CN112935414A

CN112935414A - Method for optimizing motion speed fluctuation of gear hobbing electronic gear box

Info

Publication number: CN112935414A
Application number: CN202110256797.1A
Authority: CN
Inventors: 丁国龙; 叶梦传; 吴熙; 李天一; 詹明儒
Original assignee: Hubei University of Technology
Current assignee: Hubei University of Technology
Priority date: 2021-03-09
Filing date: 2021-03-09
Publication date: 2021-06-11
Anticipated expiration: 2041-03-09
Also published as: CN112935414B

Abstract

The invention discloses a method for optimizing the movement speed fluctuation of an electronic gear box for hobbing, which comprises the following steps: (1) constructing an equation of the hob tooth profile under a hob coordinate system; (2) constructing a cutting track of the hob under a workpiece coordinate system in the machining process; (3) determining instantaneous cutting planes of the hob and the workpiece in a workpiece coordinate system and calculating to obtain the change of instantaneous cutting force along with time and the speed fluctuation of the electronic gearbox in the machining process; (4) and (4) adjusting the machining parameters, and re-executing the steps (1) to (3) until the machining parameters meeting the requirement of the speed fluctuation of the electronic gearbox, namely the optimized machining parameters, are obtained. The invention can solve the problems that the motion speed of the electronic gear box fluctuates greatly in the existing high-speed gear hobbing process, and accurate control, feedback and compensation are difficult to carry out. The optimized processing parameters can reduce the speed fluctuation of the electronic gear box, so that the movement speed of the electronic gear box is more stable, and the processing efficiency is improved.

Description

Method for optimizing motion speed fluctuation of gear hobbing electronic gear box

Technical Field

The invention belongs to the technical field of hobbing, and particularly relates to a method for optimizing the movement speed fluctuation of an electronic gear box for hobbing.

Background

The hobbing belongs to intermittent machining, and the main shaft generates speed fluctuation due to impact in the machining. Different from other gear machining methods such as numerical control gear shaping and numerical control gear milling, a hobbing machining main shaft needs to participate in generating motion to form a tooth profile, the main shaft generally works in a speed mode, in order to guarantee hobbing machining precision, a commonly-known electronic gear box motion control algorithm is generally adopted, namely, hobbing cutter rotation, hobbing cutter tangential movement and hobbing cutter axial movement along a workpiece are defined as a driving shaft, a workpiece rotating shaft is defined as a driven shaft, and a master-slave follow motion control model is established to realize high-precision motion control.

With the development of hobbing technology, the high-speed, dry-cut hard-rolling technology is more and more accepted by the market. However, during high-speed hard rolling, the rotation speed of the main shaft of the hob also fluctuates greatly due to large fluctuation of the hobbing force, so that the following motion precision of the main shaft and the auxiliary shaft is reduced, and the high-precision machining requirement of the gear cannot be guaranteed. In order to ensure the machining precision of the high-speed dry cutting hard roller, the fluctuation of cutting force is controlled from the aspect of hobbing machining dynamics and process parameters through process parameter optimization, so that the movement speed of a main shaft is smoother, the speed fluctuation is smaller, the master-slave following movement precision of an electronic gear box is ensured, and the market demand is met.

Generally, an empirical model is established for researching the hobbing force, the hobbing force is acquired through multiple experiments, and a relation between the hobbing force and relevant machining parameters is obtained through a linear fitting method.

Disclosure of Invention

In order to solve the problems pointed out in the background art, the invention provides a method for optimizing the movement speed fluctuation of an electronic gear box for hobbing, and the method is applied to hobbing, so that the movement speed fluctuation of the electronic gear box can be reduced, and the high-precision hobbing is ensured.

