1. Introduction
In modern mechanical engineering, gear transmission systems are widely used in various fields such as automotive, aerospace, and industrial machinery. Cylindrical gears, as a key component of gear transmission, their transmission accuracy directly affects the performance, reliability, and efficiency of the entire mechanical system. However, in actual operation, factors like elastic deformation and manufacturing errors of gears can lead to transmission errors, which not only reduce the transmission accuracy but also cause vibrations and noises, affecting the normal operation of the equipment.
Previous research on gear transmission errors mainly focused on either the finite – element method or the analytical method. The finite – element method can achieve high – precision solutions, but it is time – consuming due to complex modeling and dense mesh generation. The analytical method, on the other hand, can improve the solution efficiency but has limitations in considering the structural elasticity of gears. To address these issues, this paper presents a semi – analytical contact model considering elastic errors, aiming to provide a more accurate and efficient way to analyze and optimize the transmission precision of cylindrical gears.
2. Literature Review
2.1 Existing Modeling Methods for Gear Transmission Errors
Table 1: Comparison of Common Modeling Methods for Gear Transmission Errors
| Modeling Method | Advantages | Disadvantages |
|---|---|---|
| Finite – Element Method | High – precision solutions, can accurately simulate complex geometric shapes and boundary conditions | Complex modeling process, time – consuming due to dense mesh generation, high computational cost |
| Analytical Method | Simple calculation, can quickly obtain results, suitable for preliminary design and analysis | Limited consideration of gear structure elasticity, low – precision solutions, unable to accurately simulate complex contact conditions |
| Semi – Analytical Method | Combines the advantages of the above two methods, improves solution efficiency while ensuring accuracy | Requires a certain amount of theoretical basis and computational skills, and the establishment of the model is relatively complex |
Scholars at home and abroad have conducted extensive research on gear transmission error modeling methods. For example, Korta et al. [1] used the finite – element method to explore the influence of materials with different qualities on the static transmission error curve of gears. However, this method has the disadvantages of complex modeling and long calculation time. Dong et al. [13] proposed a semi – analytical method to establish a gear transmission model, which effectively improved the solution efficiency. But most of these studies did not consider elastic errors comprehensively.
2.2 Research on Influencing Factors of Transmission Errors
| Influencing Factor | Research Content | Researcher |
|---|---|---|
| Material Quality | Influence of different material qualities on static transmission error curves | Korta et al. [1] |
| Gear Eccentricity | Influence of different degrees of gear eccentricity on transmission errors | 邹帅东等 [7] |
| Elastic Error | Little research considering elastic error comprehensively | – |
In the analysis of influencing factors of transmission errors, although some scholars have studied the influence of factors such as material quality and gear eccentricity on transmission errors, the research on elastic errors is still relatively scarce. Elastic errors can have a significant impact on the transmission accuracy of gears, so it is necessary to conduct in – depth research on this aspect.
3. Establishment of the Tooth Surface Error Model of Involute Cylindrical Gears
3.1 Tooth Surface Equation of Involute Cylindrical Gears
The tooth surface of an involute cylindrical gear is formed by a curve stretching and transforming along the helical direction in space. The involute helical surface equation can be expressed as: \(\left\{\begin{array}{l} x=r_{b}\sin(u_{k}+\theta)+r_{b}u_{k}\cos(u_{k}+\theta) \\ y=r_{b}\cos(u_{k}+\theta)-r_{b}u_{k}\sin(u_{k}+\theta) \\ z = p\theta \end{array}\right.\) where \(r_{b}\) is the base – circle radius of the gear, \(\theta\) is the rotation angle of the generatrix around the axis, p is the helical – line parameter, and \(u_{b}\) is the involute generating angle.
