CN112883485B - Non-circular face gear limited slip differential and escaping operation method - Google Patents
Non-circular face gear limited slip differential and escaping operation method Download PDFInfo
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Abstract
The invention discloses a non-circular face gear limited slip differential, which comprises two identical non-circular face gears, a planet carrier and a plurality of involute cylindrical gears, wherein the non-circular face gears and the involute cylindrical gears rotate around the same axis, and the non-circular face gears are respectively and fixedly connected with automobile driving wheels. The invention also discloses a escaping operation method based on the analysis of the dynamic traction force of the whole vehicle, namely, the input rotating speed of the planet carrier is continuously increased to improve the dynamic traction force of the whole vehicle. The non-circular face gear limited slip differential provided by the invention has the characteristics of good interchangeability, large overlap ratio, low installation precision, no axial force generation in the operation process and the like, and the provided escaping operation method can highlight the advantage of high limited slip performance of the non-circular face gear limited slip differential and has the advantage of being easy for a driver to operate through reasonable structural change. Aims to solve the manufacturing and installation problems of the existing variable transmission ratio differential and provide a difficult-escaping operation method capable of exerting the high slip-limiting capacity of the non-circular face gear slip-limiting differential to the maximum extent.
Description
Technical Field
The invention belongs to the field of vehicles, and particularly relates to a non-circular face gear limited slip differential and a trapped-removal operation method.
Background
The terrain commonly encountered by the vehicle in the driving process is more in plains, mountains, plateaus, basins and hills, the high-trafficability vehicle plays an irreplaceable role in social production, and the traditional circular differential does not have a variable torque distribution characteristic and cannot meet the actual trapped-free requirement of the vehicle. The differential with the antiskid and escaping functions is a core driving component of a two-wheel drive automobile, and can actively or passively reduce the rotation speed difference when the driving wheels generate a large rotation speed difference, and most or even all the torque is distributed to the non-slip driving wheels, so that the traction force of the whole automobile is improved. The limited slip mechanism and the differential configuration principle based on the limited slip mechanism are the core problems of limited slip differential design and innovation, and research on limited slip differentials has never been interrupted.
The electronic control limited slip differential mechanism senses the slip state of the wheel by means of an electronic sensor, and drives a friction plate clutch to act by means of a motor, electro-hydraulic, electromagnetic and the like, so that the aim of actively controlling the torque distribution process of the differential mechanism is fulfilled, the electronic control limited slip differential mechanism is outstanding in control performance and is commonly used for high-grade civil automobiles, but the electronic sensor is easy to break down in bad road conditions; the free wheel type limited slip differential redistributes the torque according to the rotating speed difference of the wheel vehicle, can lock the half-axle gear on the slip side, has the limited slip performance which is comparable to that of a differential lock, but can not realize the accurate distribution of the torque; the Eton limited slip differential mechanism triggers the combination of friction plates by means of inertia induction, has the limited slip performance equivalent to that of a free wheel type limited slip differential mechanism, but has slower reaction time; the viscous limited slip differential mechanism forces the friction plates to be attached by viscous liquid usually by using the shearing force generated by heating and pressing silicon oil, so that the transmission torque is smaller and the response speed is slower; the Torsen differential utilizes the high friction of a worm gear and worm pair and the irreversibility in the transmission process to realize the slip limiting capability, has the advantages of reliable slip limiting, high response speed and no need of electric control, and is expensive in manufacturing cost.
The variable transmission ratio differential is a torque induction type limited slip differential, can autonomously sense the slipping state of wheels without any electronic sensor and control system and realize the rapid slip suppression function, has the advantages of convenient structural maintenance, small abrasion, long service life, high reliability and the like, has great value for off-road vehicles running in severe environment in the field, and is particularly suitable for military off-road vehicles with extremely high requirements on slip limiting capacity and reliability. In addition, the variable transmission ratio differential mechanism also has a large share in the fields of civil high-end automobiles, type off-road automobiles and the like.
