9 research outputs found
ΠΠΈΠ·Π½Π°ΡΠ΅Π½Π½Ρ Ρ Π°ΡΠ°ΠΊΡΠ΅ΡΠΈΡΡΠΈΠΊ Π²`ΡΠ·ΠΊΠΎΠ³ΠΎ ΡΠ΅ΡΡΡ Π² ΠΎΠΏΠΎΡΠ°Ρ ΠΊΠΎΠ²Π·Π°Π½Π½Ρ ΠΌΠ΅ΡΠΎΠ΄ΠΎΠΌ ΠΌΠ°ΡΡΠ½ΠΈΠΊΠ°
We analyzed the methods of determining the characteristics of friction based on the experimental studies using the damped oscillations of a pendulum. It was established that the available studies into characteristics of viscous friction lack the analytical description of the process of damped oscillations at viscous resistance and recommendations regarding practical calculation of the characteristics of friction. Here we propose a theoretical model of the swinging pendulum in the cylindrical sliding supports with a lubricant. It is demonstrated that for a pendulum in the lubricated sliding supports, the process of oscillations is described by a second order differential equation with viscous resistance, proportional to the deflection velocity of the pendulum.It is found based on the solution of the equation that the ratio of adjacent amplitudes of damped oscillations is a constant magnitude, hence it follows that the absorption coefficient is constant over the entire process. We established, based on the theoretical model of pendulum oscillations, that for the viscous friction the absorption coefficient is equal to the doubled logarithmic damping decrement and is determined by one or a cycle of oscillations. The formulas are received for calculating the indicator of dynamic viscosity of a lubricant in the contact by the decrement of pendulum oscillations damping. The developed procedures for determining the characteristics of viscous friction are applied to examine the contact- viscous properties of different combinations of lubricating and design materials. The results received are aimed at searching for design and technological solutions in order to reduce the energy losses to friction in the sliding supports of machines.Π’Π΅ΠΎΡΠ΅ΡΠΈΡΠ΅ΡΠΊΠΈ ΠΏΠΎΠΊΠ°Π·Π°Π½ΠΎ, ΡΡΠΎ Π΄Π»Ρ ΠΌΠ°ΡΡΠ½ΠΈΠΊΠ° Π² ΡΠΌΠ°Π·Π°Π½Π½ΡΡ
ΠΎΠΏΠΎΡΠ°Ρ
