CN107945626B - Mechanical type micro-dynamic inclined plane friction coefficient measuring experiment instrument - Google Patents
Mechanical type micro-dynamic inclined plane friction coefficient measuring experiment instrument Download PDFInfo
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- G—PHYSICS
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- G09B—EDUCATIONAL OR DEMONSTRATION APPLIANCES; APPLIANCES FOR TEACHING, OR COMMUNICATING WITH, THE BLIND, DEAF OR MUTE; MODELS; PLANETARIA; GLOBES; MAPS; DIAGRAMS
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Abstract
The invention relates to a friction coefficient measurement experiment instrument which comprises a horizontal table and an inclined plane experiment table, wherein the inclined plane experiment table comprises a base, a rotating inclined plane arranged on the base, an inclined plane rotating fixed rod arranged on one end of the base far away from the horizontal table, an inclined plane inclination angle thick screw rod and an inclined plane inclination angle thin screw rod. The friction coefficient measurement experiment instrument has the advantages of high precision, small error, convenience in operation, low manufacturing cost and the like.
Description
Technical Field
The invention relates to a teaching experiment instrument, in particular to a mechanical micro-inclined plane friction coefficient measuring experiment instrument.
Background
The method for measuring the dynamic friction coefficient and the static friction coefficient is various, and the inclined plane method is definitely the simplest and most convenient one.
Although measuring instruments for dynamic and static friction coefficients of various materials are already available on the market, no instrument for measuring dynamic and static friction coefficients by continuously and accurately changing the inclination angle of an inclined plane is adopted in laboratories of universities and middle schools at present. Even abroad, no mechanical instrument is adopted for continuous and accurate inclined plane inclination angle adjustment experiment. The old method for measuring the inclined plane inclination angle by manually lifting the inclined plane to rotate around the low-end rotating shaft is widely adopted, the inclined plane inclination angle is changed by using the operation, the accuracy is low, the error is large, and the operation of continuously changing the inclined plane inclination angle is difficult to control. At present, the photoelectric method is adopted to accurately measure the inclined plane inclination angle in the market, so that the power is consumed, and the energy conservation and the environmental protection are not facilitated. The applicant applied for patent number ZL201310328276.8, "high-precision fine-tuning slope measuring static and dynamic and cylinder rolling friction coefficient experiment instrument", in 12 months of 2015, has the following defects although a mechanical screw is adopted to continuously and accurately change the slope inclination angle to measure the dynamic and static friction coefficients of various materials: (1) The inclined plane terminal fixed shaft slideway and the vernier slideway are adopted at one side of the inclined plane, so that great inconvenience is caused to the operation of an experimenter, and the experimenter is difficult to observe experimental phenomena and measure; (2) A plurality of slide ways and a major scale with large diameter are adopted, so that materials are wasted and the manufacturing cost is high; (3) Fixing the vernier on the side of the rotating inclined plane is difficult and unstable; (4) The vernier slide way and the inclined plane terminal sliding shaft slide way frame are fixed on the experiment instrument support, so that great inconvenience is brought to an experimenter in observing experimental phenomena and measuring parameters; (5) The adoption of single cursor reading can bring an indelible system error to the measurement of the inclination angle of the rotating inclined plane; in view of this, the applicant has invented a "mechanical type micro-inclined plane measuring friction coefficient experimental apparatus", which is an improvement (innovation) of the above-mentioned defects of the prior patent of patent number ZL201310328276.8, and the innovative patent of the invention is more beneficial to the experimenter to observe experimental phenomena and parameter measurement easily and to operate conveniently.
The invention can also be used in the related field of research by the related scientific researchers through changing the inclination angle. Based on the above, the instrument and the equipment produced by the technology of the patent can bring very great economic benefit to manufacturers.
Disclosure of Invention
In order to solve the technical problems, the invention aims to provide the friction coefficient measurement experiment instrument which has the advantages of high precision, small error, convenient operation, low manufacturing cost and the like.
