Transmission performance and fault analysis of a vehicle universal joint

Abstract

The universal joint is one of the most critical parts of both the engine and the transmission system of a vehicle. After long-term use, however, some vibration and abnormal noise might occur in it, which may lessen safety while driving. In this article, we investigate faults associated with the double cross universal joint, including looseness, wear, and intermediate shaft torsional deformation. First, we propose a transmission model and a new fault model for this joint. Then, the model parameters of the optimal transmission performance are analyzed. Finally, the main contribution of this article is in discussing the transmission performance as related to looseness, wear, and the intermediate shaft torsional deformation. Our results show that when the angle of the two universal joints is consistent, the phase angle equals 90 and the angular velocity of the output shaft becomes constant, which indicates an optimal transmission performance. When the universal joint is exhibiting looseness, the performance of the angular velocity of the output shaft and the transmission becomes worse as the looseness increases. For both wear and the intermediate shaft torsional deformation, the output angular velocity is also unstable. If looseness occurs at the same time as one of these two faults, the instability will be superimposed and the transmission performance will be even worse. This article provides reference for analysis of faults of the universal joint and its diagnosis; for example, it provides suggestions for when the universal joint should be inspected for repairs or replaced.

Introduction

The rapid development of the automobile industry and the high expectations of drivers has meant that better driving experiences have become the goal of the automobile industry; they need to provide cars that drive well, are comfortable, and are easy to control.^1–3 In recent years, the manufacturing industry technologies of parts used to build vehicles have developed rapidly due to the pursuit of both lightweight materials and quiet and energy-efficient engines.^4,5 The universal transmission system is an important part of any vehicle and needs to be considered during the design process. The most critical part of this system is the universal joint, as it is used in the engine and steering system. ⁶ It is important to design it with consideration to its strength, durability, noise, and efficiency. ⁷

The cross shaft universal joint is used for the power transmission when the input and output shaft are not on the same line, is one of the main components of the vehicle transmission system. ⁸ It has a number of advantageous features, such as its simple structure, low wear, high transmission power, and it can bear a large load and strong torque. ⁹ However, after a car has been used for a long time, the effectiveness of its engine begins to diminish; the transmission efficiency becomes reduced, the tires wear away faster and fuel consumption increases. ¹⁰ How well the transmission and the drive axle work is also affected. It is therefore important to study and analyze the reasons behind why this occurs.

In a universal joint, since the rotation of the torque transmission is consistent, the direction of the applied stress in the joint is also consistent. After long-term usage, unilateral wear occurs at a joint’s shaft journal; this eventually leads to grooves forming on the contact surface of the universal joint, which in turn causes looseness and noise. Furthermore, the wear and bending of the shaft journal, along with the load being borne, will cause each axle of the cross shafts to be in a different plane to one another, or it will even cause the two adjacent two axes to no longer be vertical to one another. Therefore, the larger the gap in the shaft journal and the larger the bearing, the more severe the looseness will become. The center line of the whole drive shaft could even deviate from the center line of the rotating center and produce vibrations, abnormal noises, and other undesirable phenomena at the transmission shaft during driving.

The main faults associated with universal transmission devices are abnormal noise, vibrations, and torsional deformations. These faults will affect, among other things, the ride stability and the power transmission. The probability of a fault in the universal joint causing faults in the engine and transmission is higher than in other parts of a vehicle. ¹¹ The study of the influence of faults in the universal joint is therefore important.

A number of studies have been conducted on universal joints. Pantazopoulos et al. ¹² found that abnormal functioning of a vehicle’s lubrication was a major contributor to this failure. Bayrakceken et al., ¹³ meanwhile, conducted a fracture analysis on a universal joint yoke and the drive shaft of an automobile’s power transmission system. Lu et al.^14,15 presented new models of the cross shaft type universal joint with clearance. Su et al. ¹⁶ studied the motion of a universal joint using a simulation method. However, the quantitative relation between the faults and the performance of the transmission has still not been adequately investigated.

