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78-427: Shaft couplings are used in machinery for several purposes. A primary function is to transfer power from one end to another end (ex: motor transfer power to pump through coupling). Other common uses: A beam coupling, also known as helical coupling, is a flexible coupling for transmitting torque between two shafts while allowing for angular misalignment, parallel offset and even axial motion, of one shaft relative to

156-534: A force is allowed to act through a distance, it is doing mechanical work . Similarly, if torque is allowed to act through an angular displacement, it is doing work. Mathematically, for rotation about a fixed axis through the center of mass , the work W can be expressed as W = ∫ θ 1 θ 2 τ   d θ , {\displaystyle W=\int _{\theta _{1}}^{\theta _{2}}\tau \ \mathrm {d} \theta ,} where τ

234-483: A pipe whose bore is finished to the required tolerance based on the shaft size. Based on the usage of the coupling a keyway is made in the bore in order to transmit the torque by means of the key. Two threaded holes are provided in order to lock the coupling in position. Sleeve couplings are also known as box couplings . In this case shaft ends are coupled together and abutted against each other which are enveloped by muff or sleeve . A gib head sunk keys hold

312-473: A cut put too much force against the screw. Any spring light enough to allow slide movement at all would allow cutter chatter at best and slide movement at worst. These screw-adjusted split-nut-on-an-Acme-leadscrew designs cannot eliminate all backlash on a machine slide unless they are adjusted so tight that the travel starts to bind. Therefore, this idea can't totally obviate the always-approach-from-the-same-direction concept; nevertheless, backlash can be held to

390-443: A flexible beam coupling to join two rotating shafts is to reducing vibration and reaction loads which in turn will reduce overall wear and tear on machinery and prolong equipment life. Bush pin flange coupling is used for slightly imperfect alignment of the two shafts. This is modified form of the protected type flange coupling. This type of coupling has pins and it works with coupling bolts. The rubber or leather bushes are used over

468-419: A flexible coupling can protect the driving and driven shaft components (such as bearings) from the harmful effects of conditions such as misaligned shafts, vibration, shock loads, and thermal expansion of the shafts or other components. At first, flexible couplings separate into two essential groups, metallic and elastomeric. Metallic types utilize freely fitted parts that roll or slide against one another or, on

546-413: A flexible plate to the inside diameter, across the spool or spacer piece, and then from inside to outside diameter. The deforming of a plate or series of plates from I.D. to O.D accomplishes the misalignment. Disc couplings transmit torque from a driving to a driven bolt tangentially on a common bolt circle. Torque is transmitted between the bolts through a series of thin, stainless steel discs assembled in

624-420: A given space while universal joints induce lower vibrations . The limit on torque density in universal joints is due to the limited cross sections of the cross and yoke. The gear teeth in a gear coupling have high backlash to allow for angular misalignment. The excess backlash can contribute to vibration. Gear couplings are generally limited to angular misalignments, i.e., the angle of the spindle relative to

702-408: A lever multiplied by its distance from the lever's fulcrum (the length of the lever arm ) is its torque. Therefore, torque is defined as the product of the magnitude of the perpendicular component of the force and the distance of the line of action of a force from the point around which it is being determined. In three dimensions, the torque is a pseudovector ; for point particles , it is given by

780-409: A mechanism that is supposed to transmit motion accurately. Instead of gear teeth, the context is screw threads . The linear sliding axes (machine slides) of machine tools are an example application. Most machine slides for many decades, and many even today, have been simple (but accurate) cast-iron linear bearing surfaces , such as a dovetail- or box-slide, with an Acme leadscrew drive. With just

858-536: A pack. Misalignment is accomplished by deforming of the material between the bolts. An elastic coupling transmits torque or other load by means of an elastic component. One example is the coupling used to join a windsurfing rig (sail, mast, and components) to the sailboard. In windsurfing terminology it is usually called a "universal joint", but modern designs are usually based on a strong flexible material, and better technically described as an elastic coupling. They can be tendon or hourglass-shaped, and are constructed of

