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46-466: The company produces lines of both powered parachutes and paramotors that are noted for their wide choice of engine, propeller and reduction drive combinations. This Estonian corporation or company article is a stub . You can help Misplaced Pages by expanding it . This article about transport in Estonia is a stub . You can help Misplaced Pages by expanding it . Reduction drive A reduction drive

92-534: 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

138-485: A complete assembly into the ship. While finally others will have the gears dismantled, shipped and reassembled in the ship. These three methods are the most common used by shipbuilders to achieve proper alignment and each of them work based upon the assumption that proper alignment was correctly achieved at the manufacturer. Because of the involvement in the process of aligning reduction drives, there are two main sources of responsibility to achieve proper alignment. That of

184-471: A direct-drive engine may never achieve full output, as the propeller might exceed its maximum permissible rpm . For instance, a direct-drive aero engine (such as the Jabiru 2200 ) has a nominal maximum output of 64  kW (85 bhp ) at 3,300 RPM , but if the propeller cannot exceed 2,600 rpm, the maximum output would be only about 70 bhp. By contrast, a Rotax 912 has an engine capacity of only 56% of

230-415: A ship's reduction gearbox are usually double helical gears . This design helps lower the amount of required maintenance and increase the lifetime of the gears. Helical gears are used because the load upon it is more distributed than in other types. The double helical gear set can also be called a herringbone gear and consists of two oppositely angled sets of teeth. A single set of helical teeth will produce

276-762: 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

322-407: A thrust parallel to the axle of the gear (known as axial thrust) due to the angular nature of the teeth. By adding a second set opposed to the first set, the axial thrust created by both sets cancels each other out. When installing reduction gears on ships the alignment of the gear is critical. Correct alignment helps ensure a uniform distribution of load upon each pinion and gear. When manufactured,

368-492: A twist applied to turn 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

414-496: Is a mechanical device to shift rotational speed. A planetary reduction drive is a small scale version using ball bearings in an epicyclic arrangement instead of toothed gears . Reduction drives are used in engines of all kinds to increase the amount of torque per revolution of a shaft: the gearbox of any car is a ubiquitous example of a reduction drive. Common household uses are washing machines, food blenders and window-winders. Reduction drives are also used to decrease

460-406: Is a cheap and lightweight option with built-in damping of power surges. Most of the world's ships are powered by diesel engines which can be split into three categories, low speed (<400 rpm), medium speed (400-1200 rpm), and high speed (1200+ rpm). Low speed diesels operate at speeds within the optimum range for propeller usage. Thus it is acceptable to directly transmit power from the engine to

506-648: 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

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552-483: Is applied by the screwdriver rotating around its axis . A force of three newtons applied two metres from 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

598-407: 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 the cross product of the displacement vector and the force vector. The direction of the torque can be determined by using

644-462: 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 a lever multiplied by its distance from the lever's fulcrum (the length of the lever arm ) is its torque. Therefore, torque

690-425: 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

736-405: 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

782-1748: 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

828-451: 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

874-814: 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

920-406: Is typically τ {\displaystyle {\boldsymbol {\tau }}} , 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

966-506: 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

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1012-624: 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

1058-460: 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 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

1104-414: 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

1150-518: The Jabiru 2200, but its reduction gear (of 1 : 2.273 or 1 : 2.43) allows the full output of 80 bhp to be exploited. The Midwest twin-rotor wankel engine has an eccentric shaft that spins up to 7,800 rpm, so a 2.96:1 reduction gear is used. Aero-engine reduction gears are typically of the gear type, but smaller two-stroke engines such as the Rotax 582 use belt drive with toothed belts, which

1196-721: 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

1242-472: The capacitor drive has backlash, when one attempts to tune in a station, the tuning knob will feel sloppy and it will be hard to perform small adjustments. Gear-drives can be made to have no backlash by using split gears and spring tension but the shaft bearings have to be very precise. Piston-engined light aircraft may have direct-drive to the propeller or may use a reduction drive. The advantages of direct-drive are simplicity, lightness and reliability, but

1288-439: 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

1334-411: 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

1380-544: The first edition of Dynamo-Electric Machinery . Thompson motivates the term as follows: Just as 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

1426-426: The gears and pinions, and denoting all steps performed, making measurements of parts at the different steps and final assembly then forwarding this data to the shipbuilder so that they may assure the degree of accuracy required by the gear designer in the resulting shipboard assembly. Thrust bearings do not commonly appear on reduction drives on ships because axial loading is handled by a thrust bearing separate from

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1472-420: The gears are assembled in such a way as to obtain uniform load distribution and tooth contact. After completion of construction and delivery to shipyard it is required that these gears achieve proper alignment when first operated under load. Some shipbuilders will have the gears transported and installed as a complete assembly. Others will have the gears dismantled, shipped, reassembled in their shops and lowered as

1518-568: 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

1564-586: 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,

1610-404: The lube oil in the reduction gears stay this way a lube oil purifier will be installed with the drive. Types of reduction drives include cycloidal , strain wave gear , and worm gear drives. 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

1656-433: The normal wear down of the stern tube will not induce significant movement of the reduction gear coupling from its proper alignment. The gear manufacturer is then responsible for ensuring basic gear alignment, such that the final assembly measurements are taken carefully and recorded for the reduction drive to be installed correctly, proper tooth contact in the factory, where the manufacturer accurately and precisely assembles

1702-487: The number of teeth on each gear. For example, a pinion with 25 teeth, turning a gear with 100 teeth, must turn 4 times in order for the larger gear to turn once. This reduces the speed by a factor of 4 while raising the torque 4 fold. This reduction factor changes depending on the needs and operating speeds of the machinery. The reduction gear aboard the Training Ship Golden Bear has a ratio of 3.6714:1. So when

1748-683: 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 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

1794-404: The propeller. For medium and high speed diesels, the rotational speed of the crankshaft within the engine must be reduced in order to reach the optimum speed for use by a propeller. Reduction drives operate by making the engine turn a high speed pinion against a gear , turning the high rotational speed from the engine to lower rotational speed for the propeller. The amount of reduction is based on

1840-528: 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

1886-507: The reduction drive assembly. But on smaller reduction drives attached to auxiliary machinery or if the design of the ship demands it, one can find thrust bearings as a part of the assembly. In order to ensure a reduction drive's smooth working and long lifetime, it is vital to have lubricating oil . A reduction drive that is run with oil free of impurities like water, dirt, grit and flakes of metal, requires little care in comparison to other type of engine room machinery. In order to ensure that

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1932-448: The rotational speed of an input shaft to an appropriate output speed. Reduction drives can be a gear train design or belt driven. Planetary reduction drives are typically attached between the shaft of the variable capacitor and the tuning knob of any radio , to allow fine adjustments of the tuning capacitor with smooth movements of the knob. Planetary drives are used in this situation to avoid "backlash", which makes tuning easier. If

1978-427: The shipbuilder and that of the gear manufacturer. The shipbuilder must provide a foundation that is sufficiently strong and rigid so that the gear mounting surface does not deflect greatly under operating conditions, a shaft alignment drawing that details the positions of line bearing and the method for aligning the forward piece of line shafting to the reduction gear coupling and the location of stern tube being such that

2024-875: 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

2070-406: The two Enterprise R5 V-16 diesel engines operate at their standard 514 rpm, the propeller turns at 140 rpm. A large variety of reduction gear arrangements are used in the industry. The three arrangements most commonly used are: double reduction utilizing two pinion nested, double reduction utilizing two-pinion articulated, and double reduction utilizing two-pinion locked train. The gears used in

2116-733: 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} }

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