A method for calculating speed pulsation of an internal curve hydraulic motor

Abstract

The application discloses a kind of inner curve hydraulic motor speed pulsation calculation method.First, the machine-liquid coupling dynamics framework is constructed to determine the speed pulsation;Then the leakage loss of the inner curve hydraulic motor flow distribution shaft interface is analyzed by analytical method, and the leakage loss of the piston ring interface is calculated by numerical method;Finally, the obtained leakage loss is substituted into the machine-liquid coupling dynamics framework for calculation, and the speed pulsation of the inner curve hydraulic motor is finally obtained.The method can reveal the mechanism of speed pulsation in depth, provide accurate guidance for the design optimization of inner curve hydraulic motor, and is especially suitable for performance analysis and improvement of low-speed large-torque inner curve hydraulic motor.

Description

Technical Field

[0001] This invention belongs to the field of hydraulic motor performance analysis and optimization technology, and particularly relates to a method for calculating the speed pulsation of an internal curve hydraulic motor, which is applicable to the speed pulsation calculation, multi-interface influence analysis and design optimization of low-speed, high-torque internal curve hydraulic motors. Background Technology

[0002] Speed ​​pulsation not only severely affects the control accuracy of motors, but severe pulsation can even lead to motor jamming or malfunction of the entire mechanical equipment. Existing methods primarily focus on the cam ring profile that determines the kinematics of the motor piston, analyzing the impact of cam ring profile design on speed pulsation based on kinematic angles, or using torque pulsation as a substitute evaluation index for speed pulsation, but neglecting power loss and pressure changes. Other methods analyze the impact of piston motion on torque pulsation by establishing a piston cavity pressure dynamics model, but still rely on kinematic calculations of piston motion, without considering piston dynamics. In recent years, although methods have been developed to establish lumped parameter models considering pressure and piston dynamics for speed pulsation analysis, and similar models have been used to study the impact of flow distribution structures on hydraulic motor torque pulsation, most of these models do not consider the leakage characteristics of various lubrication interfaces inside the hydraulic motor, resulting in significant deviations in the calculation results of existing models.

[0003] The lubrication interfaces inside internal curved hydraulic motors are typically studied separately due to their complex leakage characteristics. The distributor shaft interface and piston ring interface are key lubrication interfaces within the motor. Existing methods have conducted leakage characteristic analyses on each interface individually, such as using elastohydrodynamic lubrication models, computational fluid dynamics simulations, and experimental methods to study the characteristics of a single interface. However, none of these methods consider the coupling effect between speed pulsation and the leakage characteristics of each interface. Due to the complex structure and lubrication characteristics of internal curved hydraulic motors, a comprehensive and systematic method for studying their speed pulsation behavior is still lacking.

[0004] In summary, it is essential to propose a calculation method for the multi-interface coupled velocity pulsation model of an internal curve hydraulic motor that comprehensively considers leakage losses at multiple interfaces, can accurately calculate velocity pulsation, and quantifies the influence of each interface. Summary of the Invention

[0005] The purpose of this invention is to address the problems of existing internal curve hydraulic motor speed pulsation calculation models neglecting the influence of multi-interface leakage, insufficient calculation accuracy, and lack of in-depth explanation of the speed pulsation mechanism. This invention proposes a speed pulsation calculation method for internal curve hydraulic motors, which can accurately calculate speed pulsation and provide a scientific basis for the design optimization of internal curve hydraulic motors.

[0006] This invention is achieved through the following technical solution: a method for calculating the speed pulsation of an internal curve hydraulic motor, the method comprising the following steps:

[0007] (1) Construct a mechanical-hydraulic coupling dynamics framework, which includes the fluid dynamics of the hydraulic oil inside the internal curved hydraulic motor and the rigid body dynamics of the plunger assembly and cam ring;

[0008] (2) Analyze the leakage loss of the distribution shaft interface of the internal curve hydraulic motor by analytical method, including the external leakage from the high pressure window of the distribution shaft to the hydraulic motor housing and the internal leakage from the high pressure window to the low pressure window.

[0009] (3) Based on the flow balance equation of the oil hole and piston ring interface, the distribution of pressure and oil film thickness is solved by numerical method to obtain the leakage loss of the piston ring interface of the inner curve hydraulic motor.

