Photo Nissan LEAF NISMO improved new model (20MY)

### [Nissan Leaf NISMO New Test Drive] The appearance of "ePlus NISMO" is awaited ... Yoichiro Watanabe

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The steering gear ratio was also changed quickly, reducing the steering angle by 20%.** **

The characteristic of electric vehicles such as the "Leaf" is that they have excellent environmental performance, but the accelerator pedal is depressed to drive the motor.** → Continue reading**

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# Gear ratio

**Gear ratio**(Hagurumahi) has twogearorRoller chainTwo connected bysprocketOf the number of teethratio, Or driveBeltTwo connected bypulley OfPerimeterIs the ratio of.Number of teeth ratio, gear (gear) ratio, gear (gear) ratio (British: gear ratio) Is sometimes called.

## Overview

In the photo on the right, a small gear (Pinion) Has 13 teeth, and the big gear next to it (idler,Idler wheel) Has 21 teeth.In this case, the gear ratio will be 21/13 or 1.62 / 1 (sometimes written as 1.62: 1).

This means that the pinion gear makes 1 revolutions while the idler gear makes one revolution.

In other words, each rotation of the pinion gear causes the idler gear to rotate 1 / 1, or 1.62.In simple terms, idler gears mean that they rotate slower than pinion gears.

右の写真に一部が写っている大きな歯車の歯数が42だとすると、この歯車とアイドラ歯車の歯車比は21/42 = 1/2であり、ピニオン歯車が1回転するときに大きな歯車は0.62/2 = 0.31回転する。したがって、この3つの歯車全体の減速比は約 1:3.23となる。

Since the idler gear in the middle touches both the large and small gears, this can be ignored in gear ratio calculations, and the gear ratio for all three gears is the teeth of the largest and smallest gears. The ratio of numbers can be calculated as 3/42 = 13.

Since the number of teeth is proportional to the circumference of the gear (the larger the ring, the larger the number of teeth), the gear ratio can also be expressed as the ratio of the circumferences of the two wheels.*d* The diameter of the small gear,*D* The diameter of the large gear,*gr* When is the gear ratio

BecomesradiusExpressed in

*r*Is a small gearradius,*R*Is the radius of the large gear

It can also be expressed as.

Peripheral speed of small gear*v _{d}* , Peripheral speed of large gear

*V*, Each angular velocity is ω

_{d}_{d}、ω

_{D}Then,

And combined with the above calculation,

Can be expressed by.In other words, the gear ratio is also the ratio of the diameter of the gear, and by extension, the ratio of the radius of the gear.

Gear-shaped pulleys connected by a belt with teeth,Bicycle,オ ー ト バ イThe same calculation can be performed when a special gear called a sprocket is connected with a chain as in.

Timing beltA belt with teeth called is an internal combustion engineCamshaftとCrankshaftSynchronize the movement ofvalveIs used to open and close accurately according to the movement of the cylinder.

In other applications, the camshaft and crankshaft are often directly connected by gears, whileTiming chainと 呼 ば れ るRoller chainOr silent chains are used for this purpose in automobiles.Either way4-stroke engineThen, the gear ratio between the camshaft and the crankshaft is always 2: 1 and the camshaft makes one rotation for every two rotations of the crankshaft.

In automobiles, the speed of the vehicle is usually adjusted mainly by switching the combination of many gears (speed stage).ト ラ ン ス ミ ッ シ ョ ンAnd the final reducer (usually) that increases the torque of the wheels with another set of gearsDifferential gear) Gears are used as speed adjusters in two places^{[1]}..These two devices are separatedPropeller shaftIt is integrated with the method connected byTransaxleThere are two types of methods.

The 2004 Chevrolet Corvette C6 Z5 with a 06-speed manual transmission is equipped with a transmission with gear ratios as shown in the table below.

Speed stage | Gear ratio |
---|---|

1 speed | 2.97:1 |

2 speed | 2.07:1 |

3 speed | 1.43:1 |

4 speed | 1.00:1 |

5 speed | 0.84:1 |

6 speed | 0.56:1 |

Backward | 3.28:1 |

In the case of 1st speed, the engine rotates 1 rotations per rotation of the output shaft of the transmission. The gear ratio of 2.97th gear is 4: 1 which means that the engine speed and the rotation speed of the transmission output shaft are the same, and in 1th and 5th speed called overdrive, the transmission output shaft is faster than the engine. Rotate.

In the Corvette example above, the gear ratio of the final reduction gear is 3.42: 1, and the transmission output shaft rotates 1 for each tire rotation.By multiplying the gear ratio of the transmission and the differential, the gear ratio of the entire power train is calculated. In the case of the 3.42st speed in this example, 1: 10.18, that is, every 1 rotations of the engine, the tire rotates once.

