Method for dynamic determination of injection pressure for external gear motor for hoisting

Abstract

The application discloses a dynamic determination method for injection pressure of an external gear motor for hoisting, which comprises the following steps: step one, determining fluctuating output hydraulic rotating speed and output hydraulic torque from gear pair meshing process; step two, calculating angular acceleration of the output hydraulic rotating speed from the fluctuating output hydraulic rotating speed; step three, calculating dynamic hoisting load torque from the angular acceleration of the output hydraulic rotating speed; and step four, calculating dynamic injection pressure from the hoisting load torque equal to the output hydraulic torque coupling. The application provides a simple formula for injection pressure under hoisting load, clearly shows the coupling mechanism among the working conditions of the injection pressure, the rated injection flow and the rated back pressure, the hoisting involute gear-shaft geometric parameters of the base circle radius, the pitch circle radius, the tooth width and the shaft end radius, and the hoisting load mass, and makes up for the deficiency in the calculation of the output hydraulic torque and its fluctuation coefficient of the gear motor, thereby improving the design quality of the gear motor and the evaluation quality of hoisting characteristics.

Description

Technical Field

[0001] This invention relates to the field of hydraulic motor technology, and more specifically to a method for dynamically determining the injection pressure of an external gear motor used for hoisting. Background Technology

[0002] External gear motors (or simply gear motors) are positive displacement hydraulic power components with a working principle opposite to that of external gear pumps (or simply gear pumps), but with a basically the same structure. Their core structure consists of a large-backlash external gear pair (or simply gear pair) composed of two gears of the same size. They are widely used in lifting and hoisting applications, although their speed is relatively low. Considering the need for forward and reverse rotation in this type of lifting gear motor, the double-trapped oil unloading grooves corresponding to the large backlash are generally symmetrically arranged. The large output fluctuation determined by the periodic meshing of the gear pair is a structural problem inherent in the coexistence of gear pumps and motors. Just as the output pressure of a gear pump is determined by the load, the injection pressure of a gear motor should also be determined by the lifting load. However, current research and performance evaluations are primarily focused on specific injection pressures and flow rates, such as calculating the output hydraulic speed and torque of lifting gear motors and their fluctuation coefficients. These studies treat the gear motor as a separate object, ignoring the lifted load, leading to results that differ significantly from actual lifting applications. The reason is that the output hydraulic speed and its fluctuation are mainly determined by the injection flow rate and the geometric parameters of the gear pair, while the output hydraulic torque and its fluctuation are mainly determined by the injection pressure and the geometric parameters of the gear pair. The fluctuation of the output hydraulic speed will cause the gear pair-shaft and the lifted load to generate inertial torque. These inertial torques will directly affect the fluctuation of the injection pressure and the lifted load torque. That is, the injection pressure and the lifted load torque are coupled. The injection pressure should be determined by the integrated dynamic lifting characteristics of the gear pair-shaft and the lifted load under the rated injection flow rate. Summary of the Invention

[0003] To address the shortcomings of the prior art, this invention provides a dynamic determination method for the injection pressure of an external gear motor used for lifting, namely, a dynamic determination method for the injection pressure of the gear motor and the lifting load torque. The purpose is to clarify the coupling mechanism between the injection pressure and the dynamic characteristics of the lifted load by accurately calculating and analyzing the injection pressure to match the actual lifting conditions, thereby improving the design quality of the gear motor and the evaluation quality of its lifting characteristics.

[0004] The method for dynamically determining the injection pressure of an external gear motor for lifting involves a gear pair-shaft, including a lifting involute gear-shaft and a loose involute gear-shaft. The lifting involute gear and the loose involute gear have the same dimensions and structure, determined by the previous gear motor design results. The shaft extension of the lifting involute gear-shaft is used to output hydraulic speed and hydraulic torque for lifting the load, and the shaft extension of the lifting involute gear-shaft is longer than the shaft extension of the loose involute gear-shaft.

[0005] The method for dynamically determining the injection pressure of an external gear motor used for lifting includes the following steps:

[0006] Step 1: Determine the fluctuating output hydraulic speed and output hydraulic torque from the gear pair meshing process; Step 2: Calculate the angular acceleration of the output hydraulic speed from the fluctuating output hydraulic speed;

[0007] Step 3: Calculate the dynamic lifting load torque from the angular acceleration of the output hydraulic speed;

[0008] Step 4: Calculate the dynamic injection pressure by coupling the lifting load torque with the output hydraulic torque.