Let the tangent point of the straight generatrix of the involute cylindrical gear and the cylinder on the x – axis be s, and there is a moving point k on this straight generatrix. Let the distance from point k to point s be l, and the angle between the straight generatrix and the end – section be \(\alpha\). Then the parameter equation of the straight generatrix is: \(\left\{\begin{array}{l} x=r_{b} \\ y = l\cos\alpha \\ z = l\sin\alpha \end{array}\right.\) Substituting the straight – generatrix equation into the above formula, the tooth – surface parameter equation of the involute cylindrical gear can be obtained: \(\left\{\begin{array}{l} x=r_{b}\cos\theta – l\cos\alpha\sin\theta \\ y=r_{b}\sin\theta + l\cos\alpha\cos\theta \\ z = l\sin\alpha + p\theta \end{array}\right.\)
3.2 Error Tooth Surface Equation
The tooth – profile error value of an involute cylindrical gear can be determined by looking up the table [15]. The involute – gear tooth – profile curve is discretized into points, and the distance \(r_{0}\) from each point on the tooth – profile to the gear center is calculated. Taking the distance r from each point on the tooth – profile to the gear center as the abscissa and the tooth – profile error as the ordinate, a tooth – profile curve considering the tooth – profile error is constructed, as shown in Figure 1. [Insert Figure 1: Tooth Profile Curve Considering Gear Error]
The expression of the tooth – profile error is: \(\Delta f=f\sin((r – r_{0})w)\) where \(\Delta f\) is the tooth – profile error of point K on the tooth – profile, f is the maximum value of the tooth – profile error, \(r_{0}\) is the distance from the first discrete point on the tooth – profile curve to the gear center, \(r_{e}\) is the distance from the end – point of the tooth – profile curve to the gear center, and \((x_{k},y_{k})\) is the coordinate of any discrete point K on the tooth – profile.
As shown in Figure 1, taking the tooth – profile error of the corresponding point as the offset distance, the discrete points of the tooth – profile curve are offset along the normal direction to obtain new discrete points \(K'(x_{k}’,y_{k}’)\) of the tooth – profile. Distributing these new discrete points along the helical – line direction can obtain the error tooth surface. The coordinates of the discrete points \(K'(x_{k}’,y_{k}’)\) of the tooth – profile after adding the error can be expressed as: \(\left\{\begin{array}{l} x_{k}’=x_{k}+\Delta f\cos\phi_{k} \\ y_{k}’=y_{k}+\Delta f\sin\phi_{k} \end{array}\right.\) where \(\phi_{k}\) is the angle between the normal direction of the discrete point K on the tooth – profile and the x – axis.
4. Semi – Analytical Contact Model of Involute Cylindrical Gears Considering Elastic Errors
4.1 Derivation of Gear Deformation Coordination Equation
During the rotation of the gear, the contact can be equivalent to the contact of elastic bodies. The deformation coordination equation of each point on the contact line can be expressed as: \(Q_{i}=\varepsilon_{i}+\sigma_{i}-U_{i}\) where \(Q_{i}\) is the final clearance between the contact point i and the corresponding point, \(\varepsilon_{i}\) is the initial contact clearance caused by errors, including tooth – profile errors and modification amounts, \(U_{i}\) is the displacement generated by the six – degree – of – freedom rigid – body motion of the contact point i, and \(\sigma_{i}\) is the elastic – deformation amount at the contact point i.
Under the action of load, the elastic deformation at the gear contact point includes overall deformation and local contact deformation. The overall deformation refers to the bending – shear deformation. The elastic deformation of the involute cylindrical gear can be expressed as: \(\sigma_{i}=\sigma_{h i}+\sigma_{b1}+\sigma_{b2}\) where \(\sigma_{h i}\) is the contact deformation at the contact point i, and \(\sigma_{b1}\), \(\sigma_{b2}\) are the bending – shear deformations of the driving and driven wheels, respectively.
The contact problem of an involute cylindrical gear at a certain position can be regarded as the contact problem of two cylinders. During the contact process, the normal – curvature radii of the driving and driven wheels at the contact point are the radii of the cylinders. According to the statistical contact theory, the local deformation at the contact point under the action of force can be expressed as: \(u_{i}=\frac{2F_{i}}{\pi l_{i}E}(\ln\frac{2w_{i}}{B_{i}} + 0.148)\) where \(u_{i}\) is the local deformation at the contact point i (mm), \(F_{i}\) is the load at the contact point i (N), \(l_{i}\) is the distance of the contact line (mm), \(\mu_{1}\), \(\mu_{2}\) are the Poisson’s ratios of the driving and driven wheels, respectively, \(E_{1}\), \(E_{2}\) are the elastic moduli of the driving and driven wheels (Pa), \(w_{i}\) is the thickness of the gear corresponding to the contact point (mm), and \(B_{i}\) is the contact half – width (mm).
