MMM 03 Mecanismos PDF

# MECANISMOS ## Introducción When we observe a machine, we identify it by its shape and dimensions, but if we were to study it in depth, we would observe that it is made up of a series of mechanisms that generate the final assembly. We could define "mechanism" as the combination of parts or pieces...

# MECANISMOS ## Introducción When we observe a machine, we identify it by its shape and dimensions, but if we were to study it in depth, we would observe that it is made up of a series of mechanisms that generate the final assembly. We could define "mechanism" as the combination of parts or pieces that produce a determined action. We will limit ourselves to studying those that are normally found in machines, tools, etc. To understand what a mechanism is, we will do so through the exposition of some examples: - **Image "a"** A clamp is a tool that serves to hold parts together by applying a certain force (image "a"). The assembly formed by a spindle and a nut constitutes a mechanism that allows the transformation of a circular motion into another linear motion. We can quickly observe that through a mechanism (screw-nut) we achieve a pre-designed purpose (clamp). - **Image "b"** Another example similar to the previous one is found in micrometers (image "b"). Using the same system, we can take precise measurements. - **Image "c"** By combining mechanisms, we achieve more complex machinery, such as a lathe, a milling machine, a column drill or even an excavator (image "c”), etc. In the latter case, through a series of mechanisms that transmit, transform and regulate the movement, pressure is exerted determinedly. To understand the function of mechanisms, we need to know some basic concepts. ## El movimiento We understand movement as the state of bodies while they change position or location. To study it, we follow the displacement made by a single point of the element and we say: a movement is a change of place or position of a point with respect to a set. ### Types of movement If we examine the trajectory traveled by a point in motion, we will distinguish: - Discretional movement (Fig. 1). - Rectilinear movement (Fig. 2). - Circular movement (Fig. 3). - Helical or spiral movement (Fig. 4). ### Velocidad When we talk about speed, we understand it as the distance that can be traveled in a given time. If we study speed in relation to movement we can differentiate: - When the movement is discretional, the speed changes arbitrarily. - When the movement is uniform, the speed is constant throughout time. - When the movement is accelerated, speed increases. - When the movement is delayed, the speed decreases. Finally, we can establish a final differentiation: alternative movement. ## Medios de funcionamiento de los mecanismos Essentially, mechanisms can perform their mission in the following ways: - By mechanical means. This is the most common case of mechanisms (Figs. 5, 6, 7). - Through a hydraulic (liquid pressure) or pneumatic (air pressure) medium (Fig. 8). - Using electrical systems (Fig. 9). All the cases mentioned above can be combined, achieving machines with a variety of operating methods. ## Los mecanismos All mechanisms are mainly used to transmit movement and therefore, we can call them "transmission mechanisms". In addition to this task, they can also transform movement. So when this happens, they can be defined as transmission and transformation mechanisms. The transformation is achieved by: - Varying revolutions (Fig. 5). - Inverting the direction of rotation (Fig. 6). - Transforming a determined movement into another (Fig. 7). A clear example can be found in a car, as the mechanisms that compose it achieve, among many other applications, acquiring different speeds and being able to move forward or backward. All this is achieved from a linear movement developed by the pistons inside the cylinders. To carry out a study in an orderly way, although we already know that the main function of almost all mechanisms is the transmission of movement and that in many cases they also manage to transform it, we can particularize in the following types: - **Control mechanisms**. They are used to regulate or limit certain movements (Fig. 10). They are also used in the start-up and shutdown of machines (Fig. 11). - **Clutch mechanisms**. They are mainly used to establish a transmission between two shafts or to cancel that transmission without stopping the movement coming from the engine. In short, they are used to engage or disengage machine parts (Fig. 12). - **Brake mechanisms**. With them, we achieve a reduction in the speed of a body, managing to stop its movement when necessary. - **Reversal