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936-819: A shaft is better than the more complex notion of applying a linear force (or a pair of forces) with a certain leverage. Today, torque is referred to using different vocabulary depending on geographical location and field of study. This article follows the definition used in US physics in its usage of the word torque . In the UK and in US mechanical engineering , torque is referred to as moment of force , usually shortened to moment . This terminology can be traced back to at least 1811 in Siméon Denis Poisson 's Traité de mécanique . An English translation of Poisson's work appears in 1842. A force applied perpendicularly to

1014-489: A simple nut, some backlash is inevitable. On manual (non- CNC ) machine tools, a machinist's means for compensating for backlash is to approach all precise positions using the same direction of travel, that is, if they have been dialing left, and next want to move to a rightward point, they will move rightward past it, then dial leftward back to it; the setups, tool approaches, and toolpaths must in that case be designed within this constraint. The next-more complex method than

1092-762: A single point particle is: L = r × p {\displaystyle \mathbf {L} =\mathbf {r} \times \mathbf {p} } where p is the particle's linear momentum and r is the position vector from the origin. The time-derivative of this is: d L d t = r × d p d t + d r d t × p . {\displaystyle {\frac {\mathrm {d} \mathbf {L} }{\mathrm {d} t}}=\mathbf {r} \times {\frac {\mathrm {d} \mathbf {p} }{\mathrm {d} t}}+{\frac {\mathrm {d} \mathbf {r} }{\mathrm {d} t}}\times \mathbf {p} .} This result can easily be proven by splitting

1170-491: A small amount (1 or 2 thousandths of an inch or), which is more convenient, and in some non-precise work is enough to allow one to "ignore" the backlash, i.e., to design as if there were none. CNCs can be programmed to use the always-approach-from-the-same-direction concept, but that is not the normal way they are used today , because hydraulic anti-backlash split nuts, and newer forms of leadscrew than Acme/trapezoidal -- such as recirculating ball screws -- effectively eliminate

1248-452: A spring and/or a second bearing to provide a compressive axial force that maintains bearing surfaces in contact despite reversal of the load direction. Torque In physics and mechanics , torque is the rotational analogue of linear force . It is also referred to as the moment of force (also abbreviated to moment ). The symbol for torque is typically τ {\displaystyle {\boldsymbol {\tau }}} ,

1326-559: A strong and durable elastic material. In this application, the coupling does not transmit torque, but instead transmits sail-power to the board, creating thrust (some portion of sail-power is also transmitted through the rider's body). Flexible couplings are usually used to transmit torque from one shaft to another when the two shafts are slightly misaligned. They can accommodate varying degrees of misalignment up to 1.5° and some parallel misalignment. They can also be used for vibration damping or noise reduction. In rotating shaft applications

1404-554: A third shaft, called the spindle. Each joint consists of a 1:1 gear ratio internal/external gear pair. The tooth flanks and outer diameter of the external gear are crowned to allow for angular displacement between the two gears. Mechanically, the gears are equivalent to rotating splines with modified profiles. They are called gears because of the relatively large size of the teeth. Gear couplings and universal joints are used in similar applications. Gear couplings have higher torque densities than universal joints designed to fit

1482-409: A whole revolution of the larger of a pair of mating gears. Backlash in gear couplings allows for slight angular misalignment. There can be significant backlash in unsynchronized transmissions because of the intentional gap between the dogs in dog clutches . The gap is necessary to engage dogs when input shaft (engine) speed and output shaft (driveshaft) speed are imperfectly synchronized. If there

1560-417: Is wear . Factors affecting the amount of backlash required in a gear train include errors in profile, pitch, tooth thickness, helix angle and center distance, and run-out . The greater the accuracy the smaller the backlash needed. Backlash is most commonly created by cutting the teeth deeper into the gears than the ideal depth. Another way of introducing backlash is by increasing the center distances between

