CN113944728A - Unequal-pressure-angle end face double-arc gear mechanism driven by parallel shafts - Google Patents

Abstract

The invention discloses an unequal pressure angle end face double-arc gear mechanism driven by parallel shafts and a design method, belonging to the field of gear transmission, wherein the double-arc gear mechanism comprises a small gear and a large gear which are parallel in axis, the end face tooth profiles of the small gear and the large gear are respectively composed of a convex arc tooth profile, a straight line tooth profile, a concave arc tooth profile and a tooth root transition curve, and the specific structure of the tooth profiles is determined by a meshing line parameter equation and parameters such as contact ratio, tooth number, transmission ratio and the like; when the driving device is correctly installed, the convex-concave arcs of the small wheel and the large wheel simultaneously realize double-point meshing contact on the end faces of the wheel teeth, the two meshing points have unequal pressure angles, and the small wheel and the large wheel rotate under the driving of the driving device to realize transmission between two shafts. The design method disclosed by the invention can be used for designing the unequal pressure angle double-arc gear mechanism for parallel shaft transmission, has the advantages of simple design, easiness in lubrication, high tooth root bending strength, large transmission ratio and contact ratio, strong bearing capacity and the like, and can be widely applied to the design of transmission systems of engineering machinery such as double-wheel milling machines and the like.

Description

Double arc gear mechanism with unequal pressure angle end face driven by parallel shafts

technical field

The invention relates to the field of gear transmission, in particular to an unequal pressure angle end face double arc gear mechanism for parallel shaft transmission.

Background technique

As the core basic components of machinery, gears are widely used in machine tools, automobiles, robots, wind power, coal mines, aerospace and other equipment manufacturing fields and the main battlefield of the national economy. Their performance directly determines the quality of major equipment and high-end industrial products. performance and reliability. Research on core basic components such as high-performance gears is a key factor in promoting industrial transformation and upgrading and enhancing the core competitiveness of national industries. Especially with the economic growth, construction machinery is developing towards high power, which puts forward higher requirements for the design of its core transmission components such as gearbox gear transmission.

At present, the main problem facing my country's gear industry is that the design and manufacturing capabilities of high-efficiency, large-carrying capacity, lightweight, and high-reliability high-performance gear products are obviously insufficient. Parallel shaft gear transmission is the most common application form of gear transmission, among which, involute gears are the most widely used. However, since the development of involute gears, there have always been transmission failures such as friction and wear, gluing, and plastic deformation caused by the relative sliding of tooth surfaces, which seriously affects the transmission efficiency, service life and reliability of gear products, especially high-speed and heavy-duty gears. performance, which restricts the performance improvement of "high-end precision" mechanical equipment. Especially in the case of heavy load, the relative sliding of the involute gear tooth tip is very serious, which is easy to cause transmission failure.

In order to solve the above problems of involute gear transmission, domestic and foreign scholars have gradually developed single-arc gears and double-arc gears for parallel shaft transmission forms, including end-face double-arc gears and normal double-arc gears, such as China The patent document, the application number is 202110318591.7, discloses "a double-arc small tooth difference deceleration transmission device and the method for forming double-arc teeth", the application number is 201810893876.1, discloses "a double-arc gear", the application number is 201620553083.1, discloses "a double arc gear" and so on. Compared with involute gears, double arc gears driven by parallel shafts have greater tooth surface contact strength and tooth root bending strength, as well as good lubricating properties. However, the tooth profiles of the small wheel and the large wheel of the above-mentioned double arc gear are based on the same hob cut by Fan Cheng method, and in order to ensure the correct meshing of the large and small gears, the pressure angle of the two meshing points of the tooth profile of the hob is set as equal value. Therefore, the limitation of the existing double arc gear mechanism is that the pressure angle of the two meshing points of the tooth profile is limited to be equal, so that its structure is not an optimal bearing design structure, and the construction machinery such as double-wheel milling in the construction of underground diaphragm walls In the case of heavy-duty transmission, the root of the gear teeth may be broken, resulting in construction accidents. In addition, if it is simply to increase the bending strength of the double arc gear root and improve the safety factor, it is necessary to increase the gear module, which will make the transmission structure of these devices too large, thus affecting the design and performance of the whole machine.

SUMMARY OF THE INVENTION

The purpose of the present invention is to solve the problems existing in the prior art of the double arc gear mechanism in the field of mechanical transmission, and propose a parallel shaft transmission of a double arc gear mechanism with an unequal pressure angle end face and a design method thereof. The double-arc gear mechanism with angular end face has the advantages of simple design, easy lubrication, high bending strength of the tooth root, large transmission ratio and coincidence degree, and strong bearing capacity. It can be widely used in the transmission system design of construction machinery such as double-wheel milling.

In order to achieve the above purpose, the technical solution adopted in the present invention is: a unequal pressure angle end face double arc gear mechanism driven by parallel shafts is proposed, which includes a pair of gear pairs composed of a small wheel and a large wheel, and the small wheel is connected to the input shaft through the input shaft. The driver is fixedly connected, the large wheel is connected to the output shaft, the axes of the small wheel and the large wheel are parallel, and the tooth profiles on the end surfaces of the small wheel and the large wheel have an axisymmetric form. The top to the tooth root is composed of convex circular arc tooth profile, straight tooth profile, concave circular arc tooth profile and tooth root transition curve; the meshing mode of the small wheel and the large wheel is the concave-convex meshing transmission with double-point contact on the end surface , and the two meshing points have unequal pressure angles; the small wheel rotates under the drive of the driver, and realizes the connection between the parallel shafts through the continuous meshing between the two pairs of convex circular arc tooth profiles and concave circular arc tooth profiles. The smooth meshing transmission, the meshing points of the two unequal pressure angles respectively form two contact lines with equal pitches on the tooth surfaces of the small wheel and the large wheel, both of which are cylindrical helical lines; the small wheel and the large wheel respectively form two contact lines of equal pitch. The tooth flanks of the large wheel are all helical flanks obtained by the cylindrical helical motion of the end face tooth profile along the respective contact lines, the pitch of the helical flank is equal to the pitch of the contact line, and the small wheel It is opposite to the helical direction of the teeth of the large gear.

Further, in the concave-convex meshing transmission in which the end faces of the small wheel and the large wheel are in double-point contact, the two meshing points are respectively the convex arc tooth profile of the small wheel teeth and the concave circle of the large wheel teeth. The meshing point M _R1 of the arc tooth profile and the meshing point M _R2 of the concave circular arc tooth profile of the adjacent gear teeth of the small wheel and the convex circular arc tooth profile of the adjacent gear teeth of the large wheel; these two pairs of concave and convex circular arcs The normal line of the meshing point of the tooth profile on the end face intersects at the same point, which is the tangent point of the pitch circle of the pair of double arc gears, that is, the node; the horizontal distance from the two meshing points to the node is PM; when the pair of parallel shafts drive When the unequal pressure angle end face double arc gear mechanism is driven, the two meshing points M _R1 and M _R2 have the same axial movement speed, respectively forming two meshing lines K _R1 -K _R1 and K _R2 -K _R2 in space, And two contact lines of the tooth surfaces of the small wheel and the large wheel are respectively formed.