mechanisms**. They are used to reverse the direction of rotation (Fig. 13). - **Regulation mechanisms**. With these, we can regulate a determined movement, limiting it to a specific usage value. We can highlight among these the speed variators, which offer the possibility of choosing from a wide range of speeds. - **Locking mechanisms**. They are the only ones, along with brakes, whose purpose is not the transmission of movement. They are mainly used to: - Ensure the positioning of an element (Fig. 14). - Prevent a machine from being operational while the safety features are removed. - That two incompatible parts of a machine are not activated simultaneously, etc. - **Coupling mechanisms**. They are used to couple and decouple shafts, achieving the transmission of movement (Fig. 15). ## Mecanismos de transmisión If we study in more depth how to transmit the movement, we would need to begin by observing the relative position that the shafts occupy on which we want to materialize the transmission. In this way, we can discuss the following dispositions: - Aligned shafts or forming a small angle between them (Figs. 16 and 17) - Shafts forming an angle greater than 5º - Parallel shafts (Fig. 18) - Intersecting shafts (Fig. 19). - Shafts that intersect (Fig. 20). ### Ejes alineados In this case, the way to transmit the movement is mainly done through couplings. We can distinguish between the following types: - **Flexible couplings** They are used to transmit movements with stiffness and torsion of medium level, admitting slight angular, axial and parallel misalignments. They also perform certain torsional shock absorption. Even some of these mechanisms under intense overload break cleanly, acting as "mechanical fuses", protecting the operator and the equipment. Below, are several types of flexible couplings: - **Oldham Coupling** During the rotation of the coupling, the transmitting disk rotates to the force. Its design allows for misalignments of the shaft without requiring heavy loads on the coupling. - **JawFlex Transmission Flexible Couplings** These couplings, comprising three parts, consist of two aluminum drums and an elastic element (spider). The polyurethane element in the shape of a spider cushions impact loads, minimizing impact on the motor and other sensitive equipment. - **Flexible Couplings of the Bellows Type** It consists of a series of corrugations connected to each other, like an accordion. These membranes are rigid against torsion, each one being capable of performing a certain angular flexion, and the sum of all these flexions gives the coupling its capacity to overcome angular displacements, in parallel or axials. - **Flexible Couplings of Helical Grooving Transmission.** Designed for applications where high speeds, lack of alignment and limitations in lubrication would exceed the limits supported by other couplings. - **Rigid couplings** With these, we can join the shafts at any angle. The coupling joint surface can be in a plane perpendicular to the shaft (Fig. 21) or in one that contains it (Fig. 22). In this type of mechanism, the alignment of the shafts is extremely important due to its high rigidity. - **Clutch and release couplings** With these mechanisms, we can achieve or cancel the transmission of movement between two shafts or aligned elements without stopping one of them. To carry out the study more specifically We should distinguish between two types: - The couplings that allow for disengagement with the shafts in motion, but the shafts or pieces to be joined will be stopped to perform the union of the system (Fig. 23). This type of mechanism is called a tooth clutch. - The mechanisms that allow for coupling and disengagement with the shafts stationary or in rotation. There are different types that are based on the friction between surfaces. The most commonly used are cone clutches (Fig. 24), disc clutches (Fig. 25) and multi-disk clutches (Fig. 26). If we study their actuation, we could discuss about mechanical, hydraulic and electromagnetic clutches. - **Torque limiting couplings.** They interrupt the continuity between the power source and the load when it reaches a predetermined value; they even favor the absorption of the inertia of the starting motor (Fig. 27). - **Couplings with intermediate reducers.