CN106640500B - Power generation facility based on roll motion - Google Patents
Power generation facility based on roll motion Download PDFInfo
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- CN106640500B CN106640500B CN201710140255.1A CN201710140255A CN106640500B CN 106640500 B CN106640500 B CN 106640500B CN 201710140255 A CN201710140255 A CN 201710140255A CN 106640500 B CN106640500 B CN 106640500B
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- F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
- F03—MACHINES OR ENGINES FOR LIQUIDS; WIND, SPRING, OR WEIGHT MOTORS; PRODUCING MECHANICAL POWER OR A REACTIVE PROPULSIVE THRUST, NOT OTHERWISE PROVIDED FOR
- F03B—MACHINES OR ENGINES FOR LIQUIDS
- F03B13/00—Adaptations of machines or engines for special use; Combinations of machines or engines with driving or driven apparatus; Power stations or aggregates
- F03B13/12—Adaptations of machines or engines for special use; Combinations of machines or engines with driving or driven apparatus; Power stations or aggregates characterised by using wave or tide energy
- F03B13/14—Adaptations of machines or engines for special use; Combinations of machines or engines with driving or driven apparatus; Power stations or aggregates characterised by using wave or tide energy using wave energy
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- F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
- F03—MACHINES OR ENGINES FOR LIQUIDS; WIND, SPRING, OR WEIGHT MOTORS; PRODUCING MECHANICAL POWER OR A REACTIVE PROPULSIVE THRUST, NOT OTHERWISE PROVIDED FOR
- F03B—MACHINES OR ENGINES FOR LIQUIDS
- F03B11/00—Parts or details not provided for in, or of interest apart from, the preceding groups, e.g. wear-protection couplings, between turbine and generator
- F03B11/06—Bearing arrangements
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- F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
- F05—INDEXING SCHEMES RELATING TO ENGINES OR PUMPS IN VARIOUS SUBCLASSES OF CLASSES F01-F04
- F05B—INDEXING SCHEME RELATING TO WIND, SPRING, WEIGHT, INERTIA OR LIKE MOTORS, TO MACHINES OR ENGINES FOR LIQUIDS COVERED BY SUBCLASSES F03B, F03D AND F03G
- F05B2220/00—Application
- F05B2220/70—Application in combination with
- F05B2220/706—Application in combination with an electrical generator
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- F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
- F05—INDEXING SCHEMES RELATING TO ENGINES OR PUMPS IN VARIOUS SUBCLASSES OF CLASSES F01-F04
- F05B—INDEXING SCHEME RELATING TO WIND, SPRING, WEIGHT, INERTIA OR LIKE MOTORS, TO MACHINES OR ENGINES FOR LIQUIDS COVERED BY SUBCLASSES F03B, F03D AND F03G
- F05B2260/00—Function
- F05B2260/40—Transmission of power
- F05B2260/403—Transmission of power through the shape of the drive components
- F05B2260/4031—Transmission of power through the shape of the drive components as in toothed gearing
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- Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
- Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
- Y02E—REDUCTION OF GREENHOUSE GAS [GHG] EMISSIONS, RELATED TO ENERGY GENERATION, TRANSMISSION OR DISTRIBUTION
- Y02E10/00—Energy generation through renewable energy sources
- Y02E10/20—Hydro energy
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- Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
- Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
- Y02E—REDUCTION OF GREENHOUSE GAS [GHG] EMISSIONS, RELATED TO ENERGY GENERATION, TRANSMISSION OR DISTRIBUTION
- Y02E10/00—Energy generation through renewable energy sources
- Y02E10/30—Energy from the sea, e.g. using wave energy or salinity gradient
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- Chemical & Material Sciences (AREA)
- Combustion & Propulsion (AREA)
