A hydraulic gear pump

Abstract

The present invention discloses a hydraulic gear pump, comprising a driving gear shaft, a lip seal, a front end cover, a front "8" type sleeve, a pump body, a rear "8" type sleeve, a rear end cover, a driven gear shaft, a positioning pin hole, a pump outlet, and a fixing bolt hole. Compared with the prior art, its beneficial effects are as follows: dynamic compensation of the radial force of the bearing is performed, an oil film is formed between the rotating shafts, wear between the bearing and the shaft during rotation is resolved, and a dynamic pressure floating state of the rotating shaft is achieved; the axial force generated when the helical gears rotate and engage to convey the medium is compensated, and the axial movement of the gears due to the axial force is resolved; the tilting caused by the high and low pressure difference of the contact end faces of the gears is effectively alleviated; an open loop is formed from high pressure to medium pressure to low pressure, dynamic high-pressure oil is introduced, constant dynamic pressure is maintained, and high-temperature oil is taken away to reduce the internal temperature of the hydraulic gear pump, thereby playing a role in lubrication and cooling.

Description

Technical Field

[0001] The present invention relates to the technical field of hydraulic gear pumps, in particular to a hydraulic gear pump. Background Art

[0002] Hydraulic gear pumps are widely used in high-end engineering fields such as defense and military industry, ship propulsion, aerospace, mobile machinery, medical equipment, and heavy equipment. As one of the core components providing power to hydraulic systems, their performance directly determines the quality of the hydraulic system and impacts the performance of high-end engineering equipment. Gear pump leakage can affect the pump's volumetric efficiency, while gear pump wear can directly or indirectly reduce the pump's volumetric efficiency and operating life, and generate noise. This noise not only affects the overall system's performance but also has certain adverse effects on people's physical and mental health. Therefore, low leakage, low noise, and low wear during the operation of hydraulic gear pumps are crucial to the safety and stability of the entire hydraulic system. Therefore, during the hydraulic gear pump design phase, it is important to understand the mechanisms that cause leakage, noise, and wear, prevent them, and ultimately improve the performance of the hydraulic gear pump. The radial force, axial force, and high and low pressure zones that occur in hydraulic gear pumps during operation are all causes of wear and noise in the pump. The shaft and bearing sleeves wear severely after long periods of operation, and the rotation generates heat and noise, making it impossible to achieve high-speed operation. The heat generated inside the pump cannot be eliminated in time, which changes the viscosity of the medium, reduces the pump's performance and increases leakage. If the above problems can be solved together, the problems of leakage, wear, and noise can be effectively solved at the same time. At present, both domestic and foreign research focuses on one point to improve the performance of hydraulic gear pumps, but the improvement effect is low, and the performance improvement of other problems is not obvious. It is impossible to effectively reduce the leakage, wear, noise, and life of the gear pump at the same time. Summary of the Invention

[0003] The object of the present invention is to provide a hydraulic gear pump to solve the problems raised in the above background technology.

[0004] To achieve the above-mentioned purpose, the present invention provides the following technical solutions: comprising a driving gear shaft, a lip seal ring, a front end cover, a front "8"-shaped sleeve, a pump body, a rear "8"-shaped sleeve, a rear end cover, a driven gear shaft, a positioning pin hole, a pump outlet, and a fixing bolt hole; the front end cover and the rear end cover are provided with a through "8"-shaped through groove on the side in contact with the pump body, and a sealing O-ring is installed in the through groove; the front end cover is installed on the left side of the pump body; the front "8"-shaped sleeve is installed on the left side inside the pump body; the driving gear shaft passes through the front end cover and the front "8"-shaped sleeve and is installed inside the pump body, and the left side of its gear segment is aligned with the front "8"-shaped sleeve The right side is in contact; the rear "8"-shaped sleeve is in contact with the right side of the gear segment of the driving gear shaft and is located on the right side inside the pump body; the driven gear shaft passes through the front "8"-shaped sleeve and the rear "8"-shaped sleeve and is installed inside the pump body, and its gear segment is meshed with the gear segment of the driving gear shaft; the rear end cover is installed on the right side of the pump body; the lip seal ring passes through the left shaft segment of the driving gear shaft and is installed on the left side of the front end cover; the pump outlet is installed in the center of the upper and lower sides of the pump body; the locating pin hole is located at the connection between the front end cover and the rear end cover and the pump body respectively; the fixing bolt hole passes through the front end cover, pump body and rear end cover and is fixed with a nut.