** Besides direct couplings, the transmission can be achieved through intermediate reducers. These systems are applied when it is necessary to transmit a movement in which the speed of the input shaft is different from the output shaft (Fig. 28). In the following images, we can observe a transmission of movement between aligned shafts. Through this mechanism, a lower output speed and a higher power than that provided by the motor is achieved. ### Ejes formando entre sí un ángulo superior a 5° When we need to transmit movement between two shafts with angular misalignments greater than 5º the "Cardan" universal joints are used. In these articulated couplings, an angular misalignment exceeding 30º is not recommended. - **Simple Cardan Joint** It is used to connect a wide variety of high speed or high precision equipment, where angular misalignments greater than 5 degrees are expected. - **Double Cardan Joint** It is often used so that the shaft connecting them forms similar angles with the driven and driving shafts. Among its applications are the connection of line shafts, motor shafts, conveyor belts, and countless types of machinery. - **Double Cardan Joint with Telescopic Shaft** This shaft connecting the two joints can be telescopic, allowing, in addition to angular deviation, a variation in its length. ### Ejes paralelos The most common transmission that we will find is the one that is carried out between shafts located in parallel. To carry out this transfer of movement, we can find the following systems: - Friction wheels. - Belts and pulleys (Fig. 29). - Geared wheels (Fig. 30). - Chains and chain wheels. In these, the types of circular movement can have many peculiarities. The following are listed as the most significant: - The direction of rotation of the shafts can be the same or the opposite. - Movement can be achieved through simple or compound transmission. - Through a series of mechanisms, the speed of the driven shaft may be constant or variable. - Depending on the elements that make up the transmission, losses of movement by slipping (friction wheels, belts and pulleys), or transmissions without loss of movement by slipping (geared wheels, chains, etc.) can occur. ### Ejes que se cruzan Many times, within machines, we find that movement is transmitted between intersecting shafts. To achieve this purpose, we will come across one of the following systems: - Belts and pulleys (Fig. 31). - A worm gear and a wheel (Fig. 32). It is a very common method, as it not only transmits movement between two shafts positioned perpendicularly but it also produces a large reduction in the speed of the output shaft. Also, movement transmission is usually irreversible and achieved only from the worm gear to the wheel. - Two helical gears (Fig. 33). This allows the angle formed between the shafts to be equal to or greater than 90º. ### Ejes que se cortan To establish a connection between two shafts that intersect, we must use one of the following methods: - Friction wheels. - Bevel gears (Fig. 34). It is also possible to carry out movement transfers between intersecting shafts with an angle different from 90º. ## Mecanismos de transformación de movimiento Once we have studied the transmission of movement, we will see what kind of transformations it can undergo. Normally, what is intended is to achieve the transformation of a circular movement into a linear one or vice versa. In this way we differentiate: - **Connecting Rod and Crank Mechanisms** They can have a fixed stroke or with the possibility of regulation. We consider that the connecting rod-crank mechanism with a fixed stroke (Fig. 35) is used to transform the circular movement into a reciprocating rectilinear movement. The crank "1-2" rotates around a fixed axis that passes through "1”. The slider "3" describes a rectilinear movement and the connecting rod "2-3” a limited angular movement. If we study the figure "35a", we will realize that, in this case, the connecting rod-crank system has the possibility of regulation. So, the distance "L" traveled by the piston is a function of the radius "r" of the circumference described by point "1". Another, example is the figure "35b", where we can observe the trajectory of a connecting rod anchored to a wheel. This point of attachment can sometimes be varied, producing linear trajectories of different magnitudes. - **Rack and Pinion Mechanisms (Fig. 36)** In this case, the linear displacement can be achieved by the rack or the pinion. - **Screw-nut mechanisms** Similar to above, it is possible that the linear displacement is achieved by the screw or the nut. If the screw does not have the possibility of axial displacement, as it rotates, it linearly displaces the nut. If, on the other hand, the nut is axially locked, the linear displacement is suffered by the screw (Fig. 37). - **Cam Mechanisms:** Rectilinear alternating movement can be obtained through several devices. One of the most common is the cam. A cam is a mechanism generally composed of a driver called a "cam", which, by direct contact, moves another piece called a follower, in such a way that it performs a specific alternating movement. These mechanisms are simple and economical; through their design, the follower can achieve almost any desired movement. - **Cam of the disc type (Fig. 38.)