In order to achieve the above purpose, the present invention adopts the following technical scheme:
the mechanical type micro-dynamic inclined plane friction coefficient measuring experiment instrument comprises a horizontal table and an inclined plane experiment table, wherein the inclined plane experiment table comprises a base, a rotating inclined plane arranged on the base, an inclined plane rotating fixed rod arranged on one end of the base far away from the horizontal table, an inclined plane inclination angle thick screw rod and an inclined plane inclination angle thin screw rod; the lower end of the inclined plane inclination angle coarse screw rod is connected with the inclined plane inclination angle fine screw rod through a fine screw rod spiral ring, the inclined plane inclination angle fine screw rod is hinged with the base through a rotating shaft I, the inclined plane rotation fixing rod is hinged with the base through a rotating shaft II, and the distance between the rotating shaft I and the horizontal table is larger than the distance between the rotating shaft II and the horizontal table; one end of the rotating inclined plane is hinged with the horizontal table through a rotating shaft III, and the other end of the rotating inclined plane is connected with the inclined plane inclination angle coarse screw rod through a coarse screw rod spiral ring; the thin screw rod spiral ring is arranged on the inclined-plane inclined-angle thin screw rod and can move up and down along the inclined-plane inclined-angle thin screw rod, and the thick screw rod spiral ring is arranged on the inclined-plane inclined-angle thick screw rod and can move up and down along the inclined-plane inclined-angle thick screw rod; a main scale disc and a vernier disc are also fixed on the rotating shaft III, wherein the main scale disc (8) is fixed, and the vernier disc (9) rotates along with the rotating inclined plane (4); the main scale disc is circular, main scales are engraved on the outer edge of the main scale disc, a left vernier and a right vernier which are matched with the main scale disc are arranged on the outer edge of the vernier disc, and a connecting line at the center of the left vernier and the right vernier passes through the center of the rotating shaft III; the inclined plane rotates and sets up the dead lever spout along its length direction on the dead lever, is provided with the dead lever in the dead lever spout and rotates the slide shaft, the both ends that the dead lever rotated the slide shaft can be fixed on rotating the inclined plane.
Preferably, leveling support legs are arranged at the bottoms of the horizontal table and the inclined surface experiment table, and leveling horizontal bubbles are arranged on the rotating inclined surface.
Preferably, the leveling support leg comprises a support leg seat, a leveling threaded rod, a leveling lifting sleeve and a leveling lifting rod, wherein the upper end of the leveling lifting rod is fixed on the lower end face of the horizontal table or the base, the leveling lifting sleeve is sleeved on the leveling lifting rod and is in threaded connection with the leveling threaded rod, and the lower end of the leveling threaded rod is fixed on the support leg seat.
Preferably, a support column is arranged at one end, close to the horizontal platform, of the base, the rotating shaft III is arranged on the support column, and the height of the position where the rotating shaft III is located is consistent with the height of the horizontal platform.
Preferably, the main scale disc shaft is arranged on the rotating shaft III and is fixed on the support column through six screws.
Preferably, the vernier disc shaft is arranged on the rotating shaft III and is tightly attached to the main scale disc.
Preferably, the lower end of the inclined-plane inclination angle thick screw rod is kept fixed with the thin screw rod spiral through the left and right tightening nuts, and the outer sides of the thick screw rod spiral and the thin screw rod spiral are respectively provided with a rotating handle.
Compared with the prior art, the invention has the beneficial effects that:
(1) The rotating inclined plane terminal and the base are connected through thick and thin screw rods by adopting a double-rotating-shaft structure and the combination adjustment of thick and thin screw rings, so that the continuous micro-motion of the rotating inclined plane around the rotating shaft III is realized;
(2) The main scale (0-360 degrees) and the vernier scale (0 ' -30 ') are adopted for matching reading, so that the accurate reading (the accuracy reaches 1 ') of rotating the inclined plane to a certain angle (namely, the inclination angle of the rotating inclined plane relative to the horizontal plane) is improved;
(3) The novel invention patent avoids the inconvenience brought to experimental operation and experimental measurement because the inclined plane terminal moving shaft and the vernier slide way are arranged on the side face in the original invention patent of patent number ZL 201310328276.8; according to the novel invention, a main ruler with the diameter of 20cm is adopted, and an inclined plane rotation fixing rod is adopted to support and stably rotate an inclined plane, so that the operation and measurement of an experimenter are not affected;
(4) The reading of the double vernier system is adopted to measure the rotating angle of the rotating inclined plane, which is beneficial to eliminating the system error caused by the misalignment (namely the eccentric difference) of the rotating main shaft and the geometric main shaft;
(5) In a specific experiment, the tightening nuts adopted at different positions ensure the stability of the whole instrument;
(6) The dynamic and static friction coefficients of various materials can be accurately measured, such as: testing dynamic and static friction coefficients of various materials such as various metals, wood, paper, plastic films, sheets and the like;
(7) The special design structure adopted by the novel invention greatly saves the manufacturing materials of experimental instruments and reduces the production cost for manufacturers.