Further, the tooth surface contact line of the small wheel and the large wheel is determined by the following method:

角，所述大轮绕z_g轴转过

角；In the three spatial coordinate systems of o _p --x _p , y _p , z _p , o _k --x _k , y _k , z _k and o _g --x _g , y _g , z _g , where o _p , o _k and o _g are the origins of the three spatial coordinate systems, respectively, x _p , x _k and x _g are the x-axis of the three spatial coordinate systems, and y _p , y _k and y _g are the three spatial coordinate systems, respectively. The _x -axis, zp, zk and _zg are respectively the _z -axis of the three spatial coordinate systems, the _zp -axis coincides with the rotation axis of the small wheel, the _zg -axis coincides with the rotation axis of the large wheel, and _zk The axis coincides with the meshing line K _R1 - K _R1 passing through the meshing point M _R1 , and the z _k axis is parallel to the z _p and z _g axes, the x _p and the x _g axis are coincident, the x _k and the x _g axis are parallel, and the o _p is parallel to the x g axis. The distance of o _g is a; the coordinate system o ₁ --x ₁ , y ₁ , z ₁ is fixed with the small wheel, and the coordinate system o ₂ --x ₂ , y ₂ , z ₂ is fixed with the big wheel , the small wheel coordinate system o ₁ --x ₁ , y ₁ , z ₁ and the large wheel coordinate system o ₂ --x ₂ , y ₂ , z ₂ are respectively at the starting position with the coordinate system o _p --x _p ,y _p , z _p and o _g -- x _g , y _g , z _g coincide, the small wheel rotates clockwise around the z _p axis at a constant angular velocity ω ₁ , and the large wheel rotates around the z _g axis at a constant angular velocity ω ₂ inversely Clockwise rotation, after a period of time from the starting position, the coordinate systems o ₁ --x ₁ , y ₁ , z ₁ and o ₂ -- x ₂ , y ₂ , z ₂ rotate respectively, and the meshing points are M _R1 and M _R2 , the small wheel rotates around the _zp axis

angle, the large wheel rotates around the z _g axis

horn;

When the small wheel and the large wheel are engaged for transmission, the meshing point M _R1 is set to move along the meshing line K _{R1 -K R1} from the coordinate origin ok, and the parameter equation for the movement of the M _R1 point is:

At the same time, the meshing point M _R2 moves along the meshing line K _R2 -K _R2 at the same moving speed, and the parameter equation for the movement of the M _R2 point is:

In formulas (1) and (2), t is the motion parameter variable of the meshing point M _R1 , 0≤t≤Δt, Δt is the maximum value of the motion parameter variable; c1 is the undetermined coefficient _of the meshing point motion, the unit is mm, PM is the horizontal distance from the meshing point to the node; in order to ensure the fixed transmission ratio meshing, the rotation angle of the small wheel and the large wheel and the movement of the meshing point must be in a linear relationship, and the rotation angle of the small wheel and the large wheel is the same as The relationship of the meshing point is as follows:

In formula (3), k is the linear proportional coefficient of the motion of the meshing point, and its unit is radian; _i12 is the transmission ratio between the small wheel and the large wheel;

When the meshing point M _R1 moves along the meshing line K _R1 -K _R1 , the point M _R1 simultaneously forms the contact lines C _R1p and C _R1g on the convex circular arc tooth surface of the small wheel and the concave circular arc tooth surface of the large wheel; when the meshing point M When _R2 moves along the meshing line K _R2 -K _R2 , point M _R2 simultaneously forms contact lines C _R2p and C _R2g on the concave arc tooth surface of the small wheel and the convex arc tooth surface of the large wheel respectively; according to the coordinate transformation, the coordinate system o is obtained _p --x _p , y _p ,z _p , o _k --x _k ,y _k ,z _k and o _g --x _g ,y _g ,z _g , o ₁ --x ₁ ,y ₁ ,z ₁ And the homogeneous coordinate transformation matrix between o ₂ --x ₂ , y ₂ , z ₂ is:

in,

In formulas (5) and (6), R ₁ is the pitch cylinder radius of the small wheel, R ₂ is the pitch cylinder radius of the large wheel, PM is the distance from the meshing points M _R1 and M _R2 to the node P, and α _t1 is the meshing point The end face pressure angle of _MR1 , α _t2 is the end face pressure angle of the meshing point _MR2 ;

From equations (1) and (4), the parametric equation of the contact line C _R1p of the pinion cam tooth surface is obtained as:

From equations (1) and (4), the parameter equation of the contact line C _R1g of the concave arc tooth surface of the large wheel can be obtained as:

From equations (2) and (4), the parametric equation of the contact line C _R2p of the concave circular arc tooth surface of the pinion is obtained as:

From equations (2) and (4), the parametric equation of the tooth surface contact line C _R2g of the large wheel camber is obtained as:

Further, the tooth profile of the end face of the small wheel and the large wheel is determined by the following method:

The local coordinate systems S _a1 (o _a1 -x _a1 y _a1 z _a1 ) and S _b2 (o _b2 are established respectively at the center o _a1 of the small wheel convex arc tooth profile ar1 and the circle center o _b2 of the large wheel concave arc tooth profile br2 -x _b2 y _b2 z _b2 ), the parametric equations of the small wheel convex circular arc tooth profile ar1 and the large wheel concave circular arc tooth profile br2 are respectively:

In equations (11) and (12), ρ _a1 is the arc radius of the pinion end face convex arc tooth profile ar1, ξ _a1 is the angle parameter of ar1, ξ _a1a and ξ _a1b are the minimum and maximum values of ξ _a1 , respectively ;ρ _b2 is the arc radius of the concave circular arc tooth profile br2 on the end face of the large wheel, ξ _b2 is the angle parameter of br2, ξ _b2a and ξ _b2b are the minimum and maximum values of ξ _b2 , where the value of ξ _a1b is determined by the small wheel The intersection of the addendum circle and the pinion convex arc tooth profile ar1 is obtained by solving;

ξ _a1a =ξ _a1b -π/5.5; (13)

ξ _b2a =ξ _b2b -π/6.5; (14)

The local coordinate systems S _b1 (o _b1 -x _b1 y _b1 z _b1 ) and S _a2 (o _a2 -x) are established respectively at the center o _b1 of the small wheel concave arc tooth profile Br1 and the center o _a2 of the large wheel convex arc tooth profile Ar2 _a2 y _a2 z _a2 ), then the parametric equations of the small wheel convex circular arc tooth profile Br1 and the large wheel concave circular arc tooth profile Ar2 are:

In formulas (15) and (16), ρ _b1 is the arc radius of the concave circular arc tooth profile Br1 on the pinion end face, ξ _b1 is the angle parameter of Br1, ξ _b1a and ξ _b1b are the minimum and maximum values of ξ _b1 respectively ;ρ _a2 is the arc radius of the convex arc tooth profile Ar2 on the end face of the big wheel, ξ _a2 is the angle parameter of Ar2, ξ _a2a and ξ _a2b are the minimum and maximum values of ξ _b2 , where the value of ξ _a2b is determined by the big wheel The intersection point of the addendum circle and the tooth profile Ar2 of the big wheel camber arc is obtained by solving;

ξ _a2a = ξ _a2b -π/5.5 (17)

ξ _b1a =ξ _b1b -π/6.5; (18)

The parametric equation of the convex arc tooth profile ar1 on the right side of the pinion tooth end face in the _Sp coordinate system is obtained by coordinate transformation:

The parametric equation of the concave circular arc tooth profile br1 on the right side of the pinion tooth end face in the _Sp coordinate system is obtained from the coordinate transformation:

The parametric equation of the concave circular arc tooth profile br2 on the right side of the tooth end face of the large gear in the S _g coordinate system is obtained by coordinate transformation:

The parametric equation of the convex arc tooth profile ar2 on the right side of the tooth end face of the large gear in the S _g coordinate system is obtained by coordinate transformation:

The transition curve hr1 on the right side of the pinion tooth end face is determined by the points P _0P and P _1P and their tangent vectors T _0P and T _1P , and the point P _0P is determined by R _h1 , so the value ξ _b1b of the tooth profile br1 can be obtained by solving, P _1P is determined by the pinion root circle radius R _f1 and the angle δ _1R , and the parametric equation of the transition curve hr1 on the right side of the pinion tooth end face is obtained as:

In formulas (23) and (24), x _p (P _0P ), y _p (P _0P ), z _p (P _0P ) are the three-coordinate components of the point P _0P , x _p (P _1P ), y _p (P _1P ), z _p (P _1P ) are the three-coordinate components of the point P _1P , respectively, x _p (T _0P ), y _p (T _0P ), z _p (T _0P ) are the unit cuts of the point P _0P The three-coordinate components of the vector T _0P , x _p (T _1P ), y _p (T _1P ), z _p (T _1P ) are the three-coordinate components of the unit tangent vector T _1P of the point P _1P , m _t is the end face Modulus, b ₁ , b ₂ , b ₃ , b ₄ are calculation parameters, _TH is the shape control parameter of the tooth root transition curve, 0.2≤TH ≤1.5, t _H is the calculation parameter, _{0≤t H ≤1} ;

The transition curve hr2 on the right side of the tooth end face of the large gear is determined by the points P _0G and P _1G and their tangent vectors T _0G and T _1G , and the point P _0G is determined by R _h2 , so the value ξ _b2b of the tooth profile br2 can be obtained by solving, P _1G is determined by the tooth root circle radius R _f2 of the large gear and the angle δ _2R . The parametric equation of the transition curve hr2 on the right side of the tooth end face of the large gear is obtained as follows:

In formula (25), x _g (P _0G ), y _g (P _0G ), z _g (P _0G ) are the three-coordinate components of the point P _0G , respectively, x _g (P _1G ), y _g (P _1G ) , z _g (P _1G ) are the three-coordinate components of the point P _1G respectively, x _g (T _0G ), y _g (T _0G ), z _g (T _0G ) are the unit tangent vector T _0G of the point P _0G respectively The three-coordinate components, x _g (T _1G ), y _g (T _1G ), and z _g (T _1G ) are respectively the three-coordinate components of the unit tangent vector T _1G of the point P _1G ;

When determining the number of pinion teeth Z ₁ , the transmission ratio i ₁₂ , the normal modulus m _n , the degree of coincidence ε, the linear proportionality coefficient k, the pressure angles α _t1 and α _t2 of the two meshing points of the pinion, the diameter coefficient Φ _d , the teeth When the transition curve shape control parameter _TH is used, the undetermined coefficient c ₁ of the meshing point motion and the motion law, the contact line and the meshing line, the tooth profile of the end face of the small wheel and the large wheel and the correct installation distance are also determined accordingly. The gear tooth surface structure of the wheel can also be determined, so as to obtain the unequal pressure angle end face double arc gear mechanism of parallel shaft transmission.