1638-429: Is a clearance or lost motion in a mechanism caused by gaps between the parts. It can be defined as "the maximum distance or angle through which any part of a mechanical system may be moved in one direction without applying appreciable force or motion to the next part in mechanical sequence." An example, in the context of gears and gear trains , is the amount of clearance between mated gear teeth. It can be seen when

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1716-427: Is a cheap solution, but professional grade CNCs use the more expensive backlash-eliminating drives mentioned above. This allows them to do 3D contouring with a ball-nosed endmill, for example, where the endmill travels around in many directions with constant rigidity and without delays. In mechanical computers a more complex solution is required, namely a frontlash gearbox . This works by turning slightly faster when

1794-441: Is a form of keyless shaft locking device that does not require any material to be removed from the shaft. The basic idea is similar to a clamp coupling but the moment of rotation is closer to the center of the shaft. An alternative coupling device to the traditional parallel key , the tapered lock removes the possibility of play due to worn keyways. It is more robust than using a key because maintenance only requires one tool and

1872-648: Is a general proof for point particles, but it can be generalized to a system of point particles by applying the above proof to each of the point particles and then summing over all the point particles. Similarly, the proof can be generalized to a continuous mass by applying the above proof to each point within the mass, and then integrating over the entire mass. In physics , rotatum is the derivative of torque with respect to time P = d τ d t , {\displaystyle \mathbf {P} ={\frac {\mathrm {d} {\boldsymbol {\tau }}}{\mathrm {d} t}},} where τ

1950-427: Is calculated as the minimum transverse backlash at the operating pitch circle allowable when the gear teeth with the greatest allowable functional tooth thickness are in mesh with the pinion teeth with their greatest allowable functional tooth thickness, at the smallest allowable center distance, under static conditions. Backlash variation is defined as the difference between the maximum and minimum backlash occurring in

2028-453: Is composed of two shaft hubs, a metallic grid spring, and a split cover kit. Torque is transmitted between the two coupling shaft hubs through the metallic grid spring element. Like metallic gear and disc couplings, grid couplings have a high torque density . A benefit of grid couplings, over either gear or disc couplings, is the ability their grid coupling spring elements have to absorb and spread peak load impact energy over time. This reduces

2106-511: Is named for John Oldham who invented it in Ireland , in 1821, to solve a problem in a paddle steamer design. Rag joints are commonly used on automotive steering linkages and drive trains . When used on a drive train they are sometimes known as giubos . Rigid couplings are used when precise shaft alignment is required; any shaft misalignment will affect the coupling's performance as well as its life span, because rigid couplings do not have

2184-430: Is perpendicular to the tongue and groove on the other. The middle disc rotates around its center at the same speed as the input and output shafts. Its center traces a circular orbit, twice per rotation, around the midpoint between input and output shafts. Often springs are used to reduce backlash of the mechanism. An advantage to this type of coupling, as compared to two universal joints, is its compact size. The coupler

2262-425: Is the moment of inertia of the body and ω is its angular speed . Power is the work per unit time , given by P = τ ⋅ ω , {\displaystyle P={\boldsymbol {\tau }}\cdot {\boldsymbol {\omega }},} where P is power, τ is torque, ω is the angular velocity , and ⋅ {\displaystyle \cdot } represents

2340-405: Is the newton-metre (N⋅m). For more on the units of torque, see § Units . The net torque on a body determines the rate of change of the body's angular momentum , τ = d L d t {\displaystyle {\boldsymbol {\tau }}={\frac {\mathrm {d} \mathbf {L} }{\mathrm {d} t}}} where L is the angular momentum vector and t