** We will study the movements that occur with this type of cam. - **Cam of the wedge type (Fig. 39.)** As we can see in the diagram, depending on the lateral displacement of the wedge, the rise and fall of the stem is achieved. - **Drum cam (Fig. 40.)** This type of cam, along with the lateral ones, it produces a movement similar to that of the disk, being used in automatic systems. ## Other mechanisms - **Step-by-step mechanisms:** These mechanisms produce intermittent movements. We can highlight the following types: - **Pawls.** There are many, but the basis of their operation is similar (Fig. 41). The rotary movement of a plate produces a fraction of a turn in the pawl. On occasion this rotation can be regulated by offsetting the arm on the plate. Normally, pawls produce these intermittent movements in a single direction (Fig. 42), but reversible pawls can exist, in which, through the rotation of the locking mechanism, rotations occur in both directions (Fig. 41). We can also find them as clamping or locking systems (Fig. 42a). - **Maltese cross:** In its different constructions, it can be used to produce an intermittent output movement from a constant speed input. As we can see in the following figures, the movement coming from the motor makes the crank rotate, whose stem goes in and out alternately in the slots of the "Maltese cross", producing movement when both elements are in contact, and canceling the transmission when the stem leaves the slot. As we can see, the constant rotation movement is transformed into another intermittent rotation movement (Fig. 43) or linear intermittent movement (Fig. 44). - **Brake mechanisms** These elements are widely used in machines. Their mission is to control the rotary movement of a component, going as far as stopping it if necessary. They achieve their objective by frictioning one fixed element against another mobile element, in such a way that the kinetic energy is transformed into heat because of the friction. This heat is dissipated into the atmosphere We can divide brakes into two classes: - **Brake shoes:** the shoes are the fixed friction elements, which, pressing against a wheel, commonly called a drum, stop its movement. The shoes can be positioned externally (Fig. 46) or internally (Fig. 45) with respect to the drum; they are shaped like a half-moon and are equipped with brake lining. The drum is usually made of cast iron or a light alloy, and is machined externally and internally to balance it. - **Disc brakes (Fig. 47):** These are made up of a rotating brake disc, considered the mobile element of the braking system. This is clamped by the caliper, which is the static element that houses the brake pads. When these pads are activated, either by a mechanical or hydraulic system, they rub against the disc producing its stop. - **Reducers and geared motors.** In all machines, movement originates from motors, which usually provide high revolutions, approximately between 1,500 and 3,000 rpm. These speeds, on many occasions, are too high for the proper operation of the equipment; therefore, it is necessary to apply reducers or geared motors that reduce the speed to acceptable operating values, such as 50, 60, 100, rpm, etc. In short, we will say that reducers are gear mechanisms capable of modifying the speeds of motors; they will usually be electric. Geared motors are purchased as a whole, i.e., an asynchronous electric motor coupled to a reduction unit (Fig. 48a.). All this equipment will be enclosed and protected electrically. On the other hand, individual reduction units can be purchased (Fig. 48b), to which a motor that generates the initial movement will need to be coupled later. To achieve speed reductions, transmission by belts, chains or gears can also be used. These systems have certain disadvantages and, when replacing them with reducers, space is saved, noise emitted and maintenance are reduced, while the torque output and equipment life increase. ### Classification of speed reducers Generally, reducers can be classified according to the type of gears that make up the mechanism; we could talk about: worm and wheel, gear and planetary. - **Worm and wheel reducer** This is the simplest reducer. It consists of a worm that may have one or more entries and that properly meshes with a wheel. The wheel is composed of a steel core and a bronze periphery. If we assume a worm with one