Further, the meshing mode of the small wheel and the large wheel is a concave-convex meshing transmission with double-point contact on the end surfaces, the two meshing points have unequal end surface pressure angles, and the end surface pressure angle of the meshing point of the small wheel concave arc tooth profile. It is smaller than the pressure angle of the end face of the tooth profile meshing point of the pinion cam, so as to enhance the bending strength of the tooth root, that is, α _t2 <α _t1 .

Further, the coincidence degree of the unequal pressure angle end face double arc gear mechanism of the parallel shaft transmission is twice that of the single-point contact meshing, the coincidence degree of the single-point contact meshing needs to be greater than 1, and the unequal pressure of the double-point meshing is required. The formula for calculating the coincidence degree of the double arc gear mechanism on the angular end face is:

Obtain the maximum value of the kinematic parameter variable of the meshing point of the unequal pressure angle end face double arc gear mechanism driven by the parallel shaft.

When designing, it is necessary to comprehensively determine the maximum value Δt of the motion parameter variable of the meshing point M _R1 according to the value ε of the coincidence degree, the linear proportional coefficient k and the number of teeth Z ₁ of the pinion.

Further, the input shaft and the output shaft connected with the small wheel and the large wheel are interchangeable, that is, the small wheel is used to connect the input shaft, the large wheel is used to connect the output shaft, or the large wheel is used to connect the input shaft, The small wheel is connected to the output shaft, respectively corresponding to the speed reduction transmission or speed increase transmission mode of the unequal pressure angle end face double arc gear mechanism driven by the parallel shaft; only when the number of teeth of the small wheel and the large wheel is equal, the mechanism can be realized Constant speed transmission applications with a gear ratio of 1.

Further, the rotation direction of the input shaft connected to the driver is clockwise or counterclockwise, so as to realize the forward and reverse transmission of the small wheel or the large wheel.

The unequal pressure angle end-face double arc gear mechanism of the parallel shaft transmission of the present invention is a gear mechanism fundamentally innovative in the theory of the traditional double arc gear transmission mechanism, and its design method is also different from the existing gear mechanism based on curved surface meshing. Equation design method, but an active design method based on meshing line parametric equations. The meshing mode of the unequal pressure angle end-face double-arc gear mechanism driven by the parallel shaft of the present invention is a point meshing mode based on the meshing line parameter equation of equal slip rate, and the relative sliding speeds of all meshing points on the two meshing lines are respectively equal. It can ensure uniform friction and wear of the tooth surface. The most prominent feature of the unequal pressure angle end face double arc gear mechanism of the parallel shaft transmission of the present invention is that the unequal pressure angle design of the end face double arc end face and the tooth root transition curve design can effectively improve the bending strength of the gear root.

Compared with the prior art, the unequal pressure angle end face double arc gear mechanism of the parallel shaft transmission of the present invention has the following beneficial effects:

1. The design of the unequal pressure angle end-face double-arc gear mechanism driven by the parallel shaft of the present invention is based on the active design method of the meshing line parameter equation, constructing the double-point concave-convex meshing tooth surface on the end surface, and the relative sliding of all meshing points on the two meshing lines. The speeds are all equal, so the tooth flanks wear the same amount and are easy to lubricate.

2. The two pressure angles of the meshing point of the end face tooth profile of the unequal pressure angle end face double arc gear mechanism driven by the parallel shaft of the present invention are designed to be unequal, which can increase the bending strength of the tooth root and maximize the service life of the gear. Reduce the size of the structure, which is conducive to the transmission of heavy-duty power.

3. The coincidence degree of the unequal pressure angle end face double arc gear mechanism driven by the parallel shaft of the present invention is free to design, and the structure and shape of the tooth profile can be determined through the pre-design of the coincidence degree, so as to realize the uniform distribution of the load and improve the dynamic performance.

4. The unequal pressure angle end face double arc gear mechanism of the parallel shaft transmission of the present invention has no undercut, and the minimum number of teeth is 1. Compared with the existing parallel shaft involute gears and other mechanisms, it can achieve a single-stage large transmission ratio and high coincidence. At the same time, since the number of teeth can be designed to be smaller, the tooth thickness and module can be designed with the same gear diameter, so as to have higher bending strength and greater bearing capacity, suitable for micro/micro machinery, conventional mechanical transmission And the promotion and application in the field of high-speed and heavy-duty transmission.

5. The unequal pressure angle end face double arc gear mechanism of the parallel shaft transmission of the present invention can make the small wheel and the large wheel have similar tooth root bending strength by adjusting the optimal design of the shape control parameters of the tooth root transition curve, so as to realize the transmission mechanism. The equal strength design further improves the service life of the equipment.

Description of drawings

The present invention will be further described below in conjunction with the accompanying drawings and embodiments, in which:

FIG. 1 is a schematic structural diagram of the unequal pressure angle end face double arc gear mechanism of the parallel shaft transmission of the present invention.

FIG. 2 is a schematic diagram of the spatial meshing coordinate system of the unequal pressure angle end face double arc gear mechanism of the parallel shaft transmission of the present invention.

Fig. 3 is the tooth profile composition structure and the coordinate system of the end face of the large wheel and the small wheel in Fig. 1 and Fig. 2 of the present invention.

FIG. 4 is a partial detail and enlarged view of FIG. 3 .

Fig. 5 is a three-dimensional view of the small wheel in Fig. 1 of the present invention.

FIG. 6 is a three-dimensional view of the large wheel in FIG. 1 of the present invention.

FIG. 7 is a schematic structural diagram of the present invention when the large wheel is connected to the input shaft to drive the small wheel to increase the speed transmission.

In the above picture: 1- driver, 2- small wheel, 3- input shaft, 4- output shaft, 5- large wheel, 6- small wheel section cylinder, 7- small wheel contact line C _R2p , 8- big wheel contact line C _R2g , 9-mesh line K _R2 -K _R2 , 10- big wheel contact line C _R1g , 11-mesh line K _R1 -K _R1 , 12- small wheel contact line C _R1p , 13- big wheel pitch cylinder, 14- The right tooth root transition curve of the pinion tooth, 15- the right concave arc tooth profile of the pinion tooth, 16- the right straight tooth profile of the pinion tooth, 17- the right convex arc tooth profile of the pinion tooth , 18- the right tooth root transition curve of the large gear tooth, 19- the right concave arc tooth profile of the large gear tooth, 20- the right straight tooth profile of the large gear tooth, 21- the right convex circle of the large gear tooth Arc profile.

Detailed ways

Various exemplary embodiments of the present invention will be described in detail below with reference to the accompanying drawings. It should be noted that the relative arrangement of components and steps, the numerical expressions and numerical values set forth in these embodiments do not limit the scope of the invention unless specifically stated otherwise.

Meanwhile, it should be understood that, for the convenience of description, the dimensions of various parts shown in the accompanying drawings are not drawn in an actual proportional relationship.

The following description of at least one exemplary embodiment is merely illustrative in nature and is in no way intended to limit the invention, its application, or uses.

In order to make the objectives, technical solutions and advantages of the present invention clearer, the present invention will be further described in detail below with reference to specific embodiments and accompanying drawings.

Techniques, methods, and devices known to those of ordinary skill in the relevant art may not be discussed in detail, but where appropriate, such techniques, methods, and devices should be considered part of the authorized description.

In all examples shown and discussed herein, any specific value should be construed as illustrative only and not as limiting. Accordingly, other examples of exemplary embodiments may have different values.

It should be noted that like numerals and letters refer to like items in the following figures, so once an item is defined in one figure, it does not require further discussion in subsequent figures.

Embodiment 1: The present invention provides an unequal pressure angle end-face double arc gear mechanism for parallel shaft transmission, which is applied to the transmission with a transmission ratio of 2 between parallel shafts, and their coincidence degree is designed to be ε=4. Its structure is shown in Figure 1, including a small wheel 2 and a large wheel 5, the small wheel 2 and the large wheel 5 form a pair of transmission pairs, the small wheel 2 is connected to the input shaft 3, the input shaft 3 and the drive motor 1 are fixedly connected, and the large wheel is connected. 5. Connect the output shaft 4, that is, the large wheel 5 is connected with the driven load through the output shaft 4; the axes of the small wheel 2 and the large wheel 5 are parallel to each other. FIG. 2 is a schematic diagram of the space meshing coordinate system of the unequal pressure angle end face double arc gear mechanism driven by the parallel shaft of the present invention.

Referring to Figures 1, 2, 3, 4, and 5, the pitch cylinder 6 of the pinion has a radius of R ₁ , the tip circle radius of the pinion is R _a1 , the root circle radius is R _f1 , and the outer surface of the pinion cylinder is evenly distributed. There are helical gear teeth, and the tooth profile on the end face of the gear tooth is in the form of axisymmetric, that is, the tooth profile on the left side of the end face and the tooth profile on the right side are axisymmetric. Taking the tooth profile on the right side of the pinion end face as an example, from the tooth tip to the tooth root, there are 17 convex arc tooth profiles on the right side of the pinion teeth, 16 straight tooth profiles on the right side of the pinion teeth, and 16 on the right side of the pinion teeth. The concave arc tooth profile 15 and the right tooth root transition curve 14 of the pinion teeth are composed.

Referring to Figures 1, 2, 3, 4, and 6, the pitch cylinder 13 of the large wheel has a radius of R ₂ , the tip circle radius of the pinion is R _a2 , the root circle radius is R _f2 , and the outer surface of the large gear root cylinder is evenly distributed There are helical gear teeth, and the tooth profile on the end face of the gear tooth is in the form of axisymmetric, that is, the tooth profile on the left side of the end face and the tooth profile on the right side are axisymmetric. Taking the tooth profile on the right side of the end face of the big wheel as an example, from the top of the tooth to the root of the tooth, there are 21 convex arc tooth profiles on the right side of the big wheel teeth, 20 on the right side of the big wheel teeth, and 20 on the right side of the big wheel teeth. The concave arc tooth profile 19 and the tooth root transition curve 18 on the right side of the large gear teeth are formed.

The teeth of the small wheel and the large wheel are all helical teeth, and the tooth surface of the pinion is obtained by performing a helical motion along the contact line C _R1p 12 of the pinion end face, and the pitch of the helical motion is related to the contact line C _R1p 12 . The same; the tooth surface of the large wheel is obtained by the helical motion of the tooth profile of the end face of the large wheel along the contact line C _R1g 10 of the large wheel, and the pitch of the helical motion is the same as the contact line C _R1g 10 of the large wheel; at any end face, the small wheel and the large wheel The tooth profile of the end face meshes at two points M _R1 and M _R2 at the same time, and the spatial movement of these two meshing points forms meshing lines K _R1 -K _R1 11 and meshing lines K _R2 -K _R2 9 respectively;

The small wheel 2 is connected to the input shaft 3 and rotates under the drive of the driver 1, so that the convex circular arc tooth profile and the concave circular arc tooth profile on the small wheel and the big wheel are meshed at the meshing points M _R1 and M _R2 at the same time, realizing parallel shafts. For the transmission between the movement and the power, the driver 4 in this embodiment is an electric motor.

角，大轮绕z_g轴转过

角； _Wherein , the _{contact line} of the _tooth surface of the small wheel and the large wheel and the _tooth profile structure of the end surface of the small wheel and the large wheel are determined by the following methods: In the three space coordinate systems of _k , y _k , z _k and o _g --x _g , y _g , z _g , the z _p axis coincides with the rotation axis of the small wheel, the z _g axis coincides with the rotation axis of the large wheel, and the z p axis coincides with the rotation axis of the large wheel. The _k axis coincides with the meshing line K _R1 -K _R1 passing through the meshing point M _R1 , and the z _k axis is parallel to the z _p and _{z g} axes, and the x _p and x _g axes are coincident, and the x _k and x _g axes are parallel. The distance of o _g is a; the coordinate system o ₁ -- x ₁ , y ₁ , z ₁ is fixed with the small wheel, the coordinate system o ₂ -- x ₂ , y ₂ , z ₂ is fixed with the large wheel, the small wheel, The big wheel coordinate systems o ₁ --x ₁ , y ₁ , z ₁ and o ₂ -- x ₂ , y ₂ , z ₂ are respectively at the starting position with the coordinate systems o _p --x _p , y _p , z _p and o _g --x _g , y _g , z _g coincide, the small wheel rotates clockwise around the z _p axis at a uniform angular velocity ω ₁ , and the large wheel rotates counterclockwise around the z _g axis at a uniform angular velocity ω ₂ . After time, the coordinate system o ₁ -- x ₁ , y ₁ , z ₁ and o ₂ -- x ₂ , y ₂ , z ₂ rotate respectively. At this time, the meshing points are M _R1 and M _R2 , and the small wheel revolves around the z _p axis turn around

angle, the large wheel rotates around the z _g axis

horn;

When the small wheel and the large wheel are engaged in the transmission, the meshing point M _R1 is set to move along the meshing line K _{R1 -K R1} from the coordinate origin ok, and the parameter equation of the movement of the M _R1 point is:

At the same time, the meshing point M _R2 moves along the meshing line K _R2 -K _R2 at the same moving speed, and the parameter equation for the movement of the M _R2 point is:

In formulas (1) and (2), t is the motion parameter variable of the meshing point M _R1 , 0≤t≤Δt; c1 is the undetermined coefficient _of the meshing point motion, in millimeters (mm); in order to ensure the meshing of the fixed transmission ratio, the smaller There must be a linear relationship between the rotation angle of the wheel and the big wheel and the movement of the meshing point. The specific relationship is as follows:

In formula (3), k is the linear proportional coefficient of the motion of the meshing point, and its unit is radian (rad); i ₁₂ is the transmission ratio between the small wheel and the large wheel;

When the meshing point M _R1 moves along the meshing line K _R1 -K _R1 , the point M _R1 simultaneously forms the contact lines C _R1p and C _R1g on the convex circular arc tooth surface of the small wheel and the concave circular arc tooth surface of the large wheel; when the meshing point M When _R2 moves along the meshing line K _R2 -K _R2 , the point M _R2 forms the contact lines C _R2p and C _R2g on the concave arc tooth surface of the small wheel and the convex arc tooth surface of the large wheel at the same time; according to the coordinate transformation, the coordinate system can be obtained o _p --x _p ,y _p ,z _p , o _k --x _k ,y _k ,z _k and o _g —x _g ,y _g ,z _g , o ₁ —x ₁ ,y ₁ ,z ₁ and The homogeneous coordinate transformation matrix between o ₂ —x ₂ , y ₂ , z ₂ is:

in,

In formulas (5) and (6), R ₁ is the pitch cylinder radius of the small wheel, R ₂ is the pitch cylinder radius of the large wheel, PM is the distance from the meshing points M _R1 and M _R2 to the node P, and α _t1 is the meshing point The end face pressure angle of _MR1 , α _t2 is the end face pressure angle of the meshing point _MR2 ;

From equations (1) and (4), the parametric equation of the contact line C _R1p of the pinion cam tooth surface is obtained as:

From equations (1) and (4), the parameter equation of the contact line C _R1g of the concave arc tooth surface of the large wheel can be obtained as:

From equations (2) and (4), the parametric equation of the contact line C _R2p of the concave circular arc tooth surface of the pinion is obtained as:

From equations (2) and (4), the parametric equation of the tooth surface contact line C _R2g of the large wheel camber is obtained as:

The tooth profile of the end face of the small wheel and the large wheel is determined by the following method:

