CN111005865B - Method for accurately measuring trapped oil area of external-meshing straight gear pump - Google Patents

Abstract

The invention provides a method for accurately measuring the trapped oil area of an external gear pump. The method solves a tooth profile equation and a meshing equation of the end face of the straight gear by using a coordinate transformation principle, realizes parametric modeling of a gear pair by applying an ANSYS software programming language, and derives the oil trapping area in a meshing period by means of an ASUM command.

Description

Method for accurately measuring trapped oil area of external-meshing straight gear pump

Technical Field

The invention belongs to the field of measurement of oil trapping area of a gear pump, and particularly relates to an accurate measurement method of oil trapping area of an external meshing straight gear pump.

Background

The external gear pump has the advantages of simple structure, easy manufacture, low price and the like, and is widely applied in the mechanical field. During operation of the gear pump, vibration and noise of the pump are further increased by the presence of trapped oil excitation. The accurate acquisition of the trapped oil area of the gear pump is a precondition for excitation analysis of trapped oil of the gear pump, and has important significance for optimizing the dynamic performance of the gear pump. At present, the method for solving the oil trapping area of the gear pump mainly comprises programming calculation or virtual measurement by utilizing three-dimensional software. The first method has higher requirement on programming capability, simplifies the calculation process greatly and has low solving precision; the second method cannot realize parameterization and has low measurement efficiency.

Therefore, it is necessary to develop a method for accurately measuring the oil trapping area of an external meshing spur gear pump.

Disclosure of Invention

The invention aims to provide a method for accurately measuring the trapped oil area of an external gear pump, which aims to solve the problems in the prior art.

The technical scheme adopted for achieving the aim of the invention is that the method for accurately measuring the trapped oil area of the external meshing straight gear pump comprises the following steps:

1) obtaining basic parameters of an internal gear pair of the gear pump, and determining the structure of the rack-type cutter, wherein the basic parameters of the gear pair comprise the number of teeth z, the modulus m, the pressure angle α, the tooth width B and the tooth crest height coefficient ha^*Coefficient of head clearance c^*And a shift coefficient x.

2) And deducing to obtain a meshing equation and an end face tooth profile equation through coordinate transformation.

3) And establishing a gear pair solid model.

4) And establishing a gear pair grid model.

5) And measuring the oil trapping area in different meshing states to obtain the oil trapping area in one meshing period.

Further, the rack tool profile of the rack-type tool includes a top edge circular arc section and a top edge straight section. The top edge arc section is used for machining and cutting a tooth root transition curve F of the machined gear. And enveloping the straight line segment of the top blade to obtain an involute tooth profile G of the tooth surface of the gear to be processed.

Further, the step 2) specifically comprises the following steps:

1.1) establishing a straight gear machining coordinate system. The processing coordinate system comprises a moving coordinate system S connected with the end face of the shaping rack₁And a moving coordinate system S connected with the end face of the gear to be processed₂And a fixed coordinate system S connected with the end face of the gear to be processed_f。

1.2) deriving a meshing equation and an end face tooth profile equation in a coordinate system S₂And (4) a middle expression. Wherein the tooth root transition arc part of the meshing equation is in a coordinate system S₂The middle expression is shown as formula (1)

Tooth surface involute profile part of meshing equation in coordinate system S₂The expression is shown as formula (2).

Root transition arc part of end face tooth profile equation in coordinate system S₂The expression is shown as formula (3).

End face tooth profile equation tooth surface involute tooth profilePartially in a coordinate system S₂The expression is shown as formula (4).

In the formula, r is the radius of a pitch circle of the gear, and is mm; phi is a coordinate system S₂Angle of rotation, °; a is pi m/2; rho is the radius of the arc part of the cutter, and is mm; theta is an angle change parameter, °; l is the length variation parameter, mm.

Further, the step 5) specifically comprises the following steps:

and 5.1) selecting an oil trapping area consisting of the teeth of the driving wheel and the corresponding teeth of the two driven wheels as a research object.

5.2) creating oil trapping areas.

5.3) calculating the area of the oil trapping area.

And 5.4) rotating the gear pair to obtain different meshing states and derive the trapped oil area in one meshing period.

The technical effects of the invention are undoubted:

A. the straight gear end face tooth profile equation deduced according to the coordinate transformation principle is used for establishing a gear pair solid model, so that the accuracy of gear tooth modeling is improved, and the accuracy of oil trapping area measurement is further improved;

B. for gear pumps of different models, corresponding gear models can be generated only by modifying corresponding gear parameters, and then corresponding oil trapping areas are obtained;

C. the created model can also be used for the development of subsequent work such as the mechanical property analysis of the gear pump and the like, so that the workload of designers is reduced to a certain extent, and the working efficiency is improved;

D. the gear pump oil trapping excitation analysis device has the advantages of being high in precision, high in efficiency and the like, and is favorable for improving the gear pump oil trapping excitation analysis precision, and further improving the gear pump dynamic performance optimization effect.