[0010] (4) The leakage amount and leakage loss in steps (2) and (3) are substituted into the mechanical-hydraulic coupling dynamics framework constructed in step (1) for calculation, and finally the speed pulsation of the inner curve hydraulic motor is obtained.

[0011] Furthermore, the piston cavity pressure p in fluid dynamics is calculated based on the continuity equation and the state equation, as follows:

[0012]

[0013] Among them, Q l K represents the leakage rate of the hydraulic motor. e V is the bulk modulus of hydraulic oil. p This refers to the volume of the plunger cavity;

[0014] Q hp and Q lp The flow rates flowing into and out of the plunger cavity are respectively calculated based on the orifice flow equation:

[0015]

[0016]

[0017] Among them, C d The orifice flow coefficient is... Let be the fluid density, sgn be the sign function, and p be the fluid density. in and p out These represent import and export pressures, A hp and A lp The flow channel area is determined by the distribution shaft structure;

[0018] Q l The calculation formula is:

[0019]

[0020] In the formula q d q represents the leakage at the distribution shaft interface. pThe leakage at the piston ring interface is given; substituting the leakage of the hydraulic motor into the above fluid dynamics equations yields the pressure change in the motor plunger chamber.

[0021] V p Represented as:

[0022]

[0023] Among them, V dead d is the volume of the plunger cavity when the plunger assembly is at the lower end termination point. p ρ is the diameter of the plunger. φ ρ is the theoretical extreme diameter of the profile corresponding to the rotation angle φ of the cam ring. φ (0) is the radius of the theoretical profile base circle. , This refers to the speed of the hydraulic motor;

[0024] In rigid body dynamics, the dynamic equations of the plunger assembly only consider radial acceleration, and the formula is:

[0025]

[0026]

[0027] Where, m p It is the mass of the plunger assembly, F n F is the contact force between the roller and the guide rail. t The contact force between the roller and the guide plate. The pressure angle between the cam roller and the cam ring is determined by the cam ring profile.

[0028] The dynamic equation of the cam ring is expressed as:

[0029]

[0030] The first item on the left is the driving torque T generated by the sum of all contact forces between the roller and the cam ring. L J is the load torque acting on the hydraulic motor, and J is the moment of inertia of the hydraulic motor.

[0031] Solving the fluid dynamics equations and the plunger assembly dynamics equations simultaneously yields the motor speed. Based on the above equations, a machine-fluid coupled dynamics framework is established, and the speed pulsation of the hydraulic motor can be obtained by solving it.

[0032] Furthermore, the internal leakage from the high-pressure window to the low-pressure window includes leakage from the first high-pressure window to the low-pressure window and leakage from the high-pressure window of the distribution shaft to the low-pressure window of the distribution shaft.

[0033] Furthermore, the formula for calculating the leakage at the distribution shaft interface is:

[0034]

[0035] Where q e This refers to the external leakage from the high-pressure window of the distribution shaft to the hydraulic motor housing; during operation, the distribution shaft window is rotatably connected to the fixed cylinder window, and its sealing length l a The leakage q of the distribution axis window changes periodically. e Represented as:

[0036]

[0037] For different distribution shaft high-pressure windows, the sealing length l a They have different phases, with a phase difference of 60 degrees. e p is the sealing length between the distribution shaft window and the housing. case η is the housing pressure inside the hydraulic motor; η is the dynamic viscosity of the hydraulic oil; δ s This refers to the clearance between the distribution shaft and the cylinder block;

[0038] q i This refers to the internal leakage from the high-pressure window to the low-pressure window, including the leakage q from the first high-pressure window to the low-pressure window. ig And leakage q from the high-pressure window of the distribution shaft to the low-pressure window of the distribution shaft ip , is represented as:

[0039]

[0040] Among them, l ig The sealing length between the first high-pressure window and the low-pressure window is given. Internal leakage in the high-pressure window of the distribution shaft can leak to the two adjacent low-pressure windows of the distribution shaft, where the sealing length to the left window is l. il The sealing length to the right window is l ir .