In this article, we investigate faults associated with the double cross universal joint faults, including looseness, wear, and intermediate shaft torsional deformation. First, we propose a transmission model and a new model for faults associated with the double cross universal joint. Then, we carry out a transmission performance analysis. The optimal transmission angle relations are derived, and the effects of the angle between the input and output shafts, and the phase angle on the angular velocity of the output shaft, are analyzed. Finally, the main contribution of this article is to discuss the transmission performance with regard to looseness, wear, and the intermediate shaft torsional deformation, before analyzing the working condition and reliability.

Analysis of the transmission model and the fault model of the double cross universal joint

Transmission model

The movement mechanism of the transmission shaft of the double cross universal joint is shown in Figure 1. The angle between the input shaft, S₁, and the intermediate shaft, S₂, is defined as α, while the angle between S₂ and the output shaft S₃ is defined as β. The angular positions and velocities of the input shaft, intermediate shaft, and output shaft are $[{\theta }_1,{\theta }_2,{\theta }_3,{\omega }_1,{\omega }_2,{\omega }_3]$ , respectively. The phase angle between the two planes, P₂ and P₃, of the joint forks at both ends of the intermediate shaft is $\phi$ . The angle between the two planes, S₁O₁S₂ and S₂O₂S₃, is defined as γ which is equivalent to the reverse angle that between the two planes, P₂ and P₃. Therefore, the angle $\phi$ is designed to reduce the influence of the angle γ on the transmission and compensate this angle to make a constant speed transmission. The new phase angle can be obtained by φ-γ. Here, we set γ = 0.

Figure 1.

The movement mechanism of the transmission shaft of the double cross universal joint.

The configuration in which plane P₁ is vertical to plane S₁O₁S₂ (ΦO₁⊥S₁O₁S₂) is defined as the initial configuration of the transmission shaft, where ${\theta }_1=0$ . The angle unit used in this article is degrees (°).

From the view of the projection plane that is vertical to the plane of the intermediate shaft S₂ at O₁, the trajectory of the intermediate shaft fork Θ is a circle, and the trajectory of the input shaft fork, Φ, is an ellipse (Figure 2). The following equations can be obtained, where increases in the input shaft angle and the intermediate shaft angle are $\mathrm{\Delta }{\theta }_1$ and $\mathrm{\Delta }{\theta }_2$ , respectively ¹⁷

$$\frac{\tan \mathrm{\Delta }{\theta }_1}{\tan \mathrm{\Delta }{\theta }_2}=\frac{{\mathrm{\Phi }}_2\mathrm{\Omega }/O_1\mathrm{\Omega }}{{\mathrm{\Phi }}_1\mathrm{Q}/O_1\mathrm{\Omega }}$$

(1)

$$\frac{{\mathrm{\Phi }}_2\mathrm{\Omega }}{{\mathrm{\Phi }}_1\mathrm{\Omega }}=\frac{O_1{\mathrm{\Phi }\prime }_2}{O_1{\mathrm{\Phi }\prime }_1}$$

(2)

$$\frac{O_1{\mathrm{\Phi }\prime }_2}{O_1{\mathrm{\Phi }\prime }_1}=\frac{1}{\cos \alpha }$$

(3)

Figure 2.

The relation between the input shaft and the intermediate shaft.

Equations (1)–(3) yields

$$\frac{\tan \mathrm{\Delta }{\theta }_1}{\tan \mathrm{\Delta }{\theta }_2}=\frac{1}{\cos \alpha }$$

(4)

In the motion system, the initial rotation angle is $O_1{\mathrm{\Phi }}_0$ , and the rotation angle of the fork of the input angle is

$${\theta }_1=\mathrm{\Delta }{\theta }_1$$

(5)

The rotation angle of the fork of the intermediate angle is

$${\theta }_2=\mathrm{\Delta }{\theta }_2+90°=\mathrm{acrtan}(\tan ({\theta }_1+90°)·\cos \alpha )$$

(6)