- Mechanical Engineering (AREA)
- General Engineering & Computer Science (AREA)
- Connection Of Motors, Electrical Generators, Mechanical Devices, And The Like (AREA)
- Other Liquid Machine Or Engine Such As Wave Power Use (AREA)
Abstract
一种基于横摇运动的发电装置,可以安装于横摇式波浪发电设备或横摇式消波堤中,属于利用海洋能发电的新能源领域。该发电装置包括第一转轴、第一单向轴承、大齿轮、小齿轮、第二转轴、发电机、轴承、第二单向轴承、横摇设备。第一转轴与横摇设备固定连接,第一单向轴承固定嵌套在第一转轴上,大齿轮固定嵌套在第一单向轴承上,发电机和轴承固定连接在横摇设备上,第二转轴连接发电机和轴承,第二单向轴承固定嵌套在第二转轴上,小齿轮又固定嵌套在第二单向轴承上,并位于发电机和轴承之间,与大齿轮紧密啮合在一起。该发电装置结构简单,造价低廉,效能比高,可靠性高,无污染,在规则波与不规则波下均可有效发电,并且具有良好的消波能力。
The utility model relates to a power generation device based on rolling motion, which can be installed in a rolling wave power generation device or a rolling wave breaker, and belongs to the field of new energy using ocean energy to generate electricity. The power generating device includes a first rotating shaft, a first one-way bearing, a large gear, a small gear, a second rotating shaft, a generator, a bearing, a second one-way bearing, and rolling equipment. The first rotating shaft is fixedly connected to the rolling equipment, the first one-way bearing is fixedly nested on the first rotating shaft, the large gear is fixedly nested on the first one-way bearing, the generator and the bearing are fixedly connected to the rolling equipment, and the first one-way bearing is fixedly nested on the first one-way bearing. The two rotating shafts are connected to the generator and the bearing, the second one-way bearing is fixedly nested on the second rotating shaft, and the pinion is fixedly nested on the second one-way bearing, and is located between the generator and the bearing, and is closely meshed with the large gear together. The power generation device has the advantages of simple structure, low cost, high efficiency ratio, high reliability, no pollution, can generate electricity effectively under regular waves and irregular waves, and has good wave absorbing ability.
Description
技术领域technical field
本发明涉及一种基于横摇运动的发电装置,可以安装于横摇式波浪发电设备或横摇式消波堤中,属于利用海洋能发电的新能源领域。The invention relates to a power generation device based on rolling motion, which can be installed in a rolling wave power generation device or a rolling wave breaker, and belongs to the field of new energy using ocean energy to generate electricity.
背景技术Background technique
1974年工程师Salter发明了一种横摇式波能转换装置,该装置的设计严谨,横截面轮廓呈非对称型式,其前端(迎浪面)较小,后部(背浪面)较大,水下部分为圆弧形,装置在波浪作用下绕转动轴发生横摇运动,并且可以将几乎所有的短波拦截下来,此波能转换装置在短波时的一级转换效率可以接近于100%。In 1974, engineer Salter invented a rolling wave energy conversion device. The design of the device is rigorous and the cross-sectional profile is asymmetrical. The underwater part is arc-shaped, and the device rolls around the rotation axis under the action of waves, and can intercept almost all short waves. The first-order conversion efficiency of this wave energy conversion device in short waves can be close to 100%.
虽然波浪发电研究经过几十年的发展,先后出现过几十种不同的发电装置的设计,以提高发电效率。但是现有的波浪发电机依然存在以下缺点:结构复杂,摩擦过多,制造成本高昂,易发生故障,使用寿命低,波浪能损耗大,并且当波浪较小时,极易停止工作导致其有效工作时间较短。此外,一些消波设备在消波过程中,具有横摇运动,此横摇动能源自波浪能,但是通常被浪费。通过安装本发明中的发电装置,即可将波浪能转化为电能,进而加以利用。Although wave power research has been developed for decades, dozens of different power generation device designs have emerged to improve power generation efficiency. However, the existing wave generator still has the following shortcomings: complex structure, excessive friction, high manufacturing cost, easy failure, low service life, large wave energy loss, and when the wave is small, it is easy to stop working and cause it to work effectively. shorter time. In addition, some wave-dissipating devices have a rolling motion during wave-dissipation, and the rolling energy is derived from wave energy, but is usually wasted. By installing the power generation device in the present invention, the wave energy can be converted into electric energy and then utilized.