The complete flexibility matrix of the involute cylindrical gear includes the overall flexibility matrix and the local flexibility matrix. The complete flexibility matrix can be expressed as: \([\lambda_{w}]=[\lambda_{b1}]+[\lambda_{b2}]+[\lambda_{h}]\) where \(\lambda_{w}\) is the complete flexibility matrix, \(\lambda_{b1}\), \(\lambda_{b2}\) are the bending – shear flexibility matrices of the driving and driven wheels, respectively, and \(\lambda_{h}\) is the contact – point contact flexibility matrix.
The elastic – deformation amount of the involute cylindrical gear is: \([\sigma]=[\lambda_{w}][F]\) where \(\sigma\) is the gear elastic – deformation amount matrix, and F is the normal – force matrix at the contact point.
During the meshing process of the involute cylindrical gear, due to the influence of the six – degree – of – freedom motion of the gear, the points on the contact line generate rigid displacements along the normal direction. By constructing a projection matrix, the rigid displacement of the gear is projected onto the normal direction. The rigid displacement generated during the meshing process of the gear can be expressed as: \([U]=[G_{1}\ G_{2}]\left[\begin{array}{l}\Phi_{1} \\ \Phi_{2}\end{array}\right]\) where U is the projection of the gear rigid displacement in the normal direction, \(G_{1}\), \(G_{2}\) are the six – degree – of – freedom projection vectors of the driving and driven wheels, and \(\Phi_{1}\), \(\Phi_{2}\) are the rigid displacements of the driving and driven wheels.
4.2 Derivation of Gear Force – Balance Equation
To solve the contact force of the actual contact points of the involute cylindrical gear under the influence of elastic deformation, it is necessary to establish the force and moment balance equations of the driving and driven wheels.
When the driving wheel is subjected to a load, it needs to be balanced by the contact force between the driving and driven wheels and the bearing support force. Projecting the contact force between the driving and driven wheels onto the coordinate system of the corresponding gear, the force – balance equation of the driving wheel can be obtained: \([T_{1}]=[G_{1}^{T}][F_{12}]+[K_{1}][\Phi_{1}]\) where \([T_{1}]\) is the external – load matrix of the driving wheel, \([F_{12}]\) is the contact force of the driven wheel on the driving wheel, and \([K_{1}]\) is the support – stiffness matrix of the driving wheel.
Similarly, the force – balance equation of the driven wheel can be obtained: \([T_{2}]=[G_{2}^{T}][F_{21}]+[K_{2}][\Phi_{2}]\) where \([T_{2}]\) is the external – load matrix of the driven wheel, \([F_{21}]\) is the contact force of the driving wheel on the driven wheel, and \([K_{2}]\) is the support – stiffness matrix of the driven wheel.
Integrating the force – balance equations of the driving and driven wheels, the overall force – balance equation can be obtained: \(\left[\begin{array}{l}T_{1} \\ T_{2}\end{array}\right]=\left[\begin{array}{cc}G_{1}^{T}&0 \\ 0&G_{2}^{T}\end{array}\right]\left[\begin{array}{l}F_{12} \\ F_{21}\end{array}\right]+\left[\begin{array}{cc}K_{1}&0 \\ 0&K_{2}\end{array}\right]\left[\begin{array}{l}\Phi_{1} \\ \Phi_{2}\end{array}\right]\)
4.3 Calculation of Gear Elastic Deformation
Since the parameters of the driving and driven gears are the same, only the complete and local finite – element models of the driving wheel need to be established in ANSYS software to obtain the bending – shear deformation coefficients of the driving and driven gears [19]. Taking a helical gear as an example, its overall finite – element model adopts a five – tooth model, as shown in Figure 2(a). Full constraints are applied to the center hole of the gear to obtain the complete flexibility matrix, and the elastic moduli of the gear body and the tooth body are the same. The local finite – element model of the helical gear is shown in Figure 2(b). Full constraints are applied to the non – contact tooth surface, and the elastic modulus of the tooth body is 1000 times that of the tooth surface to ensure that the contact tooth surface only contains local contact deformation. The node coordinates and elements on the contact tooth surfaces of the driving and driven wheels are completely consistent.