For the transmission system, $\alpha$ is a fixed angle. Equation (6) yields

$$\frac{d{\theta }_2}{\mathrm{dt}}=\frac{\cos \alpha }{{\cos }^2({\theta }_1+90°)·(1+{\cos }^2\alpha ·{\tan }^2({\theta }_1+90°))}·\frac{d{\theta }_1}{\mathrm{dt}}$$

(7)

From equation (7), we can obtain

$$\frac{d{\theta }_2}{\mathrm{dt}}=\frac{\cos \alpha }{1-{\sin }^2\alpha ·{\cos }^2{\theta }_1}·\frac{d{\theta }_1}{\mathrm{dt}}$$

(8)

The relation of the angular velocity between the intermediate and input shafts can now be derived ³

$$\frac{{\omega }_2}{{\omega }_1}=\frac{\cos \alpha }{1-{\sin }^2\alpha ·{\cos }^2{\theta }_1}$$

(9)

Therefore, the relation of the angular velocity between the output and input shafts can be obtained

$${\omega }_3=\frac{\cos \beta }{1-{\sin }^2\beta {\cos }^2({\theta }_2+\phi )}\times \frac{\cos \alpha }{1-{\sin }^2\alpha {\cos }^2{\theta }_1}{\omega }_1$$

(10)

The fault model of the double cross universal joint

The main faults of the universal transmission device are abnormal noise, vibration, and deformation; these are mainly caused by the faults such as looseness, wear, and intermediate shaft torsional deformation. When looseness and wear of the universal joint occur, the central axes in the universal joint will not be consistent, and a small distance $\mathrm{\Delta }d$ between the central axes will appear, as shown in Figure 3.

Figure 3.

Sectional diagram of the universal shaft with faults.

In this article, we suppose that the fault is in the universal joint between the intermediate and output shafts. Therefore, for this faulty universal joint, the angle between the intermediate and output shafts, $\beta$ , will deviate from its normal value. If the fault angle is defined as $\beta \prime$ , there will be a relation of $\beta \prime =f(\mathrm{\Delta }d)$ . Equation (11) defines $\overline{\beta }$ as the non-dimensional variation value of the angle, and $\overline{{\omega }_3}$ as the non-dimensional variation value of the angular velocity of the output shaft. In the following sections on the analysis of the faults of the universal joint, we will discuss the relations between these parameters

$$\{\begin{array}{c}\overline{\beta }=\frac{\mathrm{\Delta }\beta }{\beta }=\frac{\beta \prime -\beta }{\beta }\hfill \\ \multicolumn{1}{c}{\overline{{\omega }_3}=\frac{\mathrm{\Delta }{\omega }_3}{{\omega }_3}=\left|\frac{{\omega \prime }_3-{\omega }_3}{{\omega }_3}\right|}\end{array}$$

(11)

In practical applications, if the joint clearance between the universal joint cross shaft journal and bearing is more than 0.25 mm, then abnormal noise and vibrations will be produced. This indicates that when Δd > 0.25 mm, the fault angle between the intermediate output shafts, $\beta \prime$ , is out of the acceptable range, the angular velocity of the output shaft, ${\omega }_3$ , will be not smooth. This may result in some faults, such as looseness or wear, developing in the universal joint, which may require the universal joint to be replaced or repaired.

Model parameter analysis of the double cross universal joint

The constant relation between the angular velocities of the input and output transmission shafts is shown in equation (5). From this, we can find a set of model parameters that specify a constant input angular velocity that obtains a stable output angular velocity. We will therefore investigate the influence of the model parameters on the output angular velocities and obtain their optimal values. We set the constant angular velocity of the input shaft to be ${\omega }_1=1\mathrm{rad}/\mathrm{s}$ , which is shown in Figure 4.

Figure 4.

Constant angular velocity of input shaft.

With a fixed $\alpha$ that is equal to 30 and the parameters in Table 1 giving $\phi$ equal to 80, 90, 110 and $\beta$ equaling 25, 30, 35, and 40, respectively, the angular velocity relationship between the intermediate and output shafts is analyzed.