The local coordinate systems S _a1 (o _a1 -x _a1 y _a1 z _a1 ) and S _b2 (o _b2 are established respectively at the center o _a1 of the small wheel convex arc tooth profile ar1 and the circle center o _b2 of the large wheel concave arc tooth profile br2 -x _b2 y _b2 z _b2 ), the parametric equations of the small wheel convex circular arc tooth profile ar1 and the large wheel concave circular arc tooth profile br2 are respectively:

In equations (11) and (12), ρ _a1 is the arc radius of the pinion end face convex arc tooth profile ar1, ξ _a1 is the angle parameter of ar1, ξ _a1a and ξ _a1b are the minimum and maximum values of ξ _a1 , respectively ;ρ _b2 is the arc radius of the concave circular arc tooth profile br2 on the end face of the large wheel, ξ _b2 is the angle parameter of br2, ξ _b2a and ξ _b2b are the minimum and maximum values of ξ _b2 , where the value of ξ _a1b is determined by the small wheel The intersection of the addendum circle and the pinion convex arc tooth profile ar1 is obtained by solving;

ξ _a1a =ξ _a1b -π/5.5; (13)

ξ _b2a =ξ _b2b -π/6.5; (14)

The local coordinate systems S _b1 (o _b1 -x _b1 y _b1 z _b1 ) and S _a2 (o _a2 -x) are established respectively at the center o _b1 of the small wheel concave arc tooth profile Br1 and the center o _a2 of the large wheel convex arc tooth profile Ar2 _a2 y _a2 z _a2 ), then the parametric equations of the small wheel convex circular arc tooth profile Br1 and the large wheel concave circular arc tooth profile Ar2 are:

In formulas (15) and (16), ρ _b1 is the arc radius of the concave circular arc tooth profile Br1 on the pinion end face, ξ _b1 is the angle parameter of Br1, ξ _b1a and ξ _b1b are the minimum and maximum values of ξ _b1 respectively ;ρ _a2 is the arc radius of the convex arc tooth profile Ar2 on the end face of the big wheel, ξ _a2 is the angle parameter of Ar2, ξ _a2a and ξ _a2b are the minimum and maximum values of ξ _b2 , where the value of ξ _a2b is determined by the big wheel The intersection point of the addendum circle and the tooth profile Ar2 of the big wheel camber arc is obtained by solving;

ξ _a2a =ξ _a2b -π/5.5; (17)

ξ _b1a =ξ _b1b -π/6.5; (18)

The parametric equation of the convex arc tooth profile ar1 on the right side of the pinion tooth end face in the _Sp coordinate system is obtained by coordinate transformation:

The parametric equation of the concave circular arc tooth profile br1 on the right side of the pinion tooth end face in the _Sp coordinate system is obtained from the coordinate transformation:

The parametric equation of the concave circular arc tooth profile br2 on the right side of the tooth end face of the large gear in the S _g coordinate system is obtained by coordinate transformation:

The parametric equation of the convex arc tooth profile ar2 on the right side of the tooth end face of the large gear in the S _g coordinate system is obtained by coordinate transformation:

The transition curve hr1 on the right side of the pinion tooth end face is determined by the points P _0P and P _1P and their tangent vectors T _0P and T _1P , and the point P _0P is determined by R _h1 , so the value ξ _b1b of the tooth profile br1 can be obtained by solving, P _1P is determined by the pinion root circle radius R _f1 and the angle δ _1R , and the parametric equation of the transition curve hr1 on the right side of the pinion tooth end face is obtained as:

In formulas (23) and (24), x _p (P _0P ), y _p (P _0P ), z _p (P _0P ) are the three-coordinate components of the point P _0P , x _p (P _1P ), y _p (P _1P ), z _p (P _1P ) are the three-coordinate components of the point P _1P , respectively, x _p (T _0P ), y _p (T _0P ), z _p (T _0P ) are the unit cuts of the point P _0P The three-coordinate components of the vector T _0P , x _p (T _1P ), y _p (T _1P ), z _p (T _1P ) are the three-coordinate components of the unit tangent vector T _1P of the point P _1P , m _t is the end face Modulus, b ₁ , b ₂ , b ₃ , b ₄ are calculation parameters, _TH is the shape control parameter of the tooth root transition curve, 0.2≤TH ≤1.5, t _H is the calculation parameter, _{0≤t H ≤1} ;

The transition curve hr2 on the right side of the tooth end face of the large gear is determined by the points P _0G and P _1G and their tangent vectors T _0G and T _1G , and the point P _0G is determined by R _h2 , so the value ξ _b2b of the tooth profile br2 can be obtained by solving, P _1G is determined by the tooth root circle radius R _f2 of the large gear and the angle δ _2R . The parametric equation of the transition curve hr2 on the right side of the tooth end face of the large gear is obtained as follows:

In formula (25), x _g (P _0G ), y _g (P _0G ), z _g (P _0G ) are the three-coordinate components of the point P _0G , respectively, x _g (P _1G ), y _g (P _1G ) , z _g (P _1G ) are the three-coordinate components of the point P _1G respectively, x _g (T _0G ), y _g (T _0G ), z _g (T _0G ) are the unit tangent vector T _0G of the point P _0G respectively The three-coordinate components, x _g (T _1G ), y _g (T _1G ), and z _g (T _1G ) are respectively the three-coordinate components of the unit tangent vector T _1G of the point P _1G ;

In this example:

t-the motion parameter variable of meshing point M, and t∈[0, Δt];

k- is the linear scale coefficient;

Z ₁ - the number of pinion teeth;

Z ₂ - the number of teeth of the large gear;

m _n - normal modulus;

R ₁ - is the pitch cylinder radius of the small wheel, R ₁ =m _t Z ₁ /2; (26)

R ₂ - is the pitch cylinder radius of the large wheel, R ₂ =i ₁₂ R ₁ ; (27)

i ₁₂ - is the transmission ratio of the small wheel to the large wheel,

a- The relative position of the axis installation of the small wheel and the large wheel: a=R ₁ +R ₂ ; (29)

b-The width of the teeth of the small wheel and the large wheel: b=c ₁ Δt=2Φ _d R ₁ ; (30)

Φ _d — diameter coefficient;

β-pitch circle helix angle,

m _t - modulus of end face, m _t = m _n /cosβ; (32)

R _a1 —— the radius of the pinion tip circle, R _a1 =R ₁ +m _t ; (33)

R _f1 ——pinion root circle radius, R _f1 =R ₁ -1.25m _t ; (34)

R _h1 —— the radius from the starting point P _0P of the transition curve at the root of the small wheel to the rotation center of the small wheel, R _h1 =R ₁ -m _t ; (35)

R _a2 —— the radius of the tooth tip circle of the large gear, R _a2 =R ₂ +m _t ; (36)

R _f2 —— the radius of the tooth root circle of the large gear, R _f2 =R ₂ -1.25m _t ; (37)

R _h2 —— the radius from the starting point P _0G of the transition curve at the root of the big wheel to the rotation center of the big wheel, R _h2 =R ₂ -m _t ; (38)

PM - the horizontal distance from the meshing point to the node,

ρ _a1 —— the arc radius of the convex arc tooth profile on the end face of the pinion, ρ _a1 = PM; (40)

ρ _a2 —— the arc radius of the convex arc tooth profile of the big wheel end face, ρ _a2 = ρ _a1 ; (41)

ρ _b2 —— the arc radius of the concave arc tooth profile on the end face of the big wheel, ρ _b2 =ρ _a1 +Δρ; (42)

Δρ——The difference between the concave and convex arc radius, Δρ=0.5m _t ; (43)

ρ _b1 —— the arc radius of the concave arc tooth profile on the end face of the pinion, ρ _b1 =ρ _b2 ; (44)

δ ₁ ——The central angle between the tooth root arcs of the adjacent two teeth of the small wheel,

δ ₂ ——The central angle between the tooth root arcs of the two adjacent gear teeth of the big wheel,

δ _1R ——the acute angle between the radius corresponding to the point P _1P on the transition curve hr1 of the right root of the pinion tooth and the x _p axis,

δ _2R ——the acute angle between the radius corresponding to the point P _1G on the transition curve hr2 of the right root of the large gear tooth and the x _p axis,

β，ξ_a1，ξ_b1，ξ_a2，ξ_b2角度的单位为弧度(rad)；压力角α_t1，α_t2的单位为度(°)；Among them: each coordinate system axis, a, b, m _n , m _t , ρ _a1 , Δρ, R ₁ and R ₂ and other lengths, radii or distances are in millimeters (mm); k,

β, ξ _a1 , ξ _b1 , ξ _a2 , ξ _b2 The unit of angle is radian (rad); the unit of pressure angle α _t1 , α _t2 is degree (°);

When determining the number of pinion teeth Z ₁ , the transmission ratio i ₁₂ , the normal modulus m _n , the degree of coincidence ε, the linear proportionality coefficient k, the pressure angles α _t1 and α _t2 of the two meshing points of the pinion, the diameter coefficient Φ _d , the teeth When the transition curve shape control parameter _TH is used, the undetermined coefficient c1 and motion law of the meshing point motion, the contact line and the meshing line, the tooth profile of the end face of the small wheel and the large wheel and their correct installation distance are also determined accordingly. The gear tooth surface structure of the big wheel can also be determined, so as to obtain a double-arc gear mechanism with an unequal pressure angle end face driven by a parallel shaft.