The bending – shear flexibility matrix of the nodes on the contact tooth surfaces of the driving and driven wheels can be expressed as: \([\eta_{b}^{\beta}]=[\eta_{i}^{f}]-[\eta_{i}^{f}]\) where \(\eta_{b, fe}\) is the bending – shear flexibility matrix of the nodes, \(\eta_{1,6}\) is the bending – shear flexibility matrix of the overall finite – element model, and \(\eta_{L.60}\) is the bending – shear flexibility – matrix coefficient of the local finite – element model.
After constructing the overall and local finite – element models of the gear, the flexibility – coefficient matrix is extracted using the sub – structure method in ANSYS software . When using the sub – structure method, external and internal nodes are involved. Since the degrees of freedom of the internal nodes are not considered in this paper, the condensation method can be used to ignore the internal nodes. When assembling each sub – structure into a whole, only external nodes are included, and the equation dimension is much smaller than that of the original model.
The flexibility matrix is calculated using the shape – function interpolation operation method. For any grid node, after determining the position relationship between the tooth – surface contact point and the grid node, the flexibility coefficient of the contact point is obtained by interpolating the known flexibility coefficients. For the flexibility matrices of contact points on different tooth surfaces, they can be obtained through the position relationship between the tooth – surface contact points and the overall grid nodes, and finally, they are reassembled into a flexibility matrix according to the contact – point order [21].
4.4 Analysis of Gear Transmission Accuracy Considering Elastic Errors
Based on the above – established semi – analytical contact model of involute cylindrical gears, the influence of elastic errors on their transmission errors is analyzed [22], and an analysis process for gear transmission accuracy is constructed, as shown in Figure 3. [Insert Figure 3: Analysis Process of Involute Cylindrical Gear Transmission Accuracy]
The analysis steps of the transmission accuracy of cylindrical gears considering elastic errors are as follows:
- First, according to the basic parameters of the gear, a gear geometric model is established to calculate the position of the gear contact line. The contact line is discretized to obtain uniformly distributed discrete points and determine their position coordinates.
- Based on the coordinates of the obtained discrete contact points, considering the tooth – profile error, the amplitude of the tooth – profile error corresponding to each contact point is determined by the distance from the contact point to the gear center. The obtained tooth – profile error amplitude is substituted into the contact clearance, and the new contact – point coordinates are obtained by combining with the coordinates of the initial discrete contact points. Then, the overall deformation equation of the gear is derived.
- Assume that the initial load acts equally on all potential contact points to obtain the displacement, overall flexibility matrix, and local contact flexibility matrix at each contact point, and then integrate them to obtain the complete flexibility matrix of the gear.
- Determine whether the contact point participates in meshing according to the contact force of the contact point: \(F_{i}<0\ N\) indicates that the point on the contact line does not participate in meshing, and \(F_{i}>0\ N\) indicates that the point on the contact line participates in meshing. All contact points are obtained through iteration, and the flexibility matrix is updated.
5. Analysis of Involute Cylindrical Gear Transmission Accuracy Based on the Semi – Analytical Model
5.1 Verification of the Semi – Analytical Model
To verify the accuracy of the semi – analytical contact model of cylindrical gears constructed above, an example analysis is carried out according to the parameters of the helical gear shown in Table 3. The calculation results of the transmission errors based on the semi – analytical model and finite – element simulation are compared. Table 3: Basic Parameters of the Helical Gear
| Parameters | Driving Wheel | Driven Wheel |
|---|---|---|
| Number of Teeth z | 36 | 36 |
| Module \(m/mm\) | 3 | 3 |
| Pressure Angle \(\alpha/(^{\circ})\) | 20 | 20 |
| Tooth Width \(B/mm\) | 30 | 30 |
| Helical Angle \(\beta/(^{\circ})\) | 15 | 15 |
| Profile Shift Coefficient x | 0 | 0 |
| Clearance Coefficient \(c^{*}\) | 0.25 | 0.25 |
| Elastic Modulus \(E/GPa\) | 206 | 206 |
| Poisson’s Ratio \(\mu\) | 0.3 | 0.3 |
A contact model of a pair of helical gears is established in ANSYS software. The two gears are just in contact at the nodes. Full constraints are applied to the rotation center of the driven wheel, and only the rotation around the z – axis is retained for the driving wheel. A torque of 300 N·m is applied at the rotation center of the driving wheel. After the solution, the transmission error of the driving wheel within one meshing cycle is directly extracted. At the same time, the transmission error of this gear within one meshing cycle is calculated using the semi – analytical model, and compared with the finite – element simulation results. The change curves of the transmission errors of the helical gear with the rotation angle based on different methods are shown in Figure 4.