Drawings
Fig. 1 is a front view of the experimental apparatus in full view.
Fig. 2 is a schematic structural view of the leveling foot.
Fig. 3 is a top view of the experimental apparatus in an initial state.
Fig. 4 is a diagram of a method of nesting a main scale disc with a left support bar, a vernier disc, and a main scale disc connected with a rotating shaft of the vernier disc.
FIG. 5 is a main scale disk a fixed schematic.
Fig. 6 is a schematic structural view of the vernier disc.
Fig. 7 is a diagram showing the rotation of the rotary inclined plane of the experimental instrument to a certain inclination angle.
Fig. 8 is a schematic structural view of a support column.
Fig. 9 is a schematic diagram of the cooperation of the fixed rod slide shaft and the rotating inclined plane.
Fig. 10 is a schematic view of the structure of the inclined surface rotation fixing lever.
FIG. 11 is a diagram showing the connection of a rotating ramp to a ramp angle thick lead screw.
FIG. 12 is a schematic diagram showing the connection between a base and a thin inclined-angle screw rod, and between a thick inclined-angle screw rod and a thin inclined-angle screw rod.
FIG. 13 is a schematic view of a circular slider.
Fig. 14 is a schematic diagram of reading accuracy of the reading system.
Fig. 15 is a schematic diagram showing the state of reading the initial and final positions corresponding to the vernier with a certain inclination angle by rotating the inclined plane.
Fig. 16 is a schematic diagram of a dual vernier correction of different axes.
FIG. 17 is an example analysis of high accuracy measurement of dynamic and static friction coefficients on a rotating ramp.
FIG. 18 is a schematic diagram of the rolling force of a cylinder on a rotating ramp.
Detailed Description
The following describes the embodiments of the present invention in detail with reference to the drawings.
The mechanical type micro-dynamic inclined plane friction coefficient measuring experiment instrument shown in fig. 1, 3 and 7 comprises a horizontal table 1 and an inclined plane experiment table 2. The inclined plane experiment table 2 comprises a base 3, a rotating inclined plane 4 arranged on the base 3, an inclined plane rotating fixed rod 5 arranged on the base 3 and far away from one end of the horizontal table 1, an inclined plane inclination angle thick screw rod 6 and an inclined plane inclination angle thin screw rod 7. In order to facilitate the adjustment of the level, leveling support legs 10 are arranged at the bottoms of the horizontal table 1 and the inclined surface experiment table 2, and leveling horizontal bubbles 11 of the same type are arranged on the rotary inclined surface 4 and the horizontal table 1.
Wherein, the thick screw pole of inclined plane inclination 6 lower extreme is connected with the thin screw pole of inclined plane inclination 7 through thin screw pole helicoidal 71, and the thin screw pole of inclined plane inclination 7 is connected and is articulated with base 3 through pivot I41, and inclined plane rotation dead lever 5 is articulated with base 3 through pivot II 42. And, the distance between the rotating shaft I41 and the horizontal table 1 is larger than the distance between the rotating shaft II 42 and the horizontal table 1. One end of the rotating inclined plane 4 is hinged with the horizontal table 1 through a rotating shaft III 43, and the other end of the rotating inclined plane 4 is connected with the inclined plane inclination angle coarse screw rod 6 through a coarse screw rod screw ring 61. Wherein, the thin screw rod screw ring 71 is arranged on the inclined-angle thin screw rod 7 and can move up and down along the inclined-angle thin screw rod 7, and the thick screw rod screw ring 61 is arranged on the inclined-angle thick screw rod 6 and can move up and down along the inclined-angle thick screw rod 6.
