Influence of the brake lining position on the efficiency of the centrifugal friction roller

Brake roller is one of the safety elements of a pallet flow rack. At present, most widely used construction of brake roller is centrifugal friction roller (CFR). Efficiency of the CFR is ability to limit speeds of a pallet with different masses in pallet flow rack, and while the lower the speed, the higher efficiency of CFR. One of the parameters that affect to CFR efficiency is frictional lining position on the brake pads of CFR, which can be define with angle of brake lining position. The article is devoted to calculation the influence of angle of a brake lining position, its operating range finding. Analytical research was conducted for the CFR prototype. It is reported that effective areas of the angles is lies closer to the boundaries of operating range and it is non-effective to install a brake lining in the middle of the operating range.


Introduction
Pallet flow rack is one of the block storage or deep-lane storage systems [1][2][3][4][5], which consists of static part (metal construction) and dynamic part (rollers, stopping mechanism with pallet separators, brake rollers, etc) [6]. The utilization of the pallet flow rack can reduce travelling distance of the forklift by 25% in compare with single-deep racks [7] and therefore such racks can be used in automated warehouse [8][9][10].
There are many publication is devoted to static parts of the rack [11][12][13][14]. However, the literature is not sufficiently covered issues concerning dynamic part and safety elements -brake roller and stopping mechanism with pallet separators.
Stopping mechanism with pallet separator is need to avoid the pressure on the unloading pallet from the following behind it and therefore allow reducing the requirement for the quality of forklift drivers. Thus, it can be minimize the human factor, which is one of the main factor of accidents on the production [15].
The brake rollers serves as speed limiter, which does not allow damage of the stopping mechanism with pallet separator. Therefore, stopping mechanism with pallet separator and brake rollers is works as a system. Most widely used construction of brake roller ( Figure 1) is centrifugal friction roller (CFR), consisting of axis 5 and brake insert 1 with planetary multiplier 3 and centrifugal brake 4, installing in shall 2 [e.g. 16]. The efficiency of the CFR is determined by the speed V of the moving of a pallet on the CFR, while the lower the speed, the higher the efficiency of it. Thus, safety of the pallet flow rack is determine of the efficiency of the CFR. As known, brake efficiency in common depends from material of friction pair [17], coefficient of friction and its instability [18], as well as temperature on the friction surface [19][20][21]. In addition to the above, efficiency of the CFR also depends from the position of the brake lining on the brake pad of centrifugal brake.
Look at the scheme of the centrifugal brake of the CFR shown in Figure 2. Speed V of the moving of a pallet on the CFR can be calculated as [22]: where D -outside diameter of CFR shall, u -gear ratio of planetary multiplier, r -radius of action of centrifugal force Pcf, c -arm of the centrifugal force Pcb relative to axis A of rotation brake pad, mmass of the brake pad, M -mass of the pallet, tan α -inclination of the roller bed of pallet flow rack, w -coefficient of resistance to movement of a pallets on the roller bed, i -quantity of the brake pads (i = 2), d -inside diameter of CFR shall, f -coefficient of friction between CFR shall and lining, ηcoefficient of efficiency of CFR, a and b -arms of a normal force N and a friction force Nf respectively, K -elastic force, k1 and k2 -arms of elastic forces K of the springs.  (1) shows that the speed V of the moving of a pallet on the CFR depends on the arms a and b, which are defined by lining position on the brake pad, as well as parameters of springs and points of its mountings, which defined initial speed V0 of activation of centrifugal brake (contact of frictional lining with CFR shall). The V0 can be calculated with (1) for mass of the pallet M = 0.

Brake lining position
To exclude the effect of initial speed of activation of CFR brake in the analysis of influence of the lining position on the efficiency of CFR, the form of brake pads was chosen so that if lining is fixed in different positions, the initial speed of activation remains constant. In this case, the elastic forces K of the springs, as well as the arms k1 and k2 of its actions, are constants.

Angle of a brake lining position
Taking into account mentioned above, look at scheme, where position of the brake lining on the brake pad is determined with angle β of a brake lining position ( Figure 3). Considering the mass of the brake lining significantly less than the mass of the brake pad, changing of the position of the center of gravity can be neglected.
Than (1) takes the form Taking into account (2) and Figure 3 the arms a and b of a normal force N and friction force Nf can be founded as: where l0 -distance between the axis of rotation of CFR and brake pad (see Figure 3).

Angle of a brake lining position
The range of the angle of a brake lining position can be calculated considering the fact that speed V of the moving pallet on the CFR can not be less than initial speed V0 of activation CFR, or taking into account (3): Taking into account (4) the range of the angle of a brake lining position can be calculated from inequality After transformations of the (6) the operating range of the β can be calculated by solving square inequality √1 − (cos ) 2 + cos > Placing the friction lining on the brake pad outside the operating range, the CFR is jammed. In addition, it is necessary to make sure that it is constructively possible to install the friction lining within the boundaries of the operating range.

Results and discussion
An analytical research of the influence of the brake lining position on the efficiency of CFR was conducted for the parameters of CFR, pointed in Table 1. The operating range of the angle of a brake lining position, calculated with (7), Table 1 and design restriction of CFR, is equal β = 20…127 .
Results of the calculation of the speed V of the moving of a pallet on the CFR with (2) taking into account (3) and Table 1, is shown in Figure 4.   Figure 4 shows that efficiency of the CFR is depend from the position of the brake lining and effective areas of angle β is varies from 20…40 ̊ and 100…120 ̊ (Figure 4,b). It must be noted, that in the middle of the operating range of the angle β the speed V of the moving of a pallet on the CFR takes high values with the maximum at β=70 .

Conclusions
Efficiency of the CFR is determined by the speed of the moving of a pallet on CFR, while the lower the speed, the higher the efficiency of it. Brake lining position, which is one of the parameters of the CFR, affecting on its work efficiency, can be defined by angle β. The operating range of its angle, depending from the inside diameter of the CFR shall, distance between the axis of rotation of CFR and brake pad, as well as, coefficient of friction between CFR shall and brake lining, is calculated with equation (7). An analytical research, conducted for the CFR prototype, showed: