Study of a Plate-Type Friction Vibration Damper
Abstract Generated abstract
This paper examines a plate-type friction vibration damper intended to improve the running behavior of freight cars, particularly empty and lightly loaded cars where dynamic overloads are relatively high. It develops force and relative-friction relations for empty and loaded operating conditions, distinguishing upward and downward motion, and applies the calculations to MT-50 and TsNII-KhZ-O bogies. The analysis indicates that the proposed damper can provide greater relative friction during upward motion than downward motion and greater damping for empty cars than loaded ones, including a possible one-sided damping characteristic. A removable design is also described, with an operating characteristic aimed at maintaining favorable acceleration and oscillation behavior, and the paper argues that such dampers may offer advantages over wedge dampers in reliability, adaptability, and running safety.
Full Text
Study of a Plate-Type Friction Vibration Damper
A. A. Dychko
(Presented by the scientific seminar of the Department of Applied Mechanics)
Despite the urgency of the problem and continuous research work aimed at finding improved friction vibration dampers, it has still not been possible to create a friction vibration damper that would make it possible to solve the issues of smooth running of cars, especially empty and lightly loaded ones.
In operation, the coefficient of dynamic overload in empty cars on TsNII-KhZ-O bogies is twice as large as in loaded ones.
As will be shown below, this drawback can be eliminated by means of a plate-type friction vibration damper (Fig. 1), which forms a single whole with the central spring suspension of the freight bogie.
The friction plate is suspended at the top from the side frame of the bogie by means of a roller, and at the bottom rests on a spring; therefore it is a lever of the second kind (Fig. 1). In an empty car the center plate beam is closer to the hinge of the friction plate, whereas in a loaded car it is closer to the elastic support. As a result, in an empty car the friction plates are pressed more strongly against the bolster beam than in a loaded one.
Fig. 1
The force with which the friction plate presses on the center plate beam, according to Fig. 1, is equal to:
a) for an empty car
\[ N_{\mathrm{in}} = N \frac{l}{a + f_{\mathrm{n}} \pm \mu \cdot b}, \tag{1} \]
where
\[ N = 750\ \text{kg} \]
is the initial compression of the spring of the friction plate,
\(a = 10\ \mathrm{cm}\) — distance from the upper hinge of the friction plank to the middle of the bolster beam,
\(l = 21\ \mathrm{cm}\) — distance from the hinge to the elastic support of the friction plank,
\(f_p = 0.5\ \mathrm{cm}\) — deformation of the main springs for an empty car;
b) for a loaded car
\[ N_{ig}=N\frac{l}{a+f_g\pm \mu b}. \tag{2} \]
Because the friction plank is suspended eccentrically on the side frame:
- The friction force during downward motion contributes to a reduction of the pressure of the friction plank on the bolster beam:
a) for an empty car
\[ N_{np}=N\frac{l}{a+f_p+\mu_n b}, \tag{3} \]
where
\(\mu_n\) — coefficient of friction during downward motion;
\(b=10\ \mathrm{cm}\) — eccentricity of application of the friction force;
b) for a loaded car
\[ N_{ng}=N\frac{l}{a+f_g+\mu_n b}. \tag{4} \]
\(f_g=46\ \mathrm{cm}\) — deformation of the main springs for a loaded car.
- The friction force during upward motion contributes to an increase of the pressure of the friction plank on the bolster beam:
a) for an empty car
\[ N_{vp}=N\frac{l}{a+f_p-\mu_v b}, \tag{5} \]
where
\(\mu_v=0.2\) — coefficient of friction during upward motion;
b) for a loaded car
\[ N_{vg}=N\frac{l}{a+f_g-\mu_v b}. \tag{6} \]
Consequently, the coefficient of relative friction for an empty car during downward
\[ \varphi_{np}=\frac{2\mu\cdot N_{np}}{zh\cdot f_p} \tag{7} \]
and upward motion
\[ \varphi_{vp}=\frac{2\mu\cdot N_{vp}}{zh\cdot f_p}; \tag{8} \]
for a loaded car during downward
\[ \varphi_{ng}=\frac{2\mu\cdot N_{ng}}{zh\cdot f_g} \tag{9} \]
and upward motion
\[ \varphi_{vg}=\frac{2\mu\cdot N_{vg}}{zh\cdot f_g}, \tag{10} \]
where
\(zh\) — stiffness of the spring assembly.
The results of calculations of the coefficients of relative friction for the MT-50 and TsNII-Kh3-O bogies, equipped with a plate-type vibration damper, are presented in Table 1.
It follows from the table that the coefficient of relative friction in a plate-type friction vibration damper depends on its parameters \(a, l, f_{\mathrm{n}}, f_{\mathrm{g}}, \mu_{\mathrm{n}}\), and \(\mu_{\mathrm{v}}\). The operating diagram of this vibration damper is shown in Fig. 2.
