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preface
In modern industry, mechanical transmission is an indispensable part, and gear transmission as a common and efficient transmission method, its tooth shape design has an important impact on transmission efficiency and stability.
However, in practical applications, traditional gear transmission often has some problems, such as high noise, low efficiency, short life, etc.
In order to solve these problems, the researchers in our team have begun to conduct in-depth research on the tooth shape design of gear transmission, where the number of teeth plays a key role in transmission performance.
In the past design, more teeth were often used to improve the smoothness of the transmission, but this also brought some disadvantages, more teeth will increase manufacturing costs and friction losses, and also increase the possibility of noise.
Therefore, the gear shape design of the gear transmission with less gear count faces a series of challenges, such as the control of tooth shape error and the improvement of tooth surface contact.
In order to overcome these challenges, some people in our team have adopted a variety of methods and technologies, among which, tooth shape design based on numerical simulation and optimization algorithms has become a research hotspot, and through the help of computer simulation and optimization algorithms, the optimal tooth profile parameters can be quickly obtained, so as to achieve the optimal design of gear transmission with less teeth.
So, what method should be used to optimize gear transmission with low tooth count, and what are the pros and cons?
The load carrying capacity of the gear drive
Gear transmission is one of the most important mechanisms in the field of mechanical transmission, can transmit power and movement, to achieve variable speed, torque and direction change and other needs, its transmission precision is high, high efficiency, high power, long service life and compact structure, with a wide range of applications, although it has a history of thousands of years, but is still the core component of many electromechanical products.
In recent years, with the rapid development of computing science and CNC machine tool technology, new methods and technologies have emerged, bringing new vitality and methods to the design and processing of gears, and gear transmission has also developed towards the trend of lightweight, miniaturization, diversification, extreme and intelligence.
To this end, our research team has done a lot of work on the research and application of gear transmission in new tooth shapes, new structures, new theories, new analysis methods and new processing technologies, and has achieved rich results.
Among them, single-stage large transmission applied under extreme conditions and gear transmission with less number of teeth are hot spots in the field of gear transmission research and application in recent years, but some practical problems in practical applications have yet to be solved.
In the application of gear transmission, there are often some extreme design situations, such as under the condition of limited space and quality, the number of pinion teeth in the gear pair is required to be as small as 6 or less, so as to meet the larger transmission ratio.
With the development of instruments, equipment and equipment in the direction of miniaturization and lightweight, the design and application of gear pairs with fewer teeth composed of pinions has put forward new requirements, and gear transmission with less teeth has a wide range of applications, such as reduction devices and micro reducers and precision instruments in the field of aerospace and robot transmission.
However, too few pinion teeth will cause the bearing capacity of gear transmission to decrease, the meshing performance will deteriorate, and the pinion shaft is slender and easy to break, the tooth top becomes sharp and the root cut is serious.
The gear transmission with less gear count and worm gear transmission have the characteristics of large transmission ratio, compact mechanism and line contact, but there are also essential differences, less gear transmission belongs to plane parallel shaft gear transmission, transmission power is dependent on the tangential division of the tooth contact point, and worm gear worm belongs to the space staggered shaft gear transmission, the transmission of power is dependent on the axial component of the gear tooth contact point.
For worm gear transmission compared with parallel shaft gear transmission, the relative sliding speed between the teeth of the meshing wheel is large, the friction loss of the tooth surface is large, and the transmission efficiency is low, so it is necessary to carry out research on the gear transmission with a large transmission ratio, small size, lighter weight, more compact structure and wide application prospects.
At present, the vast majority of studies regard the gear with less tooth count as an extreme case of involute gear transmission, and there are deficiencies in the gear transmission of the involute as the tooth profile curve by correcting the tooth profile curve or the cutting edge curve of the machining tool.
In terms of tooth shape design theory, the tooth design theory for the characteristics of gear transmission with less teeth has not been deepened and improved, and it has not been able to get rid of the limitation of involute gear, and lacks targeted research ideas and results.
Therefore, some people in our team have conducted relevant research on involute gears and made in-depth analysis of their possible problems, in order to solve the most basic problems.
Involute in gear transmission
Low-tooth-count gears are an extreme case of gear transmission, and involute lines are still used as the tooth profile curve in most studies.
