Torque Transmitting Joints PDF

Gépelemek 1. TORQUE TRANSMITTING JOINTS Form & Force closing elements Authors: Dr. Kerényi György Molnár László, Dr. Marosfalvi János, Dr. Horák Péter, & Dr. Baka Ernő Nyomatékkötések | GÉPELEMEK 1. előadás 1 Power transmission (shafting) Gépelemek 1. Function: to transfer power & torque betw...

Gépelemek 1. TORQUE TRANSMITTING JOINTS Form & Force closing elements Authors: Dr. Kerényi György Molnár László, Dr. Marosfalvi János, Dr. Horák Péter, & Dr. Baka Ernő Nyomatékkötések | GÉPELEMEK 1. előadás 1 Power transmission (shafting) Gépelemek 1. Function: to transfer power & torque between shaft & hub and sometimes with axial force. Based on effects: • Form-locking; • Force-locking; • Material-closing. Based on structure: • Connection with transmission element; • Direct connection. Based on regulation • Adjustable; • Non adjustable. Nyomatékkötések | GÉPELEMEK 1. előadás 2 Form-locking joints Gépelemek 1. With transmitting element: • key joints • square, feather key • woodruff key • sledge runner key (in case of axial movement) • pin joints Direct connections. • splined • geared • polygon Nyomatékkötések | GÉPELEMEK 1. előadás 3 Key joint Gépelemek 1. Advantages: • Simple structure; • Simple assembly; • Standardized; • Trusted calculation methods. Disadvantages: • Causes eccentricity, therefore hogh revs not possible; • Not economical, because relatively big shaft diameter is needed; • Not proper fro alternating torque transmission. Square key Woodruff key Nyomatékkötések | GÉPELEMEK 1. előadás 4 Calculation of the torque transmitting elements Gépelemek 1. Steps of calculation are the same as the form closing joints: • Determination of load case & constraints • Determination of acting surfaces (loaded, compressed surfaces, weakest cross section) based on the flow of Flux. • Determination of the load per unit area (average pressure, state of stress) • Comparison with Ultimate strenght (alowable stress) → n = … (safety factor) • Calculation of extraordinaries eg.: ring stress state. This methodology is valid for all torque transmitting element, therefore we show it for the key connections. Nyomatékkötések | GÉPELEMEK 1. előadás 5 Calculation of the key connection Gépelemek 1. 2M d where M is the transmitting torque, F is the loading force of the joint. 1. Determination of load case: F= Nyomatékkötések | GÉPELEMEK 1. előadás 6 Calculation of key connection Gépelemek 1. 2. Determination of acting surfaces: • Pressed surface: A p = (l − b )  (h − t − f ) • Weakest cross-section: (notations from figure) A  b  l 3. Determination of load per unit surface: • Average surface pressure: • Average shearing stress: p=  = F Ap F A p  p meg    meg 4. Comparison with the limit state: 5. Other: M  =   meg • Normal shearing stress: cs Kp where Kp polar cross-section factor of the shaft. • Checking of thickness of the hub (v): v = 0,3..0,35d from experience: Nyomatékkötések | GÉPELEMEK 1. előadás 7 Engineering of key connections Gépelemek 1. The real pressure distribution along the length and height of the key: The utilization of the length of the latch depends on the place of torque acting points. Nyomatékkötések | GÉPELEMEK 1. előadás 8 Different pins Gépelemek 1. a) Dowel pin b) Taper pin c) Groove pin Nyomatékkötések | GÉPELEMEK 1. előadás 9 Different pins Gépelemek 1. The pressured surface & the weakest cross section in case of normal pins & parallel pins shaft. Nyomatékkötések | GÉPELEMEK 1. előadás 10 Spline shaft-spline plate Gépelemek 1. Advantages: • Power transmission distribution is even along the perimeter; • Big transmittable power with small dimensions; • Good for alternating torque distribution; • There is not really eccentricity; • Proper for