As shown in fig. 1, 4, 5, 6, and 7, a main scale disk 8 and a vernier disk 9 are also fixed to the rotation shaft iii 43. The main scale 8 is circular and has a main scale 81 engraved on its outer periphery. The outer fringe of vernier disc 9 is provided with left vernier 91 and right vernier 92 that match with main scale disc 8, and the line in left vernier 91 and right vernier 92 center department passes the center of pivot III 43.
As shown in fig. 1, 7, 9 and 10, a fixed rod sliding groove 51 is formed in the inclined surface rotation fixed rod 5 along the length direction thereof, a fixed rod sliding shaft 52 is arranged in the fixed rod sliding groove 51, and both ends of the fixed rod sliding shaft 52 are fixed on the rotation inclined surface 4. The base 3 is close to the one end of horizontal stand 1 and is provided with support column 31, and pivot III 43 sets up on support column 31 and pivot III 43 place highly is unanimous with horizontal stand 1 height. The main scale 8 is journalled on the spindle iii 43 and secured to the support column 31 by six screws. The vernier disc 9 is arranged on the rotating shaft III 43 in a shaft way and is tightly attached to the main scale disc 8. The vernier disc (9) is fixed relative to the rotary inclined plane 4 and can rotate along with the rotation of the rotary inclined plane 4.
As shown in fig. 2, the leveling foot 10 includes a foot base 101, a leveling threaded rod 102, a leveling lift sleeve 103, and a leveling lift rod 104. The upper end of a leveling lifting rod 104 is fixed on the lower end face of the horizontal table 1 or the base 3, a leveling lifting sleeve 103 is sleeved on the leveling lifting rod 104 and is in threaded connection with a leveling threaded rod 102, and the lower end of the leveling threaded rod 102 is fixed on a supporting foot seat 101.
As shown in fig. 12, 1 and 7, the lower end of the inclined-angle thick lead screw 6 is fixed to the end of the thin lead screw coil 71 by left and right tightening nuts 62, and the outer sides of the thick lead screw coil 61 and the thin lead screw coil 71 are provided with rotation handles 63.
The principle of correcting the eccentricity ratio by adopting double cursors is as follows:
as shown in fig. 16, a dual cursor correction different axis schematic is shown. Because the center (geometric center) of the main scale of the instrument dial is not necessarily completely coincident with the rotating main shaft (namely, the eccentric difference exists), the reading of the rotating inclined plane from a single micro scale always has errors (namely, instrument errors) in the rotating process, and two vernier scales are designed and symmetrically installed for measuring the inclination angle of the rotating inclined plane, so that the instrument errors caused by the eccentric difference can be corrected. Let O be the geometric center of the main scale and the main scale disk, O 1 If left and right vernier scales are used, the initial readings before rotation of the rotating inclined plane are respectively theta Left 1 、θ Right 1 The end readings of the vernier with the inclined plane rotated to a certain inclination angle are respectively theta Left 2 、θ Right 2 The rotating inclined plane rotates by the angle of
And (3) proving: as shown in FIG. 16, the center of the circle is O when the geometric center of the main scale disk is coincident with the center of the fixed rotation shaft at the lower end of the rotation inclined plane, and the center of the fixed rotation shaft at the lower end of the rotation inclined plane is O when the geometric center of the main scale disk is not coincident with the center of the fixed rotation shaft at the lower end of the rotation inclined plane 1 O is used as two diameters of AC and CD respectively, O is used as 1 As EF// AB and JH// CD, it can be seen that as long as the two centers are coincident, the reading AC arc length or BD arc length read by any vernier is error-free, if the two centers are not coincident, the reading is EJ arc length or HF arc length, and both arc lengths are inaccurate, but EA arc length=fb arc length; JC arc length = HD arc length, there are: AC arc length=bd arc length= (aj+jc) arc length= (df+fb) arc length= (aj+hd) arc length= (df+ea) arc length,
therefore, the expression (1) holds. When the geometric center of the instrument dial main scale is not completely coincident with the fixed rotating shaft at the lower end of the rotating inclined plane, double vernier scale reading is adopted, and 1-type calculation is adopted, so that the rotating angle of the rotating inclined plane around the fixed rotating shaft at the lower end can be accurately measured.
