Parametric Optimization Design Method for Friction Plates of Hydro-Viscous Clutches

Summary

This study combines numerical analysis software with response surface methodology (RSM) to systematically explore the optimization design method for friction plates of hydro-viscous clutches.

Abstract

The hydro-viscous clutch (HVC) operates based on the theory of liquid viscous transmission, using viscous fluid as the working medium to transmit power through the shearing force of the oil film between friction plates. The groove structure on the friction plates directly affects the torque transmission capacity and rise in the shear-induced temperature of the oil film. Therefore, designing friction plate structures that balance efficient torque transmission and low temperature rise is of great significance. To address this issue, this study analyzes the impact of the groove structure on the oil film characteristics and identifies the key influencing factors. Subsequently, simulation software was used to calculate the torque and temperature rise of the oil film under different groove structures. The structural parameters of the friction plates were then optimized using the Box-Behnken design of the response surface methodology (RSM). The results show that the optimized friction plate design, featuring a groove depth of 0.214 mm, an arc length of 5 mm, 16 radial arc-shaped grooves, and 5 circumferential grooves, can significantly reduce the oil film temperature while ensuring high torque transmission. This design approach provides a reference for the optimized design of friction pairs in hydro-viscous clutches of various sizes.

Introduction

With the rapid development of social productivity, an increasing number of large heavy-load machines are being utilized in construction and manufacturing processes. These machines require high-power dynamic speed regulation while also considering low energy consumption.

In recent years, a new type of speed control device has been proposed and used in heavy machinery, specifically the Hydro-Viscous Clutch. This device integrates mechanical, electronic control, and hydraulic technologies, incorporating both fluid shear transmission and mechanical friction transmission. Its energy-efficient characteristics have led to increasingly widespread applications^1,2,3.

The working principle of the Hydro-Viscous Clutch is based on Newton's internal friction law, utilizing the torque generated by shearing the oil film to achieve power transmission and smooth speed regulation. Therefore, the Hydro-Viscous Clutch can accomplish stable power transmission and control^4,5. The key factors affecting the oil film are the surface structure of the friction plate. The surface of the Hydro-Viscous Clutch friction plates is not smooth but contains grooves of various forms. The presence of these grooves ensures the formation of a dynamic pressure oil film and good heat dissipation performance; however, the oil film formed by grooved friction plates affects the theoretical viscous shear torque. Additionally, the groove structure not only affects the uniformity of the formed oil film but also relates to the temperature generated by the oil film shear, subsequently impacting the cooling effect of the friction plate. Excessive temperature can cause warping and deformation of the friction plates, leading to permanent failure⁶. Therefore, the structural design of the Hydro-Viscous Clutch primarily focuses on the design of the friction plates, with the key challenge being to optimize the following parameters: transmitted torque, oil film load capacity, oil film uniformity, oil film temperature, friction plate temperature, and friction plate strength^7,8.

The design of the oil groove structure for Hydro-Viscous Clutch friction plates mainly includes various arrangements, such as circumferential grooves, radial grooves, and arc-shaped grooves^9,10,11. Previous research indicates that, in addition to differences in arrangement forms, the cross-sectional designs of the oil grooves also vary, including rectangular, trapezoidal, and arc-shaped grooves. The structural differences of the oil grooves have various impacts on the oil film characteristics^{12,13,14,15,16}. Under specific conditions, the oil film formed by different groove structures can have varying impacts on the performance of the clutch. The dimensions of clutches used in different mechanical devices are not unique; thus, the performance of friction plates with the same structure can significantly differ when used in clutches of different sizes and operating conditions. Therefore, the design of Hydro-Viscous Clutch friction plates for various machinery and different operational conditions requires a cost- and time-efficient design and evaluation scheme.

The design approach for Hydro-Viscous Clutch friction plates encompasses various aspects, including theoretical analysis, experimental research, and numerical simulations, focusing on how the pressure fields, temperature fields, and velocity fields of the oil film affect performance^{8,17,18,19,20,21}. Additionally, numerous scholars have based their research on the micro-texture of the friction plate surface and the materials used in the friction plates to improve the performance of the Hydro-Viscous Clutch^22,23. Many scholars have studied the relationship between the cavitation characteristics of the rotating flow field in hydro-viscous clutches and the cross-sectional shape of the oil reservoir. They have analyzed the initiation positions of oil film shear cavitation under different groove structural parameters, providing a theoretical basis and technical support for predicting the onset of oil film shear cavitation^24,25. Among these methods, numerical simulation has become a key research tool, and with the development of simulation software, research has progressively become more refined. The Fluent module is primarily utilized to simulate and analyze the impact of different oil groove structures on flow field performance, with a specific goal of optimizing oil film properties through changes in groove structures^26,27,28. However, the simulation analyses and experimental results obtained for specific requirements have consistently met expectations but have not been validated for their applicability to friction plate design in Hydro-Viscous Clutches of different sizes.