directional changes; • Easy assembly; • standardized. Disadvantages: • Pricy, economical only at mass production. Nyomatékkötések | GÉPELEMEK 1. előadás 11 Spline shaft-spline plate (connection) Gépelemek 1. on inner side (inner-outer diameters) on sides of splines (fit on the ribs) Nyomatékkötések | GÉPELEMEK 1. előadás 12 Spline shaft-spline plate (connection) Gépelemek 1. a) Wedge (kerb tooth) joint b) Involute tooth joint a; Advantages: • Better load efficiency than spline; • For manufacturing and contol the gear b; production tools can be used • No eccentricity; • Proper for axial position variations; • Simple assembly; • Standardized. Disadvantages: • Rather for mass production. Nyomatékkötések | GÉPELEMEK 1. előadás 13 Polygon shaft connections Gépelemek 1. Advantages: • Self-centering construction; • The cross section of the shaft is simple, stress peaks are small, therefore efficient for alternating load cases; • No eccentricity. Torque transmit sections Nyomatékkötések | GÉPELEMEK 1. előadás 14 Polygon shaft connections Gépelemek 1. Disadvantages: • Production is only with special machines; • Because of the big local surface pressure peaks, the hub can be machined from strong materials; • The FEM checking of the hub is difficult; • Expensive. Calculation as at form closing joints: Transmitting surface in this case: where Ap = hbz h = (D − d ) / 2 , z : number of angles of polygon, b : width of the hub. Nyomatékkötések | GÉPELEMEK 1. előadás 15 Other form-locking connections (Hirth joint) Gépelemek 1. Hirth serrated shaft joint is a form-locking, self-centering and easily detachable connection component connects shafts, disks, rotors, wheels and cranks with remarkable precision and maximum torque capacity. • Big torques, small dimensions; • No radial space demand. Nyomatékkötések | GÉPELEMEK 1. előadás 16 Force-locking joints Gépelemek 1. Principle: as a result of the elastic clamping perpendicular to the connected surface, the frictional force is in the direction opposite to the load acting in the direction of the tangent of surface prevents the hub and the shaft from moving relative to each other. Properties: Frictional force works always on the opposite direction to the load, therefore the joint can transmit torque & force. Frictional force can not be bigger than, the boundary force of slippage, therefore joint can be used as sefety connection. Gaining the pre-tensional force: − Interference fit; − Preload with axial force; − Tangential preload; − Hydraulic preload. Nyomatékkötések | GÉPELEMEK 1. előadás 17 Force-locking joints Gépelemek 1. Adjustable Hub-shaft Non-adjustable Cylinder-cylinder Direct touch Interference fit eg: clamping joint Touch via in-between element eg: Spieth clamping sleeve Clamping ring joint Taper shaft-hub Cylinder-cone Taper ring pair Nyomatékkötések | GÉPELEMEK 1. előadás 18 Interference fit (shaft-hub connection) Gépelemek 1. Fit between two parts in which the external dimension of one part slightly exceeds the internal dimension of the part into which it has to fit. From assembly side can be: press-fitting; shrink-fitting (heat up the hub or cool down the shaft). Advantages: • Easy machining; • Self-centering; • Smooth cross sections of the shaft therfore no stress peaks; • No imbalancing. Disadvantages: • Tolerances & fittings are strict; • Hard to machine the surfaces accurately. Nyomatékkötések | GÉPELEMEK 1. előadás 19 Interference fit (shaft-hub connection) Gépelemek 1. Shaft deformation: f1 = d1 − d Hub deformation: f 2 = d − d2 Sum of deformations is the overlap: f = f1 + f 2 Nyomatékkötések | GÉPELEMEK 1. előadás 20 Interference fit (shaft-hub connection) Gépelemek 1. In case of elastic deformation it is linear connection between