Table 1
| Bogie type | Parameters of the plate-type vibration damper | Coefficient of friction | Empty car \(\varphi_{\mathrm{n}}\) | Empty car \(\varphi_{\mathrm{v}}\) | Loaded car \(\varphi_{\mathrm{n}}\) | Loaded car \(\varphi_{\mathrm{v}}\) |
|---|---|---|---|---|---|---|
| MT-50 | \(a=b=100\) mm \(l=210\) mm \(f_{\mathrm{n}}=5\) mm \(f_{\mathrm{g}}=22\) mm \(\varkappa=900\) kg/mm \(N=750\) kg |
\(0,2\) | \(0,11\) | \(0,16\) | \(0,02\) | \(0,03\) |
| MT-50 | \(a=b=100\) mm \(l=210\) mm \(f_{\mathrm{n}}=5\) mm \(f_{\mathrm{g}}=22\) mm \(\varkappa=900\) kg/mm \(N=750\) kg |
\(0,3\) | \(0,15\) | \(0,28\) | \(0,03\) | \(0,05\) |
| MT-50 | \(a=b=100\) mm \(l=210\) mm \(f_{\mathrm{n}}=5\) mm \(f_{\mathrm{g}}=22\) mm \(\varkappa=900\) kg/mm \(N=750\) kg |
\(0,4\) | \(0,19\) | \(0,43\) | \(0,38\) | \(0,76\) |
| MT-50 | \(a=b=100\) mm \(l=210\) mm \(f_{\mathrm{n}}=5\) mm \(f_{\mathrm{g}}=22\) mm \(\varkappa=900\) kg/mm \(N=750\) kg |
\(\mu_{\mathrm{n}}=0,2\) \(\mu_{\mathrm{v}}=0,4\) |
\(0,11\) | \(0,43\) | \(0,02\) | \(0,076\) |
| TsNII-KhZ-O | \(a=b=100\) mm \(l=220\) mm \(f_{\mathrm{n}}=12\) mm \(f_{\mathrm{g}}=64\) mm \(\varkappa=312\) kg/mm \(N=750\) kg |
\(0,2\) | \(0,13\) | \(0,19\) | \(0,18\) | \(0,023\) |
| TsNII-KhZ-O | \(a=b=100\) mm \(l=220\) mm \(f_{\mathrm{n}}=12\) mm \(f_{\mathrm{g}}=64\) mm \(\varkappa=312\) kg/mm \(N=750\) kg |
\(0,3\) | \(0,18\) | \(0,32\) | \(0,025\) | \(0,037\) |
| TsNII-KhZ-O | \(a=b=100\) mm \(l=220\) mm \(f_{\mathrm{n}}=12\) mm \(f_{\mathrm{g}}=64\) mm \(\varkappa=312\) kg/mm \(N=750\) kg |
\(0,4\) | \(0,25\) | \(0,51\) | \(0,031\) | \(0,044\) |
| TsNII-KhZ-O | \(a=b=100\) mm \(l=220\) mm \(f_{\mathrm{n}}=12\) mm \(f_{\mathrm{g}}=64\) mm \(\varkappa=312\) kg/mm \(N=750\) kg |
\(\mu_{\mathrm{n}}=0,2\) \(\mu_{\mathrm{v}}=0,4\) |
\(0,13\) | \(0,51\) | \(0,018\) | \(0,044\) |
In a plate-type vibration damper it is possible to obtain the condition \(\varphi_{\mathrm{v}} \gg \varphi_{\mathrm{n}}\), i.e., a one-sided vibration damper.
Fig. 2
One-sided and two-sided vibration dampers, under the action of a disturbing force, can ensure stability of the vibration process if the condition is imposed that the magnitude of deformation from the impact impulse be equal to the reduction of the vibration amplitude by the resistance forces over one period for the two-sided damper,
\[ z_s=\frac{4\varphi_{\mathrm{d}}}{1-\varphi_{\mathrm{d}}^{2}}\cdot f_{\mathrm{d}} . \tag{11} \]
and for the one-sided damper
\[ z_s=\frac{2\varphi_{\mathrm{o}}}{1-\varphi_{\mathrm{o}}}\cdot f_{\mathrm{o}}, \tag{12} \]
where
\[ \varphi_{\mathrm{d}} \]
is the coefficient of relative friction for the two-sided vibration damper;
\[ \varphi_{\mathrm{o}} \]
is the coefficient of relative friction for the one-sided vibration damper;
\[ f_{\mathrm{d}}=\frac{P}{\varkappa(1+\varphi_{\mathrm{d}})} \]
is the static deflection of the spring set in a two-sided vibration damper;
\[ f_0=\frac{P}{\zh} \]
is the static deflection of the spring set with a one-sided damper;
\(P\) is the static load;
\(\zh\) is the stiffness of the spring set.
