## 1 Introduction
[PERSON] [17; 18] presented a transient 3D CFD simulation model, which enabled to calculate the flow behaviour and drag torque of a disengaged wet clutch disk. [PERSON] [19; 20] presented a mathematical model of the drag torque of the disengaged wet clutch by considering the effects of grooves and waviness on the friction plates. [PERSON] [21; 22] established a comprehensive numerical model, which took radial grooves, hydrodynamic, mechanics of elasticity, plasticity contact, and thermal effect into consideration. This model solved the domain decomposition of groove area by coupled finite element method. [PERSON] [23; 24] investigated the friction and wear performance of commercially available unidirectional CFRP plates in contact with the roughened mold steel plates through a comprehensive experiment. However, this simplified model lacked test verification. Especially for the new type of conical groove friction disk, the friction calculation model and experimental data are even less. Recently, [PERSON] [25] investigated the friction coefficient of multi-cone friction pair under different loads and different speeds, and research shows that the multi-cone structure influences the frictional behaviors of the friction specimens. In this paper, the friction model of conical groove friction disk is established, and the friction coefficient is calculated by equivalent radius and is developed based on the previous work by [PERSON] et al. [25]. An experimental investigation is designed to analyze the influences of different cone configuration parameters on behaviors of conical groove friction disks. Frictional specimens with different configuration parameters are designed and the influences of configurations parameters are obtained. The results can be suitable for the friction components in engineering practice. In the process of contact, the two cone surfaces of the single cone friction element contact with each other. The clearance between the friction disk and the separator disk is \(h_{0}\), the inner diameter of the friction element is \(R_{\rm i}\), the outer diameter is \(R_{\rm o}\), the cone angle is \(\alpha\), the equivalent inner diameter is \(r_{1}\), and the equivalent outer diameter is \(r_{D}\). The rotation speed of friction disk is \(\omega_{1}\), the separator disk starts to rotate under the action of oil film shear torque, the rotation speed is \(\omega_{2}\), and the hydraulic load of the separator disk is \(F\). As shown in Figure 2, \(R_{\rm i}\) are \(R_{\rm o}\) are the inner and outer radius, respectively; \(r_{1}\), \(r_{2}\), \(r_{3}\), and \(r_{4}\) are the vertices of the conical surfaces. The normal force is applied on the back of the friction disk. All calculations are based on the Reynolds equation, and the pressure distribution is assumed to be constant. According to the cone friction calculation method [25], the equivalent radius calculation of conical friction element is carried out. The equivalent radius is used to describe the conical feature. As shown in Figure 1, the conical friction surface is equivalent to a plane disk with an external radius of \(r_{D}\) and an internal radius of \(r_{1}\). The equivalent radius \(r_{D}\) of the cone surface can be calculated as Equation (1). \[r_{D}=\frac{2}{3\sin\left(\frac{\alpha}{2}\right)}\left[\frac{r_{4}^{3}-r_{3} ^{3}}{r_{4}^{2}-r_{3}^{2}}+\frac{r_{2}^{3}-r_{1}^{3}}{r_{2}^{2}-r_{1}^{2}} \right]+r_{1} \tag{1}\]  
The instantaneous friction coefficient \(\mu\) can be calculated as Equation (2):  
\[\mu=\frac{T}{F(r_{D}-r_{1})} \tag{2}\]  
where, \(T\) is the belt torque, which can be obtained by the test. \(F\) is the hydraulic load of the separator disk. (The equivalent radius \(r_{D}\) and internal radius of \(r_{1}\) are shown in Figure 1b)  
Figure 1: Friction model for conical groove friction element (**a**) single cone ring friction element, (**b**) simplified contact model [25]. Figure 2: Equivalent radius of single conical groove friction element.