The configuration mode of the variable transmission ratio differential is similar to that of a common circular differential, and a noncircular bevel gear is mainly adopted as a core transmission element at present. A high performance variable ratio differential is disclosed, as in the patent publication CN 1043981A. The invention is the earliest variable transmission ratio differential mechanism structure adopting non-conical gears in China, and comprises a driving wheel, a transmission shaft, a differential mechanism, a half axle gear and a planetary gear, wherein the half axle gear and the planetary gear are both non-conical gears. The locking device is simple in structure, the locking coefficient can reach 2.9-3.1, and the locking device is suitable for heavy engineering vehicles and cross-country vehicles. However, the change of the transmission ratio takes one cycle of the gear as a change period, the change amplitude is small, and meanwhile, the design method of the non-conical gear section curve is not mature enough, so that the improvement space is provided. A later-developed patent of the invention, publication No. CN1418784A, discloses a variable ratio limited slip differential. The invention aims to solve the problems of a single-circle-pitch variable transmission ratio differential, and the differential comprises a differential shell, a built-in planetary gear, a half axle gear, a flat gasket and a butterfly spring piece, wherein the flat gasket is arranged on the outer side of the built-in half axle gear, the butterfly spring piece is arranged between the flat gasket and the differential shell, the half axle gear and the planetary gear are non-conical gears, the number of teeth is an integral multiple of 3, and two adjacent high teeth are added with one low tooth or two adjacent low teeth are added with one high tooth to form a group. The change period of the transmission ratio of the invention is increased to three cycles of the gear, and the change amplitude is increased. However, the change period of the transmission ratio of the two inventions is always limited by the number of the gear teeth, so that the limited slip performance is greatly influenced, and the special tooth form reduces the strength of the gear teeth and influences the service life of the differential mechanism.
An inventive patent publication No. CN101886695A discloses a non-bevel gear limited slip differential. The invention relates to a variable transmission ratio differential specially designed for off-road vehicles, which comprises a differential shell, 2 non-circular planetary gears, non-circular half-shaft gears and a straight shaft, wherein the 2 non-circular planetary gears and the non-circular half-shaft gears adopt specially designed non-conical gears, and the gear ratio is 1: 2. The invention has the outstanding advantages that the limitation of the change rule of the transmission ratio by the tooth number universal joints is broken through, the limited slip capability of the non-conical gear limited slip differential is greatly improved, and the use requirement of the off-road vehicle is met, but the non-conical gear adopted by the invention has higher requirements on the processing precision and the installation precision, the part standardization degree is low, and the use and maintenance cost is higher.
Patent publication No. CN104728387A discloses a three-pronged non-bevel gear limited slip differential. The invention aims to overcome the technical defects of a noncircular bevel gear differential, and the configuration of the noncircular bevel gear differential comprises a differential shell, a first noncircular bevel side gear, a second noncircular bevel side gear, 3 noncircular planetary gears and a Y-axis, wherein the number of teeth of the 3 noncircular planetary gears is the same as that of the first noncircular bevel side gear and the second noncircular bevel side gear. Compared with a straight-shaft type noncircular bevel gear differential mechanism, the noncircular bevel gear differential mechanism has the advantages of convenience in processing, low cost, high structural strength and the like, but the design difficulty of a noncircular bevel gear pitch curve is greatly improved, and the problems of high processing difficulty, difficulty in installation, inconvenience in maintenance and the like are not fundamentally solved.
In summary, in terms of differential configuration, the existing variable transmission ratio differentials mostly adopt non-conical gears as core driving components, and the gear transmission has three problems: firstly, the meshing condition of the section curve of the non-conical gear is harsh, so that the design work is complex and the requirements on manufacturing and mounting precision are high; the standardization degree of parts of the non-conical gear pair is low, and the interchangeability and the universality are greatly influenced; and thirdly, the noncircular bevel gear generates axial force in the transmission process, so that the lightweight design of a supporting mechanism of the noncircular bevel gear is not facilitated, and the problems cause that the core element of the differential with the variable transmission ratio is difficult to manufacture and install and difficult to replace due to failure. In addition, the existing method for the two-wheel drive vehicle carrying the variable transmission ratio differential to get rid of the trouble when the single-side drive wheel slips is derived from the static torque distribution analysis of two output ends of the variable transmission ratio differential, and the maximum driving force of the vehicle is considered to be only equal to a static locking coefficient (K ═ i) in the design21max/i21minWherein i21To the ratio of the planetary gear to the side gear in a variable ratio differential), resulting in limited slip performance of the variable ratio differential, which is not comparable to tosenIn contrast to differentials and dog-ear differentials, the above problems have limited the practical application of variable ratio differentials.
Disclosure of Invention
The invention provides a slip-limiting differential based on a non-circular face gear and an efficient difficulty-removing operation method, aiming at the two problems of difficult manufacturing and installation and difficulty-removing operation methods of the existing variable transmission ratio differential, which can not play the high slip-limiting performance of the variable transmission ratio differential, and can solve the problems of high requirements on manufacturing and installation precision and poor interchangeability of parts of the variable transmission ratio differential, and meanwhile, the slip-limiting difficulty-removing capability of the variable transmission ratio differential is greatly improved.