Due to many problems such as small number of pinion teeth, small shaft diameter and large transmission ratio, such as serious root cutting, low bearing capacity, poor meshing performance and processing difficulties, there has been no systematic research at present, and there is no clear reveal, which causes the root cause of low bearing capacity of gear transmission with low involute line and low number of teeth, and poor meshing performance.
Taking the involute gear with less teeth as the research object and revealing the main failure form of the gear with the number of teeth is the basis and entry point of the research.
To this end, some people in our team have carried out research on this problem, on the geometric modeling and processing of gear pairs with low number of teeth in involute line, transmission test research, to solve the geometric problems of gear with low number of teeth and obtain the main failure form of gear transmission with low number of teeth.
When the number of teeth of standard involute gears is less than 17, root cutting will occur, and the number of teeth of the gear with less teeth in this study is between 2-6, and if the design parameters are not adjusted, serious root cutting will inevitably occur, and the tooth top will also appear sharpened.
Because the coincidence of gear sub-faces is generally less than 1 if the involute has fewer teeth, if spur gears are used, it is necessary to increase the degree of coincidence by increasing the tooth top height and reducing the meshing angle to ensure continuous transmission.
In practical applications, most gear transmission with less teeth will use helical gears, mainly because helical gear transmission is more stable than spur gear transmission, its transmission is stable, noise is small, the meshing performance is good, the total coincidence is large, the tooth surface meshing imprint is long, and the load of single pairs of gears can be reduced and the bearing capacity of gears can be improved.
Therefore, this study is mainly for the study of helical teeth and cylindrical gears with few teeth, so it is necessary to establish a end face model and a tooth surface mathematical model.
It is in this way that this gear end face model can visually reflect the profile of the gear, and the end tooth profile consists of a tooth top arc, an involute line, a transition curve and a cogging bottom arc, where the top arc is determined by the tooth blank.
In the gear with a small number of teeth, the tooth top appears sharpened, the end face tooth profile has no tooth top arc, and the groove bottom arc is generally a tooth root arc segment tangent to the transition curve, and the end face model needs to establish the involute equation and the transition curve equation respectively.
In terms of testing, the main reasons for the low bearing capacity of the gear transmission with a small number of teeth, as well as the poor meshing performance and the main failure form of the transmission have not been clearly revealed.
In this case, our team has carried out research on the modeling of gears with low tooth count, transmission tests, strength analysis, tooth shape design and new tooth shape analysis.
Among them, involute gears are favored in the selection of gear profiles due to their advantages of high transmission efficiency, easy interchangeability, theoretical research and mature design and manufacturing technology.
Studies have shown that when the number of teeth of involute gears is less than 7, the tooth top of the gear in displacement begins to sharpen, which was once thought to be the limit number of teeth of involute gears, and gears with less than 7 teeth will cause many problems due to the small number of teeth.
For this reason, our team has conducted in-depth research on gears with a low number of teeth, and after machining and testing them, the results obtained are not what they originally wanted.
Machining test of gears
Therefore, it can be seen from the solid model that the pinion root cutting problem can be solved by large radial displacement.
Although it can meet the transmission needs under certain conditions, due to the characteristics of small wheel shaft diameter and easy deformation, it is easy to lead to insufficient bearing capacity and other problems, and subsequent tests and theoretical analysis will be carried out for research.
The low number of teeth gear is a problem for machining the application of low number of teeth, and the trial production of test gears is carried out using special hob cutters and hobbing machines with large mounting angles.
In the gear processing method, hobbing has the characteristics of high efficiency and good precision, and it is applied to machining gears with a small number of teeth, which requires specific requirements for the movement of machine tools and hobs.
Therefore, this becomes a low-tooth-count gear that can be machined efficiently and with high precision, and for high-efficiency CNC gear hobbing machines, our team has a special hob design.
Therefore, according to the given basic parameters of the test gear pair and the design method of the hob, the relevant parameters of the hob are designed, and the hob material will be used in the corresponding technology.
According to the test needs, the CNC gear hobbing machine and special hob are used to hobbing the gears with the given parameters with a small number of teeth, and the gear material is carburized and quenched heat treatment.
Finally, after testing, the gear accuracy is to meet the design requirements, it can be seen that the pinion presents a small shaft diameter and a pointed tooth top, and the transmission test will be carried out to study its bearing capacity and meshing performance.
Due to the special shape of the pinion, it leads to gear transmission with a small number of teeth, and uncertainty in terms of load carrying capacity and meshing performance.