[0005] As a preferred technical solution of the present invention, the front contact surface of the front "8" type sleeve is the contact surface with the gear segment, and the rear contact surface is the contact surface with the pump body; the front "8" type sleeve is provided with a through hole and a blind hole, the through hole is provided with the driving gear shaft, and the blind hole is provided with the driven gear shaft; the rear contact surface has two positioning holes I, positioning holes II and a sealing groove; the upper arc surface of the front "8" type sleeve is provided with drainage arc grooves I and drainage arc grooves II, and a plane opening II between the arc surfaces is connected with the positioning hole II ... front "8" type sleeve is provided with a through hole A hole I is formed on the lower arc surface of the sleeve, which is connected to the through hole and the blind hole respectively; an arc groove I is formed beside the through hole on the front contact surface, and is connected to the drainage arc groove II through an internal opening; an arc groove II is formed beside the blind hole on the front contact surface, and is connected to the drainage arc groove I through an internal opening; an arc groove III is formed on the inner wall of the blind hole near the front contact surface, and is connected to the drainage arc groove II through an internal opening; an arc groove IV is formed on the inner wall of the through hole near the front contact surface, and is connected to the drainage arc groove I through an internal opening.

[0006] As a preferred technical solution of the present invention, the angle of the circular arc groove I is 40°, the angle of the circular arc groove II is 80°, and the outer diameter of the two circular arc grooves is smaller than the root circle radius of the gear segments of the driving gear shaft and the driven gear shaft; the angle of the circular arc groove III is 60°, and the angle of the circular arc groove IV is 90°.

[0007] As a preferred technical solution of the present invention, the difference between the rear "8"-shaped sleeve and the front "8"-shaped sleeve is that a sealing groove II is opened in the center of the sealing groove I on the rear contact surface. The sealing groove II is a gourd-shaped groove, and both holes are blind holes. The angle of the arc groove I is 80°, the angle of the arc groove II is 40°, the angle of the arc groove III is 90°, and the angle of the arc groove IV is 60°.

[0008] As a preferred technical solution of the present invention, the front "8"-shaped sleeve and the rear "8"-shaped sleeve are respectively installed on the left and right sides of the driving gear shaft and the driven gear shaft, and the front "8"-shaped sleeve and the rear "8"-shaped sleeve are installed symmetrically on the left and right.

[0009] Compared with the prior art, the present invention has the following beneficial effects:

[0010] 1. Perform dynamic compensation for the radial force of the bearing, form an oil film between the rotating shafts, avoid the eccentricity of the two meshing shafts, solve the wear between the bearing and the shaft during rotation, and achieve the dynamic pressure floating state of the rotating shaft;

[0011] 2. Compensate for the axial force generated when the helical gear rotates and engages with the conveying medium, and solve the problem of axial movement of the gear due to the axial force;

[0012] 3. Effectively alleviate the tilt caused by the high and low pressure difference of the gear contact end surface;

[0013] 4. This creates an open loop from high pressure to medium pressure and then to low pressure, introducing dynamic high-pressure oil to maintain constant dynamic pressure. This removes high-temperature oil, lowering the internal temperature of the hydraulic gear pump and providing lubrication and cooling. Solving the above problems can effectively reduce leakage, wear, and noise in the hydraulic gear pump, thereby improving its overall performance and extending its service life. BRIEF DESCRIPTION OF THE DRAWINGS

[0014] Figure 1 It is a three-dimensional schematic diagram of the present invention;

[0015] Figure 2 It is a cross-sectional view of the present invention;

[0016] Figure 3 This is a perspective schematic diagram of the front "8" type sleeve of the present invention I;

[0017] Figure 4 This is a perspective diagram II of the front "8" type sleeve of the present invention;

[0018] Figure 5 This is a perspective diagram III of the front "8" type sleeve of the present invention;

[0019] Figure 6 This is a three-dimensional schematic diagram of the rear "8" type sleeve of the present invention;