In order to achieve the above object, a first aspect of the present invention provides a non-circular face gear limited slip differential, which includes two identical sun gears, a planet carrier and a plurality of planet gears, wherein the sun gears and the planet carrier rotate around the same axis, the two sun gears are respectively and fixedly connected with an automobile driving wheel, the sun gears are multi-period non-circular face gears, the planet gears are involute cylindrical gears, and a pitch curve equation of the non-circular face gears is as follows:
wherein r is the pitch curve radial diameter of the non-circular face gear1，ε2，ε3，....，εnIs the eccentricity of the non-circular face gear,
is the rotation angle of the non-circular face gear, n is the order of the non-circular face gear, when n is fixed, the value is divided by epsilonnThe eccentricity ratios except the eccentricity ratios are all 0; the number of the involute cylindrical gears is n, and the number of teeth of the non-circular face gear is z2Is a multiple of n when z2N is an odd number, and the number of teeth z of the cylindrical gear is1Is odd when z is2N is an even number, and the number of teeth z of the cylindrical gear1Is an even number; the cylindrical gears are uniformly distributed along the circumferential direction of the non-circular face gears, and each cylindrical gear is meshed with two non-circular face gears simultaneously; two of the above two areThe initial phase angle difference of the circular face gears on a plane vertical to the axes of the two non-circular face gears is 180 degrees/n, and two nodes between each involute cylindrical gear and the two non-circular face gears are respectively superposed with the direction passing maximum extreme point L (1+ epsilon) and the direction passing minimum extreme point L (1-epsilon) of the two non-circular face gears.
Preferably, the value range of the pitch curve periodicity n of the non-circular face gear is 2-4, and the eccentricity ratio is not more than 0.3.
Further, when the non-circular face gear is a 2-step non-circular face gear, the non-circular face gear limited slip differential comprises a first non-circular face gear and a second non-circular face gear which are used as sun gears, a first standard involute straight tooth cylindrical gear and a second standard involute straight tooth cylindrical gear which are used as planet gears, and a planet carrier which is composed of a first differential housing, a second differential housing and a planet shaft.
Preferably, in the automobile drive axle, the first non-circular face gear is connected with the first drive wheel through the first drive shaft of the automobile drive axle, the second non-circular face gear is connected with the second drive wheel through the second drive shaft of the automobile drive axle, wherein the first non-circular face gear is installed on the inner side of the first differential case through a cylindrical roller bearing, the second non-circular face gear is installed on the inner side of the second differential case through a cylindrical roller bearing, the first standard involute straight tooth cylindrical gear and the second standard involute straight tooth cylindrical gear are respectively installed on two end parts of the planetary shaft through sliding bushings, the planetary shaft is fixed on the second differential case through a limiting block, and the driven reduction gear and the first differential case are connected together through bolts.
Further, the integration of the first differential case and the second differential case enables the rotation axes of the first non-circular face gear and the second non-circular face gear to be kept on the same straight line; when the non-circular face gear differential works, the first standard involute straight-tooth cylindrical gear and the second standard involute straight-tooth cylindrical gear are simultaneously meshed with the first non-circular face gear and the second non-circular face gear, the first standard involute straight-tooth cylindrical gear and the second standard involute straight-tooth cylindrical gear both perform space point-winding rotation, and the first non-circular face gear and the second non-circular face gear perform fixed-axis rotation.