Combining existing research methods, this study leverages Fluent simulation software and RSM response surface methodology (RSM) parameter optimization to propose a design scheme suitable for oil groove structures in friction plates of various sizes. This involves analyzing the characteristics of the oil film under different groove parameters using Fluent, discussing the key factors that significantly influence these characteristics, calculating the torque and temperature changes of the oil film formed by different groove parameters, and statistically optimizing the friction plate structural parameters using the Box-Behnken method.

This study demonstrates the optimization analysis of friction plates with a composite groove structure, which includes rectangular cross-section circumferential grooves combined with radial grooves of arc-shaped cross-section. The goal is to design friction plates that can simultaneously achieve high torque transmission and low oil film temperature. Future designs for different sizes of friction plates will only require changes to the initial dimensions of the model while maintaining the same research plan and procedures.

Protocol

NOTE: The technical route of the design scheme is shown in Figure 1, which mainly includes model establishment, simulation analysis, and parameter optimization. Model establishment includes two main categories: models required for single-factor analysis and models derived from the experimental design given by the response surface methodology (RSM) after determining the influencing factors. The model establishment is completed in SolidWorks, the simulation analysis is performed in Fluent, and the parameter optimization is conducted in Design-Expert.

1. Model establishment

1. Determine the basic dimensions of the friction pad, and set the inner radius of the friction pad to 110 mm, the outer radius to 160 mm, and the oil film thickness to 0.3 mm.
2. Establish a basic model by creating a circular sketch with an inner diameter of 110 mm and an outer diameter of 160 mm on the XY plane, and then extrude the circle to 0.3 mm. Create a basic model by ensuring the resulting annular shape forms an oil film model without oil grooves.
3. On one side surface of the annular model, create sketch 2 and draw 5 circular faces with a uniform distribution and a width of 3 mm, then extrude them to 0.3 mm. Form the oil film with a rectangular cross-section created by the circumferential oil groove.
4. Create sketch 3 on the YZ plane, drawing a semicircular arc with an arc length of 3 mm, which is tangent to the oil film formed by the circumferential oil groove, then extrude it radially to the outer surface of the oil film and array the solid along the circumference of the inner loop to form 14 components.
5. Create sketch 4 on the XY plane, drawing a circle with a radius of 110 mm, then cut away the excess model using the sketch, completing the establishment of 14 radial semicircular oil groove oil films.
6. Save the established model as the geometric model of the oil film formed by the original oil groove parameters.
7. Modify sketch 2 to draw 3-7 uniformly distributed circumferential oil grooves, each with a width of 3 mm, and generate five oil film models that differ only in the circumferential oil grooves. Save these models in STEP format.
8. Modify sketch 3 to adjust the arc length of the semicircular arc to 3-6 mm, increasing the arc length by 0.5 mm each time, and generate seven oil film models that differ only in the radial semicircular structure. Save these models in STEP format.
9. Modify sketch 2 by adjusting the extrusion thickness to 0.1-0.4 mm, increasing the thickness by 0.05 mm each time, and generate seven oil film models that differ only in the depth of the oil grooves. Save these models in STEP format.
10. Adjust the circumferential array quantity in sketch 3 to modify the number of radial oil grooves to 10-16, and generate seven oil film models that differ only in the number of radial grooves. Save these models in STEP format.

2. Simulation analysis

NOTE: The simulation analysis includes model pre-processing, mesh partitioning, and simulation calculations. All steps are completed in ANSYS Workbench.