[0020] In the figure: driving gear shaft 1, lip seal 2, front end cover 3, front "8"-shaped sleeve 4, positioning hole I401, positioning hole II402, sealing groove I403, hole I404, hole II405, drainage arc groove I406, drainage arc groove II407, arc groove I408, arc groove II409, arc groove III410, arc groove IV411, pump body 5, rear "8"-shaped sleeve 6, sealing groove II601 and rear end cover 7, driven gear shaft 8, positioning pin hole 9, pump outlet 10, and fixing bolt hole 11. DETAILED DESCRIPTION

[0021] Example 1

[0022] like Figures 1 to 6As shown, the present invention discloses a hydraulic gear pump, comprising a driving gear shaft 1, a lip seal ring 2, a front end cover 3, a front "8"-shaped sleeve 4, a pump body 5, a rear "8"-shaped sleeve 6, a rear end cover 7, a driven gear shaft 8, a positioning pin hole 9, a pump outlet 10, and a fixing bolt hole 11; the front end cover 3 and the rear end cover 7 are provided with a through "8"-shaped through groove on the side in contact with the pump body 5, and a sealing O-ring is installed in the through groove; the front end cover 3 is installed on the left side of the pump body 5; the front "8"-shaped sleeve 4 is installed on the left side inside the pump body 5; the driving gear shaft 1 passes through the front end cover 3 and the front "8"-shaped sleeve 4 and is installed inside the pump body 1, and the left side of its gear segment is aligned with the right side of the front "8"-shaped sleeve 4 Side contact; the rear "8"-shaped sleeve 6 contacts the right side of the gear segment of the driving gear shaft 1 and is located on the right side inside the pump body 5; the driven gear shaft 8 passes through the front "8"-shaped sleeve 4 and the rear "8"-shaped sleeve 6 and is installed inside the pump body 5, and its gear segment is engaged with the gear segment of the driving gear shaft 1; the rear end cover 7 is installed on the right side of the pump body 5; the lip seal 2 passes through the left shaft segment of the driving gear shaft 1 and is installed on the left side of the front end cover 3; the pump outlet 10 is installed in the center of the upper and lower sides of the pump body 5; the locating pin hole 9 is located at the connection between the front end cover 3 and the rear end cover 7 and the pump body 5 respectively; the fixing bolt hole 11 passes through the front end cover 3, the pump body, and the rear end cover 7 and is fixed with a nut. The front contact surface of the front "8" type sleeve 4 is the contact surface with the gear segment, and the rear contact surface is the contact surface with the pump body 5; the front "8" type sleeve 4 is provided with a through hole and a blind hole, the through hole is provided with the driving gear shaft 1, and the blind hole is provided with the driven gear shaft 8; the rear contact surface has two positioning holes I401, positioning holes II402 and a sealing groove I403; the upper arc surface of the front "8" type sleeve 4 is provided with drainage arc grooves I406 and drainage arc grooves II407, and the plane opening II405 between the arc surfaces is connected with the positioning hole II402; the lower side of the front "8" type sleeve 4 is provided with a plurality of positioning holes I401, a positioning hole ... II407, and the plane opening II405 between the arc surfaces is connected with the positioning hole II402; the lower side of the front "8" type sleeve 4 is provided with a plurality of positioning holes I401, a positioning hole II402 and a sealing groove I403; the upper arc surface of the front "8" type sleeve 4 is provided with drainage arc grooves I406 and II407, and the plane opening II405 between the arc surfaces is connected with the positioning hole II402; the lower side of the front "8" type sleeve 4 is provided with a plurality of positioning holes I401, a positioning hole II402 and a sealing groove I403; the upper arc surface of Each arcuate surface has a hole I404, connected to the through hole and the blind hole, respectively. On the front contact surface, an arcuate groove I408 is provided adjacent to the through hole, and its internal opening connects to the drainage arcuate groove II407. On the front contact surface, an arcuate groove II409 is provided adjacent to the blind hole, and its internal opening connects to the drainage arcuate groove I406. On the inner wall of the blind hole, an arcuate groove III410 is provided near the front contact surface, and its internal opening connects to the drainage arcuate groove II407. On the inner wall of the through hole, an arcuate groove IV411 is provided near the front contact surface, and its internal opening connects to the drainage arcuate groove I406. The difference between the rear "8"-shaped sleeve 6 and the front "8"-shaped sleeve 4 is that a gourd-shaped sealing groove II601 is provided in the center of the sealing groove I403 on the rear contact surface. The front "8" shaped sleeve 4 and the rear "8" shaped sleeve 6 are respectively installed on the left and right sides of the driving gear shaft 1 and the driven gear shaft 8, and the front "8" shaped sleeve 4 and the rear "8" shaped sleeve 6 are installed symmetrically.Two symmetrically mounted front and rear "8"-shaped sleeves replace conventional bearings to support and secure the driving and driven gear shafts. Fluid in the high-pressure zone is channeled through side grooves and small holes into the internal arc grooves of the "8" sleeves, forming a high-pressure oil film between the gear shafts. This not only enhances lubrication, compensates for radial forces, and reduces wear on the gear shafts, but also improves lubrication. The angle of the arc groove I 408 is 40°, and the angle of the arc groove II 409 is 80°. The outer diameter of these two arc grooves is smaller than the root radius of the gear segments of the driving and driven gear shafts 1 and 8. The angle of the arc groove III 410 is 60°, and the angle of the arc groove IV 411 is 90°. This creates an open loop from high pressure to medium pressure to low pressure, introducing dynamic high-pressure oil to maintain constant dynamic pressure. This removes high-temperature oil, lowering the internal temperature of the hydraulic gear pump and providing both lubrication and cooling. This solution effectively reduces leakage, wear, and noise in the hydraulic gear pump, thereby improving its overall performance and extending its service life.

