Method and system for analyzing and optimizing viscous resistance loss of planetary reducer grease lubrication

Abstract

This invention belongs to the field of simulation technology and micro-miniature precision transmission equipment, specifically disclosing a method and system for analyzing and optimizing the viscous resistance loss of grease lubrication in planetary reducers. The method includes: constructing a non-Newtonian fluid constitutive model; using a non-Newtonian transient thermo-elasto-fluidic model of gear line contact to solve for the oil film thickness distribution and grease temperature rise, calculating the lubrication and cooling requirements of each gear pair, and determining the gear pair with the largest total demand; using the MPS method for thermo-fluid coupling simulation, iteratively optimizing the liquid level height by comparing the supply flow rate and the demand flow rate to obtain the optimal grease filling volume; and calculating the overall viscous resistance loss power under this filling volume. This invention can accurately predict the viscous resistance loss of planetary reducers under grease lubrication conditions, achieving a balance between transmission efficiency and lubrication reliability.

Description

Technical Field

[0001] This invention belongs to the field of simulation technology and micro-precision transmission equipment, specifically relating to a method and system for analyzing and optimizing the viscous resistance loss of grease lubrication in planetary reducers. Background Technology

[0002] Planetary gear reducers are widely used in industrial robots, aerospace, new energy vehicles, and construction machinery due to their compact structure, large transmission ratio, and high load-bearing capacity. Within the enclosed reducer housing, the lubrication system is crucial for ensuring the transmission efficiency of key components such as gears and bearings. However, due to its non-Newtonian fluid properties, the viscosity of the grease changes when it is agitated by the high-speed rotating gears and planetary carrier inside the reducer, generating viscous resistance losses and thus reducing the overall transmission efficiency of the reducer.

[0003] Currently, the main methods for calculating the churning loss of planetary reducers include empirical formulas and the finite element method (FEM). Empirical methods are based on empirical formulas for churning losses of Newtonian fluids (such as lubricating oil), but these formulas cannot accurately handle the complex rheological properties of non-Newtonian fluids (such as lubricating grease). The FEM is a traditional mesh-based CFD method. When dealing with the complex geometry of the gear meshing area, mesh generation is extremely complex and time-consuming. Simulating the churning of lubricating grease by gears results in poor computational stability and long calculation times. Furthermore, it cannot directly calculate the resistance torque of each component, making it difficult to efficiently apply to the calculation of overall reducer losses.

[0004] To address the aforementioned issues, this invention calculates the agitation loss of a planetary reducer under grease lubrication conditions based on the semi-implicit MPS method of moving particles, studies the influence of different operating parameters on viscous resistance loss, and combines the amount of grease required for lubrication and cooling between the meshing surfaces of the gear pair to provide theoretical support for the overall machine optimization design. Summary of the Invention

[0005] This invention provides a method for analyzing and optimizing the viscous resistance loss of grease lubrication in planetary gear reducers, comprising the following steps: S1: The rheological properties of the selected grease are measured by a rotational rheometer, and the rheological index, plastic viscosity and yield stress of the grease are fitted as a function of temperature to construct a non-Newtonian fluid constitutive model. S2: Based on the non-Newtonian fluid constitutive model obtained in step S1, the non-Newtonian transient thermo-elasto-hydrodynamic model of gear line contact is adopted to solve the Reynolds equation, film thickness equation, energy equation, viscosity-pressure-temperature equation, density-pressure-temperature equation and load balance equation simultaneously to obtain the oil film thickness distribution and grease temperature rise in the meshing area of ​​each gear pair. S3: Based on the oil film thickness distribution and grease temperature rise obtained in step S2, calculate the required lubrication amount for each gear pair using the following formula. and the amount of cooling required And calculate the total amount of grease required. Identify the gear pair with the largest total demand as the target gear pair: In the formula These are the position coordinates along the line of engagement. Let be the oil film thickness distribution function. For tooth width, For rotational speed, Number of teeth This is the actual length of the line of engagement; (b) In the formula This refers to the power loss due to meshing friction in the gear pair. For the density of the grease, For the specific heat of lubricating grease, For the temperature rise of the lubricating grease; S4: Establish a three-dimensional geometric model of the planetary reducer, modify the gear pair, set the initial grease level, and use the moving particle semi-implicit MPS method for thermal-fluid coupling simulation to calculate the grease supply flow rate in the meshing region of the target gear pair. ;like If so, lower the liquid level; If this is done, the liquid level will rise; through multiple simulation iterations, the method to achieve this will be determined. and The optimal liquid level height is determined by minimizing the absolute value of the difference between the two values, and the optimal grease filling volume is calculated accordingly. ; S5: Optimal grease filling volume obtained from step S4 The MPS method was used to simulate and calculate the viscous resistance loss power of the entire machine. ,in This represents the summation over all rotating parts. This refers to the serial number of the rotating component. For the first The rotational speed of each rotating component For the first Viscous resistance torque of a rotating component.