[0041] Furthermore, the oil in the oil groove at the piston ring interface is considered as static pressure oil with constant pressure. Based on the flow balance equation, the flow rate from the oil hole and piston ring interface should be equal to the flow rate from the oil groove. Based on the average Reynolds equation and the flow balance equation, the distribution of pressure and oil film thickness can be solved by the finite difference method, and the friction and leakage at the piston ring interface can be obtained.

[0042] Furthermore, the piston ring contains an oil groove that can hold the pressurized oil ejected from the oil hole. The oil in the oil groove can be considered to have a constant pressure of p. g The static pressure oil; to solve this pressure problem, a flow balance equation is needed, whereby the flow rate from the oil hole and piston ring interface should be equal to the flow rate from the oil groove, expressed as:

[0043]

[0044] Where, q p This refers to the leakage flow rate at the piston ring interface, where q1 and q2 are the amounts of oil flowing into and out of the oil sump, respectively. The calculation formula is as follows:

[0045]

[0046] in, It is the oil film pressure, σ p It is the composite surface roughness, v p It is the speed at which the piston rings reciprocate with the plunger assembly; φ y It is the pressure-flow factor, φ s y1 and y2 are arbitrary coordinate values ​​of the piston ring at the first or second sealing length, respectively; h is the nominal oil film thickness. T It is the average thickness of the local film layer.

[0047] The flow rate from the oil hole can be calculated using the following formula:

[0048]

[0049] Among them, C d It is the flow coefficient of the orifice, A g It is the flow area of ​​the oil hole.

[0050] Based on the average Reynolds equation and the flow balance equation, the distribution of pressure and oil film thickness is solved by the finite difference method, and the leakage situation at the piston ring interface is obtained.

[0051] Furthermore, the machine-hydraulic coupled dynamics framework is established through ordinary differential equations, which are solved using the Runge-Kutta method with variable time steps. When the time for solving the ordinary differential equations equals the final time, all calculations are completed, and the leakage loss and speed pulsation in the multi-interface of the hydraulic motor are finally obtained.

[0052] The beneficial effects of this invention are as follows: By constructing a mechanical-hydraulic coupled dynamic framework, this invention comprehensively utilizes analytical and numerical methods to incorporate leakage losses at multiple interfaces such as the distribution shaft and piston rings, thus solving the problem of insufficient calculation accuracy caused by neglecting the influence of multiple interfaces in existing models. It can accurately calculate the speed pulsation of the internal curve hydraulic motor. Attached Figure Description

[0053] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0054] Figure 1 This is a flowchart illustrating the process of calculating and solving the speed pulsation of an internal curve hydraulic motor.

[0055] Figure 2 This is a schematic diagram of the distribution shaft and piston ring lubrication interface of an internal curve hydraulic motor.

[0056] Figure 3 The result is the calculation result of the speed pulsation of the internal curve hydraulic motor. Detailed Implementation

[0057] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described below with reference to the accompanying drawings and examples. It should be understood that the specific examples described herein are merely illustrative and not intended to limit the invention.

[0058] like Figure 1 and Figure 2 As shown, this invention provides a method for calculating the speed pulsation of an internal curve hydraulic motor, with the following specific steps:

[0059] (1) Construct a mechanical-hydraulic coupling dynamics framework, which includes the fluid dynamics of the hydraulic oil inside the internal curved hydraulic motor and the rigid body dynamics of the plunger assembly and cam ring;

[0060] In fluid dynamics, the plunger cavity pressure p is calculated based on the continuity equation and the state equation, using the following formula:

[0061]

[0062] Among them, K e V is the bulk modulus of hydraulic oil. p V is the volume of the plunger cavity. p It can be represented as:

[0063]

[0064] Among them, V dead d is the volume of the plunger cavity when the plunger assembly is at the lower end termination point. p ρ is the diameter of the plunger. φ ρ is the theoretical extreme diameter of the profile corresponding to the rotation angle φ of the cam ring. φ (0) is the radius of the theoretical profile base circle. , This refers to the rotational speed of the hydraulic motor.

[0065] Q hp and Q lp The flow rates flowing into and out of the plunger cavity are respectively, and the calculation formula based on the orifice flow equation is as follows:

[0066]

[0067]

[0068] Among them, C d The orifice flow coefficient, Let be the fluid density, sgn be the sign function, and p be the fluid density. in and p out These represent import and export pressures, A hp and A lp The flow channel area is determined by the distribution shaft structure.