1. Model pre-processing
   1. Open the Workbench workstation and drag the geometry from Toolbox > Component Systems > Geometry into the project schematic area.
   2. Right-click on the Geometry, select Import Geometry Model to import the completed model, and then click to edit the geometry model in Space Claim.
   3. In the Space Claim toolbar, click on Repair, then select Additional Edges and Split Edges to complete the repair, merging the affected split lines.
   4. Sequentially click on Toolbar > Design > Selection in Selection, then select the inner surface of the model and click Create NS in the group, naming it Inlet.
   5. Using the same process, click on the outer surface and name its Outlet; click on the smooth lower wall surface and name its B as the wall surface where the oil film contacts the passive friction pad; select all unnamed surfaces and name them Z as the rotating wall surface where the oil film contacts the active friction pad.
   6. Exit Space Claim and save the file to complete the pre-processing of the model.
      NOTE: All pre-processing of the geometric model before the simulation is completed according to the steps above. The only difference is that the active wall model is inconsistent, but it does not affect any operations.
2. Mesh partitioning
   1. In the Workbench workstation, drag Fluent from Toolbox > Component Systems > Fluent into the project schematic area where the geometry has been added.
   2. Click on Geometry and drag the mouse to the mesh in the Fluent project to link its Mesh Module to the Upstream Data of the geometry.
   3. Double-click to open the mesh and select Watertight Geometry for mesh partitioning. Follow the workflow step-by-step to import the geometry model and add Local Sizing.
   4. Click Generate Surface Mesh, set the Minimum Size to 0.3 mm, the maximum size to 8 mm, and the Curvature Norm Angle to 10. After setting these parameters, click Generate the Surface Mesh.
   5. Check the surface mesh quality by right-clicking on the generated surface mesh and selecting Insert Improved Surface Mesh Quality. Set the Minimum Mesh Quality to 0.7 and click OK to complete the improvement of the surface mesh.
   6. Click Describe Geometry Model, selecting the geometry model as consisting solely of a fluid region with no gaps, keeping other options at their default settings.
   7. Sequentially click Describe Geometry Structure and Update Region Type Settings, maintaining the default settings and completing the process.
   8. Click Add Boundary Layer, selecting 3 for the number of layers, while keeping other settings at their defaults.
   9. Click Generate Volume Mesh and insert an Improved Volume Mesh Quality to ensure its quality exceeds 0.12.
      NOTE: The completed mesh partitioning is shown in Supplementary Figure 1.
   10. After generating the mesh, click Switch to the Solver Mode. Wait for the mesh partitioning and import to the analysis module to complete.
       NOTE: The quantity and quality of mesh elements are critical to the accuracy of the computational results. Watertight geometry is used to control the number and quality of the mesh by changing the cell size. As shown in Figure 2, reducing the specified minimum mesh element size from 0.8 mm to 0.1 mm increases the number of elements from 534,595 to 2,649,371. As the number of elements changes, the average temperature of the oil film and the transmitted torque result remain stable, indicating that further increases in mesh quality have minimal impact on the results. Therefore, a minimum element size of 0.3 mm is chosen for meshing.
3. Simulation solving
   1. Switch from Mesh Partitioning to Solver Mode. Once the mesh has finished loading, click on Check Case in the General menu to validate the effectiveness of the finite element model and check whether the mesh has any negative volume.
   2. Open the Energy Equation in the model settings. Enter the viscous model settings interface, select the Laminar Model, and enable the Viscous Heating option.
      ​NOTE: The choice of viscous model is determined by the flow state of the oil film flow field, typically assessed using the Reynolds number. When the Reynolds number is low, the fluid particles are unaffected, resulting in laminar flow. Conversely, a high Reynolds number indicates that disturbances among the fluids are amplified, transforming laminar flow into turbulent flow. Based on the flow theory around the rotating disk, the Reynolds number associated with the tangential velocity at the outer radius is calculated using the formula Re = R²ω/v. Where Re is the Reynolds number, R is the outer diameter of the friction discs, ω is the rotational speed of the friction plate, and v is the kinematic viscosity. When Re < 1 × 10⁵, the flow is laminar; when 2 × 10⁵ < Re < 3 × 10⁵, the flow is turbulent. For the fluid studied in this paper, with v = 30 mm²/s and R = 160 mm, the following can be derived. When the rotating speed of the friction plate is ω = 1000 rpm, the Reynolds number of the oil film flow field Re < 1 × 10⁵, indicating that the oil film is in a laminar flow state.
   3. Modify the material parameters in the settings according to the properties of the two materials listed in Table 1. Modify the liquid material parameters named "Air" in the system, and for the solid material, modify the parameters named "Aluminum."
      NOTE: The liquid will be selected as hydraulic oil #8 for the oil film material, and the solid will use copper-based material for the friction pad material.
   4. Click the Boundary Conditions, select the active friction pad wall surface named "Z," click on Momentum Settings, and set it as a rotating wall surface that rotates 100 rad/s around the Y-axis, with a shear condition of No Slip.
   5. Click the Boundary Conditions, select the passive friction pad wall surface named "B," click on Momentum Settings, and set it as a stationary wall surface with a shear condition of No Slip.
   6. Set the energy transfer-related boundary conditions through System Coupling.
   7. Set the inlet and outlet boundary conditions by clicking on the Outlet and setting it to Pressure Outlet, with the Gauge Pressure set to 0, which corresponds to standard atmospheric pressure.
   8. Set the inlet boundary conditions by clicking on the inlet, setting it as a Velocity Inlet with a flow velocity of 1 m/s and an inlet temperature of 30 °C.
   9. Click on the Solution settings, selecting the SIMPLE algorithm for the solution method model. Choose the First-Order Upwind format for the Momentum and Energy, and keep the residual values at their default settings.
   10. After completing the above steps, set the state of the computational domain at the initial moment, for example, with an initial temperature of 26 °C, pressure of 0 Pa, and velocities in the XYZ directions set to 0.
   11. Set the Number of Iterations to 300 steps, click the Calculate button to start the calculation, and wait for the results.
   12. Once the iterative calculations are complete, click Results > Reports > Fluxes. Select the Mass Flow Rate in Fluxes, check the mass flow rates for Inlet and Outlet, ensuring that the error between the two is less than 0.1% to validate the accuracy of the computational results.
   13. Complete the above steps and then analyze the results of the simulation. Click Results > Reports > Forces, select the torque around the Y-axis for the wall surface B, and interpret the resulting viscous value as the shear torque transmitted by the oil film.
   14. Exit the fluid flow calculation module, and in the Workbench workstation, drag Results from Toolbox > Component Systems > Results into the project schematic area that has completed the fluid flow simulation calculations. Click on the solution in the fluid flow module and drag the mouse to the results.
   15. Enter the results, click on Calculators, and select Function Calculator to solve for the Average Temperature of the entire oil film. Click on Calculate to obtain the overall average temperature of the oil film.