the bearing pressure and radial deformation. f1 = K1  d  p and f 2 = K2  d  p where K1 & K2 are geometrical and material dependent constants. For determination of these constants we use the thick-wall tubes theory:  1  1 + 0 K1 =  − 1  E1  1 −  0  and  1  1 + 0 K2 =  + 2  E2  1 − 0  where E is the materials Young’s modulus, ν is the Poisson’s ratio  d0   d   0   2 and d  D 2 0   here d0 in case of tube the inner diameter of it. Nyomatékkötések | GÉPELEMEK 1. előadás 21 Interference fit (shaft-hub connection) Gépelemek 1. We can also use the pre-tension triangle as we applied it at bolt joints.: If we depict the tolerance fields, it can be seen the smallest bearing pressure happens at minimum overlap, the highest bearing pressure happens at maximum overlap. pmin = 1  f min d  ( K1 + K 2 ) pmax = 1  f max d  ( K1 + K 2 ) Nyomatékkötések | GÉPELEMEK 1. előadás 22 Interference fit (shaft-hub connection) Gépelemek 1. The transmittable torque: • Calculated with minimum overlap: d 2 T =   pmin  l 2 l width of hub • Force needed for axial movement: Fax =   pmin  d  l • Axial force (Fax) and perimetral force (from torque): perimetral force: Fk = 2 T d F = Fax2 + Fk2 resultant force which loads the joint: F =   pmin  d  l The assembly force (as worst case) calculated as (highest force, with maximum overlap): Fax =   pmax  d  l Nyomatékkötések | GÉPELEMEK 1. előadás 23 Interference fit (shaft-hub connection) Gépelemek 1. Stress checking of hub: Main state of stress of the hub is internal pressure, and as a result of this: the biggest reduced stress acts at the fitting diameter d:  red 2  pmax =   meg 1 − 0 In case of solid shaft. in case of high revolutions the hub needs to be checked for tangetial stress derived from the centrifugal force. Effects of assembly: During pressing-on a smearing effect happens on the surface. The surface roughness changes because of the ductile deformation which, in the end, reduces the transmittable power. Nyomatékkötések | GÉPELEMEK 1. előadás 24 Clamping joint Gépelemek 1. Two-part hub Grooved arm Nyomatékkötések | GÉPELEMEK 1. előadás 25 Conical joint (assembly situation) Gépelemek 1. The hub with a conical bore is pressed onto the conical shaft end with axial force. The size of the axial force can be used to control the surface pressure, i.e. the transmittable torque It can be 2 phases: - pre-tensioned situation; - torque loaded situation. Force play of the pre-tensional situation: According to left figure the pressing force of the surfaces: Fn = Fa 0 sin  +   cos where: Fa0 : pre-tensional force, α : half cone angle, μ : friction coefficient. Nyomatékkötések | GÉPELEMEK 1. előadás 26 Conical joint (torque loaded situation) Gépelemek 1. Force play of the torque loaded situation: • Rigid pre-tension: In here the axial force reduces, because the Fs frictional force turns into normal position unto the slant of the cone : Axial force from the left figure: Fa = Fn  sin  where Fa : is the reduced axial force!!! • Elastic pre-tension: in here the axial force is kept by disc springs, therefore the normal force increases: Fa 0 F = sin   n where Fn* is the increased normal force!!! Nyomatékkötések | GÉPELEMEK 1. előadás 27 Conical joint Gépelemek 1. The transmittable torque: • The frictional force because of the small cone angle & the even pressure distribution is acting on the middle diameter. dk T = Fs  2 After replacing: where d1 + d 2 dk = 2 Fa 0 d1 + d 2 T =   sin  +   cos  4 Nyomatékkötések | GÉPELEMEK 1. előadás 28 Conical joint Gépelemek 1. Strenght checking of the hub: p= Assuming: even pressure distribution: Reduced stress in the hub:  red = 2 p 1 − 2 where  d2  2 =   D Fa d 22 − d12  4 2 D: outer diameter of the hub Nyomatékkötések | GÉPELEMEK 1. előadás 