[0069] Q l The leakage flow rate within the hydraulic motor is calculated using the following formula:

[0070]

[0071] In the formula q d q represents the leakage at the distribution shaft interface. p This represents the leakage at the piston ring interface.

[0072] Furthermore, in rigid body dynamics, the dynamic equations of the plunger assembly only consider radial acceleration, and the formula is:

[0073]

[0074]

[0075] Where, m p It is the mass of the plunger assembly, F n F is the contact force between the roller and the guide rail. t This is the contact force between the roller and the guide plate. The pressure angle between the cam roller and the cam ring is determined by the cam ring profile.

[0076] The dynamic equation of the cam ring can be expressed as:

[0077]

[0078] The first item on the left is the driving torque T generated by the sum of all contact forces between the cam roller and the cam ring. LLet J be the load torque acting on the hydraulic motor. J is the moment of inertia of the hydraulic motor. Based on the above equation, a mechanical-hydraulic coupled dynamic framework is established, and the velocity pulsation of the hydraulic motor can be obtained by solving it.

[0079] (2) The leakage loss at the distribution shaft interface of the internal curve hydraulic motor is analyzed using analytical methods; the formula for calculating the leakage at the distribution shaft interface is:

[0080]

[0081] Where, q e This refers to the external leakage from the high-pressure window of the distributor shaft to the hydraulic motor housing. During operation, the distributor shaft window is rotatably connected to the fixed cylinder block window, with a sealing length l. a The leakage q of the distribution axis window changes periodically. e It can be represented as:

[0082]

[0083] For different distribution shaft high-pressure windows, the sealing length l a They have different phases, with a phase difference of 60 degrees. e p is the sealing length between the distribution shaft window and the housing. case η is the housing pressure inside the hydraulic motor, η is the dynamic viscosity of the hydraulic oil, and δ is... s This refers to the clearance between the distribution shaft and the cylinder block.

[0084] q i This refers to the internal leakage from the high-pressure window to the low-pressure window, including the leakage q from the first high-pressure window to the low-pressure window. ig And leakage q from the high-pressure window of the distribution shaft to the low-pressure window of the distribution shaft ip The formula is:

[0085]

[0086] Among them, l ig The sealing length between the first high-pressure window and the low-pressure window is given. Internal leakage in the high-pressure window of the distribution shaft can leak to the two adjacent low-pressure windows of the distribution shaft, where the sealing length to the left window is l. il The sealing length to the right window is l ir .

[0087] (3) Calculate the leakage loss at the piston ring interface using numerical methods; the piston ring contains an oil groove that can hold the pressurized oil ejected from the oil hole. The oil in the oil groove can be considered to have a constant pressure p. g The static pressure oil. To solve this pressure problem, a flow balance equation is needed. The flow rate from the oil hole and piston ring interface should be equal to the flow rate from the oil groove, which can be expressed as:

[0088]

[0089] Where, q p This refers to the leakage flow rate at the piston ring interface, where q1 and q2 are the amounts of oil flowing into and out of the oil sump, respectively. The calculation formula is as follows:

[0090]

[0091] in, It is the oil film pressure, σ p It is the composite surface roughness, v p It is the speed at which the piston rings reciprocate with the plunger assembly; φ y It is the pressure-flow factor, φ s y1 and y2 are the shear flow factor, and y1 and y2 are arbitrary coordinate values ​​of the piston ring at the first or second sealing length, respectively. h is the nominal oil film thickness. T It is the average thickness of the local film layer.

[0092] The flow rate from the oil hole can be calculated using the following formula:

[0093]

[0094] Among them, C d It is the flow coefficient of the orifice, A g This refers to the flow area of ​​the oil orifice. Based on the average Reynolds equation and the flow balance equation, the pressure and oil film thickness distribution can be solved using the finite difference method, thus obtaining the friction and leakage conditions at the piston ring interface.