2418-1748: Is time. For the motion of a point particle, L = I ω , {\displaystyle \mathbf {L} =I{\boldsymbol {\omega }},} where I = m r 2 {\textstyle I=mr^{2}} is the moment of inertia and ω is the orbital angular velocity pseudovector. It follows that τ n e t = I 1 ω 1 ˙ e 1 ^ + I 2 ω 2 ˙ e 2 ^ + I 3 ω 3 ˙ e 3 ^ + I 1 ω 1 d e 1 ^ d t + I 2 ω 2 d e 2 ^ d t + I 3 ω 3 d e 3 ^ d t = I ω ˙ + ω × ( I ω ) {\displaystyle {\boldsymbol {\tau }}_{\mathrm {net} }=I_{1}{\dot {\omega _{1}}}{\hat {\boldsymbol {e_{1}}}}+I_{2}{\dot {\omega _{2}}}{\hat {\boldsymbol {e_{2}}}}+I_{3}{\dot {\omega _{3}}}{\hat {\boldsymbol {e_{3}}}}+I_{1}\omega _{1}{\frac {d{\hat {\boldsymbol {e_{1}}}}}{dt}}+I_{2}\omega _{2}{\frac {d{\hat {\boldsymbol {e_{2}}}}}{dt}}+I_{3}\omega _{3}{\frac {d{\hat {\boldsymbol {e_{3}}}}}{dt}}=I{\boldsymbol {\dot {\omega }}}+{\boldsymbol {\omega }}\times (I{\boldsymbol {\omega }})} using

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2496-451: Is torque, and θ 1 and θ 2 represent (respectively) the initial and final angular positions of the body. It follows from the work–energy principle that W also represents the change in the rotational kinetic energy E r of the body, given by E r = 1 2 I ω 2 , {\displaystyle E_{\mathrm {r} }={\tfrac {1}{2}}I\omega ^{2},} where I

2574-818: Is torque. This word is derived from the Latin word rotātus meaning 'to rotate', but the term rotatum is not universally recognized but is commonly used. There is not a universally accepted lexicon to indicate the successive derivatives of rotatum, even if sometimes various proposals have been made. Using the cross product definition of torque, an alternative expression for rotatum is: P = r × d F d t + d r d t × F . {\displaystyle \mathbf {P} =\mathbf {r} \times {\frac {\mathrm {d} \mathbf {F} }{\mathrm {d} t}}+{\frac {\mathrm {d} \mathbf {r} }{\mathrm {d} t}}\times \mathbf {F} .} Because

2652-457: Is unavoidable in nearly all reversing mechanical couplings, although its effects can be negated or compensated for. In many applications, the theoretical ideal would be zero backlash, but in actual practice some backlash must be allowed to prevent jamming. Reasons for specifying a requirement for backlash include allowing for lubrication , manufacturing errors, deflection under load, and thermal expansion . A principal cause of undesired backlash

2730-506: Is valid for any type of trajectory. In some simple cases like a rotating disc, where only the moment of inertia on rotating axis is, the rotational Newton's second law can be τ = I α {\displaystyle {\boldsymbol {\tau }}=I{\boldsymbol {\alpha }}} where α = ω ˙ {\displaystyle {\boldsymbol {\alpha }}={\dot {\boldsymbol {\omega }}}} . The definition of angular momentum for

2808-624: Is zero because velocity and momentum are parallel, so the second term vanishes. Therefore, torque on a particle is equal to the first derivative of its angular momentum with respect to time. If multiple forces are applied, according Newton's second law it follows that d L d t = r × F n e t = τ n e t . {\displaystyle {\frac {\mathrm {d} \mathbf {L} }{\mathrm {d} t}}=\mathbf {r} \times \mathbf {F} _{\mathrm {net} }={\boldsymbol {\tau }}_{\mathrm {net} }.} This

2886-427: The cross product of the displacement vector and the force vector. The direction of the torque can be determined by using the right hand grip rule : if the fingers of the right hand are curled from the direction of the lever arm to the direction of the force, then the thumb points in the direction of the torque. It follows that the torque vector is perpendicular to both the position and force vectors and defines

2964-405: The pinion (the smaller of the two gears) is significantly smaller than the gear it is meshing with then it is common practice to account for all of the backlash in the larger gear. This maintains as much strength as possible in the pinion's teeth. The amount of additional material removed when making the gears depends on the pressure angle of the teeth. For a 14.5° pressure angle the extra distance