[0023] The working principle of the present invention is as follows: when installing the present invention, the gear segments of the driving gear shaft 1 and the driven gear shaft 8 are first meshed and installed in the pump body 5, and the front "8"-shaped sleeve 4 and the rear "8"-shaped sleeve 6 are installed on both sides of the gear segment and installed in the pump body 5, and then the front end cover 3 and the rear end cover 7 are installed on the left and right sides of the pump body 5 in sequence, and fixed with bolts to complete the sealing of the pump body, finally, the lip seal 2 is installed at the front end cover 3 and the outlet of the driving gear shaft 1 to complete the sealing of the driving gear shaft, and the installation of the gear pump is completed.

[0024] In the front "8"-shaped sleeve of the present invention, high-pressure oil at the rear contact end face is introduced through hole II405. The outlet high-pressure oil then enters positioning hole II402, and then reaches the rear contact surface through positioning hole II402, forming a high-pressure oil film. High-pressure oil is introduced through drainage arc groove II407, and is respectively connected to the corresponding arc groove III410 on the inner surface of the hole and the arc groove I408 on the front contact surface, providing high-pressure oil, and finally entering the oil inlet through hole I404. High-pressure oil is introduced through drainage arc groove I406, and is respectively connected to the corresponding arc groove IV411 on the inner surface of the hole and the arc groove II409 on the front contact surface, providing high-pressure oil, and finally entering the oil inlet through hole I404.

[0025] The introduction of high-pressure oil from the arc groove on the front contact surface of the "8"-type sleeve can not only offset part of the axial force but also make the gear shaft float axially to reduce wear; the introduction of high-pressure oil from the rear contact surface of the "8"-type sleeve can solve the axial force generated by different gear shafts according to the size of the high-pressure oil contact area; the outer seals of the rear contact surfaces of the front and rear "8"-type sleeves effectively isolate oils in different pressure ranges to reduce leakage; the inner sealing groove on the rear contact surface of the rear "8"-type sleeve prevents leakage of high-pressure oil while creating high-pressure oil contact surfaces of different sizes on the rear contact surfaces of the two blind holes. The rear contact surface area of ​​the driving gear shaft 1 corresponding to the rear "8"-type sleeve is larger than the rear contact surface area of ​​the driven gear shaft 8 corresponding to the rear "8"-type sleeve. In order to compensate for the axial force on the driving gear shaft 1, dynamic pressure suspension is formed through the holes and grooves on the "8"-type sleeve, which effectively solves the problem of balancing the radial and axial forces of the gear shaft, reduces wear on the "8"-type sleeve, reduces the overall noise of the hydraulic gear pump, can adapt to higher speeds, and improves the overall life of the gear pump.