The invention provides a method for optimizing the movement speed fluctuation of an electronic gear box for gear hobbing, which comprises the following steps of:

(1) constructing an equation f (x) of the hob tooth profile under a hob coordinate system;

(2) constructing a cutting track of the hob under a workpiece coordinate system in the machining process; the method comprises the following specific steps:

any cutter tooth is selected to be defined as a reference cutter tooth, the tooth profile curve of the reference cutter tooth is dispersed into equidistant tooth profile points, and a space matrix H of the tooth profile points under a hob coordinate system is constructed_h；H_hThe first, second and third rows of the tooth profile point are respectively x, y and z axis coordinates of the tooth profile point under a hob coordinate system, and the fourth row is an additional unit row vector;

based on the positional relationship of the reference cutter tooth and other cutter teeth, using H_hConstructing a space matrix H of tooth profiles of other cutter teeth under a hob coordinate system_hp；

Will space matrix H_hpConverting the space matrix into a workpiece coordinate system to obtain a space matrix H of the tooth profile of any cutter tooth in the workpiece coordinate system_g；

H at successive time instants_gForming a cutting track in the hob processing process;

(3) determining instantaneous cutting planes of the hob and the workpiece in a workpiece coordinate system and calculating to obtain the change of instantaneous cutting force along with time and the speed fluctuation of the electronic gearbox in the machining process; the method comprises the following specific steps:

at each time, based on the space matrix H_gThe non-collinear tooth profile points form a plane J (x, y, z); constructing an equation K (x, y, z) of the workpiece outline under a workpiece coordinate system; calculating the intersection area of J (x, y, z) and K (x, y, z); calculating the instantaneous cutting area by using the calculus; obtaining instantaneous cutting force based on the instantaneous cutting area, thereby simulating the change of the instantaneous cutting force along with time and the speed fluctuation of the electronic gear box;

(4) optimizing parameters, wherein the method specifically comprises the following steps:

and (4) adjusting the machining parameters, and re-executing the steps (1) to (3) until the machining parameters meeting the requirement of the speed fluctuation of the electronic gearbox, namely the optimized machining parameters, are obtained.

Further, the equation of the constructed hob tooth profile under the hob coordinate system is as follows:

in the formula:

x represents an x-axis value of a point on the hob tooth profile on a hob coordinate system, f (x) represents a y-axis value corresponding to the point, and s represents the hob tooth thickness;

g (x) and g (-x) represent positive and negative tooth equations of the x-axis, respectively;

d₁is the reference circle diameter of the hob, h_aIs the top height of hob₁The radius of a transition circle of the hob tooth top, alpha is the angle of the point on the profile rotating around the x axis of the hob coordinate system, h_fThe tooth root of the hob is high.

Further, the spatial matrix

Wherein s represents the hob tooth thickness, k_sFor a set tooth pitch, n_sThe number of tooth profile points;

the space matrix H_hp＝M_pH_h，

M_pIs a transformation matrix;

α_pthe relative rotation angle of any cutter tooth and the reference cutter tooth along the ox axis under the hob coordinate system;

up is the relative distance between any cutter tooth and the reference cutter tooth along the oy axis under the hob coordinate system(ii) a k is the number of the hob chip grooves; p is the number of the cutter teeth, the reference cutter tooth number is 0, and other cutter teeth are numbered as 1, 2 and … i in sequence along the cutting direction of the hob₁The cutter teeth are numbered as-1, -2 … -i in sequence deviating from the cutting direction of the hob₂；m_nThe modulus of the normal surface of the hob is;

said space H_g＝M_cH_hp；M_cIn order to convert the matrix, the first and second matrices,

A＝u_xcosβ+u_y sinαsinβ+u_z cosαsinβ，B＝u_ycosα-u_zsinα，

C＝-u_x sinβ+u_y sinαcosβ+u_zcosαcosβ；

alpha, beta and gamma are respectively the rotating angles of any cutter tooth around the ox, oy and oz axes under the hob coordinate system; u. of_x、u_y、u_zRespectively the translational displacement of any cutter tooth along the ox, oy and oz axes under the workpiece coordinate system.

Compared with the prior art, the invention has the following main advantages and beneficial effects:

the invention can solve the problems that the motion speed of the electronic gear box fluctuates greatly in the existing high-speed gear hobbing process, and accurate control, feedback and compensation are difficult to carry out. The invention predicts the instantaneous hobbing force based on the cutting area, optimizes hobbing processing parameters based on the change of the instantaneous hobbing force, and can reduce the fluctuation of the speed of the electronic gear box by the optimized parameters, so that the movement speed of the electronic gear box is more stable, thereby improving the processing efficiency.

Drawings

FIG. 1 is a schematic view of a vertical gear hobbing machine;

FIG. 2 is a reference tooth definition diagram;

FIG. 3 is a schematic view of the positional relationship of the hob and the workpiece during machining;

FIG. 4 is a hob tooth profile chart in a hob coordinate system;

FIG. 5 is a diagram of the instantaneous cutting area for the hobbing process;

FIG. 6 is a partial tooth profile development view of an embodiment;

FIG. 7 is a sectional view of a single-tooth cutting in the embodiment;

FIG. 8 is a graph showing the change of the cutting area with time in the example;

FIG. 9 is a graph showing the change of instantaneous cutting force with time in the example;

FIG. 10 is a graph showing the variation of the movement speed of the main shaft of the hob in the electronic gear box in the embodiment;

fig. 11 is a graph of the instant cutting force as a function of time after optimization in the example.

FIG. 12 is a graph of the change of the movement speed of the main shaft of the hob of the electronic gearbox after optimization in the embodiment;

in the figure, 1-workpiece, 2-hob, 3-hob main shaft, 4-tool rest rotary table, 5-chip groove, 6-hobbing force, 7-workbench and 8-axial feed ram.

Detailed Description

In order that those skilled in the art will better understand the present invention, the following detailed description of the technical solution of the present invention will be clearly and completely described, and it is obvious that the following description is only a detailed description, which does not limit the scope of the present invention.

The meanings of the character parameters referred to herein are shown in Table 1.

TABLE 1 meanings of character parameters

(symbol)	Name (R)	(symbol)	Name (R)
				m_n	Modulus of normal surface of hob	α	O_hx_hy_hz_hAngle of rotation about ox axis
k	Number of chip pocket of hob	β	O_hx_hy_hz_hAngle of rotation about oy axis
				h_a	Tooth top height of hob	γ	O_gx_gy_gz_gAngle of rotation about oz axis
h_f	Root height of hob	u_x	O_gx_gy_gz_gDisplacement of lower horizontal movement along ox axis
				r₁	Tooth top transition circle radius of hob	u_y	O_gx_gy_gz_gDisplacement of translation along the oy axis
α₁	Pressure angle of hob	u_z	O_gx_gy_gz_gDisplacement of translation along the oz axis
				d₁	Diameter of reference circle of hob	k_n	Total number of cutters for cutting out one tooth profile by generating method
s	Thickness of hob teeth	m	Total number of microelements of cutting area along xq direction
				δ	Hob lead angle	K₁	Coefficient of cutting force
n_CB	Rotating speed of hob shaft	p	Numbering of cutter teeth
				N	Number of hob heads	α(t)	O_hx_hy_hz_hLower hob turning angle during machining
L	Hob length	Q(x,y,z)	Instantaneous cutting plane of hob and workpiece
				Z₁	Number of teeth of workpiece	f	Radial feed rate
h	Width of work	O_hx_hy_hz_h	Hob coordinate system
				d₂	Diameter of reference circle of workpiece	O_gx_gy_gz_g	Coordinate system of workpiece

Fig. 1 is a schematic structural view of a vertical gear hobbing machine for gear hobbing, in which a workpiece 1 to be machined is mounted on a table 7, a hob 2 mounted on a hob spindle 3 performs gear hobbing on the workpiece 1, the hob spindle 3 is connected with a tool rest turntable 4, and the tool rest turntable 4 is mounted on an axial feed ram 8; the hob 2 is provided with chip flutes 5, and the hob 2 generates a hobbing force 6 in the cutting process in the gear hobbing process.

Before describing the embodiments, definitions of concepts of terms involved are provided.

Referring to fig. 2, a schematic diagram of a reference tooth definition is shown. Any one cutter tooth of the selected hob is defined as a reference cutter tooth, the name of the cutter tooth is No. 0, and the cutter teeth are numbered as 1, 2 and … i in sequence along the cutting direction of the hob₁The cutter teeth are numbered as-1, -2 … -i in sequence deviating from the cutting direction of the hob₂。

See fig. 3, which shows a schematic diagram of the positional relationship between the hob and the workpiece during machining, and provides a definition of the hob coordinate system and the workpiece coordinate system based on the positional relationship between the hob and the workpiece. With reference to the axis of symmetry of the cutter teeth and to the hobThe intersection point of the central axes is the origin O_hWith the cutting direction of the hob as x_hThe positive direction of the axis refers to the direction of the symmetrical axis of the cutter teeth pointing to the workpiece as y_hEstablishing a right-handed Cartesian coordinate system O in the positive direction of the axis_hx_hy_hz_hI.e. the hob coordinate system, which can also be seen in fig. 2. Using the center of a circle of the bottom surface of the workpiece as the origin O_gThe direction of the axis of rotation of the workpiece from the bottom surface of the workpiece to the upper end surface of the workpiece is z_gPositive axial direction, origin O_gThe direction away from the hob is y_gEstablishing a right-handed Cartesian coordinate system O in the positive direction of the axis_gx_gy_gz_gI.e. the object coordinate system.