[0009] In step one, during the rotation of the gear pair, due to the transmission requirement that the gear pair overlap ratio is greater than 1, its rotational operation is a periodic meshing process with alternating single and double meshing points. Let f be the vector length from the node to the previous meshing point in either the single or double meshing point, where f pointing towards the injection flow side is positive and f pointing towards the return oil back pressure side is negative. Therefore, a periodic meshing process of a large backlash gear pair with symmetrically arranged double oil trapping unloading grooves is as follows: And under the assumption of no loss in injected flow ,

[0010] Where Q is the rated injection flow rate of the gear motor, pi is the dynamic injection pressure to be determined, po is the rated return oil back pressure, ω is the output hydraulic speed, δω is the fluctuation coefficient of the output hydraulic speed, M is the output hydraulic torque, Pb is the base circle pitch circle, B is the width of the involute gear for lifting and the involute gear for empty fitting of the same size, Re is the tip circle radius of the involute gear, R is the pitch circle radius of the involute gear pair, dimensionless parameter x=Re / R, dimensionless meshing position variable y=f / R, dimensionless parameter z=0.5Pb / R. In step two, based on the forming principle of the involute gear and the first derivative of f with respect to time t, df / dt=ωRb, where Rb is the base circle radius of the gear, and the first derivative of ω with respect to f in equation (2), ,

[0011] The angular acceleration dω / dt of the output hydraulic speed is given by .

[0012] In the third step, let J, m, and e be the moment of inertia, mass, and eccentricity of the involute gear - shaft for hoisting, where J = me²; m₀ is the mass of the hoisted load, g is the acceleration due to gravity, r₀ is the radius of the shaft end of the involute gear - shaft for hoisting, F₀ is the hoisting load force, and M₀ is the hoisting load torque, with M₀ = F₀r₀. When neglecting the torque losses caused by pulleys, shaft - end friction, etc., according to the law of fixed - axis rotation of a rigid body of the involute gear - shaft for hoisting, we have ,

[0013] When F₀ ≤ 0, the traction belt will loosen, F₀ ≡ 0. At this time, according to Newton's second law, we have ,

[0014] That is ,

[0015] From this, the numerical solution y* corresponding to the dimensionless meshing position variable y is determined. If y* < -z, then y* = -z. Then, the piece - wise expression of the hoisting load torque M₀(y) is .

[0016] In the fourth step, substituting Equation (5) into Equation (8) and considering m << m₀, e << r₀, we get ,

[0017] And calculating the fluctuation coefficient of the output hydraulic torque from this numerical value. Substituting the M formula in Equation (2), Equation (4), and Equation (8) into Equation (9), the injection pressure under the hoisting load is ,

[0018] And calculating the fluctuation coefficient of the injection pressure from this numerical value.

[0019] Advantages of the present invention: Through the concise formula of the injection pressure under the hoisting load given in the present invention, the working conditions of the injection pressure, the rated injection flow rate, and the rated back - pressure of the return oil are clarified, as well as the coupling mechanism among the geometric parameters of the involute gear - shaft for hoisting, such as the base - circle radius, pitch - circle radius, tooth width, and shaft - end radius, and the mass of the hoisted load. It makes up for the deficiencies in the calculation of the output hydraulic torque and its fluctuation coefficient of the existing gear motor, and further improves the design quality of the gear motor and the evaluation quality of its hoisting characteristics. When designing a gear motor, it is necessary to focus on effectively reducing the angular acceleration of the output hydraulic speed in order to fully alleviate the inertial torque impact of the load. BRIEF DESCRIPTION OF THE DRAWINGS

[0020] Figure 1 is a schematic diagram of the gear pair - shaft structure of the gear motor for hoisting in the present invention.

[0021] Figure 2 [[ID=!44]] is a schematic diagram of the meshing position of the gear pair of the gear motor for hoisting.

[0022] Figure 3 This is a schematic diagram of the torque balance of the gear pair and shaft of a gear motor for lifting.

[0023] Figure 4 This is a schematic diagram of the force balance for lifting a load.

[0024] Figure 5 A schematic diagram of the output hydraulic speed of a gear motor used for lifting.

[0025] Figure 6 A schematic diagram of the output hydraulic torque of a gear motor used for lifting.

[0026] Figure 7 A schematic diagram of the dynamic injection pressure of a gear motor used for lifting.

[0027] Wherein: 1. Involute gear-shaft for lifting; 2. Involute gear-shaft for emptying; R, pitch circle radius of the involute gear pair. b The base circle radius of the involute gear, Q, and the known rated injection flow rate of the gear motor, p. i The dynamic injection pressure to be determined, p o Rated return oil back pressure, ω, output hydraulic speed, M, output hydraulic torque, f, vector length from the previous meshing point to the node in a single or double meshing point, y=f / R, dimensionless meshing position variable, J, moment of inertia of the lifting involute gear-shaft, m, mass of the lifting involute gear-shaft, e, eccentricity of the lifting involute gear-shaft, m0, mass of the lifted load, g, gravitational acceleration, r0, shaft end radius of the lifting involute gear-shaft, F0, lifting load force, M0, lifting load torque. Detailed Implementation

[0028] The present invention will be further described below with reference to the accompanying drawings and specific embodiments.