The coincidence degree of the unequal pressure angle end face double arc gear mechanism driven by the parallel shaft is twice that of the single-point contact meshing, and the coincidence degree of the single-point contact meshing should be greater than 1. The formula for calculating the coincidence degree of the double-arc gear mechanism on the end face of the unequal pressure angle with double-point meshing is as follows:

Obtain the maximum value of the kinematic parameter variable of the meshing point of the unequal pressure angle end face double arc gear mechanism driven by the parallel shaft.

When designing, it is necessary to comprehensively determine the maximum value Δt of the motion parameter variable of the meshing point M _R1 according to the value ε of the coincidence degree, the linear proportional coefficient k and the number of teeth Z ₁ of the pinion.

The meshing mode of the small wheel and the large wheel is the concave-convex meshing transmission with double-point contact on the end surface. The two meshing points have unequal end pressure angles, and the end pressure angle of the meshing point of the concave arc tooth profile of the small wheel is higher than that of the convex circular arc tooth profile of the small wheel. The end face pressure angle of the meshing point is small to enhance the bending strength of the tooth root, that is, α _t2 <α _t1 .

a＝85.7930毫米(mm)，b＝57.1953毫米(mm)，c₁＝257.3789毫米(mm)，PM＝4.9912 毫米(mm)；In the above formula, the relevant parameters are respectively: Z ₁ =18, i ₁₂ =2, m _n =3 millimeters (mm), ε=4, k=π radians (rad), α _t1 =25°, α _t2 = 15°, Φ _d = 1, _TH = 0.5, substituting into equations (26)-(48) to obtain

a=85.7930 millimeters (mm), b=57.1953 millimeters (mm), c1 ₌ 257.3789 millimeters (mm), PM=4.9912 millimeters (mm);

Then, substitute the above values into equations (7)-(25) to obtain the contact line parameter equation and the end face tooth profile parameter equation of the small wheel and the large wheel in this example, and then according to the spiral motion, the teeth of the small wheel and the large wheel can be obtained. structure and can be assembled with the correct center distance.

When the driver 1 drives the input shaft 3 and the small wheel 2 to rotate, because when the small wheel 2 and the large wheel 5 are installed correctly, two pairs of adjacent gear teeth are in meshing state, the preset pair of double arc gears The degree of coincidence ε=4, thus ensuring that at each instant, at least two pairs of gear teeth participate in meshing transmission at the same time, and each pair of gear teeth has a meshing point on the upper and lower arc tooth profiles, thus realizing parallel shaft transmission. The unequal pressure angle end face double arc gear mechanism continuously and stably meshes transmission in the rotating motion. The rotation direction of the input shaft connected to the motor in this embodiment is clockwise, which corresponds to the deceleration transmission mode of the unequal pressure angle end face double arc gear mechanism driven by the parallel shaft, which is used to realize the deceleration and torque increase transmission of the counterclockwise rotation of the large wheel.

Embodiment 2: The unequal pressure angle end face double arc gear mechanism of the parallel shaft transmission of the present invention is applied to the speed increase transmission of the parallel shaft. As shown in Figure 6, the large wheel 5 is used to connect the input shaft 3, the input shaft 3 and the drive motor 1 are fixedly connected, and the small wheel 2 is connected to the output shaft 4, that is, the small wheel 2 is connected to the driven load through the output shaft 4; 2 and the axis of the big wheel 5 are parallel. In this embodiment, the number of teeth of the large wheel 5 is 36, the number of teeth of the small wheel 2 is 18, and the design coincidence degree ε=4. When the input shaft 3 drives the large wheel 5 to rotate, since the two pairs of adjacent gear teeth are in meshing state when the large wheel 5 and the small wheel 2 are installed, the preset coincidence degree of the pair of double arc gears is ε=4, Therefore, it is ensured that at each instant, at least two pairs of gear teeth participate in meshing transmission at the same time, and the upper and lower arc tooth profiles of each pair of gear teeth each have a meshing point, thereby realizing the unequal pressure angle end face of parallel shaft transmission. The double arc gear mechanism has continuous and stable meshing transmission in the rotating motion. At this time, the speed increase ratio of the big wheel to the small wheel is 2, that is, the transmission ratio of the small wheel to the big wheel is 2.

a＝57.1953毫米(mm)，b＝38.1302 毫米(mm)，c₁＝171.5860，PM＝3.3275毫米(mm)；The relevant parameters are respectively: Z ₁ =18, i ₁₂ =2, m _n =2 millimeters (mm), ε = 4, α _t1 =28°, α _t2 =14°, Φ _d =1, _TH = 0.6, substituted into equation (26)-equation (48) to obtain

a=57.1953 millimeters (mm), b=38.1302 millimeters (mm), c ₁ =171.5860, PM=3.3275 millimeters (mm);

Then the above values are substituted into equations (7)-(25) to obtain the contact line parameter equation and end face tooth profile parameter equation of the small wheel and the large wheel in this example, and then the distribution is based on the helical motion, so as to obtain the wheel of the small wheel and the large wheel. tooth structure and can be assembled with the correct center distance.

The rotation direction of the input shaft connected to the driver in this embodiment is counterclockwise, which corresponds to the speed-increasing transmission mode of the unequal pressure angle end-face double-arc gear mechanism of parallel shaft transmission, which is used to realize the clockwise rotation of the small wheel.

The design of the unequal pressure angle end-face double-arc gear mechanism driven by the parallel shaft of the present invention is based on the active design method of the meshing line parameter equation, and the end-face double-point concave-convex meshing tooth surface is constructed, and the relative sliding speeds of all meshing points on the two meshing lines are equal to are equal, so the wear amount of the tooth surface is the same, and it is easy to lubricate; the pressure angle of the end face meshing point of the unequal pressure angle end face double arc gear mechanism of the parallel shaft transmission of the present invention is designed to be unequal, which can increase the bending strength of the tooth root. , maximize the service life of the gear, reduce the structure size, and facilitate the transmission of heavy-duty power; the coincidence degree of the unequal pressure angle end face double arc gear mechanism of the parallel shaft transmission of the present invention is free to design, and can be adjusted by the pressure angle and the coincidence degree. Pre-designed to determine the shape of the tooth profile structure, to achieve uniform load distribution, and to improve dynamic characteristics; the unequal pressure angle end face double arc gear mechanism of the parallel shaft transmission of the present invention has no undercut, and the minimum number of teeth is 1, compared with the existing parallel shaft. Shaft involute gears and other mechanisms can realize single-stage large transmission ratio and high coincidence transmission. At the same time, due to the small number of teeth, a larger tooth thickness can be designed for the same gear diameter, so as to have higher strength and greater bearing capacity. , suitable for the promotion and application in the fields of micro/micro machinery, conventional mechanical transmission and high-speed and heavy-duty transmission; the unequal pressure angle end-face double arc gear mechanism of the parallel shaft transmission of the present invention can also be adjusted by adjusting the optimal design of the root transition curve parameter value. In order to make the small wheel and the large wheel have similar bending strength of the tooth root, realize the equal strength design of the transmission mechanism, and further improve the service life of the equipment.

It should be noted that, herein, the terms "comprising", "comprising" or any other variation thereof are intended to encompass non-exclusive inclusion, such that a process, method, article or system comprising a series of elements includes not only those elements, It also includes other elements not expressly listed or inherent to such a process, method, article or system. Without further limitation, an element qualified by the phrase "comprising a..." does not preclude the presence of additional identical elements in the process, method, article or system that includes the element.