entry, for each turn that this element makes, one tooth of the crown will advance, which involves a considerable speed reduction. We also need to bear in mind that the input shaft is positioned at 90º with respect to the output shaft. - **Gear reducer** These reducers are made up of pairs of wheels that can be of any type, i.e., with straight, helical, bevel gears, etc. (Figs. 48d and 48e). Depending on the combination of gears, the layout between the input and output shafts may vary, i.e., parallel, perpendicular, etc. - **Planetary reducer** Although they are made of gears, their layout is different because they do not mesh in the usual way in pairs,. The layout of the gears consists of a central wheel, which is known as the "sun", and several external wheels that mesh with the central wheel and rotate on it; these wheels are called "planets". The external gears will fit on a moving arm that can rotate with respect to the central gear (Fig. 48f). They usually have input and output shafts, which are in line, due to the internal layout of the epicycloidal gears; in addition, large speed reductions can be achieved, varying from 3:1 to 7:1 when they are single-stage, reaching ratios of 10,000:1 in five-stage reducers (fig. 48g). The use of a planetary reducer in the transmission of movement is a compact and reliable option because it can be applied to small or limited spaces; due to its structural simplicity, it will ensure a proper transmission of movement. - **Variable speed reducers.** When it is necessary to equip a shaft with a variety of revolutions and that the transition between them is smooth, without steps, we resort to mechanical speed variators. There are several types, the most commonly used being those with belts that achieve their objective by progressively changing the diameters of the pulleys (Figs. 49a and 49b). Other types are friction variators (Fig. 49c). ## Cadenas cinemáticas. Relaciones de transmisión The transformation of force and movement produced, usually by a motor, is often achieved through kinematic chains. We can define "kinematic chain" as the set of mechanisms that, linked together, achieve the transmission of mechanical power from the driving element to the working point. Among the most important transmission systems, we can highlight the following: - Pulleys and belts. - Gears. - Toothed wheels and chains. - Worm and wheel. - Toothed wheel and rack, etc. Normally, kinematic chains are represented schematically using standardized symbols. The following show some examples of these symbols and kinematic chains. ## Poleas y correas ### Simple transmission When movement is transmitted directly between two shafts, the system that is established is called simple transmission. We can show, in a straightforward way, that between two connected pulleys the following equality is met: d₁n₁ = d₂n₂ d₁ = diameter of the driving pulley. n₁ = revolutions per minute of the driving pulley. d2 = diameter of the driven pulley. n₂ = revolutions per minute of the driven pulley. This equality is called the "transmission law" and in it, we can observe that the diameters are inversely proportional to the speeds of rotation. Therefore, in order for the mechanism to be a speed reducer, the driving pulley has to be smaller than the driven pulley. On the other hand, the mechanism would be a multiplier. Regardless of the speed of rotation, we must study the direction of rotation, observing that it is the same in both shafts . ### Transmission ratio The transmission ratio is designated by the letter "i", and is equal to: i = n₂/n₁ i = output speed / input speed When "i" is greater than 1 it is a multiplier system. When "i" is less than 1, it is a reducer system. We need to know that some authors obtain the transmission ratio by solving the transmission law in a reverse way, so the result is: i = d₁/d₂. In this case, when “i” is greater than one we will have a reducer system and vice versa. ### Compound transmission When a movement is transmitted between more than two shafts, we can say that it is a compound transmission, so we have the following expressions: n₁d₁ = n₂d₂ = n₃d₃ = n final n conducidas i total = n inicial n conductoras n₂n₄d conductoras d₁d₃ d₂d₄ n₁n₃d conducidas ## Ruedas dentadas y cadenas In this type of system, we can also differentiate between simple and compound transmission. ### Simple transmission ratio It’s the ratio that exists between the speed of rotation n2 of the driven shaft and n1 of the driving shaft, or vice versa, so: Transmission ratio = i = n₂/n₁ i = Z₁/Z₂ Where Z₁ and Z₂ are the numbers of teeth when dealing with gears or chain sprocket wheels. ### Compound transmission