The invention relates to a mechanical micro-dynamic inclined plane friction coefficient measuring experimental instrument, which comprises the following adjusting method:
(1) Firstly, adjusting leveling lifting sleeves 103 on four leveling support legs 10 of a base, changing thick screw rod screw rings 61, changing thin screw rod screw rings 71, enabling leveling horizontal bubbles 11 on a rotating inclined plane 4 to be positioned in the center of a circle, enabling the rotating inclined plane to be positioned in a horizontal state, and respectively reading initial readings alpha of A, B windows 1 、β 1 As shown in fig. 1, 2 and 3; if the dynamic friction coefficient is to be measured, the level of the horizontal table 1 is also adjusted, i.e. by adjusting the leveling elevator sleeves 103 of the four leveling feet 10 of the water platform. As shown in fig. 1, 2 and 3;
(2) Manufacturing a circular sliding block (with a pore at the center) with the diameter of 50.00mm and the thickness of 10.00mm, and placing the sliding block at a preset position of a rotating inclined plane;
(3) Loosening the locking screw of the terminal rotating shaft 2-21 of the rotating inclined plane and the inclined plane inclination angle thin screw rod 7 to enable the screw ring of the thick screw rod to continuously rotate along the radial direction of the thick screw rod of the inclined plane inclination angle change, after a round sliding block of a certain material placed on the rotating inclined plane slides, returning the screw ring of the thick screw rod to a small extent to enable the material sliding block 11 to be just static, and then rotating the screw ring of the inclined plane inclination angle change screw rod to enable the material sliding block to be tested to just slightly move along the rotating inclined plane, wherein the sliding force of the gravity of the sliding block along the inclined plane is equal to the maximum static friction force F of the sliding material mass block relative to the inclined plane i As shown in fig. 1, 3, 7, 12, 15;
(4) The A, B window reading of the rotating inclined plane rotated to a certain angle is respectively alpha by the scale system 2 、β 2 The angle by which the rotating inclined plane rotates (i.e. the inclination angle of the rotating inclined plane relative to the horizontal plane) isAs shown in FIGS. 1, 4 and 7Shown as 15;
(5) In a specific experiment, the inclined surface rotation fixing rod fixing nut 8-4 at the terminal of the rotation inclined surface 4, the left and right tightening nuts 2-21 of the rotation inclined surface terminal connecting shaft 2-2 at the terminal of the rotation inclined surface, the left and right tightening nuts 62 of the inclined surface inclination angle thin screw rod and the rotating shaft I (shown in figures 11 and 12) and the inclined surface rotation fixing rod fixing nut 8-4 of the inclined surface rotation fixing rod 5 (shown in figure 7) are locked so as to meet the stability of the measuring device. Meanwhile, if the coefficient of dynamic friction is to be measured, the tail end of the rotating inclined plane is required to be matched with the starting end of the horizontal table 1.
The precision index of the invention is as follows:
1. the experimental instrument is structurally composed of: mainly comprises a frame, a horizontal fine tuning combination knob, a scale system, a rotary inclined plane inclination angle coarse and fine adjustment system, an experiment horizontal plane and the like.
2. Rotating slope and horizontal plane dimensions: 500.0mm (L). Times.300.0 mm (B). Times.15.0 mm (H);
3. slider specification: manufacturing a circular sliding block with the diameter of 50.00mm (D) and the thickness of 10.00mm (h), flexibly designing the circular sliding block according to different specific measurement materials in actual measurement, wherein the thickness is generally 10.00-15.00 mm, and a clear mark is coated at the circular center of the circular sliding block so as to facilitate the convenient measurement of the positions of the initial sliding block and the final sliding block, and the standard quality of the circular sliding block is weighed out;
4. angular range: 0-85 degrees;
5. precision: 1'.