[0006] Furthermore, in step S1, the non-Newtonian fluid constitutive model is selected from the Ostwald model, Bingham model, or Herschel-Bulkley model. Different shear rates are set to obtain the shear stress-shear strain rate curves of the lubricating grease, and the rheological index in each model is fitted. Plastic viscosity and yield stress τ Functional relationship.

[0007] Furthermore, in step S4, the shaping process is a moving method shaping, specifically including: keeping the gear mounting position unchanged, using an equidistant moving method to shape the tooth profile to increase the meshing area clearance; based on the particle diameter in the MPS simulation... Determine the minimum gap size to ensure that at least 3 particles exist within the gap.

[0008] Furthermore, in step S4, the initial grease level height is set. The reference is the rotation centerline of the gear set; the grease supply flow rate in the meshing area of ​​the target gear pair Calculation of particle flux in the meshing zone using MPS simulation: In the formula This is the particle volume correction factor. This represents the number of particles passing through the meshing zone per unit time. Where is the particle radius, is the meshing frequency.

[0009] Furthermore, the optimal grease filling volume mentioned in step S4 Calculate as follows: ; in The radius of the reducer housing is (mm). The optimal liquid level height (mm). The optimal liquid level height (positive value, mm) is based on the bottom of the shell. To account for the volume occupied by solids such as planetary carriers and gears, the structural coefficient is taken in the range of 0.6 to 0.9.

[0010] Furthermore, the total viscous resistance loss power mentioned in step S5 According to the formula Calculation, where The output is directly obtained from the MPS simulation in step S4.

[0011] Furthermore, the planetary reducer is a two-stage planetary transmission reducer with a rated output torque range of 10 to 100 N·m, an input speed range of 100 to 4000 rpm, and a total transmission ratio range of 10 to 60.

[0012] The present invention also provides a system for analyzing and optimizing the viscous resistance loss of grease lubrication in planetary gear reducers for performing the method, comprising: The constitutive model construction module is used to measure the rheological properties of grease at different temperature points using a rotational rheometer, and then fit the constitutive model of the non-Newtonian fluid. The microscopic analysis module is used to solve the oil film thickness distribution and grease temperature rise in the meshing zone using a non-Newtonian transient thermo-elastohydrodynamic model of gear line contact. The quantitative calculation module is used to calculate the lubrication requirements of each gear pair based on the oil film thickness distribution and the heat balance equation. Cooling requirements and total demand And identify the target gear pair; The macroscopic simulation module is used to build a three-dimensional geometric model of the planetary reducer, perform shape modification, and use the MPS method for thermo-fluid coupling simulation to calculate the grease supply flow rate of the target gear pair. The optimal liquid level and optimal grease filling volume are determined iteratively. ; The loss calculation module is used to calculate the overall viscous resistance loss power based on the optimal filling volume. .

[0013] Compared with the prior art, the present invention has the following beneficial effects: (1) The lubrication and cooling requirements of each gear pair are accurately calculated by the thermo-elastohydrodynamic model, avoiding the blindness of empirical estimation.