タ イ ヤCan also be considered as the third speed adjuster in the drive train of an automobile.If the above Corvette is equipped with 3 / 295-35 size tires, the outer circumference of the tires is 18 mm (2,085 inches), so the vehicle will advance 82.1 mm per rotation of the tire.If this car is fitted with larger tires, it will travel a longer distance per tire revolution, as in the case of high gear ratios, and a shorter distance for smaller tires.

Gear ratio of transmission and final reduction gear, tire size, engineNumber of rotationsThe vehicle speed at a specific speed stage can be calculated from.

For example, how much the car moves for each rotation of the engine can be calculated by dividing the tire outer circumference length by the gear ratio of the entire transmission and reduction gear.Tire circumference length*c _{t}* , Transmission gear ratio

*gr*, The gear ratio of the final reduction gear

_{t}*gr*Then, it can be expressed by the following equation.

_{d}Similarly, the vehicle speed at a certain engine speed can be obtained by multiplying the engine speed by the tire outer circumference length and dividing the gear ratio of the entire power train.Vehicle speed*v _{c}* , Engine speed

*v*Then, the following formula is obtained, and the vehicle speed at each speed stage when the engine rotates at 1,000 rpm is as shown in the table below.

_{e}Speed stage | The distance the car travels with each engine revolution | Vehicle speed at 1,000 rpm |
---|---|---|

1 speed | 205.3 mm | 12.3 km / h |

2 speed | 294.6 mm | 17.7 km / h |

3 speed | 426.4 mm | 25.6 km / h |

4 speed | 609.7 mm | 36.6 km / h |

5 speed | 725.9 mm | 43.6 km / h |

6 speed | 1089 mm | 65.3 km / h |

## Wide ratio and cross ratio

A transmission with a small difference in gear ratio at each speed stage is called a cross ratio transmission (or close ratio or cross transmission), and a transmission with a large difference is called a wide ratio transmission.For example, if the gear ratio between the input to the transmission and the output to the tire is 1: 4 for 1st gear and 2: 2 for 1nd gear, compare it with the one with 1st gear 4: 1 and 2nd gear 3: 1. It becomes a wide ratio.In the case of wide ratio, the ratio of gear ratios of 1st and 2nd gears is 4/2 = 2 (= 200%), and in the case of cross ratio, the same ratio is 4/3 = 1.33 (= 133%), 133% <200. Since it is%, 133% is the cross ratio.This calculation is more complicated because the gear ratio of each speed stage is different for each car.

A cross ratio transmission generally uses an engine with a narrow output band, and frequently shifts while maintaining high revs.sports carLight trucks and light vans (especially light vans) that frequently shift gears while maintaining a constant engine speed during loading.light truck, And light cab over vans).

Since the 4-speed or 5-speed transmission achieves both city driving and high-speed driving, the gear ratio difference between each speed stage decreases as the speed stage increases.This is because the gear ratio of the final speed stage is in the high torque range of the engine so as to facilitate reacceleration in the high speed range where the air resistance is large.If the gear ratio difference in each speed stage is large, the traction force in the 1st speed can be increased, but the engine speed drops significantly during shifting.By reducing the gear ratio difference, the maximum speed under specific conditions can be increased, but the acceleration at startup becomes worse.

In the case of a 4-speed transmission, the gear ratio of 1st gear is about 2.50: 1, and that of 4th gear is 1: 1 in almost all cases. The gear ratio between the 2nd and 3rd gears is determined in consideration of the vehicle weight, usage, vehicle speed, engine characteristics, etc.

*range*Is the difference in gear ratio (torque amplification factor) between 1st and 4th gears, which is largely between 2.8 and 3.2 in the case of wide ratio.This value is the most important factor that determines the starting acceleration.

*Progression*Is the next most important factor, and refers to the change in engine speed during shifting.Most transmissions have a maximum progression between 1st and 2nd gears, which decreases as the speed increases.Progression does not always decrease linearly due to various conditions such as the availability of gears and the need to reach a certain engine speed at a certain speed.

These two factors are not contradictory, but one limits the options of others.When a high reduction ratio is required at low speed due to a small output engine, a heavy vehicle body, a low gear ratio of a differential device, etc., a wide range is often taken.In this case, the engine speed is significantly reduced each time the gear is changed, as compared with the one having a narrow range. If the 1st gear ratio is small, the starting acceleration will be low, but the progression options will be wider.

There is no combination of transmission gear ratios or differential gear ratios that provide the best performance in all speed ranges, and there are some compromises.

The advantage of the cross ratio is that there is no decrease in engine speed in the high speed range, and there is spare capacity for acceleration from the high speed range such as 160 km / h, but on the other hand, the gear ratio in the low speed stage becomes smaller and the speed is low. There is a problem that the performance in the area deteriorates.In many races, the start is made from a stop on the grid, and acceleration is also important, so reducing the gear ratio difference is not always the best method even for races.In the case of a rolling start where the start is made while running in a platoon, start acceleration is not important and a smaller gear ratio difference is preferred.