Example measurement
(1) Firstly, adjusting leveling lifting sleeves 103 on four leveling support legs 10 of a base, changing thick screw rod screw rings 61, changing thin screw rod screw rings 71, enabling leveling horizontal bubbles 11 on a rotating inclined plane 4 to be positioned in the center of a circle, enabling the rotating inclined plane to be positioned in a horizontal state, and respectively reading initial readings of A, B windows to be alpha 1 、β 1 As shown in fig. 1 and 3 (rotational incline horizontal initial position); if the dynamic friction coefficient is to be measured, the level of the horizontal table 1 is also adjusted, i.e. the leveling elevator sleeve 103 is passed through the four leveling feet 10 of the horizontal table. As shown in fig. 1, 2 and 3;
(2) Manufacturing a circular sliding block (with a pore at the center) with the diameter of 50.00mm and the thickness of 10.00mm, and placing the sliding block at a preset position on a rotating inclined plane;
(3) Loosening the locking screw of the terminal rotating shaft 2-21 of the rotating inclined plane and the inclined plane inclination angle thin screw rod 7 to enable the screw ring of the thick screw rod to continuously rotate along the radial direction of the thick screw rod of the inclined plane inclination angle change, after a round sliding block of a certain material placed on the rotating inclined plane slides, returning the screw ring of the thick screw rod to a small extent to enable the material sliding block 11 to be just static, and then rotating the screw ring of the inclined plane inclination angle change screw rod to enable the material sliding block to be tested to just slightly move along the rotating inclined plane, wherein the sliding force of the gravity of the sliding block along the inclined plane is equal to the maximum static friction force F of the sliding material mass block relative to the inclined plane i As shown in fig. 1, 3, 7, 11, 12, 17, 15;
(4) The reading of the A, B window from the inclined plane to a certain inclined angle (namely, the included angle with the horizontal plane) is alpha respectively 2 、β 2 The angle rotated by the rotating inclined plane (i.e. the included angle between the rotating inclined plane and the horizontal plane) isAs shown in fig. 7 and 15;
(5) In a specific experiment, the inclined surface rotation fixing rod fixing nut 8-4 at the terminal of the rotation inclined surface 4, the left and right tightening nuts 2-21 of the rotation inclined surface terminal connecting shaft 2-2 at the terminal of the rotation inclined surface, the left and right tightening nuts 62 of the inclined surface inclination angle thin screw rod and the rotating shaft I (shown in figures 11 and 12) and the inclined surface rotation fixing rod fixing nut 8-4 of the inclined surface rotation fixing rod 5 (shown in figure 7) are locked so as to meet the stability of the measuring device. Meanwhile, if the coefficient of dynamic friction is to be measured, the tail end of the rotating inclined plane is required to be matched with the initial end of the horizontal table 1 in height, and the horizontal table 1 is required to be adjusted.
(6) When the experiment of specifically measuring the coefficient of dynamic friction force is carried out, the sliding block on the inclined plane can be manufactured into a round shape, and a pore vertical to the round surface is punched on the round center of the sliding block, so that when the experiment of the sliding block is adopted, the starting position and the end position of the movement stop are conveniently marked with marks, and then the sliding block moving distance is measured by adopting a vernier caliper;
(7) Measuring the coefficient of static friction (mu) of the corresponding material s ). As shown in fig. 7 and 17;
(8) Measuring coefficient of kinetic friction (mu) of the corresponding material k ). As shown in fig. 7 and 17;
2. mechanical analysis and formula derivation for actual measurement
(1) Measurement of coefficient of static friction
With the adoption of the design equipment, as long as the corresponding material is made to be the same size as the horizontal plane of the rotating inclined plane and is installed. The slide block is manufactured according to proper size and is put into the corresponding position of the inclined plane to be rotated. If the two surfaces of the sliding block and the contact place are static, a strong binding force-static friction force is formed between the two surfaces, and the surface can move relative to the other surface unless the binding force is broken, so that the binding force is broken-the ratio of the force before movement to the vertical force of the surface is called the static friction coefficient mu s If f s For static friction force, F 2 For vertical forces, the breaking force is also the maximum force that causes the object to actuate, i.e., the maximum static friction, is formulated as:
f s ＝μ s F 2 ……(1)
we can decompose the slide on the rotating ramp into a force component F parallel to the ramp 1 Component F perpendicular to the inclined plane 2 I.e.