[0029] Example

[0030] The example uses a standard cylindrical gear with 17 teeth, a module of 6 mm, an addendum coefficient of 1, and a pressure angle of 20°. The parameters are: B = 50 mm; Q = 30 / 60 L / min; po = 0.5 MPa; m0 = 1000 Kg; r0 = 20 mm. Based on the geometric parameter calculation formulas for involute gears and the flow rate calculation formulas for gear motors, the following parameters are calculated: Re = 57 mm, R = 51 mm, Rb = 47.92 mm, Pb = 17.71 mm, x = 1.1176, z = 0.1737, and the contact ratio is 1.51.

[0031] like Figures 1 to 7As shown, the dynamic determination method for the injection pressure of the external meshing gear motor for lifting involves a gear pair-shaft, including lifting involute gear-shaft 1 and unloaded involute gear-shaft 2. The lifting involute gear and the unloaded involute gear have the same dimensions and structure, determined by the previous gear motor design results. The shaft extension of the lifting involute gear-shaft 1 is used to output hydraulic speed and hydraulic torque for lifting the load. The shaft extension of the lifting involute gear-shaft 1 is longer than the shaft extension of the unloaded involute gear-shaft 2.

[0032] The dynamic determination method for injection pressure of an external gear motor for lifting includes the following steps: Step 1: Determine the fluctuating output hydraulic speed and output hydraulic torque from the gear pair meshing process; Step 2: Calculate the angular acceleration of the output hydraulic speed from the fluctuating output hydraulic speed; Step 3: Calculate the dynamic lifting load torque from the angular acceleration of the output hydraulic speed; Step 4: Calculate the dynamic injection pressure by coupling the lifting load torque with the output hydraulic torque.

[0033] In step one, the fluctuating output hydraulic speed and output hydraulic torque are determined by the gear pair meshing process. During the rotation of the gear pair, because the gear pair adopts a contact ratio of 1.51, its rotational working process is a periodic meshing process with alternating single and double meshing points. Let f be the vector length from the node to the previous meshing point in the single or double meshing point, where f pointing towards the injection flow side is positive and f pointing towards the return oil back pressure side is negative. Thus, a periodic meshing process of a large backlash gear pair with symmetrically set double oil trapping unloading grooves is as follows: ,

[0034] and the assumption of no loss in injected flow ,

[0035] Where Q is the rated injection flow rate of the gear motor, pi is the dynamic injection pressure to be determined, po is the rated return oil back pressure, ω is the output hydraulic speed, δω is the fluctuation coefficient of the output hydraulic speed, M is the output hydraulic torque, Pb is the base circle pitch circle, B is the width of the involute gear for lifting and the involute gear for empty fitting of the same size, Re is the tip circle radius of the involute gear, R is the pitch circle radius of the involute gear pair, dimensionless parameter x=Re / R, dimensionless meshing position variable y=f / R, and dimensionless parameter z=0.5Pb / R.

[0036] In step two, the angular acceleration of the output hydraulic speed is calculated from the fluctuating output hydraulic speed. Based on the forming principle of involute gears and the first derivative of f with respect to time t, df / dt = ωRb, where Rb is the base circle radius of the gear, and from equation (2), the first derivative of ω with respect to f... The angular acceleration dω / dt of the output hydraulic speed is obtained as follows: .

[0037] In Step 3, the dynamic hoisting load torque is calculated from the angular acceleration of the output hydraulic speed. Let J, m, and e be the moment of inertia, mass, and eccentricity of the involute gear - shaft for hoisting, where J = me²; m0 is the mass of the hoisting load, g is the acceleration due to gravity, r0 is the radius of the shaft end of the involute gear - shaft for hoisting, F0 is the hoisting load force, and M0 is the hoisting load torque, with M0 = F0r0. When neglecting the torque losses caused by pulley, shaft - end friction, etc., according to the law of fixed - axis rotation of a rigid body of the involute gear - shaft for hoisting, we have , when F0 ≤ 0, the traction belt will become loose and F0 ≡ 0. At this time, according to Newton's second law, we have ,

[0038] That is , from which the numerical solution y* corresponding to the dimensionless meshing position variable y is determined. Among them, when Q = 30 L / min, y* = - 0.18. Since y* = - 0.18 < - z = - 0.1737, so y* = - 0.1737. When Q = 60 L / min, y* = - 0.0649. Then, the piece - wise expression of the hoisting load torque M0(y) is .