ΡΠΊΠΎΠ»ΡΠΆΠ΅Π½ΠΈΡ ΠΏΡΠΎΡΠ΅ΡΡ ΠΊΠΎΠ»Π΅Π±Π°Π½ΠΈΠΉ ΠΎΠΏΠΈΡΡΠ²Π°Π΅ΡΡΡ Π΄ΠΈΡΡΠ΅ΡΠ΅Π½ΡΠΈΠ°Π»ΡΠ½ΡΠΌ ΡΡΠ°Π²Π½Π΅Π½ΠΈΠ΅ΠΌ Π²ΡΠΎΡΠΎΠ³ΠΎ ΠΏΠΎΡΡΠ΄ΠΊΠ° Ρ Π²ΡΠ·ΠΊΠΈΠΌ ΡΠΎΠΏΡΠΎΡΠΈΠ²Π»Π΅Π½ΠΈΠ΅ΠΌ, ΠΏΡΠΎΠΏΠΎΡΡΠΈΠΎΠ½Π°Π»ΡΠ½ΡΠΌ ΡΠΊΠΎΡΠΎΡΡΠΈ ΠΊΠΎΠ»Π΅Π±Π°Π½ΠΈΠΉ. ΠΠ° ΠΎΡΠ½ΠΎΠ²Π΅ ΠΌΠΎΠ΄Π΅Π»ΠΈ ΠΊΠΎΠ»Π΅Π±Π°Π½ΠΈΠΉ ΠΌΠ°ΡΡΠ½ΠΈΠΊΠ° ΠΏΠΎΠ»ΡΡΠ΅Π½ΠΎ, ΡΡΠΎ ΠΊΠΎΡΡΡΠΈΡΠΈΠ΅Π½Ρ ΠΏΠΎΠ³Π»ΠΎΡΠ΅Π½ΠΈΡ ΡΠ½Π΅ΡΠ³ΠΈΠΈ ΡΠ°Π²Π΅Π½ ΡΠ΄Π²ΠΎΠ΅Π½Π½ΠΎΠΌΡ Π»ΠΎΠ³Π°ΡΠΈΡΠΌΠΈΡΠ΅ΡΠΊΠΎΠΌΡ Π΄Π΅ΠΊΡΠ΅ΠΌΠ΅Π½ΡΡ Π·Π°ΡΡΡ
Π°Π½ΠΈΡ. ΠΠΏΡΠ΅Π΄Π΅Π»Π΅Π½Π° ΠΏΡΠΎΡΠ΅Π΄ΡΡΠ° ΡΠ°ΡΡΠ΅ΡΠ° Π΄ΠΈΠ½Π°ΠΌΠΈΡΠ΅ΡΠΊΠΎΠΉ Π²ΡΠ·ΠΊΠΎΡΡΠΈ ΡΠΌΠ°Π·ΠΊΠΈ ΠΏΠΎ Π΄Π΅ΠΊΡΠ΅ΠΌΠ΅Π½ΡΡ Π·Π°ΡΡΡ
Π°Π½ΠΈΡ ΠΊΠΎΠ»Π΅Π±Π°Π½ΠΈΠΉΠ’Π΅ΠΎΡΠ΅ΡΠΈΡΠ½ΠΎ ΠΏΠΎΠΊΠ°Π·Π°Π½ΠΎ, ΡΠΎ Π΄Π»Ρ ΠΌΠ°ΡΡΠ½ΠΈΠΊΠ° Ρ Π·ΠΌΠ°ΡΠ΅Π½ΠΈΡ
ΠΎΠΏΠΎΡΠ°Ρ
ΠΊΠΎΠ²Π·Π°Π½Π½Ρ ΠΏΡΠΎΡΠ΅Ρ ΠΊΠΎΠ»ΠΈΠ²Π°Π½Ρ ΠΎΠΏΠΈΡΡΡΡΡΡΡ Π΄ΠΈΡΠ΅ΡΠ΅Π½ΡΡΠ°Π»ΡΠ½ΠΈΠΌ ΡΡΠ²Π½ΡΠ½Π½ΡΠΌ Π΄ΡΡΠ³ΠΎΠ³ΠΎ ΠΏΠΎΡΡΠ΄ΠΊΡ Π· Π²`ΡΠ·ΠΊΠΈΠΌ ΠΎΠΏΠΎΡΠΎΠΌ, ΠΏΡΠΎΠΏΠΎΡΡΡΠΉΠ½ΠΈΠΌ ΡΠ²ΠΈΠ΄ΠΊΠΎΡΡΡ ΠΊΠΎΠ»ΠΈΠ²Π°Π½Ρ. ΠΠ° ΠΎΡΠ½ΠΎΠ²Ρ ΠΌΠΎΠ΄Π΅Π»Ρ ΠΊΠΎΠ»ΠΈΠ²Π°Π½Ρ ΠΌΠ°ΡΡΠ½ΠΈΠΊΠ° ΠΎΡΡΠΈΠΌΠ°Π½ΠΎ, ΡΠΎ ΠΊΠΎΠ΅ΡΡΡΡΡΠ½Ρ ΠΏΠΎΠ³Π»ΠΈΠ½Π°Π½Π½Ρ Π΅Π½Π΅ΡΠ³ΡΡ Π΄ΠΎΡΡΠ²Π½ΡΡ ΠΏΠΎΠ΄Π²ΡΠΉΠ½ΠΎΠΌΡ Π»ΠΎΠ³Π°ΡΠΈΡΠΌΡΡΠ½ΠΎΠΌΡ Π΄Π΅ΠΊΡΠ΅ΠΌΠ΅Π½ΡΡ Π·Π°ΡΡΡ
Π°Π½Ρ. ΠΠΈΠ·Π½Π°ΡΠ΅Π½Π° ΠΏΡΠΎΡΠ΅Π΄ΡΡΠ° ΡΠΎΠ·ΡΠ°Ρ
ΡΠ½ΠΊΡ Π΄ΠΈΠ½Π°ΠΌΡΡΠ½ΠΎΡ Π²`ΡΠ·ΠΊΠΎΡΡΡ ΠΌΠ°ΡΡΠΈΠ»Π° ΠΏΠΎ Π΄Π΅ΠΊΡΠ΅ΠΌΠ΅Π½ΡΡ Π·Π°ΡΡΡ
Π°Π½Ρ ΠΊΠΎΠ»ΠΈΠ²Π°Π½
ΠΠΈΠ·Π½Π°ΡΠ΅Π½Π½Ρ Ρ Π°ΡΠ°ΠΊΡΠ΅ΡΠΈΡΡΠΈΠΊ Π²`ΡΠ·ΠΊΠΎΠ³ΠΎ ΡΠ΅ΡΡΡ Π² ΠΎΠΏΠΎΡΠ°Ρ ΠΊΠΎΠ²Π·Π°Π½Π½Ρ ΠΌΠ΅ΡΠΎΠ΄ΠΎΠΌ ΠΌΠ°ΡΡΠ½ΠΈΠΊΠ°
We analyzed the methods of determining the characteristics of
friction based on the experimental studies using the damped oscillations
of a pendulum. It was established that the available studies
into characteristics of viscous friction lack the analytical description
of the process of damped oscillations at viscous resistance and recommendations
regarding practical calculation of the characteristics
of friction. Here we propose a theoretical model of the swinging
pendulum in the cylindrical sliding supports with a lubricant. It is
demonstrated that for a pendulum in the lubricated sliding supports,
the process of oscillations is described by a second order differential
equation with viscous resistance, proportional to the deflection velocity
of the pendulum.