29 Conical joint Gépelemek 1. In case of angle misalignment the pressure distribution in uneven: 1) Lower contact 1. Lower contact 2. Upper contact 2) Upper contact From hub point of view the 2. case is worse, then the reduced stress in hub:  red 2  pmax = 1 − 2 where pmax  2  p Nyomatékkötések | GÉPELEMEK 1. előadás 30 Wedge joints Gépelemek 1. The essential element of the wedge joint is a sloping part, the wedge, which is pressed between the hub and the shaft with an axial force. Taper key Saddle key Gib head key Nyomatékkötések | GÉPELEMEK 1. előadás 31 Wedge joints Gépelemek 1. Transmittable torque by taper key joint: 𝐹𝑎𝑥 𝑇 = 𝜇𝐹𝑅 𝑑 = 𝜇 𝑑 𝑡𝑔 𝛼 + 𝜌 where: FR Fax μ α ρ d normal force in hub; assembly (axial) force; friction coeff. Between wedge & hub; wedge angle; half cone-angle between wedge & hub; shaft diameter. Strenght checking of the connection: tension stress in the hub: = where: v l FR 2vl athickness of hub; lenght of hub. Nyomatékkötések | GÉPELEMEK 1. előadás 32 Frictional hub-shaft connections Gépelemek 1. They are standard machine elements used to connect shafts and hubs. They are capable of transmitting torque, axial forces, radial forces and bending moments. The advantages can be the following: Backlash free connections Ideal for reversing operation Simultaneous transmission of torque and axial force Easy alignment of hub to shaft Compact solutions due to high power density Reduced costs due to simple shaft and hub geometry Connections can be released even after long operation time Nyomatékkötések | GÉPELEMEK 1. előadás 33 Conical ring pairs (built-in situations) Gépelemek 1. x x 1. 2. x x 3. 4. Nyomatékkötések | GÉPELEMEK 1. előadás 34 Ring type joints (conical ring force play) Gépelemek 1. x x 1. 2. x x 3. Vectors of the first ring pair 4. Force play of the whole assemby Nyomatékkötések | GÉPELEMEK 1. előadás 35 Ring type joints (conical ring) Gépelemek 1. Inner side pre-tensioned connection Clamping ring connection Nyomatékkötések | GÉPELEMEK 1. előadás 36 Ring type joints (conical ring) Gépelemek 1. Nyomatékkötések | GÉPELEMEK 1. előadás 37 Ring type joints (conical ring) Gépelemek 1. Nyomatékkötések | GÉPELEMEK 1. előadás 38 Ring type joints (clamping ring) Gépelemek 1. Nyomatékkötések | GÉPELEMEK 1. előadás 39 Ring type joints (star ring) Gépelemek 1. Star-ring: a. In-hub b. In-shaft Nyomatékkötések | GÉPELEMEK 1. előadás 40 Spieth clamping sets (sleeves) Gépelemek 1. Pre-tensioning of the connection a: preload from shaft b: preload from hub Nyomatékkötések | GÉPELEMEK 1. előadás 41 Spieth clamping sets (sleeves) Gépelemek 1. Nyomatékkötések | GÉPELEMEK 1. előadás 42 Spieth clamping sets (sleeves) Gépelemek 1. Nyomatékkötések | GÉPELEMEK 1. előadás 43 Star disc hub-shaft connection Gépelemek 1. Star Discs are flat-bevelled rings which are slotted on the outside and inside. An external axial actauting force is translated by the Star Disc into a much higher radial force. Nyomatékkötések | GÉPELEMEK 1. előadás 44 Star disc hub-shaft connection Gépelemek 1. Nyomatékkötések | GÉPELEMEK 1. előadás 45 Hydraulic hub-shaft connections (semi manual) Gépelemek 1. Nyomatékkötések | GÉPELEMEK 1. előadás 46 Hydraulic hub-shaft connections (semi manual) Gépelemek 1. Nyomatékkötések | GÉPELEMEK 1. előadás 47 Conical piston hub-shaft connection (hydraulic) Gépelemek 1. Construction: ETP-HYLOC is a hydromechanical joint, which consists of a double-walled steel sleeve which encloses a conical moveable piston. Mounting and dismantling is carried out with a hydraulic pump. Nyomatékkötések | GÉPELEMEK 1. előadás 48 Hydraulic hub-shaft connections Gépelemek 1. Nyomatékkötések | GÉPELEMEK 1. előadás 49 Adjustable locknuts Gépelemek 1. Nyomatékkötések | GÉPELEMEK 1. előadás 50