[0026] The rear end face of the front "8" type sleeve 4 mainly introduces high-pressure oil to compensate for the axial force. The axial forces of the driving gear shaft 1 and the driven gear shaft 8 are just opposite. Since the driving gear shaft cooperates with the through hole of the front "8" type sleeve, if the axial force points to the front "8" type sleeve, the axial force is not easy to compensate. The present invention determines the rotation direction of the driving gear shaft 1 so that the axial force received by the driven gear shaft 8 points to the front "8" type sleeve, and the driving gear shaft 1 is received by the rear "8" type sleeve. In order to effectively compensate for the axial force, the rear end face introduces high-pressure oil through the hole II405 and the positioning hole II402, and the contact surface area after the blind hole is large. The area of ​​the rear contact surface of the through hole is larger than that of the through hole, and the high-pressure area formed can compensate for the axial force on the driven gear shaft 8; in order to avoid contact wear between the front contact surface of the front "8"-shaped sleeve and the end face of the gear shaft when compensating for the axial force, the front contact surface arc groove I408 and the arc groove II409 are connected with the side drainage arc groove I406 and the drainage arc groove II407 respectively, and the drainage arc groove I406 is connected to the high-pressure area, introducing high-pressure oil contact surface to form a high-pressure floating space; since the axial force of the driving gear shaft 1 points to the rear "8"-shaped sleeve 6, the axial force received by the driven gear shaft 8 points to the front "8"-shaped sleeve 4, and the two are connected. The contact surfaces are subjected to different forces, so the angle of the arc groove II409 on the contact surface of the driven gear shaft 8 is 80 degrees, and the angle of the arc groove I408 on the contact surface of the driving gear shaft is 40 degrees. The outer diameters of the two arc grooves are smaller than the radius of the gear tooth root circle to avoid leakage. The inner surface of the through hole connecting the front "8" type sleeve 4 and the driving gear shaft 1 is provided with an arc groove III410, which is connected to the drainage arc groove II407; the inner surface of the blind hole connected to the driven gear shaft is provided with an arc groove IV411, which is connected to the drainage arc groove I406; the high-pressure oil is introduced to form an oil film with the connected shaft segments, which not only makes the rotating shaft float, but also avoids Mechanical wear is prevented by contact. Furthermore, the static pressure created by the grooves compensates for the radial forces acting on the gear shafts. Because the driven gear shaft experiences greater radial forces than the driving gear shaft, the angle of the circular arc groove IV411 is 60°, and the angle of the circular arc groove III410 is 90°. These two circular arc grooves are located near the inner surface of the oil outlet. The oil in the shaft hole is reduced in pressure and increased in temperature through force compensation and lubrication. This oil is then introduced into the low-pressure area through hole I404, forming an open-loop oil circuit. This introduced dynamic high-pressure oil maintains constant dynamic pressure and removes high-temperature oil, lowering the internal temperature of the hydraulic gear pump. The principle of the rear "8"-shaped sleeve 6 is identical to that of the front "8"-shaped sleeve 4, so it will not be described in detail.

[0027] In the description of the present invention, it should be understood that the terms "center", "longitudinal", "lateral", "up", "down", "front", "back", "left", "right", "vertical", "horizontal", "top", "bottom", "inside", "outside" and the like indicate orientations or positional relationships based on the orientations or positional relationships shown in the accompanying drawings, and are only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore cannot be understood as limiting the present invention. In addition, the terms "first", "second", etc. are only used for descriptive purposes, and cannot be understood as indicating or implying relative importance or implicitly indicating the number of the indicated technical features. Therefore, features defined as "first", "second", etc. may explicitly or implicitly include one or more of such features. In the description of the present invention, unless otherwise specified, "multiple" means two or more.

[0028] In the description of the present invention, it should be noted that, unless otherwise expressly specified or limited, the terms "installed", "connected", and "connected" should be understood in a broad sense. For example, they can refer to fixed connections, detachable connections, or integral connections; they can refer to mechanical connections or electrical connections; they can refer to direct connections or indirect connections through an intermediate medium; and they can refer to internal connections between two components. For those skilled in the art, the specific meanings of the above terms in the present invention can be understood based on specific circumstances.

[0029] Although the specific embodiments of the present invention have been described in detail above, the present invention is not limited to the above embodiments. Within the scope of knowledge possessed by ordinary technicians in this field, various changes can be made without departing from the purpose of the present invention. Modifications or deformations that do not involve creative work are still within the scope of protection of the present invention.