In a second aspect of the invention, a method for operating a vehicle in a situation where the vehicle falls into a slip trouble of a single-side driving wheel driven by a non-circular-face gear limited slip differential by using the non-circular-face gear limited slip differential is provided, wherein the operating method increases the output rotation speed of an engine by stepping on an accelerator pedal, so that the dynamic traction force of the whole vehicle is greater than the driving resistance, namely Fd>FfzDetermining the dynamic traction force F of the whole vehicledThe expression includes the following four steps:
s1, the circumferential acting force of a single planet wheel to the non-circular face gear on the sliding side is given as follows:
in the formula, F32For a single planet wheel to the peripheral force of the slipping-side non-circular face gear, JaMoment of inertia for a single wheel pair about its axis of revolution, JzMoment of inertia for a single drive shaft to its axis of revolution, J2Is the moment of inertia, omega, of the slipping non-circular face gear to its axis of rotationHInputting the rotating speed of the planet carrier of the non-circular face gear limited slip differential, j is the number of the planet wheels, r2Is the radial direction, r, of the slipping-side non-circular face gearRRadial direction of the wheel, fLFor the sliding friction to which the drive wheels are subjected, MGbIs a single driving wheel rolling resistance couple;
s2, the circumferential acting force of the set planet wheel to the non-slip non-circular face gear is as follows:
in the formula, F63For the circumferential force of the non-slipping non-circular-face gear on the planet wheel, JxxIs the moment of inertia, omega, of the planetary wheel pair to the x-axisxIs the angular velocity component, r, of the planet wheel in the x-axis3Radial direction of the planet wheel, F23For said non-slip non-circular surfaceCircumferential force of the gear on the planet wheel, wherein F23＝F32；
S3, the torque transmitted by the non-circular face gear limited slip differential to the non-slip driving wheel is given as follows:
TL9＝jF36r6+Mn (4)
in the formula, TL9Torque transmitted to non-slipping drive wheels for non-circular face gear limited slip differentials, F36Acting on the non-slip side non-circular face gear in the circumferential direction by the planetary wheel, wherein F36＝F63，r6Radial direction of said non-slip non-circular face gear, MnThe friction torque in the non-circular face gear limited slip differential is obtained;
s4, giving the expression of the dynamic traction of the whole vehicle as follows:
Fd＝(TL9-MGb)/rR+fL (5)
in the formula, FdFor the whole vehicle dynamic traction force, the formula (2) is substituted into the formula (3), the formula (3) is substituted into the formula (4), and the formula (4) is substituted into the formula (5) in sequence, so that the whole vehicle dynamic traction force expression is obtained:
wherein J is the number of the planet wheels, JxxIs the moment of inertia, omega, of the planetary wheel pair to the x-axisxIs the angular velocity component, r, of the planet wheel in the x-axis3Is the radial direction of the planet wheel, r6Is composed of
Radial direction of non-slip non-circular face gear, JaMoment of inertia for a single wheel pair about its axis of revolution, JzMoment of inertia for a single drive shaft to its axis of revolution, J2For moment of inertia, omega, of the slipping side non-circular face gear to its axis of rotationHFor the input rotational speed, f, of the planet carrier of the non-circular face gear limited slip differentialLIs the sliding friction force to which the driving wheel is subjected, rRRadial direction of the wheel, r2For slipping side non-circular face gearRadial direction of (M)nFor friction torque, M, in non-circular face gear limited slip differentialsGbIs a single driving wheel rolling resistance couple.
Drawings
FIG. 1 is a schematic structural view of a non-circular face gear limited slip differential of the present invention;
FIG. 2 is a perspective view of a 2-step non-circular face gear of the present invention;
FIG. 3 is a schematic view of the initial position of a 2-step two non-circular face gear of the present invention;
FIG. 4 is a schematic structural view of a drive axle of an automobile according to the present invention;
FIG. 5 is a torque split map of the non-circular face gear limited slip differential of the present invention;
fig. 6 is a comparison graph of vehicle driving force obtained by different analysis methods of the present invention.
Reference numerals: in FIG. 1, 1 — first differential case; 2-a first non-circular face gear; 3-a first standard involute spur gear, 4-a second standard involute spur gear; 5-planet axis; 6-a second non-circular face gear; 7 — a second differential housing; 8-a second drive shaft; 9-a second drive wheel; 10-main reduction gear; 11-driven reduction gear; 12 — a first drive wheel; 13 — a first drive shaft; t isL12Torque picked up by the first driving wheel 12; t isL9Torque obtained by the second driving wheel 9; fdmax-dynamically analyzing the obtained traction force of the whole vehicle; fd1-maximum driving force from static analysis; ffz-vehicle running resistance.
Detailed Description
The invention is further described with reference to the following figures and examples.
The invention discloses a non-circular face gear limited slip differential, which comprises two identical sun gears, a planet carrier and a plurality of planet gears, wherein the sun gears and the planet carrier rotate around the same axis, the two sun gears are respectively and fixedly connected with automobile driving wheels, the sun gears are multi-period non-circular face gears, the planet gears are involute cylindrical gears, and the number of the planet gears is equal to the number of the non-circular face gears.