3042-414: The scalar product . Algebraically, the equation may be rearranged to compute torque for a given angular speed and power output. The power injected by the torque depends only on the instantaneous angular speed – not on whether the angular speed increases, decreases, or remains constant while the torque is being applied (this is equivalent to the linear case where the power injected by a force depends only on

3120-471: The Newtonian definition of force is that which produces or tends to produce motion (along a line), so torque may be defined as that which produces or tends to produce torsion (around an axis). It is better to use a term which treats this action as a single definite entity than to use terms like " couple " and " moment ", which suggest more complex ideas. The single notion of a twist applied to turn

3198-429: The ability to compensate for misalignment. Due to this, their application is limited, and they're typically used in applications involving vertical drivers. Clamped or compression rigid couplings come in two parts and fit together around the shafts to form a sleeve. They offer more flexibility than sleeved models, and can be used on shafts that are fixed in place. They generally are large enough so that screws can pass all

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3276-417: The ability to hermetically separate two areas whilst continuing to transmit mechanical power from one to the other making these couplings ideal for applications where prevention of cross-contamination is essential. An Oldham coupling has three discs, one coupled to the input, one coupled to the output, and a middle disc that is joined to the first two by tongue and groove . The tongue and groove on one side

3354-721: The above expression for work, , gives W = ∫ s 1 s 2 F ⋅ d θ × r {\displaystyle W=\int _{s_{1}}^{s_{2}}\mathbf {F} \cdot \mathrm {d} {\boldsymbol {\theta }}\times \mathbf {r} } The expression inside the integral is a scalar triple product F ⋅ d θ × r = r × F ⋅ d θ {\displaystyle \mathbf {F} \cdot \mathrm {d} {\boldsymbol {\theta }}\times \mathbf {r} =\mathbf {r} \times \mathbf {F} \cdot \mathrm {d} {\boldsymbol {\theta }}} , but as per

3432-515: The axes of the connected shafts, of 4–5°. Universal joints are capable of higher misalignments. Single joint gear couplings are also used to connect two nominally coaxial shafts. In this application the device is called a gear-type flexible, or flexible coupling . The single joint allows for minor misalignments such as installation errors and changes in shaft alignment due to operating conditions. These types of gear couplings are generally limited to angular misalignments of 1/4–1/2°. A grid coupling

3510-448: The backlash. The axis can move in either direction without the go-past-and-come-back motion. The simplest CNCs, such as microlathes or manual-to-CNC conversions, which use nut-and-Acme-screw drives can be programmed to correct for the total backlash on each axis, so that the machine's control system will automatically move the extra distance required to take up the slack when it changes directions. This programmatic "backlash compensation"

3588-412: The cutting tool is moved in equals the amount of backlash desired. For a 20° pressure angle the distance equals 0.73 times the amount of backlash desired. As a rule of thumb the average backlash is defined as 0.04 divided by the diametral pitch ; the minimum being 0.03 divided by the diametral pitch and the maximum 0.05 divided by the diametral pitch . In metric, you can just multiply the values with

3666-439: The definition of torque, and since the parameter of integration has been changed from linear displacement to angular displacement, the equation becomes W = ∫ θ 1 θ 2 τ ⋅ d θ {\displaystyle W=\int _{\theta _{1}}^{\theta _{2}}{\boldsymbol {\tau }}\cdot \mathrm {d} {\boldsymbol {\theta }}} If

3744-411: The derivative of a vector is d e i ^ d t = ω × e i ^ {\displaystyle {d{\boldsymbol {\hat {e_{i}}}} \over dt}={\boldsymbol {\omega }}\times {\boldsymbol {\hat {e_{i}}}}} This equation is the rotational analogue of Newton's second law for point particles, and