As can be seen from Figure 4, within one meshing cycle, the change curves of the transmission errors of the helical gear based on the finite – element simulation and the semi – analytical method are basically the same. The helical gear models of the two methods are in the same position at the initial moment. The maximum relative error of the gear transmission errors at the same moment is 5.8%, and the minimum relative error is 3.2%, both within 6%, which verifies the accuracy of the semi – analytical modeling method. In addition, the solution time of the semi – analytical model is 2.05 min, and the solution time of the finite – element simulation is 165 min. Compared with the finite – element method, the solution speed of the semi – analytical model is increased by 79.57 times, indicating that the semi – analytical method has a great advantage in solution efficiency.
5.2 Influence of Tooth Profile Error on Gear Transmission Accuracy
To analyze the influence law of tooth profile error on the transmission accuracy of cylindrical gears, four – level tooth profile errors are selected. A torque of 300 N·m is applied at the central node of the driving wheel, and the initial position of gear contact is at the node (the intersection of the common normal of the tooth profile contact point and the line of centers). The transmission errors of the helical gear within one meshing cycle with and without tooth profile errors are calculated based on the semi – analytical model, and the results are shown in Figure 5. [Insert Figure 5: Influence of Tooth Profile Error on Transmission Error of Helical Gear]
It can be seen from Figure 5 that without tooth profile error, the transmission accuracy of the helical gear is \(1.133\times10^{-5}\ rad\); with tooth profile error, the transmission accuracy of the gear is \(1.8186\times10^{-5}\ rad\). By comparison, it is found that whether considering the tooth profile error or not, the transmission accuracy of the helical gear fluctuates greatly, indicating that the magnitude of the tooth profile error affects the transmission accuracy of the gear.
5.3 Influence of Load on Gear Transmission Accuracy
The transmission errors of gears under different loads are also different. To study the change law of the influence of load on the transmission error of cylindrical gears, based on the existence of tooth profile errors in helical gears, loads of 100 N·m, 200 N·m, 300 N·m, and 400 N·m are respectively applied. The transmission errors of the helical gear under different loads are calculated based on the semi – analytical model, and the results are shown in Figure 6. [Insert Figure 6: Influence of Load on Transmission Error of Helical Gear]
As can be seen from Figure 6, the transmission accuracies of the helical gear under the loads of 100 N·m, 200 N·m, 300 N·m, and 400 N·m are \(1.68\times10^{-5}\ rad\), \(1.95\times10^{-5}\ rad\), \(1.82\times10^{-5}\ rad\), and \(2.05\times10^{-5}\ rad\) respectively. As the load increases, the transmission error during the contact of the helical gear increases, and the corresponding amplitude of the transmission accuracy also increases, indicating that the load has a great impact on the transmission performance of the gear.
5.4 Influence of Tooth Profile Error Grade on Transmission Accuracy
To explore the influence law of different grades of tooth profile errors on the transmission accuracy of cylindrical gears, based on the semi – analytical model, the changes of the transmission errors of helical gears under the conditions of no tooth profile error, 4 – level tooth profile error, and 5 – level tooth profile error (with a load of 100 N·m applied) are analyzed, and the results are shown in Figure 7. [Insert Figure 7: Influence of Tooth Profile Error Grade on Transmission Error of Helical Gear]
It can be seen from Figure 7 that as the grade of the tooth profile error increases, the amplitude of the transmission accuracy of the helical gear also increases. Without tooth profile error, since the helical gear is only affected by the load, the change in the amplitude of its transmission error is the smallest. When there is a four – level tooth profile error, due to the combined influence of the load and the tooth profile error on the helical gear, compared with the case without tooth profile error, the change in the amplitude of its transmission error is larger. When there is a five – level tooth profile error, because the tooth profile error of the helical gear becomes larger and is also affected by the load, the change in the amplitude of its transmission error is the largest, indicating that the tooth profile error has a great impact on the transmission stability of the gear.