As shown in fig. 1, as a 2-step non-circular face gear limited slip differential, that is, when the non-circular face gear is a 2-step non-circular face gear, the non-circular face gear limited slip differential of the present invention includes a first non-circular face gear 2 and a second non-circular face gear 6 as sun gears, a first standard involute spur gear 3 and a second standard involute spur gear 4 as planetary gears, and a carrier constituted by a first differential case 1, a second differential case 7, and a planetary shaft 5.
As shown in fig. 2, in the 2-step non-circular face gear limited slip differential, the first non-circular face gear 2 and the second non-circular face gear 6 have the order of 2 and the eccentricity of 0.18.
The pitch curve equation of the non-circular face gear is as follows:
wherein r is the pitch curve radial diameter of the non-circular face gear1，ε2，ε3，....，εnIs the eccentricity of the non-circular face gear,
is the rotation angle of the non-circular face gear, n is the order of the non-circular face gear, when n is fixed, the value is divided by epsilonnThe eccentricity ratios except the eccentricity ratios are all 0; the number of the involute cylindrical gears is n, and the number of teeth of the non-circular face gear is z2Is a multiple of n when z2N is an odd number, and the number of teeth z of the cylindrical gear is1Is odd when z is2The number/n is even, and the number z1 of teeth of the cylindrical gear is even; the cylindrical gears are uniformly distributed along the circumferential direction of the non-circular face gears, and each cylindrical gear is meshed with two non-circular face gears simultaneously;
in the initial position, the phase angle difference between the multicycle non-circular face gears is 180 degrees/n, and the nodes of the involute cylindrical gear and the non-circular face gear respectively correspond to radial extreme values L (1+ epsilon) and L (1-epsilon) of the non-circular face gears.
As shown in fig. 3, when the 2-step noncircular face gear limited slip differential is mounted, the initial phase angles of the first noncircular face gear 2 and the second noncircular face gear 6 are different by 180 °/2, that is, by 90 °, so that the shortest radial direction of the first noncircular face gear 2 is aligned with the longest radial direction of the second noncircular face gear 6 in the initial state.
As shown in fig. 4, in the automobile drive axle with the non-circular face gear limited slip differential, the first non-circular face gear 2 is connected with the first drive wheel 12 through the first drive shaft 13 of the automobile drive axle, the second non-circular face gear 6 is connected with the second drive wheel 9 through the second drive shaft 8 of the automobile drive axle, wherein the first non-circular face gear 2 is installed inside the first differential housing 1 through a cylindrical roller bearing, the second non-circular face gear 6 is installed inside the second differential housing 7 through a cylindrical roller bearing, the first standard involute spur gear 3 and the second standard involute spur gear 4 are respectively installed on two ends of the planetary shaft 5 through sliding bushings, the planetary shaft 5 is fixed on the second differential housing 7 through a limit block, and the driven reduction gear 11 is connected with the first differential housing 1 through bolts.
The integration of the first differential case 1 and the second differential case 7 keeps the axes of revolution of the first non-circular face gear 2 and the second non-circular face gear 2 on the same straight line. When the non-circular face gear differential works, the first standard involute straight-tooth cylindrical gear 3 and the second standard involute straight-tooth cylindrical gear 4 are simultaneously meshed with the first non-circular face gear 2 and the second non-circular face gear 6, the first standard involute straight-tooth cylindrical gear 3 and the second standard involute straight-tooth cylindrical gear 4 both perform space point-winding rotation, and the first non-circular face gear 2 and the second non-circular face gear 2 perform fixed-axis rotation.
The torque of the engine is transmitted to the first drive shaft 13 and the second drive shaft 8, and finally to the first drive wheel 12 and the second drive wheel 9, via the main reduction gear 10, the driven reduction gear 11, the first differential case 1 and the second differential case 7, the planetary shaft 5, the first non-circular face gear 2, and the second non-circular face gear 6 in this order.
In order to ensure that the non-circular face gear is convenient to process, the pitch curve shapes of the first non-circular face gear 2 and the second non-circular face gear 6 are all convex, and according to the convex discriminant of the pitch curve of the non-circular gear:
in the formula, r is the radial direction of the non-circular face gear, j is the rotation angle of the non-circular face gear, and when the eccentricity e of the first non-circular face gear 2 and the second non-circular face gear 6 is calculated to be not more than 0.3, the curve shapes of the pitch curves of the first non-circular face gear 2 and the second non-circular face gear 6 can not have concave parts.