However, it is necessary to obtain the similarities and differences between its efficiency, failure and meshing performance compared with traditional gear transmission through transmission test, and then obtain a new and targeted tooth design theory, so as to get rid of the limitation of involute line and obtain targeted tooth design research ideas.
In this test, a gear transmission test bench with a low number of teeth was designed and a test test system was built to test transmission efficiency, fatigue life and meshing performance.
For the test content of the transmission test, it mainly includes the transmission efficiency, bearing capacity and meshing performance of involute gear transmission with low number of teeth to obtain the main failure form of gear with low number of teeth.
According to the needs of the transmission test and the processed gear pair parameters, it mainly includes the following components: motor, test gearbox, two torque speed sensors, magnetic powder brake and elastic column pin coupling.
The output load of the magnetic powder brake is controlled by the PAB high-precision steady current source, which can change the size of the load, and the efficiency value of the gear pair under different loads can be measured, and it can be seen from the tooth surface after the test that the pinion tooth surface has pitting corrosion.
This is due to the high meshing frequency of the pinion tooth surface, and under the combined action of varying contact stress, tooth surface friction and lubricant, cracks are generated on the tooth surface, and pits are formed by falling off.
A small amount of glued area will appear on the surface, because the pinion under high-speed operation, the tooth surface contact stress is large, the sliding speed is high, resulting in a higher temperature on the tooth surface, resulting in instantaneous sticking welding phenomenon.
After a long time test, the pinion shaft with the number of teeth of 2 will be broken as a whole, according to the cross-section analysis, it belongs to the bending fatigue fracture, the main reason is that the pinion shaft diameter is small, the bending during the transmission process, and the torsional deformation is serious.
The wear of the tooth surface of the large gear is also obvious, and some tooth surfaces are worn and a small amount of glued area appears.
The test shows that contact fatigue pitting corrosion is the main failure form of gear transmission with less teeth, the main reason is: the tooth surface contact mode formed by involute line is convex-convex meshing, and the comprehensive curvature is large, resulting in large tooth surface contact stress, because the number of pinion tooth surface stress cycles is much greater than that of large gear.
And in the meshing process stress cycle cycle is very small, tooth surface can not timely heat dissipation resulting in tooth surface temperature is too high, in addition, low tooth surface contact fatigue strength is also the main factor, this is due to the difficulty of processing, tooth surface is not subjected to high-strength heat treatment and grinding and other processing.
Therefore, when designing the parameters of gear pairs with less teeth, the parameter selection is carried out by the tooth surface contact fatigue strength calculation formula, and then checked according to the tooth root bending fatigue strength calculation formula.
The larger transmission ratio of the gear pair with less teeth also leads to the number of stress cycles of pinions is much more than that of large gears, therefore, compared with large and pinions, pinions are the weak link of the transmission system, and in order to prevent gear shaft bending or torsional fracture, it is also necessary to check the bending and torsional strength of the pinion shaft.
Therefore, by calculating the number of teeth gear, it can achieve a series of important results in the field of gear transmission and the tooth design research of gear transmission with less gear count.
epilogue
By reducing the number of teeth, this design method successfully solves some problems existing in traditional gear transmission, such as high noise, low efficiency, and short life.
First of all, by reducing the number of teeth, the gear transmission with less teeth effectively reduces noise and vibration, because the noise in gear transmission is mainly caused by tooth shape error and tooth surface contact, and reducing the number of teeth can reduce the tooth shape error and contact area in gear transmission, thereby reducing the generation of noise and vibration.
Secondly, the gear transmission with less teeth also significantly improves the transmission efficiency and life, the traditional gear transmission due to the number of teeth, there is a large friction loss, by reducing the number of teeth can reduce the friction between the tooth surfaces, improve the transmission efficiency, at the same time, reducing the number of teeth can also reduce the volume and quality of the gear, improve the strength and life of the gear.
Finally, the tooth shape design method based on numerical simulation and optimization algorithm provides important support for the optimization design of gear transmission with low tooth count. With the help of computer simulation and optimization algorithms, the optimal tooth profile parameters can be quickly obtained, so as to achieve the ideal design of gear transmission with low tooth count.
In general, the tooth design study of gear transmission with low number of teeth provides an efficient and reliable transmission solution for the industry. With the continuous in-depth research and exploration in this field, it is believed that more innovative designs and methods will emerge to bring more advanced and sustainable gear transmission technology to the industry.