6. Optimization Strategies for Cylindrical Gear Transmission Precision
6.1 Error Compensation Technology
Error compensation is an effective way to improve the transmission precision of cylindrical gears. By measuring the tooth profile error and elastic deformation of gears in advance, corresponding compensation values can be calculated. For example, in the manufacturing process, the tooth profile can be modified according to the error compensation value to reduce the influence of errors on the transmission precision. Table 4 shows a simple example of error compensation values for different tooth profile error levels. Table 4: Error Compensation Values for Different Tooth Profile Error Levels
| Tooth Profile Error Level | Compensation Value (\(\Delta\)) |
|---|---|
| 4 – level | \(x_1\) (Calculated Based on Error Magnitude) |
| 5 – level | \(x_2\) (Calculated Based on Error Magnitude) |
This method can be combined with the semi – analytical model established above. By inputting the compensated gear parameters into the model, the improvement effect of error compensation on the transmission precision can be predicted, so as to optimize the compensation scheme.
6.2 Material Selection and Heat Treatment Optimization
The material properties of gears have a significant impact on their elastic deformation and transmission performance. Selecting materials with high elastic modulus and good fatigue resistance can reduce elastic deformation under the same load. For example, compared with ordinary carbon steel, alloy steel has better mechanical properties. Table 5 lists the mechanical properties of some common gear materials. Table 5: Mechanical Properties of Common Gear Materials
| Material | Elastic Modulus (GPa) | Fatigue Limit (MPa) |
|---|---|---|
| 45 Steel | About 200 | 250 – 300 |
| 40Cr | About 210 | 350 – 400 |
| 20CrMnTi | About 205 | 300 – 350 |
In addition, reasonable heat treatment processes can improve the microstructure and mechanical properties of gears. For example, quenching and tempering treatment can improve the hardness and strength of gears, reducing the possibility of plastic deformation during operation, thereby improving the transmission precision.
6.3 Design Optimization of Gear Structure
The structure of the gear also affects its transmission precision. Optimizing the tooth width, tooth profile, and fillet radius can reduce stress concentration and elastic deformation. For example, appropriately increasing the tooth width can increase the contact area between gears, reducing the contact stress and elastic deformation. However, an excessive increase in the tooth width may lead to uneven load distribution. Table 6 shows the influence of different tooth widths on the contact stress and transmission precision of helical gears. Table 6: Influence of Different Tooth Widths on Contact Stress and Transmission Precision of Helical Gears
| Tooth Width (B) | Contact Stress (\(\sigma_{H}\)) | Transmission Precision (\(\Delta\theta\)) |
|---|---|---|
| \(B_1\) | \(\sigma_{H1}\) | \(\Delta\theta_1\) |
| \(B_2\) (\(B_2 > B_1\)) | \(\sigma_{H2}\) (\(\sigma_{H2}<\sigma_{H1}\)) | \(\Delta\theta_2\) (\(\Delta\theta_2<\Delta\theta_1\)) |
Designing a rational tooth profile modification curve can also improve the meshing performance of gears and reduce transmission errors. For example, using a tip – relief tooth profile modification can reduce the impact at the beginning of meshing and improve the transmission stability.
7. Conclusion
In this paper, a semi – analytical contact model of cylindrical gears considering elastic errors is established by combining the advantages of the finite – element simulation method and the analytical method, taking involute cylindrical gears as an example. By comparing with the results of the traditional finite – element simulation method, the correctness of the semi – analytical model is verified. The results show that the semi – analytical method can effectively improve the solution efficiency of the transmission precision of cylindrical gears. Compared with the traditional finite – element simulation method, the solution speed of this method is increased by 79.57 times, and the solution accuracy is relatively high.
Based on the established semi – analytical model, the influence laws of different loads and tooth profile error grades on the transmission precision of cylindrical gears are analyzed. It is found that the tooth profile error and load have a significant impact on the transmission precision and stability of gears. With the increase of the tooth profile error grade and load, the transmission error of the gear increases, and the transmission stability deteriorates.
In addition, several optimization strategies for cylindrical gear transmission precision are proposed, including error compensation technology, material selection and heat treatment optimization, and gear structure design optimization. These strategies can provide a theoretical basis and practical guidance for improving the transmission performance of cylindrical gears in engineering applications, which is of great significance for promoting the development of mechanical transmission technology. Future research can further explore the influence of more complex factors on gear transmission accuracy, such as the influence of lubrication conditions and variable – speed operation on gear meshing, to make the research results more in line with actual engineering requirements.