In general, engines with low displacement, long cams, head intake and exhaust, and large carburetors start up slowly from low revs, and a cross ratio is more advantageous when shifting from 3rd gear to 4th gear.A cross ratio is suitable when shifting in the high speed range where air resistance is large.For racing, if the engine is set to produce high torque at a certain speed, the gear ratio needs to be adjusted to produce torque where it is needed on the course, but in other words it has shifted up. Sometimes it is necessary to design the engine so that it does not fall into the low torque range.

Consider the case where the engine is set to 7,000 rpm and the torque starts from 5,000 rpm.If the engine speed drops by 25% due to shifting, the engine speed after shifting can be re-accelerated at 5,250 rpm without any problem, but if it drops by 30%, this becomes 4,900 rpm, and there is a problem with re-acceleration until it reaches 5,000 rpm. It will be held and needs improvement.

Although it depends on the vehicle and course, this measure is generally taken by adjusting the low speed side.In other words, if there is a problem with the 2-3rd gear, the 1-2nd gear ratio is adjusted, but the result is not constant depending on the conditions.

Since the maximum speed and corner speed are different for each circuit, the gear ratio of the intermediate speed stage is determined in consideration of the necessity of downshifting during cornering.In this case, the key to the analysis is whether there is a problem with acceleration at the start of a specific corner.The cross ratio can reduce the engine speed difference between the two speed stages, but it is necessary to consider that it is necessary to increase the speed difference between some other speed stages.

The cross ratio isLarge carThere are also examples of adoption.It is common with sports cars and racing cars in that it adopts a cross ratio for the purpose of maintaining an efficient rotation range, but many large vehicles have a narrower effective rotation range than gasoline engines.diesel engineBecause the vehicle weight and cargo are heavier than those of passenger cars, the cross ratio is used to maintain the maximum torque range and fuel efficiency range of the engine.In particularTow vehicleThen.ト ラ ク タ ーIn order to tow a towed vehicle that carries much heavier cargo than (towing vehicle), there are cases where a multi-speed transmission with 10 or more speeds is installed in combination with an auxiliary transmission.

## Gear ratio of railroad cars

Railway carIn the electric car^{[2]}as well as the Electric railcars / diesel locomotivesin the case of,Main motorIt represents the gear ratio (= B / A) of the small gear (number of gears A) on the side and the large gear driven (number of gears B).

In this case, if the gear ratio is small, the number of rotations of the wheels is large and the low speed performance (acceleration / deceleration) is low, but the high speed performance (maximum speed or acceleration / deceleration in the high speed range) is high.For this reason,Limited express train,ShinkansenVehicles and the like deserve this.

On the contrary, when the gear ratio is large, the rotational force of the wheel is large and the low speed performance is high, but the high speed performance is low.In particularcargouseElectric locomotive,Commuter trainDeserves this.

Internal combustion motor vehicleMechanical,Liquid typeBoth are the same as automobiles in that they are a combination of a transmission and a final reduction gear, but they differ in that they can run at the same gear ratio (can drive at the same speed) both forward and backward using a reverse gear.^{[3]}.

## Idler gear

It should be noted that in the case of a series of connected gears, the gear ratio of the entire system can be calculated only by the number of teeth of the first gear and the last gear.The gears in the middle are irrelevant to the overall gear ratio regardless of their size, but the rotation of the last gear is reversed for each additional gear.

The middle gear that doesn't work**Idra**gear(idler wheel,Idler wheel).The idler gear used to reverse the rotation**Reverse idler**Sometimes called.In the case of a manual transmission of an automobile, a reverse idler is inserted between the two gears to move backward.

Idler gears are also used when the output and input shafts are far apart and it is not practical to simply use two large gears.Unlike the image received from the word idler, the load applied to the shaft is larger than that of the available shaft and output shaft because it receives both driving force and reaction force, and a bearing with a sufficient load capacity is required for designing.Larger gears require more space and rotational inertia in proportion to the square of the radius (Moment of inertia) Will increase.In such cases, belts and chains can be used instead of idler gears.

## footnote

**^**さ ら にtransferAnd differential gearSub transmissionAnd those withHabriductionSome models have a system.Equipped with auxiliary transmission and hub reductionMercedes-Benz-UnimogWill have a total of four speed reduction devices.**^**Electric trainとElectric locomotive.**^**Based on a carRailroad vehicleSome also have a reversing machine.

## Related item

## 外部 リンク

- Gear ratio at How Stuff Works
- "GearCalc" --Software that calculates the theoretical maximum speed of each speed stage, the vehicle speed at 1,000 rpm.
- "Perfect Shifting" --Software that calculates vehicle speed with variable gear ratio and engine rotation.