3822-433: The direction is reversed to 'use up' the backlash slack. Some motion controllers include backlash compensation. Compensation may be achieved by simply adding extra compensating motion (as described earlier) or by sensing the load's position in a closed loop control scheme . The dynamic response of backlash itself, essentially a delay, makes the position loop less stable and thus more prone to oscillation . Minimum backlash

3900-435: The direction of movement is reversed and the slack or lost motion is taken up before the reversal of motion is complete. It can be heard from the railway couplings when a train reverses direction. Another example is in a valve train with mechanical tappets , where a certain range of lash is necessary for the valves to work properly. Depending on the application, backlash may or may not be desirable. Some amount of backlash

3978-556: The factory prior to being shipped, but they occasionally go out of balance in operation. Balancing can be difficult and expensive, and is normally done only when operating tolerances are such that the effort and the expense are justified. The amount of coupling unbalance that can be tolerated by any system is dictated by the characteristics of the specific connected machines and can be determined by detailed analysis or experience. Backlash (engineering) In mechanical engineering , backlash , sometimes called lash , play , or slop ,

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4056-953: The final product while still keeping the single piece's integrity. Changes to the lead of the helical beam provide changes to misalignment capabilities as well as other performance characteristics such as torque capacity and torsional stiffness. It is even possible to have multiple starts within the same helix. The material used to manufacture the beam coupling also affects its performance and suitability for specific applications such as food, medical and aerospace. Materials are typically aluminum alloy and stainless steel, but they can also be made in acetal , maraging steel and titanium . The most common applications are attaching rotary encoders to shafts and motion control for robotics . Beam couplings can be known by various names depending upon industry. These names include flexible coupling, flexible beam coupling, flexible shaft coupling, flexure, helical coupling, and shaft coupling. The primary benefit to using

4134-478: The fulcrum, for example, exerts the same torque as a force of one newton applied six metres from the fulcrum. The term torque (from Latin torquēre , 'to twist') is said to have been suggested by James Thomson and appeared in print in April, 1884. Usage is attested the same year by Silvanus P. Thompson in the first edition of Dynamo-Electric Machinery . Thompson motivates the term as follows: Just as

4212-400: The gears. Backlash due to tooth thickness changes is typically measured along the pitch circle and is defined by: where: Backlash, measured on the pitch circle, due to operating center modifications is defined by: The speed of the machine. The material in the machine where: Standard practice is to make allowance for half the backlash in the tooth thickness of each gear. However, if

4290-568: The infinitesimal linear displacement d s {\displaystyle \mathrm {d} \mathbf {s} } is related to a corresponding angular displacement d θ {\displaystyle \mathrm {d} {\boldsymbol {\theta }}} and the radius vector r {\displaystyle \mathbf {r} } as d s = d θ × r {\displaystyle \mathrm {d} \mathbf {s} =\mathrm {d} {\boldsymbol {\theta }}\times \mathbf {r} } Substitution in

4368-586: The instantaneous speed – not on the resulting acceleration, if any). The work done by a variable force acting over a finite linear displacement s {\displaystyle s} is given by integrating the force with respect to an elemental linear displacement d s {\displaystyle \mathrm {d} \mathbf {s} } W = ∫ s 1 s 2 F ⋅ d s {\displaystyle W=\int _{s_{1}}^{s_{2}}\mathbf {F} \cdot \mathrm {d} \mathbf {s} } However,

4446-425: The lowercase Greek letter tau . When being referred to as moment of force, it is commonly denoted by M . Just as a linear force is a push or a pull applied to a body, a torque can be thought of as a twist applied to an object with respect to a chosen point; for example, driving a screw uses torque, which is applied by the screwdriver rotating around its axis . A force of three newtons applied two metres from

4524-437: The magnitude of peak loads and offers some vibration dampening capability. A negative of the grid coupling design is that it generally is very limited in its ability to accommodate the misalignment. Highly flexible couplings are installed when resonance or torsional vibration might be an issue, since they are designed to eliminate torsional vibration problems and to balance out shock impacts. They are used in installations where