正是基于这种具有极高的波浪能与机械能转换效率横摇装置,本发明在该横摇设备中设计安装了结构简单,造价低廉,可靠性强,能效比高,有效工作时间长,经济效益好的发电装置,有效的解决了现有横摇波浪发电装置所存在的结构复杂,造价昂贵,故障率高,能量转换率低,有效工作时间较短的问题。It is precisely based on this kind of rolling device with extremely high wave energy and mechanical energy conversion efficiency that the present invention is designed and installed in the rolling device with simple structure, low cost, strong reliability, high energy efficiency ratio, long effective working time and economical. The high-efficiency power generating device effectively solves the problems of complex structure, high cost, high failure rate, low energy conversion rate and short effective working time of the existing rolling wave power generating device.
发明内容SUMMARY OF THE INVENTION
针对现有技术的诸多不足,本发明提供一种横摇式发电装置,该发电装置应结构简单、造价低廉、可靠性高、能效比高的发电装置。In view of many deficiencies in the prior art, the present invention provides a roll-type power generation device, which should be a power generation device with simple structure, low cost, high reliability and high energy efficiency ratio.
本发明采用的技术方案是:一种基于横摇运动的发电装置,它包括第一转轴、大齿轮、小齿轮、第二转轴、发电机和轴承,它还包括第一单向轴承、第二单向轴承和横摇设备,发电机和多个轴承固定连接在横摇设备上,所述第一转轴通过两个轴承与横摇设备固定连接,第一单向轴承固定嵌套在第一转轴上,大齿轮又固定嵌套在第一单向轴承上;所述第二转轴连接发电机和轴承,第二单向轴承固定嵌套在第二转轴上,小齿轮又固定嵌套在第二单向轴承上,并位于发电机和轴承之间,小齿轮与大齿轮紧密啮合在一起;第一转轴是横摇设备的旋转中心,横摇设备以第一转轴为中心并带动第一转轴一起做横摇运动,第一转轴带动第一单向轴承随之转动;当第一转轴随横摇设备顺时针转动的速度大于大齿轮的速度时,第一单向轴承带动大齿轮加速转动,当第一转轴随横摇设备逆时针方向转动的速度小于大齿轮时,第一单向轴承不再带动大齿轮转动,大齿轮在第一单向轴承带动下只沿一个方向转动;在上述过程中,大齿轮带动与其啮合的小齿轮转动,当小齿轮逆时针方向转动的速度大于第二转轴时,第二单向轴承带动第二转轴加速转动;当小齿轮顺时针方向转动的速度小于第二转轴时,第二单向轴承不再带动第二转轴转动;小齿轮的转动将动力传递给第二转轴,带动发电机工作发电。The technical scheme adopted in the present invention is: a power generation device based on rolling motion, which includes a first rotating shaft, a large gear, a small gear, a second rotating shaft, a generator and a bearing, and also includes a first one-way bearing, a second The one-way bearing and the rolling device, the generator and the plurality of bearings are fixedly connected to the rolling device, the first rotating shaft is fixedly connected to the rolling device through two bearings, and the first one-way bearing is fixedly nested in the first rotating shaft The large gear is fixedly nested on the first one-way bearing; the second rotating shaft is connected to the generator and the bearing, the second one-way bearing is fixedly nested on the second rotating shaft, and the pinion is fixedly nested on the second rotating shaft. On the one-way bearing and between the generator and the bearing, the pinion and the large gear are closely meshed together; the first rotating shaft is the rotation center of the rolling equipment, and the rolling equipment takes the first rotating shaft as the center and drives the first rotating shaft together When the rolling motion is performed, the first rotating shaft drives the first one-way bearing to rotate accordingly; when the clockwise rotation speed of the first rotating shaft with the rolling equipment is greater than the speed of the large gear, the first one-way bearing drives the large gear to accelerate the rotation. When the speed of the counterclockwise rotation of the first rotating shaft with the rolling device is lower than that of the large gear, the first one-way bearing no longer drives the large gear to rotate, and the large gear only rotates in one direction driven by the first one-way bearing; during the above process , the large gear drives the pinion that meshes with it to rotate. When the speed of the pinion rotating counterclockwise is greater than that of the second shaft, the second one-way bearing drives the second shaft to accelerate; when the speed of the pinion clockwise is less than the second When rotating the shaft, the second one-way bearing no longer drives the second rotating shaft to rotate; the rotation of the pinion transmits the power to the second rotating shaft to drive the generator to work and generate electricity.