The above-mentioned serial numbers of the embodiments of the present invention are only for description, and do not represent the advantages or disadvantages of the embodiments. In a unit claim enumerating several means, several of these means may be embodied by one and the same item of hardware. The use of the words first, second, and third, etc. do not denote any order, and these words may be construed as identifications.

The above are only preferred embodiments of the present invention, and are not intended to limit the scope of the present invention. Any equivalent structure or equivalent process transformation made by using the contents of the description and drawings of the present invention, or directly or indirectly applied in other related technical fields , are similarly included in the scope of patent protection of the present invention.

Claims (8)

1. The utility model provides a driven not equal pressure angle terminal surface double circular arc gear mechanism of parallel shaft, includes a pair of gear pair that steamboat and bull wheel are constituteed, the steamboat links firmly with the driver through the input shaft, the output shaft is connected to the bull wheel, the steamboat with the axis of bull wheel is parallel, its characterized in that: the end face tooth profiles of the small wheel and the large wheel have axial symmetry forms, and the left and right end face tooth profiles respectively consist of a convex arc tooth profile, a straight line tooth profile, a concave arc tooth profile and a tooth root transition curve from the tooth top to the tooth root; the small wheel and the large wheel are meshed in a concave-convex meshing transmission mode with end surfaces in double-point contact, and the two meshing points have unequal pressure angles; the small wheel is driven by the driver to rotate, stable meshing transmission between parallel shafts is realized through continuous meshing between two pairs of convex circular arc tooth profiles and concave circular arc tooth profiles, two meshing points with different pressure angles respectively form two contact lines with the same pitch on tooth surfaces of the small wheel and the large wheel, and the two contact lines are cylindrical spiral lines; the gear tooth flanks of the small wheel and the large wheel are spiral tooth flanks obtained by cylindrical spiral motion of end face tooth profiles along respective contact lines, the screw pitch of the spiral tooth flanks is equal to that of the contact lines, and the spiral directions of the gear teeth of the small wheel and the gear teeth of the large wheel are opposite.

2. The unequal pressure angle end face double-circular arc gear mechanism of parallel shaft transmission according to claim 1, characterized in that: the small wheel and the big wheel are in double-point contact concave-convex meshing transmission, and two meshing points of the small wheel and the big wheel are respectively a meshing point M of a convex circular arc tooth profile of the teeth of the small wheel and a concave circular arc tooth profile of the teeth of the big wheel_R1And the meshing point M of the concave circular arc tooth profile of the adjacent gear teeth of the small gear and the convex circular arc tooth profile of the adjacent gear teeth of the large gear_R2(ii) a The normal lines of the tooth profile meshing points of the two pairs of concave-convex circular arc end surfaces intersect at the same point, and the point is a tangent point of a pitch circle of the pair of double-circular-arc gears, namely a node; the horizontal distances from the two meshing points to the node are both PM; when the pair of parallel shafts drive the double-arc gear mechanism with unequal pressure angle end faces, two meshing points M_R1And M_R2Has the same axial movement speed and forms two spatial meshing lines K respectively_R1-K_R1And K_R2-K_R2And each form two contact lines of the tooth faces of the small wheel and the large wheel.

3. The unequal pressure angle end face double-circular-arc gear mechanism of parallel shaft transmission according to claim 2, characterized in that: the tooth surface contact line of the small wheel and the large wheel is determined by the following method:

at o_p--x_p,y_p,z_p、o_k--x_k,y_k,z_kAnd o_g--x_g,y_g,z_gIn three spatial coordinate systems, where o_p、o_kAnd o_gRespectively the origin, x, of three spatial coordinate systems_p、x_kAnd x_gX-axis, y of three spatial coordinate systems respectively_p、y_kAnd y_gX-axis, z, of three spatial coordinate systems, respectively_p、z_kAnd z_gZ-axes, z, of three spatial coordinate systems, respectively_pThe axis of rotation of the shaft and the small wheel coinciding, z_gThe axis of rotation of the shaft and the bull wheel coinciding, z_kShaft-to-pass meshing point M_R1Engagement line K of_R1-K_R1Coincide with and z_kAxis and z_p、z_gAxes parallel to each other, x_pAnd x_gThe axes being coincident, x_kAnd x_gAxis parallel, o_pAnd o_gA is a; coordinate system o₁--x₁,y₁,z₁Fixedly connected with the small wheel and having a coordinate system o₂--x₂,y₂,z₂Fixedly connected with the large wheel and a small wheel coordinate system o₁--x₁,y₁,z₁And a large wheel coordinate system o₂--x₂,y₂,z₂At the starting position respectively with the coordinate system o_p--x_p,y_p,z_pAnd o_g--x_g,y_g,z_gCoincident, the small wheels being at a uniform angular velocity ω₁Around z_pThe shaft rotates clockwise and the bull wheel rotates at a uniform angular velocity ω₂Around z_gThe axis rotates anticlockwise, after a period of time from the starting position, the coordinate system o₁--x₁,y₁,z₁And o₂--x₂,y₂,z₂Respectively rotate when the meshing point is M_R1And M_R2Said small wheel winding z_pThe shaft rotates through

Angle, said large wheel winding z_gThe shaft rotates through

An angle;

when the small wheel and the large wheel are in meshing transmission, a meshing point M is set_R1From the origin o of coordinates_kBeginning along the line of engagement K_R1-K_R1Exercise, M_R1The parametric equation for point motion is:

at the same time, the mesh point M_R2Along the line of engagement K at the same speed of movement_R2-K_R2Exercise, M_R2The parametric equation for point motion is:

wherein t is the meshing point M_R1T is more than or equal to 0 and less than or equal to delta t, and delta t is the maximum value of the motion parameter variable; c. C₁The undetermined coefficient of the movement of the meshing point is represented by millimeter, and PM is the horizontal distance from the meshing point to the node; in order to ensure that the fixed gear ratio is engaged, the rotation angles of the small wheel and the large wheel and the movement of the engagement point have to be in a linear relationship, and the rotation angles of the small wheel and the large wheel and the movement of the engagement point have the following relationship:

in the formula, k is a linear proportionality coefficient of the movement of the meshing point, and the unit of k is radian; i.e. i₁₂The transmission ratio between the small wheel and the large wheel is set;

when the point of engagement M_R1Along the line of engagement K_R1-K_R1While in motion, point M_R1Simultaneously, contact lines C are respectively formed on the convex circular arc tooth surface of the small wheel and the concave circular arc tooth surface of the large wheel_R1pAnd C_R1g(ii) a When the point of engagement M_R2Along the line of engagement K_R2-K_R2While in motion, point M_R2Simultaneously, contact lines C are respectively formed on the concave arc tooth surface of the small wheel and the convex arc tooth surface of the large wheel_R2pAnd C_R2g(ii) a Obtaining a coordinate system o according to the coordinate transformation_p--x_p,y_p,z_p、o_k--x_k,y_k,z_kAnd o_g--x_g,y_g,z_g、o₁--x₁,y₁,z₁And o₂--x₂,y₂,z₂The homogeneous coordinate transformation matrix in between is:

wherein,

in the formula, R₁Is the pitch cylinder radius of the small wheel, R₂Is the pitch cylinder radius of the bull wheel, and PM is the meshing point M_R1And M_R2Distance to node P, α_t1Is a meshing point M_R1End face pressure angle of alpha_t2Is a meshing point M_R2The end face pressure angle of (1);

from said M_R1The contact line C of the convex arc tooth surface of the small wheel is obtained by the parameter equation of point motion and the homogeneous coordinate transformation matrix_R1pThe parameter equation of (1) is as follows:

from said M_R1Obtaining the contact line C of the concave circular arc tooth surface of the large wheel by the parameter equation of point motion and the homogeneous coordinate transformation matrix_R1gThe parameter equation of (1) is as follows:

from said M_R2Calculating the small wheel concave arc tooth surface contact line C by using the parameter equation of point motion and the homogeneous coordinate transformation matrix_R2pThe parameter equation of (1) is as follows:

from said M_R2Calculating the contact line C of convex arc tooth surface of large wheel by using the parameter equation of point motion and the homogeneous coordinate transformation matrix_R2gThe parameter equation of (1) is as follows:

