5%; in case of wheat by 26.3%; in case of corn by 23.6%; and in case of keramzit by 18.5%. 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Cleary (2010) - Screw conveyor performance: comparison of discrete element modelling with laboratory experiments, Progress in Computational Fluid Dynamics, An International Journal (PCFD), Vol. 10, No. 5/6, 2010 Australia. doi:10.1504/PCFD.2010.035366 25 http://dx.doi.org/10.1115/1.4029864 http://dx.doi.org/10.1016/j.fuproc.2014.09.039 http://dx.doi.org/10.1016/j.powtec.2009.03.012 http://dx.doi.org/10.1016/j.powtec.2015.09.038 http://dx.doi.org/10.1680/geot.2006.56.9.605 http://dx.doi.org/10.1504/PCFD.2010.035366 Acta Polytechnica 58(1):17–25, 2018 1 Introduction 2 Materials and methods 3 Results 4 Conclusions References