Specifically, the dynamic traction analysis process of the whole vehicle driven by the non-circular face gear limited slip differential is as follows:
the first step sets the working condition that the first driving wheel of a certain type of rear-drive cross-country vehicle slips at a high speed to cause the vehicle with suddenly-reduced traction to be incapable of advancing. At this time, the first non-circular face gear 2, the first driving shaft 13 and the first driving wheel 12 are rigidly connected into a whole, the whole rotates around the rotation center of the whole in a fixed axis manner, and the circumferential acting force of the planet wheel 3 on the first non-circular face gear 2 can be obtained by a rigid body fixed axis rotation differential equation:
in the formula F32For the peripheral action of the planet wheels 3 on the first non-circular face gear 2, JaMoment of inertia for a single wheel pair about its axis of revolution, JzMoment of inertia for a single drive shaft to its axis of revolution, J2Is the moment of inertia, omega, of the first non-circular face gear 2 about its axis of revolutionHThe input rotating speed of the non-circular face gear limited slip differential is adopted, j is the number of planet wheels, r2Is the radial direction, r, of the first non-circular face gear 2RRadial direction of the wheel, fLIs the sliding friction force to which the first driving wheel is subjected, MGbIs a single driving wheel rolling resistance couple.
And step two, according to the fixed point rotation of the planet wheel around the central line of the planet shaft and the intersection point of the rotation axes of the non-circular face gear, the circumferential acting force of the second non-circular face gear 6 on the planet wheel 3 can be obtained:
in the formula F63For the circumferential force of the second non-circular face gear 6 on the planet wheels 3, JxxIs the moment of inertia of planet wheel 3 to the x axis, omegaxIs the angular velocity component, r, of the planet wheel 3 in the x-axis3Radial direction of planet wheel 3, F23Acting in the circumferential direction of the planet wheels 3 for the first non-circular face gear 2, wherein F23＝F32。
Thirdly, according to the required acting force F32The torque that can be transmitted to the first drive wheels 13 is found as:
TL13＝jF32r2 (11)
in the formula TL13For transmitting torque to the first drive wheel 13, and then according to the force F63The torque transmitted to the second drive wheels 9 can be found as:
TL9＝jF36r6+Mn (12)
in the formula TL9For transmitting torque to the second driving wheel 9, F36For the planetary wheels 3 to exert a circumferential force on the second non-circular face gear 6, wherein F36＝F63，r6Radial direction of the second non-circular face gear 6, MnThe friction torque in the non-circular face gear limited slip differential is adopted.
Fourthly, because the traction force of the whole vehicle is determined by the sliding friction force of the wheels on the sliding side, the influence of inertia torque is considered to deduce that the dynamic traction force of the whole vehicle in the escaping process is as follows:
Fd＝(TL9-MGb)/rR+fL (13)
in the formula, FdFor the dynamic traction of the whole vehicle, the formula (9) is substituted into the formula (10), the formula (10) is substituted into the formula (12), and the formula (12) is substituted into the formula (13) to obtain the final expression of the dynamic traction of the whole vehicle, wherein the final expression is as follows:
torque T transmitted by the engine to the first drive wheels 12L13And torque T of second driving wheel 9L9The variation relationship is shown in fig. 5, when the whole vehicle falls into the single-side driving wheel slipping predicament, the driving wheel will generate inertia torque when slipping at high speed, the inertia torque has great influence on the torque distribution characteristic of the differential mechanism as the load of the vehicle, the torque obtained by the first driving wheel 12 and the second driving wheel 9 is periodically fluctuated every time the non-circular face gear rotates for a whole circle, wherein the second driving wheel 9 obtains more torque and can periodically generate peak value FdmaxThe torque difference between the first 12 and the second 9 driving wheels is greatest at the peaks, and during the constant fluctuation of this torque difference, the wheels on a well-adhered road surface can obtain the maximum driving force, which is also a distinct feature from the static torque distribution.
And, for the visual expression, adopt the dynamic analysis method to obtain the whole car dynamic traction force, compare the whole car traction force that obtains with common static torque distribution method below, use common static torque distribution analysis non-circular face gear which pot of differential mechanism can obtain the whole car traction force of this back-drive cross country car and do:
Fd1＝(1+Sj0)fL+2ε/(1-ε)(fL+MGb/rR) (15)
in the formula Fd1Maximum traction of the vehicle, Sj0Is the locking coefficient of a common differential, e is the eccentricity of a non-circular face gear, fLSliding resistance of slipping wheels, rRIs the wheel radius. The driving resistance which needs to be overcome by the driving wheels during the driving process of the vehicle is as follows:
Ffz＝2MGf/rR+Ff (16)
in the formula FfzFor running resistance, MGfIs a single driven wheel rolling resistance couple, FfOther resistance during driving. The value range of the input rotating speed of the planet carrier of the non-circular face gear differential is set to be pi-10 pi (rad/s) according to the rated power of the automobile engine to obtain the conventional staticDynamic torque split map.