Table 1.

Model parameters of the double cross universal joints.

α	φ	β
30°	80°	25°	30°	35°	40°
30°	90°	25°	30°	35°	40°
30°	100°	25°	30°	35°	40°

Parameter combination: α = 30; φ = 80, 110; β = 25, 30, 35, 40

Figure 5 shows that with fixed $\alpha =30$ and $\varphi =80$ , when $\beta$ equals 25, 30, or 35, the amplitude of the angular velocity of the output shaft is smaller than that of the intermediate shaft. The large amplitude and asymmetry curve show that the transmission is performing poorly, thereby resulting in a performance that is not smooth. When $\beta$ is equal to 40, the amplitude of the angular velocity of the output shaft is larger than that of the intermediate shaft. The larger amplitude implies that the transmission is worse. For the situation where $\alpha =30$ and $\varphi =110$ , we can see the same results, which are shown in Figure 6. Therefore, when $\alpha =30$ , $\varphi =80,110$ , the optimal transmission relation cannot be found with any value of $\beta$ .

Figure 5.

The angular velocities of the intermediate shaft ${\omega }_2$ and the output shaft ${\omega }_3$ ( $\alpha =30°$ , $\phi =80°$ , $\beta =25°,30°,35°,40°$ ).

Figure 6.

The angular velocities of the intermediate shaft ${\omega }_2$ and the output shaft ${\omega }_3$ ( $\alpha =30°$ , $\phi =110°$ , $\beta =25°,30°,35°,40°$ ).

Parameter combination: α = 30; φ = 90; β = 25, 30, 35, 40

Figure 7 shows that with fixed $\alpha =30$ and $\varphi =90$ , when $\beta =\alpha$ , the angular velocity of the output shaft is constant, which is the optimal solution. We also find that the curve of the angular velocities of the intermediate shaft, ${\omega }_2$ , and the output shaft, ${\omega }_3$ , are symmetric. Therefore, in comparison to Figures 5 and 6, the smooth performance of the angular velocity of the output shaft can be improved when $\phi$ equals 90.

Figure 7.

Angular velocities of the intermediate shaft ${\omega }_2$ and the output shaft ${\omega }_3$ ( $\alpha =30°$ , $\phi =90°$ ).

From the analysis above, we know that the smaller the difference between $\beta$ and $\alpha$ , the smoother the performance of the universal joint will be. For practical designs, the difference between $\beta$ and $\alpha$ should be as small as possible. When $\alpha =30$ , $\beta =30$ , $\varphi =90$ , the optimal transmission relation can be found. Therefore, the phase angle, $\varphi =90$ , is the optimal solution.

Fault analysis of the double cross universal joint

When the universal joint is used for a long time, the fault will affect the delivery of the power, cause low transmission efficiency, increase fuel consumption and noise, and accelerate the wearing away of spare parts. Here, we analyze the influence of the three causes of universal joint failures on the output transmission, including looseness, wear, and torsional deformation.

If the universal joint exhibits looseness, the relationship between $\alpha$ and $\beta$ will change. Based on the best transmission performance ( $\alpha =30$ , $\varphi =90$ , and $\beta =30$ ) and the fault model presented in section “The fault model of the double cross universal joint,” we will first analyze looseness by adjusting $\beta$ . After the study of the looseness, we will investigate the wear and torsional deformation; this is because these two faults are accompanied by looseness.

Analysis of the looseness

Since after long-term use, the fit accuracy of the universal joint will no longer meet vehicle component assembly standard, some faults will emerge. The most common reason for a fault is looseness, for example, this looseness may appear in the moving angle of the universal joint, the fixed bolt of the connecting part, or the connecting bolt of the flange.

Based on the optimal transmission performance of $\alpha =30$ , $\varphi =90$ , and $\beta =30$ , we selected $\beta$ as being 29.5 and 30.5, where the variation is 1.7% of 30, in order to describe the looseness and analyze the angular velocity of the output shaft, ${\omega }_3$ .