[0095] (4) The mechanical-hydraulic coupling dynamics framework is established through ordinary differential equations, which are solved using the Runge-Kutta method with variable time steps. Within this framework, the leakage at the distribution shaft interface is calculated analytically, and the leakage loss at the piston ring interface is determined numerically. When the time for solving the ordinary differential equations equals the final time, all calculations are completed, and the velocity pulsation and leakage loss in the multi-interface of the hydraulic motor are finally obtained.

[0096] To illustrate with a specific example, the main input parameter is: piston chamber dead zone volume V. dead = 1.4×10 -4 m³, sealing length l between the distribution shaft window and the cylinder block e = 27 mm, orifice flow coefficient C d = 0.6, distribution axis window height l p =11.5 mm, plunger assembly mass m p= 8 kg, hydraulic motor moment of inertia J = 200 kg·m2, hydraulic oil bulk modulus K e = 1700 MPa, hydraulic oil dynamic viscosity η = 0.039 Pas, hydraulic oil density = 855 kg / m³, piston ring height l h = 3 mm, distribution shaft diameter d s = 125 mm, piston ring oil hole area A g = 0.4×10 -6 m², distribution shaft clearance δ s =15 μm, sealing length l between distribution shaft windows ig =17.6 mm. Substituting the parameters into the calculation framework, the current time is taken as t. c The calculation step size is Δt, and the calculation is performed once at each time interval. The calculation stops when the calculation time is the same as the set final time. The pulsation of the output speed of the hydraulic motor in the inner curve is obtained as follows: Figure 3 As shown.

[0097] The above embodiments are used to explain and illustrate the present invention, but not to limit the present invention. Any modifications and changes made to the present invention within the spirit and scope of the claims shall fall within the protection scope of the present invention.

Claims

1. A method for calculating the speed pulsation of an internal curve hydraulic motor, characterized in that, The method includes the following steps: (1) Construct a mechanical-hydraulic coupled dynamics framework, which includes the fluid dynamics of the hydraulic oil inside the internal curved hydraulic motor and the rigid body dynamics of the plunger assembly and cam ring; in the fluid dynamics, the plunger cavity pressure p is calculated based on the continuity equation and the state equation, and the formula is: ； Among them, Q l K represents the leakage rate of the hydraulic motor. e V is the bulk modulus of hydraulic oil. p This refers to the volume of the plunger cavity; Q hp and Q lp The flow rates are the inflow and outflow from the plunger cavity, respectively, calculated based on the orifice flow equation: ； ； Among them, C d The orifice flow coefficient, Let be the fluid density, sgn be the sign function, and p be the fluid density. in and p out These represent import and export pressures, A hp and A lp The flow channel area is determined by the distribution shaft structure; Q l The calculation formula is: ； In the formula q d q represents the leakage at the distribution shaft interface. p The leakage at the piston ring interface is given; substituting the leakage of the hydraulic motor into the above fluid dynamics equations yields the pressure change in the motor plunger chamber. V p Represented as: ； Among them, V dead d is the volume of the plunger cavity when the plunger assembly is at the lower end termination point. p ρ is the diameter of the plunger. φ ρ is the theoretical extreme diameter of the profile corresponding to the rotation angle φ of the cam ring. φ (0) is the radius of the theoretical profile base circle. , This refers to the speed of the hydraulic motor; In rigid body dynamics, the dynamic equations of the plunger assembly only consider radial acceleration, and the formula is: ； ； Where, m p It is the mass of the plunger assembly, F n F is the contact force between the roller and the guide rail. t The contact force between the roller and the guide plate. The pressure angle between the cam roller and the cam ring is determined by the cam ring profile. The dynamic equation of the cam ring is expressed as: ； The first item on the left is the driving torque T generated by the sum of all contact forces between the roller and the cam ring. L J is the load torque acting on the hydraulic motor, and J is the moment of inertia of the hydraulic motor. (2) Analyze the leakage loss of the distribution shaft interface of the inner curve hydraulic motor by analytical method, including the external leakage from the high pressure window of the distribution shaft to the hydraulic motor housing and the internal leakage from the high pressure window to the low pressure window. (3) Based on the flow balance equation of the oil hole and piston ring interface, the distribution of pressure and oil film thickness is solved by numerical method to obtain the leakage loss of the piston ring interface of the inner curve hydraulic motor. (4) The leakage amount and leakage loss in steps (2) and (3) are substituted into the mechanical-hydraulic coupling dynamics framework constructed in step (1) for calculation, and finally the speed pulsation of the inner curve hydraulic motor is obtained.