It is found based on the solution of the equation that the ratio
of adjacent amplitudes of damped oscillations is a constant magnitude,
hence it follows that the absorption coefficient is constant
over the entire process. We established, based on the theoretical
model of pendulum oscillations, that for the viscous friction
the absorption coefficient is equal to the doubled logarithmic
damping decrement and is determined by one or a cycle of oscillations.
The formulas are received for calculating the indicator of
dynamic viscosity of a lubricant in the contact by the decrement
of pendulum oscillations damping. The developed procedures for
determining the characteristics of viscous friction are applied to
examine the contact- viscous properties of different combinations
of lubricating and design materials. The results received are
aimed at searching for design and technological solutions in order
to reduce the energy losses to friction in the sliding supports of
machines. Π’Π΅ΠΎΡΠ΅ΡΠΈΡΠ½ΠΎ ΠΏΠΎΠΊΠ°Π·Π°Π½ΠΎ, ΡΠΎ Π΄Π»Ρ ΠΌΠ°ΡΡΠ½ΠΈΠΊΠ° Ρ
Π·ΠΌΠ°ΡΠ΅Π½ΠΈΡ
ΠΎΠΏΠΎΡΠ°Ρ
ΠΊΠΎΠ²Π·Π°Π½Π½Ρ ΠΏΡΠΎΡΠ΅Ρ ΠΊΠΎΠ»ΠΈΠ²Π°Π½Ρ
ΠΎΠΏΠΈΡΡΡΡΡΡΡ Π΄ΠΈΡΠ΅ΡΠ΅Π½ΡΡΠ°Π»ΡΠ½ΠΈΠΌ ΡΡΠ²Π½ΡΠ½Π½ΡΠΌ Π΄ΡΡ-
Π³ΠΎΠ³ΠΎ ΠΏΠΎΡΡΠ΄ΠΊΡ Π· Π²`ΡΠ·ΠΊΠΈΠΌ ΠΎΠΏΠΎΡΠΎΠΌ, ΠΏΡΠΎΠΏΠΎΡΡΡΠΉΠ½ΠΈΠΌ
ΡΠ²ΠΈΠ΄ΠΊΠΎΡΡΡ ΠΊΠΎΠ»ΠΈΠ²Π°Π½Ρ. ΠΠ° ΠΎΡΠ½ΠΎΠ²Ρ ΠΌΠΎΠ΄Π΅Π»Ρ ΠΊΠΎΠ»ΠΈ-
Π²Π°Π½Ρ ΠΌΠ°ΡΡΠ½ΠΈΠΊΠ° ΠΎΡΡΠΈΠΌΠ°Π½ΠΎ, ΡΠΎ ΠΊΠΎΠ΅ΡΡΡΡΡΠ½Ρ
ΠΏΠΎΠ³Π»ΠΈΠ½Π°Π½Π½Ρ Π΅Π½Π΅ΡΠ³ΡΡ Π΄ΠΎΡΡΠ²Π½ΡΡ ΠΏΠΎΠ΄Π²ΡΠΉΠ½ΠΎΠΌΡ Π»ΠΎΠ³Π°-
ΡΠΈΡΠΌΡΡΠ½ΠΎΠΌΡ Π΄Π΅ΠΊΡΠ΅ΠΌΠ΅Π½ΡΡ Π·Π°ΡΡΡ
Π°Π½Ρ. ΠΠΈΠ·Π½Π°ΡΠ΅Π½Π°
ΠΏΡΠΎΡΠ΅Π΄ΡΡΠ° ΡΠΎΠ·ΡΠ°Ρ
ΡΠ½ΠΊΡ Π΄ΠΈΠ½Π°ΠΌΡΡΠ½ΠΎΡ Π²`ΡΠ·ΠΊΠΎΡΡΡ
ΠΌΠ°ΡΡΠΈΠ»Π° ΠΏΠΎ Π΄Π΅ΠΊΡΠ΅ΠΌΠ΅Π½ΡΡ Π·Π°ΡΡΡ
Π°Π½Ρ ΠΊΠΎΠ»ΠΈΠ²Π°Π½Ρ