As shown in fig. 6, is the traction force F of the whole vehicled1Obtaining the maximum traction force F of the whole vehicle through dynamic limited slip analysisdmaxVehicle traction force comparison map of comparison relationship, maximum traction force F analyzed from static torque distributiond1Cannot overcome running resistance FfzThe reason is that the slip limiting performance of the variable transmission ratio differential cannot be fully exerted by the conventional operation method, and the inertia torque generated by the time-varying rotating speed of the wheels and the non-circular face gear is fully considered by the dynamic slip limiting analysis to obtain the maximum traction force F of the whole vehicledmaxWith the input speed w of the planet carrierHIs increased and continuously increased, and the input rotating speed w of the planet carrierHContinuously increased maximum traction force F of whole vehicle in processdmaxIs sufficient to overcome the running resistance FfzFrom FIG. 6, it can be known that when the non-circular face gear limited slip differential is used, the input rotation speed ω of the planet carrier isH>10rad/s or ωH>At 95r/min, the maximum traction force F of the whole vehicledmax>Running resistance FfzObviously, when an automobile driven by the non-circular surface gear limited slip differential falls into the slipping predicament of a single-side driving wheel, the opening of an engine throttle can be continuously increased and the air input of the engine is improved only by an operation method of continuously and slowly stepping on an accelerator pedal under the normal working state of the engine, so that the input rotating speed of the engine to a non-circular surface gear limited slip differential planet carrier is increased, finally, the traction force of the whole automobile overcomes the driving resistance to enable the whole automobile to be separated from the predicament, and the method has pertinence on the automobile driven by the non-circular surface gear limited slip differential and can furthest exert the actual high slip limiting performance of the non-circular surface gear limited slip differential.
Finally, it should be noted that: although the present invention has been described in detail with reference to the foregoing embodiments, it will be apparent to those skilled in the art that modifications may be made to the embodiments described above, or equivalents may be substituted for elements thereof without departing from the scope of the present invention.
Claims (5)
1. The utility model provides a stranded operation method that gets rid of non-circular face gear limited slip differential, its characterized in that non-circular face gear limited slip differential includes two the same sun gears, a planet carrier and a plurality of planet wheel, and sun gear and planet carrier are rotatory around same axis, and two sun gears are respectively with car drive wheel fixed connection, the sun gear is multicycle non-circular face gear, the planet wheel is involute cylindrical gear, non-circular face gear's pitch curve equation is:
wherein r is the pitch curve radial diameter of the non-circular face gear1，ε2，ε3，....，εnIs the eccentricity of the non-circular face gear,
is the rotation angle of the non-circular face gear, n is the order of the non-circular face gear, when n is fixed, the value is divided by epsilonnThe eccentricity ratios except the eccentricity ratios are all 0; the number of the involute cylindrical gears is n, and the number of teeth of the non-circular face gear is z2Is a multiple of n when z2N is an odd number, and the number of teeth z of the cylindrical gear is1Is odd when z is2N is an even number, and the number of teeth z of the cylindrical gear1Is an even number; the cylindrical gears are uniformly distributed along the circumferential direction of the non-circular face gears, and each cylindrical gear is meshed with two non-circular face gears simultaneously; the initial phase angle difference of the two non-circular face gears on a plane vertical to the axes of the two non-circular face gears is 180 DEG/n, and two nodes between each involute cylindrical gear and the two non-circular face gears are respectively superposed with the maximum extreme point L (1+ epsilon) and the minimum extreme point L (1-epsilon) of the two non-circular face gears;
the operating method increases the output rotating speed of the engine by stepping on the accelerator pedal, so that the dynamic traction force of the whole vehicle is larger than the running resistance, namely Fd>FfzDetermining the dynamic traction force F of the whole vehicledThe expression includes the following four steps:
s1, the circumferential acting force of a single planet wheel to the non-circular face gear on the sliding side is given as follows:
in the formula, F32For a single planet wheel to the peripheral force of the slipping-side non-circular face gear, JaMoment of inertia for a single wheel pair about its axis of revolution, JzMoment of inertia for a single drive shaft to its axis of revolution, J2The moment of inertia of the slipping non-circular face gear about its axis of rotation,