The following describes in detail the specific derivation and implementation of the present invention.

Firstly, establishing the tooth form of the hob on a hob coordinate system O_hx_hy_hz_hThe following functional expression, as follows:

the profile of the hob tooth profile in the hob coordinate system is shown in FIG. 4, g (x) denotes x_hTooth equation of axial positive, x_hNegative axial tooth form and positive tooth form with respect to y_hAxisymmetric, g (-x), so that the functional expression f (x) for the complete tooth profile of the hob is:

in equation (2), f (x) represents the y-axis value of the point on the hob coordinate system on the hob profile, and x is the x-axis value of the point on the profile on the hob coordinate system.

Secondly, calculating the tooth form of the hob cutter in a workpiece coordinate system O_gx_gy_gz_gAnd (4) a lower motion track.

Setting the step pitch of the tooth profile to k_sDispersing the profile curve of the reference cutter tooth into n_sEquidistant tooth profile points, teethSpace matrix H of contour points under hob coordinate system_hComprises the following steps:

in the formula (3), the reaction mixture is,

spatial matrix H_hIs along the hob coordinate system x_hAxial coordinate, second behavior profile point along hob coordinate system y_hAxial coordinate, third row being tooth profile point along hob coordinate system z_hThe coordinates in the axial direction, and the fourth row is an additional unit row vector.

Space matrix H of tooth profiles of other arbitrary cutter teeth under hob coordinate system_hpExpressed as:

H_hp＝M_pH_h (4)

in formula (4):

M_pthe method is a conversion matrix for converting a hob coordinate system into any hob tooth profile coordinate system, wherein the definition of the any hob tooth profile coordinate system is as follows: taking the intersection point of the symmetric axis of any cutter tooth and the central axis of the hob as an origin O_pWith the cutting direction of the hob as x_pThe positive direction of the axis refers to the direction of the symmetrical axis of the cutter teeth pointing to the workpiece as y_pEstablishing a right-handed Cartesian coordinate system O in the positive direction of the axis_px_py_pz_pI.e. any tooth form coordinate system, see in particular fig. 3.

α_pThe relative rotation angle of any cutter tooth and the reference cutter tooth along the axis ox of the hob under the hob coordinate system, and up is the relative distance between any cutter tooth and the reference cutter tooth along the axis oy of the hob under the hob coordinate system.

Tooth of any cutter tooth under hob coordinate systemThe shape coordinate may be represented as H in the object coordinate system_g：

H_g＝M_cH_hp (5)

In formula (5):

M_cis a transformation matrix;

A＝u_xcosβ+u_y sinαsinβ+u_z cosαsinβ；

B＝u_ycosα-u_zsinα；

C＝-u_xsinβ+u_y sinαcosβ+u_zcosαcosβ。

mixing O with_hx_hy_hz_hThe rotating angle of the lower hob along with the time t is recorded as alpha (t), when the machining time is t, the tooth profile of any cutter tooth is represented as H under a workpiece coordinate system_g(t)：

In the formula (6), each column represents a cutter tooth

The coordinates of a tooth profile point on the tooth profile are in a workpiece coordinate system.

Let the step pitch of the motion track be k_tAt t₀To t₁The rotational angle of the hob is defined by alpha (t)₀) Becomes alpha (t)₁) Motion track matrix of hobbing cutter tooth profile under workpiece coordinate system in time interval

Expressed as:

in the formula (7), the reaction mixture is,

are each t₀、t₀+k_t、…t₀+n_tk_tThe coordinates of the tooth profile point on the tooth profile of the hob at the moment are determined in a workpiece coordinate system;

and thirdly, determining an instantaneous cutting plane under the workpiece coordinate system, and calculating an instantaneous cutting area.