采用上述的技术方案,该装置的能量输入是基于横摇设备的横摇运动,横摇设备的横摇运动是发电装置的主要动力来源。发电装置将横摇设备横摇的机械能转化为电能。在上述机构中,第一转轴与横摇设备固定连接,当横摇设备横摇时可以带动第一转轴与其一起转动。当第一转轴随横摇设备转动时,通过第一单向轴承带动大齿轮随之转动,大齿轮再通过小齿轮将转速传递给第二转轴,进而带动发电机工作而发出充裕的电能。大齿轮自身的惯性矩较大,大齿轮在第一单向轴承带动下只沿一个方向转动。With the above technical solution, the energy input of the device is based on the rolling motion of the rolling equipment, and the rolling motion of the rolling equipment is the main power source of the power generating device. The power generation device converts the mechanical energy of the rolling equipment into electrical energy. In the above mechanism, the first rotating shaft is fixedly connected with the roll device, and when the roll device rolls, the first rotating shaft can be driven to rotate together with it. When the first shaft rotates with the rolling device, the first one-way bearing drives the large gear to rotate along with it, and the large gear transmits the rotational speed to the second shaft through the pinion, thereby driving the generator to work to generate sufficient electrical energy. The inertia moment of the large gear itself is relatively large, and the large gear only rotates in one direction driven by the first one-way bearing.
为确保当横摇设备转动时,大齿轮持续通过小齿轮将转速传递给第二转轴,进而带动发电机工作,则需要在第一转轴与大齿轮之间安装第一单向轴承,第二转轴与小齿轮之间安装第二单向轴承。In order to ensure that when the rolling equipment rotates, the large gear continuously transmits the rotational speed to the second rotating shaft through the pinion, and then drives the generator to work, it is necessary to install a first one-way bearing between the first rotating shaft and the large gear, and the second rotating shaft A second one-way bearing is installed between the pinion and the pinion.
第一单向轴承、第二单向轴承的作用有共同点也有不同点,共同点是:无论横摇设备遭遇何种风浪,以何种频率、幅度作横摇运动,第一单向轴承、第二单向轴承都可以将其转化为持续的单向转动,以便于发电机将机械能转化为电能。不同点是:The functions of the first one-way bearing and the second one-way bearing have similarities and differences. The common point is that no matter what kind of wind and waves the rolling equipment encounters, and at what frequency and amplitude, the first one-way bearing, The second one-way bearing can convert it into continuous one-way rotation, so that the generator can convert mechanical energy into electrical energy. The differences are:
1、所述第一单向轴承作用是:当第一转轴随横摇设备顺时针方向转动的速度大于大齿轮的速度时,第一单向轴承带动大齿轮加速转动,当第一转轴随横摇设备逆时针方向转动的速度小于大齿轮时,第一单向轴承不再带动大齿轮转动。1. The function of the first one-way bearing is: when the speed of the first rotating shaft rotating clockwise with the rolling device is greater than the speed of the large gear, the first one-way bearing drives the large gear to accelerate the rotation, and when the first rotating shaft rotates with the horizontal When the counterclockwise rotation speed of the shaking device is lower than that of the large gear, the first one-way bearing no longer drives the large gear to rotate.
2、所述第二单向轴承作用是:当小齿轮逆时针方向转动的速度大于第二转轴时,第二单向轴承带动第二转轴加速转动,当小齿轮顺时针方向转动的速度小于第二转轴时,第二单向轴承不再带动第二转轴转动。2. The function of the second one-way bearing is: when the speed of the pinion rotating in the counterclockwise direction is greater than that of the second rotating shaft, the second one-way bearing drives the second rotating shaft to accelerate the rotation; When there are two rotating shafts, the second one-way bearing no longer drives the second rotating shaft to rotate.