inputting the rotating speed of the planet carrier of the non-circular face gear limited slip differential, j is the number of the planet wheels, r2Is the radial direction, r, of the slipping-side non-circular face gearRRadial direction of the wheel, fLFor the sliding friction to which the drive wheels are subjected, MGbIs a single driving wheel rolling resistance couple;
s2, the circumferential acting force of the set planet wheel to the non-slip non-circular face gear is as follows:
in the formula, F63For the circumferential force of the non-slipping non-circular-face gear on the planet wheel, JxxThe moment of inertia of the planetary wheel pair to the x axis,
is the angular velocity component, r, of the planet wheel in the x-axis3Radial direction of the planet wheel, F23Acting on the planet wheel in the circumferential direction of the non-slipping non-circular face gear, wherein F23＝F32；
S3, the torque transmitted by the non-circular face gear limited slip differential to the non-slip driving wheel is given as follows:
TL9＝jF36r6+Mn (4)
in the formula, TL9Torque transmitted to non-slipping drive wheels for non-circular face gear limited slip differentials, F36Acting on the non-slip side non-circular face gear in the circumferential direction by the planetary wheel, wherein F36＝F63，r6Radial direction of said non-slip non-circular face gear, MnThe friction torque in the non-circular face gear limited slip differential is obtained;
s4, giving the expression of the dynamic traction of the whole vehicle as follows:
Fd＝(TL9-MGb)/rR+fL (5)
in the formula, FdFor the whole vehicle dynamic traction force, the formula (2) is substituted into the formula (3), the formula (3) is substituted into the formula (4), and the formula (4) is substituted into the formula (5) in sequence, so that the whole vehicle dynamic traction force expression is obtained:
wherein J is the number of the planet wheels, JxxThe moment of inertia of the planetary wheel pair to the x axis,
is the angular velocity component, r, of the planet wheel in the x-axis3Is the radial direction of the planet wheel, r6Radial direction of non-slip non-circular face gear, JaMoment of inertia for a single wheel pair about its axis of revolution, JzMoment of inertia for a single drive shaft to its axis of revolution, J2In order to obtain the moment of inertia of the non-circular gear on the slipping side to the axis of rotation,
for the input rotational speed, f, of the planet carrier of the non-circular face gear limited slip differentialLIs the sliding friction force to which the driving wheel is subjected, rRRadial direction of the wheel, r2For the direction of the non-circular face gear on the slipping sideDiameter, MnFor friction torque, M, in non-circular face gear limited slip differentialsGbIs a single driving wheel rolling resistance couple.
2. The operation method for overcoming the difficulty of the non-circular face gear limited slip differential according to claim 1, wherein the value range of the non-circular face gear pitch curve cycle number n is 2-4, and the eccentricity ratio is not more than 0.3.
3. The out-of-gear operation method for a non-circular face gear limited slip differential according to claim 1, wherein when the non-circular face gear is a 2-step non-circular face gear, the non-circular face gear limited slip differential includes a first non-circular face gear and a second non-circular face gear as sun gears, a first standard involute spur gear and a second standard involute spur gear as planetary gears, and a carrier composed of a first differential case, a second differential case, and a planetary shaft.
4. The out-of-band operation method for a non-circular face gear limited slip differential as claimed in claim 3, wherein in the automobile drive axle, a first non-circular face gear is connected to a first drive wheel through a first drive shaft of the automobile drive axle, a second non-circular face gear is connected to a second drive wheel through a second drive shaft of the automobile drive axle, wherein the first non-circular face gear is mounted inside a first differential case through a cylindrical roller bearing, the second non-circular face gear is mounted inside a second differential case through a cylindrical roller bearing, the first standard involute spur gear and the second standard involute spur gear are respectively mounted on both ends of the planetary shaft through a sliding bush, the planetary shaft is fixed to the second differential case through a stopper, and the driven reduction gear and the first differential case are connected together through a bolt.
5. The method of claim 4, wherein the integration of the first and second differential housings maintains the axes of rotation of the first and second non-circular gears in a common straight line; when the non-circular face gear differential works, the first standard involute straight-tooth cylindrical gear and the second standard involute straight-tooth cylindrical gear are simultaneously meshed with the first non-circular face gear and the second non-circular face gear, the first standard involute straight-tooth cylindrical gear and the second standard involute straight-tooth cylindrical gear both perform space point-winding rotation, and the first non-circular face gear and the second non-circular face gear perform fixed-axis rotation.
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