3. Parameter optimization

NOTE: The parameter optimization is completed using the response surface methodology for modeling and analysis. The response surface methodology requires selecting three factors that significantly influence the oil film's transferred torque and temperature, specifying their high- and low-level values. Modeling and analysis are then performed for the new combinations generated from the selected influencing factors and variables, followed by optimization calculations using the obtained data.

1. In Design-Expert software, click on NEW DESIGN to create a new design.
2. In the new design, select BOX-Behnken from Response Surface to establish a three-factor, two-level optimization model.
3. Click on Numeric Factors to select three factors: the number of radial oil grooves in the friction pad, the depth of the grooves, and the arc length of the oil grooves, and fill in the corresponding table.
4. Enter the High- and Low-level values obtained from the analysis of the three influencing factors into the corresponding table.
5. Set the Center points per block to five, then click on the next step to change the Response Variables to 2, which are the torque transmitted by the oil film and the average temperature of the oil film. Click Finish to generate 17 sets of random sample points.
6. Establish the model data by recombining the three influencing factors from the 17 sets of random sample points, and repeat section 1 to complete the model establishment.
7. Repeat section 2 for simulation analysis to obtain the transmitted torque and average temperature of the oil film after recombination. Merge the predicted variables A, B, and C of the three influence combinations with the simulated results of the transmitted torque and the average temperature to form a new variable table.
8. Next, select Quadratic for the Process Order in the model, and choose Polynomial for the Model Type, keeping other settings at default.
9. After completing the establishment of the response surface model, calculate both torque and average temperature.
10. After the analysis is complete, conduct an error analysis of the model. Click on Analysis of Variance (ANOVA) and analyze the values of R² and Adeq Precision in Fit Statistics to verify whether the model meets the standards.
11. Click on Optimization > Numerical > Criteria, keeping the ranges for the three influencing factors unchanged. Click on Solutions to find the maximum torque and the minimum average temperature for the approximate values.
12. Calculate the different results for the arrays, with the combination labeled 1 being the optimal solution for the model.

Results

The modeling and simulation analysis steps in the scheme aim to determine which parameters of the friction plate grooves significantly impact oil film temperature and transmitted torque. Through parameter optimization of sampled data, the combinations of parameters affecting oil film performance are adjusted, followed by repeated modeling and simulations to generate data, ultimately obtaining the optimal parameters for the friction plate grooves through response surface optimization.

Discussion

This study proposes an optimization design method for the oil groove structure of the Hydro-Viscous Clutch friction plates. Specifically, it aims to improve oil film performance by altering parameters such as the number, arrangement, and geometric dimensions of the grooves¹⁰. A combination of numerical simulations using Fluent software and Response Surface Methodology (RSM) is employed to analyze and optimize parameters such as the number of radial grooves, groove depth, and the arc length of the ...

Materials

List of materials used in this article

Name	Company	Catalog Number	Comments
Aldary	N/A	N/A	Alloy material
Ansys-Workbench	ANSYS	ANSYS 2023R1	Multi-purpose finite element method computer design program software.
Design-Expert	Stat-Ease	Design-Expert 13	An experimental data analysis tool
No.8 hydraulic oil	N/A	N/A	Liquid
PC	N/A	N/A	Computer equipment
SOLIDWORKS	Dassault Systemes	solidworks 2023	An engineering software drawing tool
Steel	N/A	N/A	Alloy material