[0014] (2) The required flow rate (mL / s) is directly compared with the actual supply flow rate (mL / s) in the MPS simulation. Quantitative optimization is achieved by iterating the liquid level height so that the amount of grease filling can meet the lubrication and cooling requirements while minimizing oil churning loss.

[0015] (3) The meshless MPS method is adopted, which avoids the generation of complex meshes and can directly output the viscous resistance torque of each component, resulting in high calculation efficiency.

[0016] (4) The system combines microscopic elastohydrodynamic analysis with macroscopic flow field simulation to form a complete closed loop of "demand calculation → supply simulation → iterative optimization", which is highly practical for engineering applications. Attached Figure Description

[0017] To more clearly illustrate the technical solutions in the embodiments of the present invention, the accompanying drawings used in the description of the embodiments 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, wherein: Figure 1 The rotational rheological instrument provided by this invention; Figure 2 A modified diagram of the gear movement method provided by this invention; Figure 3 The diagram shows the change in oil film thickness when the first-stage sun gear and planet gear mesh, as provided by this invention.

[0018] Figure 4 The diagram showing the variation of viscous drag torque of the second-stage planetary carrier provided by this invention. Detailed Implementation

[0019] The present invention will be further described in detail below with reference to the embodiments and accompanying drawings, but the implementation of the present invention is not limited thereto.

[0020] Example: Analysis and Optimization of Grease-Lubricated Viscous Resistance Loss in a Two-Stage Planetary Gear Reducer This embodiment focuses on a two-stage planetary reducer with a rated output torque of 10 N·m, an input speed of 3300 rpm, a total transmission ratio of 30, and a lithium-based grease.

[0021] 1. Construct a constitutive model for non-Newtonian fluids; Using a rotational rheometer (e.g.) Figure 1 (As shown) Rheological experiments were conducted on lithium-based grease at 25℃ to obtain shear stress-shear strain rate curves. The Herschel-Bulkley model was used for fitting. ; In the formula, Shear force, To yield shear force, Plastic viscosity, Shear strain rate Let be the rheological index. The fitted result is: , This constitutive model can accurately reflect the shear-thinning effect of grease.

[0022] 2. Non-Newtonian transient thermo-elasto-fluidic analysis of gear line contact; Based on the above constitutive model, taking the first-stage sun gear-planet gear meshing area as an example, the load per unit length is set. =1×10 5 N / m, entrainment speed =1.2 m / s, radius of curvature at the meshing point =12 mm, initial oil film temperature =40℃. Solve the following system of equations simultaneously (derivation details omitted): Reynolds equations (modified for non-Newtonian fluids) Film thickness equation: ; Energy equation: ; Viscosity-pressure-temperature equation: ; The pressure-temperature equation: ; Load balance equations: ; In the formula The rheological index; The density of the grease; room temperature Grease density at =0; Oil film thickness; This refers to the thickness of the oil film at the center of the grease. Oil film pressure; The viscosity of the grease; The viscosity of the grease at normal temperature and pressure; The equivalent radius of curvature at the contact point; The coordinates are in the same direction as the velocity; This refers to the suction speed; for Additional coordinates for the axes; Here is the line load distribution function; The combined elastic modulus of the two contact surfaces; The pressure viscosity coefficient; Thermal conductivity of the lubricant; The coordinates are along the film thickness direction; The specific heat capacity of the grease; This refers to the temperature of the lubricating film. Ambient temperature; These are empirical constants; The linear load per unit length.

[0023] The oil film thickness distribution in the meshing zone of each gear pair was obtained by solving the problem. And temperature field distribution. Taking the meshing region of the first-stage sun gear-planet gear as an example, the oil film thickness is solved as follows: Figure 3 As shown, the grease film thickness is relatively flat in the middle of the contact area, but a "neck" phenomenon occurs near the outlet area due to the sudden drop in pressure and elastic recovery.