所述发电装置的动力主要源于横摇设备的横摇,其可以安装在固定式横摇设备内,也可安装在浮式横摇设备内,这两种型式的横摇设备都可以在水面上随波浪的运动而发生横摇。The power of the power generation device mainly comes from the rolling of the rolling equipment, which can be installed in the fixed rolling equipment or in the floating rolling equipment. Both types of rolling equipment can be installed on the water surface. It rolls with the movement of the waves.
当转轴速度小于大齿轮速度时,大齿轮还可以继续保持正向转动向发电机输送能量的原因是,大齿轮的转动惯量较大,其所储存的能量也较多,不会被发电机快速消耗掉。When the speed of the rotating shaft is less than the speed of the large gear, the reason why the large gear can continue to rotate in the forward direction to transmit energy to the generator is that the large gear has a large moment of inertia and stores more energy, which will not be quickly affected by the generator. Use up.
常规上,所述发电装置需要通过稳压装置连接蓄电设备或是用户设备。Conventionally, the power generation device needs to be connected to a power storage device or user equipment through a voltage stabilizer.
本发明的有益效果是:The beneficial effects of the present invention are:
1、该发电装置是基于横摇设备,横摇设备在波浪能转化机械能方面有巨大的优势。其可以拦截住几乎所有的短波,并且在短波时的一级波能转换效率可以接近于100%。1. The power generation device is based on rolling equipment, which has huge advantages in converting wave energy into mechanical energy. It can intercept almost all short waves, and the first-order wave energy conversion efficiency at short waves can be close to 100%.
2、该发电装置能够感知较小的波浪,灵敏度高,通过大小齿轮的配合实现转速加速的效果,然后将转动传递给发电机,实现源源不断的发电。2. The power generation device can perceive small waves and has high sensitivity. The effect of speed acceleration is achieved through the cooperation of large and small gears, and then the rotation is transmitted to the generator to achieve continuous power generation.
3、该发电装置的第一单向轴承、第二单向轴承机构可以实现将横摇设备的机械能通过大小齿轮源源不断的输送给发电机。这是因为,无论横摇设备遭遇何种风浪,以何种频率、幅度作横摇运动,第一单向轴承、第二单向轴承都可以将其转化为持续的单向转动,以便于发电机将机械能转化为电能,大大延长发电装置的有效工作时间,增加发电量,提高其经济效益。3. The first one-way bearing and the second one-way bearing mechanism of the power generating device can continuously transmit the mechanical energy of the rolling equipment to the generator through the large and small gears. This is because, no matter what kind of wind and waves the rolling equipment encounters, and what frequency and amplitude the rolling motion is, the first one-way bearing and the second one-way bearing can convert it into continuous one-way rotation, so as to facilitate power generation The machine converts mechanical energy into electrical energy, greatly extending the effective working time of the power generation device, increasing the power generation and improving its economic benefits.
4、该发电装置结构简单,一方面可以使其建造成本降低,实现大面积推广应用,另一方面其可靠性强,维修率低,维护成本低,最重要的是其有效工作时间长,发电量大,可以实现极好的经济效益。4. The power generation device has a simple structure. On the one hand, it can reduce the construction cost and realize large-scale popularization and application. On the other hand, it has strong reliability, low maintenance rate and low maintenance cost. The most important thing is that it has a long effective working time and can generate electricity. Large quantity can achieve excellent economic benefits.
附图说明Description of drawings
图1是一种横摇式发电装置的正视结构图。FIG. 1 is a front structural view of a roll-type power generation device.
图2是一种横摇式发电装置的侧视结构图。FIG. 2 is a side structural view of a roll type power generation device.
图3是图1的剖面图。FIG. 3 is a cross-sectional view of FIG. 1 .