The plane of any tooth profile of the cutter tooth can be taken as H_g(t)Three different column vectors are determined, due to H_g(t)One column vector represents the coordinates of one tooth profile point in the workpiece coordinate system, and three non-collinear tooth profile points form a plane. In the gear hobbing process, the plane where any cutter tooth is located is represented as:

J(x,y,z)＝0 (8)

the equation K (x, y, z) for the workpiece in the workpiece coordinate system can be expressed as:

wherein r is the reference circle radius of the workpiece, and r is d ₂2; h is the workpiece width.

By combining equations (8) and (9), the instantaneous cutting plane of the workpiece and the cutter tooth can be obtained and is denoted as Q (x, y, z).

Boolean intersection operation is carried out on any cutter tooth and the workpiece on the plane Q (x, y, z) to obtain a common intersection region of any cutter tooth and the workpiece, the area of the intersection region is the cutting area, and the instantaneous cutting area is shown in figure 5. In FIG. 5, o_qx_qy_qThe plane rectangular coordinate system is defined as follows: by any intersection point o of the reference cutter tooth and the addendum circle of the workpiece_qAs an origin, and x is the direction of the origin pointing to the center of the workpiece_qIn the positive axial direction, the reference cutter tooth is directed from the origin to the intersection of the addendum circle of the workpieceOne intersection point is y_qIn the positive direction. The method for calculating the cutting area is as follows:

h is to be_g(t)N in (1)_sSubstituting the tooth profile coordinates of each hob into a plane equation Q (x, y, z), and solving to obtain a coordinate point matrix H_g1(t)The closed area formed, i.e., the intersection of any tooth with the workpiece, is the cutting area.

Differentiating the cutting region, referring to fig. 5, knowing that the four vertexes of the differential region are L (i, j), L (i, j +1), L (i +1, j +1), each infinitesimal area ds_(i,j)Comprises the following steps:

ds_(i,j)＝(y_L(i+1,j)-y_L(i,j)+y_L(i+1,j+1)-y_L(i,j+1))(x_L(i,j+1)-x_L(i,j))/2 (10)

at time t, the instantaneous cutting area of the jth insert is represented by S (t):

the total area of a tooth profile cut by the generating method is represented by S:

and fourthly, solving the instantaneous hobbing force and optimizing the speed fluctuation of the electronic gear box.

According to the area of each cutter tooth cutting workpiece, the instantaneous hobbing force F is solved_n(t)：

F_n(t)＝K₁S(t) (13)

K₁The coefficient of cutting force was determined by table look-up from the workpiece material, and table 2 is the coefficient of cutting force for the commonly used material.

TABLE 2 coefficient of cutting force of conventional materials

Let P be the output power of the hob main shaft, the instantaneous movement speed V (t) and the instantaneous hobbing force F of the hob main shaft of the electronic gear box_n(t) is as follows:

let us assume at t₁Time of day, j₁The cutting area of the knife is S (t)₁)，t₂Time of day, j₂The cutting area of the knife is S (t)₂) Electronic gearbox speed fluctuations can be expressed as Δ V:

it can be seen that the instantaneous hobbing force F_n(t) is inversely proportional to the movement speed V (t) of the main shaft, and the larger the fluctuation of the hobbing force is, the larger the fluctuation of the speed of each shaft of the electronic gear box is; speed fluctuation of each shaft of electronic gear box and instantaneous cutting area difference S (t)₂)-S(t₁) Is in direct proportion.

Setting a tooth profile generating workpiece rotating angle as omega, a hob rotating angle as tau, wherein omega and tau satisfy the relation:

τm_n＝ωd₂ (16)

the total number of the cutters for cutting a tooth profile by the generating method is k_n，k_nCalculated from equation (16):

from the expressions (11), (12) and (17), it can be seen that, when the total area S of a tooth profile cut by the generating method is constant, the number k of flutes of the flute is larger, the total number k of cutters of the tooth profile cut by the generating method is larger_nThe larger the instantaneous cutting area difference, the smaller the electronic gear box speed fluctuation. The feed times are increased, the radial feed amount is reduced, one tooth profile can be fed and cut for multiple times, the instantaneous cutting area difference of single feed is reduced, and the movement speed fluctuation of the electronic gear box is reduced.

A specific example will be provided below. The main parameter values of this example are shown in table 3.