4602-400: The module: In a gear train , backlash is cumulative. When a gear-train is reversed the driving gear is turned a short distance, equal to the total of all the backlashes, before the final driven gear begins to rotate. At low power outputs, backlash results in inaccurate calculation from the small errors introduced at each change of direction; at large power outputs backlash sends shocks through

4680-401: The muff or sleeve is made into two halves parts of the cast iron and they are joined by means of mild steel studs or bolts. The advantages of this coupling is that assembling or disassembling of the coupling is possible without changing the position of the shaft. This coupling is used for heavy power transmission at moderate speed. Diaphragm couplings transmit torque from the outside diameter of

4758-401: The original. One half of the gear is fixed to its shaft while the other half of the gear is allowed to turn on the shaft, but pre-loaded in rotation by small coil springs that rotate the free gear relative to the fixed gear. In this way, the spring compression rotates the free gear until all of the backlash in the system has been taken out; the teeth of the fixed gear press against one side of

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4836-413: The other hand, non-moving parts that bend to take up misalignment. Elastomeric types, then again, gain flexibility from resilient, non-moving, elastic or plastic elements transmitting torque between metallic hubs. A gear coupling is a mechanical device for transmitting torque between two shafts that are not collinear . It consists of a flexible joint fixed to each shaft. The two joints are connected by

4914-421: The other. This design utilizes a single piece of material and becomes flexible by removal of material along a spiral path resulting in a curved flexible beam of helical shape. Since it is made from a single piece of material, the beam style coupling does not exhibit the backlash found in some multi-piece couplings. Another advantage of being an all machined coupling is the possibility to incorporate features into

4992-598: The pins. The coupling has two halves dissimilar in construction. The pins are rigidly fastened by nuts to one of the flange and kept loose on the other flange. This coupling is used to connect shafts which have a small parallel misalignment, angular misalignment or axial misalignment. In this coupling the rubber bushing absorbs shocks and vibration during its operations. This type of coupling is mostly used to couple electric motors and machines. There are various types of constant-velocity (CV) couplings: Rzeppa joint , Double cardan joint, and Thompson coupling . In this coupling,

5070-405: The plane in which the two vectors lie. The resulting torque vector direction is determined by the right-hand rule. Therefore any force directed parallel to the particle's position vector does not produce a torque. The magnitude of torque applied to a rigid body depends on three quantities: the force applied, the lever arm vector connecting the point about which the torque is being measured to

5148-436: The point of force application, and the angle between the force and lever arm vectors. In symbols: τ = r × F ⟹ τ = r F ⊥ = r F sin ⁡ θ {\displaystyle {\boldsymbol {\tau }}=\mathbf {r} \times \mathbf {F} \implies \tau =rF_{\perp }=rF\sin \theta } where The SI unit for torque

5226-528: The rate of change of force is yank Y {\textstyle \mathbf {Y} } and the rate of change of position is velocity v {\textstyle \mathbf {v} } , the expression can be further simplified to: P = r × Y + v × F . {\displaystyle \mathbf {P} =\mathbf {r} \times \mathbf {Y} +\mathbf {v} \times \mathbf {F} .} The law of conservation of energy can also be used to understand torque. If

5304-681: The self-centering balanced rotation means it lasts longer than a keyed joint would, but the downside is that it costs more. A flexible coupling made from two counter-wound springs with a ball bearing in the center, which allows torque transfer from input to output shaft. Requires no lubrication to consistently run as it has no internal components. Coupling maintenance requires a regularly scheduled inspection of each coupling. It consists of: Even with proper maintenance, however, couplings can fail. Underlying reasons for failure, other than maintenance, include: External signs that indicate potential coupling failure include: Couplings are normally balanced at

5382-430: The simple nut is a split nut , whose halves can be adjusted, and locked with screws, so that the two sides ride, respectively, against leftward thread and the other side rides rightward faces. Notice the analogy here with the radio dial example using split gears, where the split halves are pushed in opposing directions. Unlike in the radio dial example, the spring tension idea is not useful here, because machine tools taking