Figure 8 shows that with a fixed $\alpha =30$ and $\varphi =90$ , when $\beta$ equals 30, the relationship between the angular velocity of the output shaft and time is delegated by a horizontal, which means that the universal joint is in an ideally smooth state. For $\beta =29.5,30.5$ , the maximum amplitude of the curve reaches 1.005 rad/s, which means that the universal joint does not work smoothly and the transmission performance is affected as a result.

Figure 8.

Angular velocity of the output shaft, ${\omega }_3$ ( $\beta =29.5°,30°,30.5°$ ).

Figure 9 shows that when $\beta$ deviates from its normal value of 30, the angular velocity of the output shaft varies. For example, when $\beta$ equals 31, the maximum variation of the angular velocity of the output shaft, $\mathrm{\Delta }{\omega }_3/{\omega }_3$ , reaches 0.01. Therefore, the greater the looseness becomes, the wider the change in the angular velocity of the output shaft. The angular velocity of the output shaft changes in a wide range, along with the change in $\beta$ , which indicates that the output is fluctuating.

Figure 9.

Relationship between $\beta$ and the maximum variation of the angular velocity of the output shaft ( $\mathrm{\Delta }{\omega }_3/{\omega }_3$ ).

For the analysis above, we know that when the universal joint is exhibiting looseness, the angular velocity of the output shaft has a large amplitude that affects the transmission performance. The performance of the angular velocity of the output shaft and the transmission become worse as the looseness increases. In this situation, noise and vibrations will occur more easily in the universal joint, which in turn will make the driving of the vehicle less safe.

Analysis of wear

Wear is a special type of looseness. Some parts of the universal joint will depress during high strength motion, and phenomena such as shaft wear, bearing wear, or even damage, may cause looseness. In this section, we study the wear of the universal joint and analyze the influence of the wear on the transmission performance.

The angle, $\beta$ , will fluctuate because of the wear of the joint between the shaft fork and the spider. We set four wear points to have the same amplitude width during the motion process in order to express a linear change in $\beta$ when passing through wear points. Figure 10(a) shows the value of β′/β as a function of time, where β′ is the fault angle.

Figure 10.

(a) β′/β versus time for four linear wear points and (b)–(d) the angular velocity of the output shaft, ${\omega }_3$ , with four wear points (β = 30°, 29.5°, and 30.5°).

Based on the optimal transmission performance $\alpha =30$ , $\varphi =90$ , and $\beta =30$ , we selected $\beta$ to be 29.5 and 30.5 so as to simulate looseness. Figure 10(b) shows the angular velocity of the output shaft, ${\omega }_3$ , with $\beta =30$ and the wear shown in Figure 10(a); in this figure, $\beta =30$ means wear without looseness. The angular velocity of the output shaft is not the same even in the same wear point situation. Although the variation of $\beta$ we set is 5%, the maximum variation of the angular velocity of the output shaft is over 1%. By comparing this to the optimal situation, we can see that the transmission performance was not good.

The variation in the angular velocity of the output shaft is obvious at the same wear points with looseness. For example, when $\beta$ equals 29.5 and t equals 1.9, the maximum variation of the angular velocity of the output shaft is 0.012 (1 − 0.988), as shown in Figure 10(c). This variation includes two parts: in the scenario where there is wear without looseness, when $\beta$ equals 30 and t equals 1.9, the variation in the angular velocity of the output shaft is 0.008, as shown in Figure 10(b). If there is looseness but no wear, then when $\beta$ equals 29.5 and t equals to 1.9, the variation in the angular velocity of the output shaft is 0.004, as shown in Figure 8.

When $\beta$ equals 30.5 and t equals 3.4, the maximum variation of the angular velocity of the output shaft is 0.017 (1 − 0.983), as shown in Figure 10(d) This includes the wear variation of 0.013, as shown in Figure 10(b), and the looseness variation of 0.004, as shown in Figure 8.