4. the unequal pressure angle end face double-circular arc gear mechanism of parallel shaft transmission according to claim 1, characterized in that: the end face tooth profiles of the small wheel and the large wheel are determined by the following method:

respectively at the circle center o of the convex circular arc tooth profile ar1 of the small wheel_a1And the circle center o of the big wheel concave circular arc tooth profile br2_b2Establishing a local coordinate system S_a1(o_a1-x_a1y_a1z_a1) And S_b2(o_b2-x_b2y_b2z_b2) The obtained parameter equations of the small wheel convex circular arc tooth profile ar1 and the large wheel concave circular arc tooth profile br2 are respectively as follows:

in the formula, ρ_a1Is the arc radius, ξ of the small wheel end face convex arc tooth profile ar1_a1Is the angular parameter, ξ, of ar1_a1aAnd xi_a1bAre respectively xi_a1Minimum and maximum values of; rho_b2Is the arc radius, xi, of the concave arc tooth profile br2 of the end surface of the bull wheel_b2Angular parameter of br2, ξ_b2aAnd xi_b2bAre respectively xi_b2Minimum and maximum values of, wherein ξ_a1bThe value of the small wheel is obtained by solving the intersection point of the addendum circle of the small wheel and the convex circular arc tooth profile ar1 of the small wheel;

ξ_a1a＝ξ_a1b-π/5.5；

ξ_b2a＝ξ_b2b-π/6.5；

respectively at the circle center o of the small wheel concave arc tooth profile Br1_b1And the circle center o of the big wheel convex circular arc tooth profile Ar2_a2Establishing a local coordinate system S_b1(o_b1-x_b1y_b1z_b1) And S_a2(o_a2-x_a2y_a2z_a2) The parameter equations of the small wheel convex arc tooth profile Br1 and the large wheel concave arc tooth profile Ar2 are respectively as follows:

in the formula, ρ_b1Is the arc radius, xi, of the small wheel end surface concave arc tooth profile Br1_b1Angle parameter, ξ, of Br1_b1aAnd xi_b1bAre respectively xi_b1Minimum and maximum values of; rho_a2Is the arc radius, xi, of the convex arc tooth profile Ar2 of the end surface of the bull wheel_a2Is the angular parameter, ξ, of Ar2_a2aAnd xi_a2bAre respectively xi_b2Minimum and maximum values of, wherein ξ_a2bThe value of the curve is obtained by solving the intersection point of the top circle of the bull gear and the convex circular arc tooth profile Ar2 of the bull gear;

ξ_a2a＝ξ_a2b-π/5.5

ξ_b1a＝ξ_b1b-π/6.5；

coordinate transformation is used for obtaining the right convex circular arc tooth profile of the end surface of the small wheel gearar1 at S_pThe parametric equation for the coordinate system is:

obtaining the right concave circular arc tooth profile br1 of the end surface of the small gear tooth at S through coordinate transformation_pThe parametric equation for the coordinate system is:

obtaining the right side concave circular arc tooth profile br2 of the end surface of the bull wheel tooth at S by coordinate transformation_gThe parametric equation for the coordinate system is:

obtaining the right convex circular arc tooth profile ar2 of the gear end surface of the bull gear at S through coordinate transformation_gThe parametric equation for the coordinate system is:

the right transition curve hr1 from point P_0PAnd P_1PAnd its tangent vector T_0PAnd T_1PDetermine, point P_0PFrom R_h1Determined so that the value xi of the tooth profile br1_b1bCan be solved to obtain_1PRadius R of small gear root_f1Angle delta of sum_1RJointly determining, the parameter equation for solving the right side transition curve hr1 of the small gear tooth end surface is as follows:

in the formula, x_p(P_0P)，y_p(P_0P)，z_p(P_0P) Are respectively a point P_0PThree coordinate axis component of (2), x_p(P_1P)，y_p(P_1P)，z_p(P_1P) Are respectively a point P_1PThree coordinate axis component of (2), x_p(T_0P)，y_p(T_0P)，z_p(T_0P) Are respectively a point P_0PUnit tangent vector T of_0PThree coordinate axis component of (2), x_p(T_1P)，y_p(T_1P)，z_p(T_1P) Are respectively a point P_1PUnit tangent vector T of_1PThree coordinate axis component of (1), m_tIs the end face modulus, b₁，b₂，b₃，b₄To calculate the parameters, T_HThe control parameter is the shape of the tooth root transition curve, T is more than or equal to 0.2_H≤1.5，t_HFor calculating the parameter, t is more than or equal to 0_H≤1；

The transition curve hr2 from the right side of the bull gear tooth end face_0GAnd P_1GAnd its tangent vector T_0GAnd T_1GDetermine, point P_0GFrom R_h2Determined so that the value xi of the tooth profile br2_b2bCan be solved to obtain_1GBy the radius R of the root circle of the big gear_f2Angle delta of sum_2RJointly determining, the parameter equation for obtaining the right transition curve hr2 of the bull gear tooth end face is as follows:

in the formula, x_g(P_0G)，y_g(P_0G)，z_g(P_0G) Are respectively a point P_0GThree coordinate axis component of (2), x_g(P_1G)，y_g(P_1G)，z_g(P_1G) Are respectively a point P_1GThree coordinate axis component of (2), x_g(T_0G)，y_g(T_0G)，z_g(T_0G) Are respectively a point P_0GUnit tangent vector T of_0GThree coordinate axis component of (2), x_g(T_1G)，y_g(T_1G)，z_g(T_1G) Are respectively a point P_1GUnit tangent vector T of_1GThree coordinate axis components of (a);

when determining the number of teeth Z of the small gear₁A transmission ratio i₁₂Normal modulus m_nCoincidence degree epsilon, linear proportionality coefficient k and pressure angle alpha of two meshing points of small wheel_t1And alpha_t2Coefficient of diameter phi_dRoot transition curve shape control parameter T_HUndetermined coefficient c of motion of meshing point₁And the motion rule, the contact line and the meshing line, the end face gear tooth profiles and the correct installation distance of the small wheel and the large wheel are correspondingly determined, and the gear tooth surface structures of the small wheel and the large wheel can be determined, so that the unequal pressure angle end face double-arc gear mechanism driven by the parallel shaft is obtained.

5. The unequal pressure angle end face double-circular arc gear mechanism of parallel shaft transmission according to claim 1, characterized in that: the small wheel and the big wheel are meshed in a concave-convex meshing transmission mode with end surfaces in double-point contact, the two meshing points have unequal end surface pressure angles, and the end surface pressure angle of the small wheel concave circular arc tooth profile meshing point is smaller than that of the small wheel convex circular arc tooth profile meshing point so as to enhance the bending strength of a tooth root, namely alpha_t2＜α_t1。

6. The unequal pressure angle end face double-circular arc gear mechanism of parallel shaft transmission according to claim 1, characterized in that: the contact ratio of the unequal pressure angle end face double-arc gear mechanism driven by the parallel shafts is twice of that of single-point contact meshing, the contact ratio of the single-point contact meshing needs to be more than 1, and the contact ratio calculation formula of the unequal pressure angle end face double-arc gear mechanism meshed with two points is

The maximum value of the motion parameter variable of the meshing point of the parallel shaft driven double-arc gear mechanism with unequal pressure angle end surfaces is obtained as

The design needs to be carried out according to the value epsilon of the contact ratio, the linear proportionality coefficient k and the number Z of the small gear teeth₁Comprehensively determining the meshing point M_R1Is measured by the motion parameter variable of (1).

7. The unequal pressure angle end face double-circular arc gear mechanism of parallel shaft transmission according to claim 1, characterized in that: the input shaft and the output shaft which are connected by the small wheel and the big wheel have interchangeability, namely, the small wheel is connected with the input shaft, the big wheel is connected with the output shaft, or the big wheel is connected with the input shaft, the small wheel is connected with the output shaft, and the speed reduction transmission mode or the speed increase transmission mode respectively corresponds to the speed reduction transmission mode or the speed increase transmission mode of the double-arc gear mechanism with unequal pressure angle end surfaces in parallel shaft transmission; the constant-speed transmission application with the transmission ratio of 1 of the mechanism is realized only when the number of teeth of the small gear and the large gear is equal.

8. The unequal pressure angle end face double-circular-arc gear mechanism of parallel shaft transmission according to claim 1 or 7, characterized in that: the rotation direction of the input shaft connected with the driver is clockwise or anticlockwise, so that forward and reverse rotation transmission of the small wheel or the large wheel is realized.

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