In addition, in order to ensure stable motion of the system at resonance, it is necessary that the influx of energy into the system in the form of the work of the disturbing force over one period be equal to the work of the resistance forces of the damper over the same interval of time for a two-sided damper,
\[ \zh z_s\cdot \frac{4\varphi_d}{1-\varphi_d^2}\cdot f_d, \]
i.e., that the equality hold
\[ \pi P_0 z_s=\zh z_s\frac{4\varphi_d}{1-\varphi_d^2}\cdot f_d,\quad \text{when } \varphi_d^2=0, \]
whence
\[ \varphi_d=\frac{\pi P_0}{4\zh\cdot f_d}. \]
This formula was obtained by I. I. Chelnokov (1) by another method. If the work of the resistance forces of a two-sided damper is equated to that of a one-sided damper, then we obtain:
\[ \zh z_s\cdot \frac{4\varphi_d}{1-\varphi_d^2}\cdot f_d = \zh z_s\frac{2\varphi_o}{1-\varphi_o}\cdot f_o, \tag{14} \]
whence, for \(\varphi_d^2=0;\ f_o=f_d\), we have
\[ \varphi_o=\frac{2\varphi_d}{1+2\varphi_d}. \tag{15} \]
Thus, the relative-friction coefficient of a two-sided vibration damper is greater than that of a one-sided damper,
\[ \varphi_d:\varphi_o=\varphi_d:\frac{2\varphi_d}{1+2\varphi_d} =\frac{1+2\varphi_d}{2}. \tag{16} \]
With this ratio, the probability of transmitting the load to the unsprung parts of the car at the moment when the disturbing load began to act during rebound of the damper will decrease.
Figure 3 shows a removable plate-type vibration damper, which consists of a yoke 1, two friction strips 2, fastened by means of rollers 3 to the base 4. This damper is installed together with the spring set between the bolster beam and the lower chord of the bogie side frame.
Fig. 3
The friction force of the friction strip on the yoke increases when the spring set is compressed. Therefore equation (1) takes the form:
\[ N_{in}=N\frac{l}{a-f_n\pm \mu b}, \tag{17} \]
i.e., as the deformation of the spring set increases, the force \(N_{in}\) increases, and consequently the friction force as well, especially when \(a-f_n\) approxi-
tends to zero. The operating diagram of this damper is shown in Fig. 4.
In this diagram, as the load increases from 0 to \(P_1\) (empty mode), the deflection of the spring changes along a straight line, and further, in the loaded mode, along the curve \(ab\) (2). The latter makes it possible to obtain constant accelerations and frequencies of oscillation provided that \(\dfrac{P}{\text{ж}}=\text{const}\), where \(\text{ж}\) is the stiffness of the spring. The condition \(\left(\dfrac{P}{\text{ж}}=\text{const}\right)\) is possible if there is the following relation between the load \(P\) and the deflection \(x\):
Fig. 4
\[ P=P_1 \cdot e^{\frac{x-f_1}{f}} . \tag{18} \]
Expression (18) is the equation of the ideal curve giving the relation between the load and the deflection in the springs that ensures constant accelerations in the empty and loaded operating modes of cars.
Conclusions
In conclusion it should be noted that the leaf-type friction vibration damper, as follows from the calculation and design, possesses certain advantages that place it above wedge dampers. Of these advantages, the following are the most important:
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The coefficient of relative friction during upward motion is greater than during downward motion.
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The coefficient of relative friction for an empty car is greater than for a loaded car.
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Elastic restraint of the center-plate beam relative to the side frames will make it possible to increase the stability of the side frames, reduce lateral oscillations, wear of the wheel rolling surfaces, and flange undercutting, if the joint between the friction plank and the center-plate beam is made in the form of a dihedral angle.
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The increased flexibility of the main springs, which will enable the springs to soften lateral rocking.
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Reliable operation of the vibration damper, i.e., absence of its jamming.
It is comparatively easy to equip existing freight bogies with a leaf-type friction vibration damper, especially a removable one with an aperiodic characteristic. These properties of the leaf-type friction vibration damper are of great importance for operation, for the running qualities of empty and lightly loaded cars, and for the safety of train movement at increased speeds.
LITERATURE
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I. I. Chelnokov. Determination of the parameters of vibration dampers for freight cars. Abstract of doctoral dissertation, L., 1955.
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M. V. Vinokurov. Investigation of oscillations and stability of cars. Proceedings of DIIT, issue 12, 1949.