Claims

1. A hydraulic gear pump, characterized in that: The invention comprises a driving gear shaft (1), a lip seal ring (2), a front end cover (3), a front "8" type sleeve (4), a pump body (5), a rear "8" type sleeve (6), a rear end cover (7), a driven gear shaft (8), a positioning pin hole (9), a pump outlet (10), and a fixing bolt hole (11); the front end cover (3) and the rear end cover (7) are provided with a through "8" type through groove on the contact side with the pump body (5), and a sealing O-ring is installed in the through groove; the front end cover (3) is installed on the left side of the pump body (5); the front "8" type sleeve (4) is installed on the left side inside the pump body (5); the driving gear shaft (1) passes through the front end cover (3) and the front "8" type sleeve (4) and is installed inside the pump body (5), and the gear section thereof is on the left side. The front "8" type sleeve (4) contacts the right side of the front "8" type sleeve (4); the rear "8" type sleeve (6) contacts the right side of the gear segment of the driving gear shaft (1) and is located on the right side of the inside of the pump body (5); the driven gear shaft (8) passes through the front "8" type sleeve (4) and the rear "8" type sleeve (6) and is installed inside the pump body (5), and its gear segment is meshed with the gear segment of the driving gear shaft (1); the front contact surface of the front "8" type sleeve (4) is the contact surface with the gear segment, and the rear contact surface is the contact surface with the pump body (5); the front "8" type sleeve (4) is provided with a through hole and a blind hole, the driving gear shaft (1) is installed in the through hole, and the driven gear shaft (8) is installed in the blind hole; the rear contact surface has two positioning holes I (401), positioning holes II ( 402) and a sealing groove I (403); the upper arc surface of the front "8" type sleeve (4) is provided with a drainage arc groove I (406) and a drainage arc groove II (407), and a plane opening II (405) is provided between the arc surfaces, which is connected to the positioning hole II (402); a hole I (404) is provided on the lower arc surface of the front "8" type sleeve (4), which is connected to the through hole and the blind hole respectively; an arc groove I (408) is provided beside the through hole on the front contact surface, and an internal opening is provided to connect with the drainage arc groove II (407); an arc groove II (409) is provided beside the blind hole on the front contact surface, and an internal opening is provided to connect with the drainage arc groove I (406); a circular arc groove is provided on the inner wall of the blind hole near the front contact surface. Arc groove III (410), and the internal opening is connected to the drainage arc groove II (407); an arc groove IV (411) is opened on the inner wall of the through hole near the front contact surface, and the internal opening is connected to the drainage arc groove I (406); the rear end cover (7) is installed on the right side of the pump body (5); the lip seal ring (2) passes through the left shaft section of the driving gear shaft (1) and is installed on the left side of the front end cover (3); the pump outlet (10) is installed in the center of the upper and lower sides of the pump body (5); the positioning pin hole (9) is located at the connection between the front end cover (3) and the rear end cover (7) and the pump body (5); the fixing bolt hole (11) passes through the front end cover (3), the pump body, and the rear end cover (7) and is fixed with a nut.

2. A hydraulic gear pump according to claim 1, characterized in that: The angle of the circular arc groove I (408) is 40°, the angle of the circular arc groove II (409) is 80°, and the outer diameters of the circular arc groove I (408) and the circular arc groove II (409) are smaller than the tooth root circle radius of the gear segments of the driving gear shaft (1) and the driven gear shaft (8); the angle of the circular arc groove III (410) is 90°, and the angle of the circular arc groove IV (411) is 60°.

3. The hydraulic gear pump according to claim 1, characterized in that: The difference between the rear "8"-shaped sleeve (6) and the front "8"-shaped sleeve (4) is that the rear "8"-shaped sleeve (6) has a sealing groove II (601) in the center of the sealing groove I (403) on the rear contact surface, and the sealing groove II (601) is a gourd-shaped groove.

4. A hydraulic gear pump according to claim 3, characterized in that: The front "8"-shaped sleeve (4) and the rear "8"-shaped sleeve (6) are respectively installed on the left and right sides of the driving gear shaft (1) and the driven gear shaft (8), and the front "8"-shaped sleeve (4) and the rear "8"-shaped sleeve (6) are installed symmetrically on the left and right sides.

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