[0024] 3. Calculate the required amount of grease for each gear pair; (a) Lubrication requirement Q1: using the formula The integral is performed along the actual meshing line length l. For each gear pair in this embodiment, the calculation yields: (b) Cooling requirement Q2: using the formula Among them, the power loss due to meshing friction in the gear pair The grease density is obtained by multiplying the frictional torque output from the thermo-elastohydrodynamic model by the rotational speed. =0.89 g / cm³, specific heat =2.1 J / (g·℃), temperature rise Calculations were performed using a thermo-elastic-fluid model. The calculated values ​​for each gear pair were... The values ​​were 0.24, 0.07, 0.10, and 0.03 mL / s, respectively.

[0025] (c) Total demand The values ​​are 1.04, 0.24, 0.38, and 0.09 mL / s, respectively. The maximum total demand is for the first-stage sun gear-planet gear pair (1.04 mL / s), which is taken as the target gear pair.

[0026] 4. MPS simulation determines the optimal liquid level height and filling volume; Establish a three-dimensional geometric model of the planetary reducer (housing, sun gear, planet gears, internal gear ring, planet carrier, bearings, etc.). Use the moving method for shape modification (e.g., ...). Figure 2 (As shown): Keeping the gear mounting position unchanged, perform equidistant movement and shaping on the tooth profile, and set the particle diameter. =0.8 mm, minimum meshing gap ensures at least 3 particles.

[0027] The initial liquid level is set to -20 mm according to the formula (the negative sign indicates that it is below the center of the gear). The liquid level reference is the center line of gear rotation.

[0028] The MPS method was used for thermal-fluid coupling simulation, with a particle diameter of 0.8 mm, a total number of 1.2 million particles, and a time step of 1×10⁻⁻⁻⁶. 5 The simulation duration was 1.2 s. The grease supply flow rate in the meshing zone of the target gear pair was calculated using particle flux. .Compare and (1.04 mL / s): at the initial liquid level =1.8 mL / s > 1.04 mL / s, indicating the liquid level is too high and should be appropriately lowered. This can be achieved through multiple iterations (lowering the liquid level → resimulating → calculating). When the liquid level is high When the diameter is 32.5 mm (based on the bottom of the shell), The flow rate is approximately 1.10 mL / s, which basically matches the demand. The reducer housing radius is 70 mm, the axial length of the housing is 70 mm, and the housing structure coefficient is... =0.75 (considering the volume of internal parts), set the optimal liquid level height (based on the bottom of the shell). =32.5 mm, at this point the optimal filling volume for the reducer is: =142mL; 5. Calculate the viscous resistance loss power of the entire machine; MPS simulation was used to determine the optimal filling volume. =142 mL was used for lubrication to obtain the viscous resistance torque of each rotating component (sun gear, planet gears, planet carrier, etc.). and according to the formula Calculations are performed. The drag torque of the second-stage planetary carrier changes with time as follows: Figure 4 As shown, the average torque after stabilization is approximately 0.0035 N·m. The total viscous resistance loss power of the entire machine was finally calculated. With approximately 5 W, a good balance between transmission efficiency and lubrication reliability is achieved.

[0029] The above embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit it. Those skilled in the art can make several adjustments based on the concept of the present invention, all of which fall within the protection scope of the present invention.