5460-402: The size and stiffness of the coupling, the flexible part may be single- or multi-row. Hirth joints use tapered teeth on two shaft ends meshed together to transmit torque. Jaw coupling is also known as spider or Lovejoy coupling. A magnetic coupling uses magnetic forces to transmit the power from one shaft to another without any contact. This allows for full medium separation. It can provide

5538-427: The systems require a high level of torsional flexibility and misalignment capacity. This type of coupling provides an effective damping of torsional vibrations, and high displacement capacity, which protects the drive. The design of the highly flexible elastic couplings makes assembly easier. These couplings also compensate shaft displacements (radial, axial and angular) and the torque is transmitted in shear. Depending on

5616-399: The teeth of the pinion while the teeth of the free gear press against the other side of the teeth on the pinion. Loads smaller than the force of the springs do not compress the springs and with no gaps between the teeth to be taken up, backlash is eliminated. Another area where backlash matters is in leadscrews . Again, as with the gear train example, the culprit is lost motion when reversing

5694-875: The torque and the angular displacement are in the same direction, then the scalar product reduces to a product of magnitudes; i.e., τ ⋅ d θ = | τ | | d θ | cos ⁡ 0 = τ d θ {\displaystyle {\boldsymbol {\tau }}\cdot \mathrm {d} {\boldsymbol {\theta }}=\left|{\boldsymbol {\tau }}\right|\left|\mathrm {d} {\boldsymbol {\theta }}\right|\cos 0=\tau \,\mathrm {d} \theta } giving W = ∫ θ 1 θ 2 τ d θ {\displaystyle W=\int _{\theta _{1}}^{\theta _{2}}\tau \,\mathrm {d} \theta } The principle of moments, also known as Varignon's theorem (not to be confused with

5772-434: The two shafts and sleeve together (this is the simplest type of the coupling) It is made from the cast iron and very simple to design and manufacture. It consists of a hollow pipe whose inner diameter is same as diameter of the shafts. The hollow pipe is fitted over a two or more ends of the shafts with the help of the taper sunk key. A key and sleeve are useful to transmit power from one shaft to another shaft. A tapered lock

5850-733: The vectors into components and applying the product rule . But because the rate of change of linear momentum is force F {\textstyle \mathbf {F} } and the rate of change of position is velocity v {\textstyle \mathbf {v} } , d L d t = r × F + v × p {\displaystyle {\frac {\mathrm {d} \mathbf {L} }{\mathrm {d} t}}=\mathbf {r} \times \mathbf {F} +\mathbf {v} \times \mathbf {p} } The cross product of momentum p {\displaystyle \mathbf {p} } with its associated velocity v {\displaystyle \mathbf {v} }

5928-543: The way through the coupling and into the second half to ensure a secure hold. Flanged rigid couplings are designed for heavy loads or industrial equipment. They consist of short sleeves surrounded by a perpendicular flange. One coupling is placed on each shaft so the two flanges line up face to face. A series of screws or bolts can then be installed in the flanges to hold them together. Because of their size and durability, flanged units can be used to bring shafts into alignment before they are joined. A sleeve coupling consists of

6006-410: The whole system and can damage teeth and other components. In certain applications, backlash is an undesirable characteristic and should be minimized. The best example here is an analog radio tuner dial where one may make precise tuning movements both forwards and backwards. Specialized gear designs allow this. One of the more common designs splits the gear into two gears, each half the thickness of

6084-465: Was a smaller clearance, it would be nearly impossible to engage the gears because the dogs would interfere with each other in most configurations. In synchronized transmissions, synchromesh solves this problem. However, backlash is undesirable in precision positioning applications such as machine tool tables. It can be minimized by choosing ball screws or leadscrews with preloaded nuts, and mounting them in preloaded bearings. A preloaded bearing uses

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