Therefore, the variation in the angular velocity of the output shaft is obvious in the scenario where wear occurs, and the transmission performance is duly affected. In addition, when the universal joint experiences both wear and looseness, the angular velocity of the output shaft becomes more unstable and the transmission performance also becomes worse; abnormal sounds, vibrations, and other faults are more likely to occur, which in turn reduce safety while driving a vehicle.

Figure 11 shows that with an increase in the variation of $\beta$ , the variation in the angular velocity of the output shaft increases. Therefore, the more serious the wear is, the wider the variation in the angular velocity of the output shaft. The output transmission will therefore fluctuate.

Figure 11.

Relationship between the angle variation, $\mathrm{\Delta }\beta /\beta$ , and the maximum variation of the angular velocity of the output shaft, $\mathrm{\Delta }{\omega }_3/{\omega }_3$ .

Analysis of the intermediate shaft torsional deformation

The intermediate shaft is indispensable during the delivery of power in the universal transmission system. The main fault in the intermediate shaft that we will discuss is due to the torsional deformation that causes abnormal sounds and vibrations to occur. In this section, we describe the torsional deformation by varying the phase angle, $\phi$ , which is an important parameter that affects the angular velocity of the output shaft, ${\omega }_3$ .

Based on the optimal transmission performance of $\alpha =30$ , $\varphi =90$ , and $\beta =30$ , we selected $\phi$ to be 88 and 92 so as to describe the torsional deformation, and we selected $\beta$ to be 29.5 and 30.5 in order to simulate looseness.

Figure 12 shows that the angular velocity of the output shaft is constant without any variation when the phase angle, $\phi$ , equals 90. Variations in the phase angle will result in the angular velocity of the output shaft becoming unstable.

Figure 12.

Relationship between the phase angle, $\phi$ , and variation of the angular velocity of the output shaft, $\mathrm{\Delta }{\omega }_3/{\omega }_3$ .

Figure 13(a) shows that in comparison to the phase angle $\phi =90$ , the angular velocity curves of the output shaft clearly vary when $\phi$ equals 88 or 92 and there is no looseness; this implies that the output fluctuates.

Figure 13.

Angular velocity of the output shaft, ${\omega }_3$ , with various phase angles, $\phi$ .

Figure 13(b) and (c) show that in the scenario for looseness, the angular velocity curves of the output shaft are unstable with all values of the phase angle. Meanwhile, when $\phi$ equals 88 or 92, in the situations where both the intermediate shaft torsional deformation and looseness occur, the angular velocity curves of the output shaft are even more unstable. Additionally, in comparison to β = 30, Figure 13(b) and (c) shows that the amplitude of the curves are larger, which means that the variation is stronger and more obvious.

Therefore, when the intermediate shaft has torsional deformation, which means that $\phi$ deviates from 90, the angular velocity clearly fluctuates. With both torsional deformation and looseness, the curve amplitude becomes larger, which causes strong and obvious vibrations.

Conclusion

In this article, we have studied faults that occur in the double cross universal joint, including looseness, wear, and intermediate shaft torsional deformation. A transmission model and a fault model of the double cross universal joint were built. An analysis of the parameters of the transmission model shows that when the angle of the two universal joints (α and β) are consistent, the phase angle, φ, equals 90; the angular velocity of the output shaft is therefore constant, which indicates optimal transmission performance.

Another contribution of this article is in the discussion on the transmission performance when affected by looseness, wear, and intermediate shaft torsional deformation. Our results show that when the universal joint is exhibiting looseness, the performance of the angular velocity of the output shaft and the transmission become worse as the looseness increases. For wear and intermediate shaft torsional deformation, the output angular velocity is also unstable. If looseness occurs at the same time as one of these two faults, the instability will be superimposed and the transmission performance will become even worse.

This article can help us to understand the faults of the universal joint. However, the drivetrain dynamics is also important for the faults analysis of the universal joint. This is the motivation that we will continue this research and try to study the mechanism of the transmission and the reasons of faults. We also will look to test the faults of real universal joints using the results of this study in order to generate guidance that is more applicable to real-world scenarios.