Drawings

FIG. 1 is a flow chart of the technical solution;

FIG. 2 is a schematic view of a rack-type cutter construction;

FIG. 3 is a spur gear machining coordinate system;

FIG. 4 is a schematic representation of the resulting root transition arc key points;

FIG. 5 is a schematic diagram of key points of a generated tooth surface involute curve;

FIG. 6 is a schematic representation of key points of the generated single tooth profile curve;

FIG. 7 is a schematic illustration of a generated single gear solid model;

FIG. 8 is a schematic illustration of a generated gear pair solid model of a gear pump;

FIG. 9 is a schematic diagram of a generated gear pair mesh model of a gear pump;

FIG. 10 is a schematic diagram illustrating oil trapping of a gear pump;

FIG. 11 is a schematic illustration of the oil trapping region of the gear pump produced;

FIG. 12 is a flowchart of the oil trapping area measurement.

In the figure: a top blade arc segment 1 and a top blade straight segment 2.

Detailed Description

The present invention is further illustrated by the following examples, but it should not be construed that the scope of the above-described subject matter is limited to the following examples. Various substitutions and alterations can be made without departing from the technical idea of the invention and the scope of the invention is covered by the present invention according to the common technical knowledge and the conventional means in the field.

Example 1:

the embodiment discloses an accurate measurement method for the trapped oil area of an external meshing straight gear pump, which comprises the following steps:

1) determining basic parameters of gear pairs inside the gear pump and determining the structure of the rack-type cutter. The basic parameters comprise tooth number, modulus, pressure angle, tooth width, tooth crest height coefficient, tip clearance coefficient and deflection coefficient. The basic parameters of the gear pair of the gear pump in the embodiment are shown in table 1.

TABLE 1

Basic parameters	Symbol	Driving wheel	Driven wheel
				Number of teeth	z		18	12
Modulus of elasticity	m	4	4
				Angle of pressure	α		20	20
Width of tooth	B	30	30
				Coefficient of tooth crest height	ha	*	1	1
Coefficient of head space	c*	0.25	0.25
				Coefficient of variation	x	-0.0528	0.2981

The rack profile is used to cut tooth shapes in the operating state. Referring to fig. 2, the rack profile of the rack-type tool includes a circular arc portion 1 for cutting a tooth root transition curve F of a gear to be machined, and a straight line portion 2 enveloping an involute tooth profile G of a tooth surface of the gear to be machined.

2) And establishing a straight gear machining coordinate system. Referring to fig. 3, the straight gear processing coordinate system comprises a moving coordinate system S connected with the end face of the shaping rack₁And a moving coordinate system S connected with the end face of the gear to be processed₂Fixed coordinate system S connected with end face of gear to be machined_f。

S₁The origin of coordinates is located on the machine tool pitch line and tangent to the gear pitch circle, X₁Along the machine pitch line, Y₁Then perpendicular to the machine tool pitch line, the moving coordinate system S₁Satisfies that s is r phi. S₂And S_fAll the origin of coordinates of (A) are located at the center of a pitch circle of the gear, X_f、Y_fAre each independently of X₁、X₂Parallel when S₂When the rotation angle phi is equal to 0, S₂And S_fAnd (4) overlapping.

3) The meshing equation and the face tooth profile equation are expressed in a coordinate system S2. Wherein the meshing equation is expressed in a coordinate system S2:

(a) root transition arc portion:

(b) tooth surface involute tooth profile part:

the face tooth profile equation is expressed in the coordinate system S2:

(a) root transition arc portion:

(b) tooth surface involute tooth profile part:

in the formula, r is the gear pitch circle radius, mm. Phi is a coordinate system S₂Angle of rotation, degree. a is pi m/2. Rho is the radius of the arc part of the cutter, and is mm. Theta is an angle variation parameter, °. l is the length variation parameter, mm.

4) And writing a modeling program by using ANSYS software, and establishing a gear pair entity model.

4.1) writing a parameterized modeling program by using an APDL programming language of ANSYS software, and establishing a plurality of key points of tooth root transition arcs and tooth surface involute tooth profiles by adopting a bottom-up modeling mode, wherein the key points are respectively shown in fig. 4 and fig. 5.

4.2) connecting the key points in sequence and creating an addendum circle by adopting a LINE command, and trimming redundant curves to obtain a single-tooth profile curve, wherein the key points of the end face tooth profile are as shown in FIG. 6.

4.3) copying a curve of the tooth profile of the single tooth, and obtaining a solid model of the single gear by sequentially adopting AREA and VOFFST commands, as shown in figure 7.

