Reliability assessment of cylindrical joints with tensioned roll band of the rolling mill

The work addresses to the problem of ensuring the operability of a composite roll made in the form of a cylindrical joint with the tension of a carbide band and a steel axis. When considering the wear processes, all the characteristics related to the surface microgeometry are combined by a dimensionless complex roughness parameter, which, along with the roughness class, includes the features of the surface treatment technology. To determine the contact pressure associated with the tension, the Lame formula for calculating thick-walled cylinders is used. When a hard-alloy bandage is placed on a steel roll with the tension between the contacting surfaces, a plastic unsaturated or saturated contact is performed, for which a method for calculating the tension values shall be proposed. Formulas are given for determining the maximum permissible torque that does not cause a change in the strength of the joint with tension under conditions of plastic saturated and unsaturated contact. In order to test the strength of the connection elements with tension, the theory of the greatest tangential stresses is applied for two dangerous points located on the inner surfaces of the covered and the covering parts: a formula is obtained for determining the maximum permissible calculated value of tension from the strength condition of the covered part. An example of fitting with the tension of a band made of hard alloy VK8 on a working roll made of improved steel 45 with a diameter of d = 100 mm is considered. The band is installed using a press with an H7/p6 fit to transmit a torque of M = 5 kNm. The minimum tension value is obtained from the condition of fixing the contact surfaces without their relative slippage, and the maximum tension value is obtained from the condition of the strength of the steel axis. As a result of the calculations, it was found that the minimum tolerance for this attachment does not provide the transmission of the specified torque since its value is less than the minimum allowable tension. Therefore, to ensure reliable operation of the connection with tension, it is recommended to use the H7/s6 fit, which provides the transmission of the specified torque without the strength of the connection elements.


Introduction
Recently, the reliability of technological machines and equipment has become one of the main engineering problems, which is becoming increasingly important for metallurgical production [1-4]. Insufficient reliability of technological machines and their components and devices not only leads to significant downtime of equipment but also significantly increases the cost of their operation. Increasing requirements for the quality of technological machines and equipment in order to reduce material, labor, and financial costs for maintenance and repair leads to the need for modernizing and reconstructing equipment [5][6][7][8][9][10]. At the same time, attention shall be paid to equipment for the base metal production [11][12][13][14].

Setting of a Problem
In the process of rolling workpieces made of refractory metals, the working rolls undergo significant thermal and mechanical pressures. Therefore, for high-temperature rolling of hard-to-deform IOP Publishing doi: 10.1088/1757-899X/1164/1/012019 2 materials, carbide rolls are often used. In order to save expensive carbide material, the working roll is often produced composite, consisting of a steel roll and a carbide band [15][16] The cylindrical connection with the tension of the band with the rolling roll should ensure that the contact surfaces are fixed without their relative slippage. This occurs by assigning the appropriate tightnesses. Due to the spread of the values of the coefficient of friction and tension, when an external (excessive) load and vibration are applied, a relative displacement of the band relative to the roll may occur, which negatively affects the further ability to transmit the full load. Under the action of variable loads, especially at the moment of starting and stopping, micro-displacements and fretting corrosion occur on the mating surfaces at the ends of the connected parts [17][18][19][20].

Purpose and Objectives of the Study
When considering the wear processes, all the characteristics related to the surface microgeometry can be combined by a complex dimensionless parameter [17][18][19] max r eq R rb    . (1) Here req is the reduced average radius of curvature of the vertices of the projections, equal to , lt eq lt rr r rr where rl и rt are the average values of the radii of curvature of the vertices of the projections in the longitudinal and transverse directions. It is fundamentally important here that, along with the roughness class, the surface treatment technology also plays a great role, on which the other characteristics included in the formula (1) depend. For the treated surfaces, which are characterized by an equilibrium roughness, the parameters of the reference curve of the profile take fairly stable values of b    2.
The contact pressure рc, MPa, is related to the tension N, m, the Lame dependence, which is derived in the course "Resistance of materials" [ (2) Here N-tension in the joint, m; d-roll diameter, m; C-coefficient, which is determined by the formula t 2 2 2 2 12 12 2 2 2 2 12 12 where d1 -the diameter of the hole of the covered part (for a solid roll d1 = 0); d2outer diameter of the covering part, m; E1 and E2elastic modulus of the material of the covered (of the roll) and covering (sleeve) surface, MPa; μ1 and μ2 are the Poisson coefficients of the material of the covered (of the roll) and covering (sleeve) surface.
Plastic saturated contact occurs in the case when where Kas is the assembly coefficient; for thermal assembly Kas = 1, for press assembly -Kas = 0.5 [20].
The maximum permissible moment [M], which does not cause a change in the strength of the joint with tension in the conditions of plastic contact, is determined by the formula where fm is the molecular component of the coefficient of friction, the value of which for practical calculations can be assumed to be equal to fm = 0.12 [17][18][19]; KScoefficient depending on the type of contact; for unsaturated plastic contact KS = 0.21, for saturated -KS = 0.45 [20]. Calculations show that for the connection of the band with the roll in the formula (6), the second term can be neglected. Then, for both types of contact, the formula for the permissible moment takes the following form The minimum allowable design tension value Nmin,р is found when the permissible torque value is equated with the corresponding values of the technological resistance moments M, i.e.
where N is the reduction of tension during press assembly [5]; The maximum design tension Nmax, р is determined from the solution of the problem of calculating thick-walled cylinders [22] and is reduced to testing for strength at dangerous points where the greatest tensile and compressive stresses act (Figure 1  on the inner surface of the covered part  According to the theory of the greatest tangential stresses, the strength condition has the form [21] экв Given this expression from formulas (9) and (10) Of the two values max p , the lower value limits the amount of allowable pressure determined by the formula (2). The dangerous element, as a rule, is the covered part [21], and therefore from (12) for a solid roll (d1 = 0), we get рmax = т1/2. Then the maximum permissible calculated value of the tension Nmax, р according to formula (2) will be equal to Because building connections smooths roughness, the maximum actual tension Nмах take more received by the formula (16), at the height of the roughness of the mating surfaces, i.e. max max,p 1 2 Usually, the surfaces of the covered parts (rolls) are treated with a roughness of Rz1 = 0.4…3.2 μm, and the covering (holes) -with a roughness of Rz2 = 0.8…6.3 μm. Therefore, According to the calculated values of the tension Nmax и Nmin, the corresponding standard fit is selected; most often, H7/p6, H7/r6, H7/s6, H7/t7, H7/z6, H7u7 landings are used.