Claims

1. A method for analyzing and optimizing the viscous resistance loss of grease lubrication in planetary reducers, characterized in that, Includes the following steps: S1: The rheological properties of the selected grease are measured by a rotational rheometer, and the rheological index, plastic viscosity and yield stress of the grease are fitted as a function of temperature to construct a non-Newtonian fluid constitutive model. S2: Based on the non-Newtonian fluid constitutive model obtained in step S1, the non-Newtonian transient thermo-elasto-hydrodynamic model of gear line contact is adopted to solve the Reynolds equation, film thickness equation, energy equation, viscosity-pressure-temperature equation, density-pressure-temperature equation and load balance equation simultaneously to obtain the oil film thickness distribution and grease temperature rise in the meshing area of ​​each gear pair. S3: Based on the oil film thickness distribution and grease temperature rise obtained in step S2, calculate the required lubrication amount for each gear pair using the following formula. and the amount of cooling required And calculate the total amount of grease required. Identify the gear pair with the largest total demand as the target gear pair: In the formula These are the position coordinates along the line of engagement. Let be the oil film thickness distribution function. For tooth width, For rotational speed, Number of teeth This is the actual length of the line of engagement; (b) In the formula This refers to the power loss due to meshing friction in the gear pair. For the density of the grease, For the specific heat of lubricating grease, For the temperature rise of the lubricating grease; S4: Establish a three-dimensional geometric model of the planetary reducer, modify the gear pair, set the initial grease level, and use the moving particle semi-implicit MPS method for thermal-fluid coupling simulation to calculate the grease supply flow rate in the meshing region of the target gear pair. ;like If so, lower the liquid level; If so, the liquid level will rise; Through multiple simulation iterations, it was determined that... and The optimal liquid level height is determined by minimizing the absolute value of the difference between the two values, and the optimal grease filling volume is calculated accordingly. ; S5: Optimal grease filling volume obtained from step S4 The MPS method was used to simulate and calculate the viscous resistance loss power of the entire machine. ,in This represents the summation over all rotating parts. This refers to the serial number of the rotating component. For the first The rotational speed of each rotating component For the first Viscous resistance torque of a rotating component.

2. The method according to claim 1, characterized in that, In step S1, the non-Newtonian fluid constitutive model is selected from the Ostwald model, Bingham model, or Herschel-Bulkley model. Different shear rates are set to obtain the shear stress-shear strain rate curves of the lubricating grease, and the rheological index in each model is fitted. Plastic viscosity and yield stress τ Functional relationship.

3. The method according to claim 1, characterized in that, In step S4, the shaping process is a moving method shaping, specifically including: keeping the gear mounting position unchanged, using an equidistant moving method to shape the tooth profile to increase the meshing area clearance; based on the particle diameter in the MPS simulation... Determine the minimum gap size to ensure that at least 3 particles exist within the gap.

4. The method according to claim 1, characterized in that, In step S4, the initial grease level height is set. The reference is the rotation centerline of the gear set; the grease supply flow rate in the meshing area of ​​the target gear pair Calculation of particle flux in the meshing zone using MPS simulation: In the formula This is the particle volume correction factor. This represents the number of particles passing through the meshing zone per unit time. Where is the particle radius, is the meshing frequency.

5. The method according to claim 1, characterized in that, In step S4, the optimal grease filling volume Calculate as follows: ； in Where is the radius of the reducer housing. To achieve the optimal liquid level height, The optimal liquid level height is based on the bottom of the shell. To account for the volume occupied by solids such as planetary carriers and gears, the structural coefficient is taken in the range of 0.6 to 0.

9.

6. The method according to claim 1, characterized in that, The total viscous resistance loss power mentioned in step S5 According to the formula Calculation, where The output is directly obtained from the MPS simulation in step S4.

7. The method according to claim 1, characterized in that, The planetary reducer is a two-stage planetary transmission reducer with a rated output torque range of 10 to 100 N·m, an input speed range of 100 to 4000 rpm, and a total transmission ratio range of 10 to 60.

8. A system for analyzing and optimizing the viscous resistance loss of a planetary reducer lubricated by grease, used to perform the method according to any one of claims 1-7, characterized in that, include: The constitutive model construction module is used to measure the rheological properties of grease at different temperature points using a rotational rheometer, and then fit the constitutive model of the non-Newtonian fluid. The microscopic analysis module is used to solve the oil film thickness distribution and grease temperature rise in the meshing zone using a non-Newtonian transient thermo-elastohydrodynamic model of gear line contact. The quantitative calculation module is used to calculate the lubrication requirements of each gear pair based on the oil film thickness distribution and the heat balance equation. Cooling requirements and total demand And identify the target gear pair; The macroscopic simulation module is used to build a three-dimensional geometric model of the planetary reducer, perform shape modification, and use the MPS method for thermo-fluid coupling simulation to calculate the grease supply flow rate of the target gear pair. The optimal liquid level and optimal grease filling volume are determined iteratively. ; The loss calculation module is used to calculate the overall viscous resistance loss power based on the optimal filling volume. .

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