2. The method for calculating the speed pulsation of an internal curve hydraulic motor according to claim 1, characterized in that, The internal leakage from the high-pressure window to the low-pressure window includes leakage from the first high-pressure window to the low-pressure window and leakage from the high-pressure window of the distribution shaft to the low-pressure window of the distribution shaft.

3. The method for calculating the speed pulsation of an internal curve hydraulic motor according to claim 1, characterized in that, The formula for calculating the leakage at the distribution shaft interface is: ； Where q e This refers to the external leakage from the high-pressure window of the distribution shaft to the hydraulic motor housing; during operation, the distribution shaft window is rotatably connected to the fixed cylinder window, and its sealing length l a The leakage q of the distribution axis window changes periodically. e Represented as: ； For different distribution shaft high-pressure windows, the sealing length l a They have different phases, with a phase difference of 60 degrees. e p is the sealing length between the distribution shaft window and the housing. case η is the housing pressure inside the hydraulic motor, η is the dynamic viscosity of the hydraulic oil, and δ is... s This refers to the clearance between the distribution shaft and the cylinder block; q i This refers to the internal leakage from the high-pressure window to the low-pressure window, including the leakage q from the first high-pressure window to the low-pressure window. ig And leakage q from the high-pressure window of the distribution shaft to the low-pressure window of the distribution shaft ip , is represented as: ； in, The diameter of the distribution shaft, For the height of the distribution axis window, l ig The sealing length between the first high-pressure window and the low-pressure window is given. Internal leakage in the high-pressure window of the distribution shaft can leak to the two adjacent low-pressure windows of the distribution shaft, where the sealing length to the left window is l. il The sealing length to the right window is l ir .

4. The method for calculating the speed pulsation of an internal curve hydraulic motor according to claim 1, characterized in that, The oil in the piston ring interface oil groove is considered to be static pressure oil with constant pressure. Based on the flow balance equation, the flow rate from the oil hole and piston ring interface should be equal to the flow rate from the oil groove. Based on the average Reynolds equation and the flow balance equation, the distribution of pressure and oil film thickness can be solved by the finite difference method, and the friction and leakage at the piston ring interface can be obtained.

5. The method for calculating the speed pulsation of an internal curve hydraulic motor according to claim 4, characterized in that, The piston ring has an oil groove that can hold the pressurized oil ejected from the oil hole. The oil in the oil groove can be considered to have a constant pressure of p. g The static pressure oil; to solve this pressure problem, a flow balance equation is needed, whereby the flow rate from the oil hole and piston ring interface should be equal to the flow rate from the oil groove, expressed as: ； Where, q p This refers to the leakage flow rate at the piston ring interface, where q1 and q2 are the amounts of oil flowing into and out of the oil sump, respectively. The calculation formula is as follows: ； in, It is the oil film pressure, σ p It is the composite surface roughness, v p It is the speed at which the piston rings reciprocate with the plunger assembly; φ y It is the pressure-flow factor, φ s y1 and y2 are arbitrary coordinate values ​​of the piston ring at the first or second sealing length, respectively; h is the nominal oil film thickness. T η is the average thickness of the local film layer, and η is the dynamic viscosity of the hydraulic oil. The flow rate from the oil hole can be calculated using the following formula: ； Among them, C d It is the flow coefficient of the orifice, A g It is the flow area of ​​the oil hole. The density of the hydraulic oil; Based on the average Reynolds equation and the flow balance equation, the distribution of pressure and oil film thickness is solved by the finite difference method, and the leakage situation at the piston ring interface is obtained.

6. The method for calculating the speed pulsation of an internal curve hydraulic motor according to claim 1, characterized in that, The machine-hydraulic coupling dynamics framework is established through ordinary differential equations, which are solved using the Runge-Kutta method with variable time steps. When the time for solving the ordinary differential equations equals the final time, all calculations are completed, and the leakage loss and speed pulsation in the multi-interface of the hydraulic motor are finally obtained.

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