图中:1、第一转轴,2、第一单向轴承,3、大齿轮,4、小齿轮,5、第二转轴,6、发电机,7、轴承,8、第二单向轴承,9、横摇设备。In the figure: 1, the first shaft, 2, the first one-way bearing, 3, the large gear, 4, the pinion, 5, the second shaft, 6, the generator, 7, the bearing, 8, the second one-way bearing, 9. Rolling equipment.
具体实施方式Detailed ways
下面结合附图和实施方式对本发明的技术方案作进一步说明。The technical solutions of the present invention will be further described below with reference to the accompanying drawings and embodiments.
图1、2、3示出了一种横摇式发电装置的结构图。图中,这种基于横摇运动的发电装置包括第一转轴1、大齿轮3、小齿轮4、第二转轴5、发电机6、轴承7、第一单向轴承2、第二单向轴承8和横摇设备9,发电机6和多个轴承7固定连接在横摇设备9上。第一转轴1通过两个轴承7与横摇设备9固定连接,第一单向轴承2固定嵌套在第一转轴1上,大齿轮3又固定嵌套在第一单向轴承2上。第二转轴5连接发电机6和轴承7,第二单向轴承8固定嵌套在第二转轴5上,小齿轮4又固定嵌套在第二单向轴承8上,并位于发电机6和轴承7之间,小齿轮4与大齿轮3紧密啮合在一起。第一转轴1是横摇设备9的旋转中心,横摇设备9以第一转轴1为中心并带动第一转轴1一起做横摇运动,第一转轴1带动第一单向轴承2随之转动。当第一转轴1随横摇设备9顺时针转动的速度大于大齿轮3的速度时,第一单向轴承2带动大齿轮3加速转动,当第一转轴1随横摇设备9逆时针方向转动的速度小于大齿轮3时,第一单向轴承2不再带动大齿轮3转动,大齿轮3在第一单向轴承2带动下只沿一个方向转动。在上述过程中,大齿轮3带动与其啮合的小齿轮4转动,当小齿轮4逆时针方向转动的速度大于第二转轴5时,第二单向轴承8带动第二转轴5加速转动。当小齿轮4顺时针方向转动的速度小于第二转轴5时,第二单向轴承8不再带动第二转轴5转动;小齿轮4的转动将动力传递给第二转轴5,带动发电机6工作发电。Figures 1, 2 and 3 show the structure diagram of a rolling type power generating device. In the figure, the power generation device based on rolling motion includes a
采用上述的技术方案,当第一转轴1速度小于大齿轮3速度时,大齿轮3还可以继续保持正向转动向发电机6输送能量的原因是,大齿轮3的转动惯量较大,其所储存的能量也较多,不会被发电机6快速消耗掉。大齿轮3、小齿轮4的直径比很大,大齿轮3、小齿轮4的配合转动起到了加速的作用,使转速达到发电机6的发电要求。Using the above technical solution, when the speed of the first
当第一转轴1随横摇设备顺时针方向转动的速度大于大齿轮3的速度时,第一单向轴承2带动大齿轮3加速转动,当第一转轴1随横摇设备9逆时针方向转动的速度小于大齿轮3时,第一单向轴承2不再带动大齿轮3转动。第一单向轴承只能带动大齿轮顺时针单向转动3。When the speed of the first
当小齿轮4逆时针方向转动的速度大于第二转轴5时,第二单向轴承8带动第二转轴5加速转动,当小齿轮4顺时针方向转动的速度小于第二转轴5时,第二单向轴承8不再带动第二转轴5转动。第二单向轴承只能带动第二转轴逆时针单向转动。When the rotation speed of the
这种基于横摇运动的发电装置的运行方式:横摇设备9以第一转轴1为中心的横摇运动带动第一转轴1往复转动,第一转轴1通过第一单向轴承2将往复转动转化为大齿轮3的顺时针方向的单向转动,经过与小齿轮4的啮合获得足够转速,转动方向也被传递成小齿轮的逆时针方向的单向转动,然后经过第二单向轴承8传递到第二转轴5上带动发电机6转动并发电,发出的电通过稳压装置连接蓄电设备或是用户设备。The operation mode of the power generation device based on rolling motion: the rolling motion of the rolling
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