Discussion of the research results
An example of fitting with the tension of a band made of hard alloy VK8 [23] on a working roll made of improved steel 45 [23]with a diameter of d = 100 mm is considered. The band is installed using a press with a H7/p6 fit to transmit a torque of M = 5 kN·m. The outer diameter of the band d2 = 170 mm, the length of the landing surface l = 145 mm. The landing surface is treated according to the 6th class of cleanliness, for which the complex roughness characteristic of the r = 0,5. The surface hardness of the roll HB = 2500 MPa. Check whether the specified torque can be transmitted.
For the H7/p6 landing [24], we find the lower and upper limit deviations of the roll and the hole, and then the lower Nlow = 2 μm and the upper Nhigh= 59 μm limit values of the tightness (Figure 2). To determine the type of contact, we use the formula (5) to determine the amount of tension that characterizes the transition condition to plastic contact, taking into account that when pressing Cas = 0.5. Therefore, in connection with the tension, both unsaturated (Nlow = 2 μm) and saturated (Nhigh= 59 μm) plastic contact can be performed. For the maximum amount of tension, according to the formula (7), we obtain the maximum permissible moment [M]   For the minimum amount of tension, using the formula (7), we obtain the minimum allowable moment [M]   Since [M]min = 1 кНм < M = 5 кН, the minimum tolerance for this fit does not provide the transmission of the specified torque.
During the press assembly, it is necessary to switch to a different type of fit to ensure the minimum allowable tension, which can be estimated using the formula (8) The value of the tension reduction N = 12 μm is taken for the 6th class of surface treatment purity, i.e. for Ra = 2.5...1.25 μm. For the H7/r6 landing, we find [8] the lower Nlow = 51 μm and the upper Nhigh = 73 μm values of the limit deviations (see Figure 2), and we determine the lower Nlow = 16 μm and the upper Nhigh= 73 μm of the tension values, which is also not enough to transmit the specified torque.
For the H7/s6 landing, we find [24] the lower Nlow = 71 μm and the upper Nhigh = 93 μm values of the limit deviations (see Figure 2), and we determine the lower Nlow = 136 μm and the upper Nhigh= 93 μm of the tension values. This landing ensures the transmission of the specified torque.

Conclusions
When considering the wear processes, all the characteristics related to the surface microgeometry are combined by a dimensionless complex roughness parameter, which, along with the roughness class, includes the features of the surface treatment technology. To determine tensed contact pressure, the Lame formula for calculating thick-walled cylinders is used. Formulas are given for determining the maximum permissible torque that does not cause a change in the strength of the joint with tension under conditions of plastic saturated and unsaturated contact. In order to test the strength of the connection elements with tension, the theory of the greatest tangential stresses is applied for two dangerous points located on the inner surfaces of the covered and the covering parts: a formula is obtained for determining the maximum permissible calculated value of tension from the strength condition of the covered part. An example of fitting with the tension of a band made of hard alloy VK8 on a working roll made of improved steel 45 with a diameter of d = 100 mm is considered. The band is installed using a press with a H7/p6 fit to transmit a torque of M = 5 kNm. Calculations have shown that the minimum tolerance for this landing does not provide the transmission of the specified torque. Therefore, to ensure reliable operation of the connection with tension, it is recommended to use the H7/s6 fit, which provides the transmission of the specified torque without the strength of the connection elements.