TABLE 3 processing essential parameters table

Parameter(s)	Parameter value
		Modulus m of normal surface of hob_n	6mm
Hob pressure angle alpha 1	20°
		Number of teeth Z of workpiece ₁	50
Width h of work	60mm
		Number k of chip grooves of hob	14
Number of hob heads N	1
		Hob lead angle delta	2°59′27″
Diameter d of reference circle of hob₁	115mm
		Hob length L	160
Speed n of the hob shaft_CB	500rpm
		Radial feed amount f	13.5mm
Workpiece material
		45 steel

In this embodiment, the function expression of the hob tooth profile in the hob coordinate system is:

for axial machining of spur gears, the rotational speed of the workpiece shaft

In this example, the partial tooth profile was developed as shown in FIG. 6, the sectional shape of the single-tooth cutting was shown in FIG. 7, and the change of the cutting area with time was shown in FIG. 8, with a minimum value of 0 and a maximum value of 9.518mm²。

In this embodiment, when the number of the chip grooves of the hob is 14 and the number of the primary cutting passes is the full depth of tooth, the instantaneous cutting force changes as shown in fig. 9, and the movement speed of the hob main shaft of the electronic gear box changes as shown in fig. 10. And repeatedly adjusting the processing parameters such as the hob feeding times, the cutting depth, the hob chip groove number and the like, and simulating the change of the instantaneous cutting force and the movement speed of the hob spindle under each set of processing parameters until the processing parameters reducing the fluctuation of the instantaneous cutting force are obtained, wherein the current processing parameters are optimized processing parameters. The optimized processing parameters obtained in this embodiment are: the number of the chip grooves of the hob is 20, the feeding times are two, the first feeding amount is 9.6mm, and the second feeding is carried out until the depth of the full tooth is reached. The change of the optimized instantaneous cutting force is shown in fig. 11, the change of the movement speed of the hob main shaft of the electronic gear box is shown in fig. 12, the movement speed ratio of the hob main shaft of the electronic gear box before and after optimization is shown in table 4, and the fluctuation difference of the movement speed after optimization is reduced by 0.11 m/s.

TABLE 4 comparison of the movement speeds of the hob spindles of an electronic gearbox

	Minimum value	Maximum value	Mean value of	Difference of fluctuation
					Before optimization	1.69m/s	2.11m/s	1.88m/s	0.42m/s
After optimization	2.31m/s	2.62m/s	2.47m/s	0.31m/s

The above description is only for the purpose of illustrating the preferred embodiments of the present invention and is not to be construed as limiting the invention, but rather as the subject matter of the invention is to be construed in all aspects and as broadly as possible, and all changes, equivalents and modifications that fall within the true spirit and scope of the invention are therefore intended to be embraced therein.

Claims

1. A method for optimizing the movement speed fluctuation of an electronic gear box for gear hobbing is characterized by comprising the following steps:

at each time, based on the space matrix H_gThe non-collinear tooth profile points form a plane J (x, y, z); constructing equations of workpiece contours in a workpiece coordinate systemK (x, y, z); calculating the intersection area of J (x, y, z) and K (x, y, z); calculating the instantaneous cutting area by using the calculus; obtaining instantaneous cutting force based on the instantaneous cutting area, thereby simulating the change of the instantaneous cutting force along with time and the speed fluctuation of the electronic gear box;

2. The method for optimizing the movement speed fluctuation of the gear hobbing electronic gearbox according to claim 1, wherein:

the equation of the constructed hob tooth profile under the hob coordinate system is as follows:

in the formula:

，

3. The method for optimizing the movement speed fluctuation of the gear hobbing electronic gearbox according to claim 1, wherein:

the space matrix

the space matrix H_hp＝M_pH_h，

M_pIs a transformation matrix;

up is the relative distance between any cutter tooth and the reference cutter tooth along the oy axis under the hob coordinate system; k is the number of the hob chip grooves; p is the number of the cutter teeth, the reference cutter tooth number is 0, and other cutter teeth are numbered as 1, 2 and … i in sequence along the cutting direction of the hob₁The cutter teeth are numbered as-1, -2 … -i in sequence deviating from the cutting direction of the hob₂；m_nThe modulus of the normal surface of the hob is;

，

A＝u_xcosβ+u_ysinαsinβ+u_zcosαsinβ，B＝u_ycosα-u_zsinα，C＝-u_xsinβ+u_ysinαcosβ+u_zcosαcosβ；