[0039] In Step 4, the dynamic injection pressure is calculated by coupling the hoisting load torque equal to the output hydraulic torque. Substituting Equation (5) into Equation (8) and considering m << m0, e << r0, we get , and from this, the fluctuation coefficient of the output hydraulic torque is calculated numerically. It can be seen that the greater the rated injection flow rate, the higher the rotational speed, and the greater the inertial torque of the load, the greater the fluctuation of the output hydraulic torque to balance it.

[0040] Substituting the M formula in Equation (2), Equation (4), and Equation (8) into Equation (9), the injection pressure under the hoisting load is , and from this, the fluctuation coefficient of the injection pressure is calculated numerically. It can be seen that the greater the rated injection flow rate, the higher the rotational speed, and the greater the inertial torque of the load, the greater the fluctuation of the output hydraulic torque to balance it, resulting in a greater fluctuation of the injection pressure, thus limiting the further increase of the rotational speed.

[0041] The above embodiments only illustrate the specific implementation schemes of the present disclosure, but the implementation schemes of the present disclosure are not limited by the above content. Any changes, modifications, substitutions, combinations, and simplifications made without substantially departing from the gist and principle of the inventive concept of the present disclosure shall be equivalent replacement methods and shall be included in the protection scope determined by the claims.

Claims

1. A method for dynamic determination of injection pressure for an external gear motor for hoisting, characterized in that: Includes the following steps: Step 1: Determine the fluctuating output hydraulic speed and output hydraulic torque from the gear pair meshing process; Step 2: Calculate the angular acceleration of the output hydraulic speed from the fluctuating output hydraulic speed; Step 3: Calculate the dynamic lifting load torque from the angular acceleration of the output hydraulic speed; Step 4: Calculate the dynamic injection pressure by coupling the lifting load torque with the output hydraulic torque; In step one, during the rotation of the gear pair, due to the transmission requirement that the gear pair overlap ratio is greater than 1, its rotational operation is a periodic meshing process with alternating single and double meshing points. Let f be the vector length from the node to the previous meshing point in either the single or double meshing point, where f pointing towards the injection flow side is positive and f pointing towards the return oil back pressure side is negative. Therefore, a periodic meshing process of a large backlash gear pair with symmetrically arranged double oil trapping unloading grooves is as follows: , and the assumption of no loss in injected flow Where Q is the rated injection flow rate of the gear motor, pi is the dynamic injection pressure to be determined, po is the rated return oil back pressure, ω is the output hydraulic speed, δω is the fluctuation coefficient of the output hydraulic speed, M is the output hydraulic torque, Pb is the base circle pitch circle, B is the width of the involute gear for lifting and the involute gear for empty fitting of the same size, Re is the tip circle radius of the involute gear, R is the pitch circle radius of the involute gear pair, dimensionless parameter x=Re / R, dimensionless meshing position variable y=f / R, dimensionless parameter z=0.5Pb / R; In step two, based on the forming principle of involute gears and the first derivative of f with respect to time t, df / dt = ωRb, where Rb is the base circle radius of the gear, and from equation (2), the first derivative of ω with respect to f... The angular acceleration dω / dt of the output hydraulic speed is obtained as follows: ; In step three, let J, m, and e be the moment of inertia, mass, and eccentricity of the involute gear-shaft used for lifting, respectively, J = me²; m0 be the mass of the load being lifted, g be the acceleration due to gravity, r0 be the radius of the shaft end of the involute gear-shaft used for lifting, F0 be the lifting load force, and M0 be the lifting load torque, M0 = F0r0. Ignoring torque losses caused by friction between the pulleys and the shaft end, the rigid body rotation law of the involute gear-shaft used for lifting is obtained as follows: ， When F0≤0, the traction belt will loosen; when F0≡0, according to Newton's second law, we get... , Right now , This determines the numerical solution y* corresponding to the dimensionless meshing position variable y. If y* < -z, then y* = -z. Therefore, the piecewise expression for the lifting load torque M0(y) is: .

2. The method for dynamically determining the injection pressure of the external meshing gear motor for lifting as described in claim 1, characterized in that: The gear pair involved includes a lifting involute gear shaft and a loose involute gear shaft. The lifting involute gear and the loose involute gear have the same size and structure, which were determined by the previous gear motor design results. The shaft extension of the lifting involute gear shaft is used to output hydraulic speed and hydraulic torque for lifting the load. The shaft extension of the lifting involute gear shaft is longer than the shaft extension of the loose involute gear shaft.

3. The method for dynamically determining the injection pressure of the external meshing gear motor for lifting as described in claim 2, characterized in that: In the fourth step, substituting Equation (5) into Equation (8) and considering m << m0, e << r0, we get , and calculating the fluctuation coefficient of the output hydraulic torque from this value. Substituting the M formula in Equation (2), Equation (4), and Equation (8) into Equation (9), the injection pressure under the hoisting load is And from this value, the fluctuation coefficient of the injection pressure is calculated.

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