ratio When in the transfer of movement there are two or more pairs of wheels, the transmission ratio will be: n₁ Z i final = n inicial n conducidas n conductoras n₂n₄Z conductoras Z₁Z₃ Z₂Z₄ n₁n₃Z conducidas In this numbering, the wheels marked with even numbers are receivers of the movement and the odd numbers are drivers. In the case of gears, the direction of rotation of the wheels is as indicated in the figure. Chains have a rotation equal to that of the belts. ### Worm and wheel Normally, it is part of a irreversible system, i.e., the movement can only be achieved in one direction, from the worm to the wheel and not vice versa. These elements help achieve high transmission ratios. ## Tornillo tuerca y Piñón cremallera The rotary motion can be transformed into rectilinear motion by means of the following devices: screw-nut (Fig. 50a) or rack-and-pinion (Fig. 50b). - **Screw-nut:** If "Ph" is the pitch of the screw and "n" is the number of turns applied, the linear displacement "D" is: D = Ph * n The variable "n" can be a whole number or a fractional number of turns. If we studied the graduated drum, "N" would correspond to the divisions of the drum and "Ph" to the pitch of the screw; the displacement "D" for each division of the drum is: D = Ph / N If the drum is fitted with Vernier calipers, with N' divisions, that coincide with (N-1) divisions of the graduated drum, the precision of the Vernier calipers will be: ap = Ph / (N - N') This procedure is used in the graduated drums of machine carriages. - **Rack and pinion:** When the linear displacement is achieved by a wheel and a rack, we should make the following calculations: If "Pc" is the circular pitch of the rack and "Z" is the number of teeth of the pinion that engages with it, the displacement "V" of the rack (or the pinion, when the rack is fixed), is: V = PZ.n, where "n" is the number of turns or fraction of a turn that the pinion makes and P = πd_p / Z, where "d_p" is the primitive diameter of the wheel. ### Calculation of the kinematic chain of gearboxes If we consider the mechanism represented in Figure 51 and we want to determine the speeds of rotation of the main shaft III, the easiest way to perform the calculation is to analyze the speeds that each shaft acquires successively, i.e., to study the mechanism in parts to finally deduce the output speeds of the kinematic chain. Obviously, we must start by calculating the transmission ratio of the pulleys; in this way, we will find the speed at which shaft I rotates; we can then see that this rotational speed can be transmitted through three different paths to shaft II and from there through two others to shaft III. A quick way to find out the number of output speeds of the output shaft is to multiply the groups of movable wheels. Therefore, we have 3 gears on shaft I and 2 gears on shaft II, so 3x2=6, the number of final speeds of the shaft. A convenient way to calculate speeds is to use the shaft tree system, as shown in the table below. ## Forms of measuring revolutions or speeds of machine elements On many occasions, we will find ourselves needing to measure the revolutions provided by a motor or those at which a shaft or machine element rotates. For this measurement, we will use an instrument called a tachometer. There are two ways to do this: ### Measurement by contact The instruments used are equipped with a conical stylus and a measurement wheel. When we set out to measure the revolutions of a shaft, we will position the conical stylus on the tachometer, which in turn will come into contact with the center of the rotating shaft (Fig. 52a). We will immediately obtain a reading of the revolutions it develops. The measurement wheel is used to determine the speed of the elements that move linearly. For example, if we want to know the speed of a conveyor belt, we just need to place the wheel in contact with the belt (Fig. 52b); we will immediately obtain the reading on the instrument display. We must be careful when the speed to be measured is very high, i.e., greater than 250 m/min., since, due to safety reasons, and also due to the difficulty in obtaining a correct reading, it is advisable to use the non-contact method. ### Measurement without contact For this, we will use a tachometer equipped with a laser or optical sensor (Fig. 53). Simultaneously, a strip of reflective material will be placed on the element that rotates (Fig. 54) so that, when the tachometer is pointed at this strip , a reading of the revolutions that the shaft acquires is produced. If the distance to be measured is small, i.e., less than 100 mm., the reading can be obtained without the need to use the adhesive strip .