4.4) moving the modeling coordinate system in ANSYS by a distance of a center distance along the end face of the generated gear, and then establishing another gear model under the current coordinate system to generate a gear pair solid model, as shown in FIG. 8.

5) Defining material properties and grid types, and establishing a gear pair grid model. Referring to table 2, gear pair material properties, gear pairs are divided by SOLID185 units to build hexahedral mesh models, as shown in fig. 9.

TABLE 2

Elastic modulus/(N/m ^2)	Poisson ratio	Density/(kg/m ^3)
			2.12E+11	0.289	7.86E+03

6) And measuring the oil trapping area of the gear pump.

6.1) based on the principle of gear pump oil trapping, as shown in FIG. 10, the oil trapping region composed of the gear teeth a, 2, b is selected as the object of study, the numbers of the nodes of the profile of the end face teeth of the driving wheel and the driven wheel are extracted, the threshold value of the meshing point is set, and the node numbers of the driving point and the meshed point are found and defined as N1, Na, N2, Nb (one driving wheel gear tooth and one driven wheel generate two meshing positions).

6.2) connecting nodes N1, Na, N2, Nb generation lines L1a, L2b, respectively, create an oil trapping region, as shown in FIG. 11.

6.3) the area of the oil trapping region is derived using ANSYS software ASUM commands.

6.4) rotating the gear pair to obtain different meshing states and lead out the trapped oil area in a meshing period.

It is worth mentioning that the trapped oil volume gradually decreases to a minimum and then gradually increases during the process of the spur gear from engagement to engagement. When the size of the oil sealing volume changes, hydraulic oil sealed in the volume is squeezed or expanded, and local high pressure or air pocket is generated in the oil sealing volume. The solution used in the embodiment is that the end covers at the two sides of the gear are provided with unloading grooves, so that when the enclosed volume is reduced, the oil chamber is communicated with the unloading groove at one side, and when the enclosed volume is increased, the oil chamber is communicated with the unloading groove at the other side, so that the pressure balance is realized.

Claims (3)

1. The method for accurately measuring the trapped oil area of the external meshing straight gear pump is characterized by comprising the following steps of:

1) obtaining basic parameters of a gear pair in the gear pump and determining the structure of the rack-type cutter, wherein the basic parameters of the gear pair comprise the number of teeth z, the modulus m, the pressure angle α, the tooth width B and the tooth crest height coefficient ha^*Coefficient of head clearance c^*And a shift coefficient x;

2) deriving a meshing equation and an end face tooth profile equation through coordinate transformation;

2.1) establishing a straight gear processing coordinate system; the processing coordinate system comprises a moving coordinate system S connected with the end face of the shaping rack₁And a moving coordinate system S connected with the end face of the gear to be processed₂And a fixed coordinate system S connected with the end face of the gear to be processed_f；

2.2) deriving the equation of engagement and the equation of tooth profile of the end face in a coordinate system S₂A middle expression; wherein the tooth root transition arc part of the meshing equation is S in the coordinate system₂The expression is shown as formula (1);

the involute tooth profile part of the tooth surface of the meshing equation is S in the coordinate system₂The expression is shown as formula (2);

the arc part of the root transition of the end face tooth profile equation is S in the coordinate system₂The expression is shown as formula (3);

the involute tooth profile part of the tooth surface of the end face tooth profile equation is S in the coordinate system₂The expression is shown as formula (4);

in the formula, r is the radius of a pitch circle of the gear, and is mm; phi is a coordinate system S₂Angle of rotation, °; a is pi m/2; rho is the radius of the arc part of the cutter, and is mm; theta is an angle change parameter, °; l is a length variation parameter, mm;

3) establishing a gear pair solid model;

4) establishing a gear pair grid model;

5) and measuring the oil trapping area in different meshing states to obtain the oil trapping area in one meshing period.

2. The method for accurately measuring the oil trapping area of the external meshing spur gear pump as claimed in claim 1, wherein: the rack tool profile of the rack-type tool comprises a top blade arc section (1) and a top blade straight section (2); the top edge arc section (1) is used for machining and cutting a tooth root transition curve F of the machined gear; and the involute tooth profile G of the tooth surface of the gear to be processed is enveloped by the straight line segment (2) of the top blade.

3. The method for accurately measuring the oil trapping area of the external meshing straight gear pump as claimed in claim 1, wherein the step 5) specifically comprises the following steps:

5.1) selecting an oil trapping area formed by the teeth of the driving wheel and the corresponding teeth of the two driven wheels as a research object;

5.2) creating an oil trapping area;

5.3) calculating the area of the oil trapping area;

and 5.4) rotating the gear pair to obtain different meshing states and derive the trapped oil area in one meshing period.

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