F 1 ＝mg sinα……(2)
F 2 ＝mg sinα……(3)
In the process of rotating the inclined plane, if the sliding block just slides down along the inclined plane, the inclination angle alpha of the inclined plane 0 Sliding force F at this time 1 (α 0 ) Just with maximum static friction force f s The same, force on perpendicular to the bevel is F 2 (α 0 ) Is obtained by the following formula (1) and formula (2):
as shown in fig. 17.
(2) Measurement of dynamic coefficient of friction
Rotating the inclined plane to a certain angle alpha 1 Due to alpha 1 ＞α 0 The sliding block is placed at a certain position (l) of the inclined plane, and the sliding block starts to slide downwards at the position under the action of gravitational potential energy until the bottom end of the inclined plane moves along the horizontal direction, and the sliding friction force acts on the sliding block in the whole movement process, so that the sliding block is opposite to the movement direction of the sliding block, and finally slides to the position s along the horizontal plane to be stationary. Set sliding friction coefficient mu k The method comprises the steps of carrying out a first treatment on the surface of the At a position l (measured by a vernier caliper) away from the bottom of the inclined plane, the potential energy mgl sin alpha of the sliding block at the initial position 0 Work f of resistance force of slide block in inclined plane sliding process k l＝μ k F j0 ＝μ k mg cosα 0 The slide block moves from the bottom of the inclined plane to the position s (measured by a vernier caliper), and the resistance performs work mgs. According to the law of conservation of energy:
mgl sinα 0 ＝μ k lmg cosα 0 +mgs……(5)
thereby obtaining the coefficient of sliding friction as
μ k ＝(l sinα 0 -s)/l cosα 0 ……(6)
Thus, it can also be demonstrated by the above measurement that the maximum static friction coefficient is larger than the dynamic friction coefficient. I.e.
μ s ＞μ k ……(7)
As shown in fig. 17.
(3) Cylindrical rigid body rolling application on inclined plane
Let the mass of the cylindrical rigid body be m, the radius be r, the moment of inertia around the central axis of the cylinder be J. The experiment is carried out by adopting a mechanical micro-dynamic inclined plane friction coefficient measuring experiment instrument, and corresponding operation is carried out according to the steps, when the cylinder is purely rolled on the inclined plane, the cylinder can be regarded as translation of the mass center and rotation motion around the mass center, and the stress condition is shown in figure 18.
From the law of mass motion and the law of rotation
mg sinθ-f＝ma c ……(8)
fr＝Jβ c ……(9)
And a c ＝β c r, wherein a c Translational acceleration, beta, of centroid c To obtain angular acceleration of rotation around the mass center
Let the length of the bevel be l. The speed and rolling time of the mass center when the cylinder rolls from the top to the bottom from the rest are
When cylinders with the same mass and radius and different rotational inertia do pure rolling from the same inclined plane, the acceleration obtained by the mass center, the speed when the mass center moves for the same distance and the required time are different, and the larger the rotational inertia J is, the smaller the acceleration of the mass center and the speed when the mass center moves for the same distance are, but the longer the time required for the movement for the same distance is.
9. Precision analysis for mechanical high-precision continuous adjustment inclined plane inclination angle precision measurement of various material dynamic, static and cylindrical rolling friction coefficient experiment instrument
1. Precision analysis of coefficient of static friction
Pair (4) mu s ＝tanα 0 Differentiating to obtain mu' s ＝(secα 0 )α′ 0 . Let mu' k ＝Δμ s 、α′ 0 ＝Δα 0 ThenThe result of the experiment corresponds to the error of
Wherein:
2. precision analysis of kinetic friction coefficient
Couple (6)Differentiation is carried out to obtain
Let mu' k ＝Δμ k ，α′ 0 ＝Δα 0 . The corresponding instrument error of the experimental result is
Wherein:and l and s are constants.
2. Precision analysis of rolling friction coefficient
(1) Precision analysis of cylinder centroid velocity
Pair (11)Differential->Let v' 0 ＝Δv 0 The mass center speed error of the cylinder is that theta' =delta theta
(2) Precision analysis of cylinder centroid rolling time
Pair (12)Differential->Let t '=Δt, θ' =Δθ, then the cylinder rolling time error is
Wherein:for a certain cylinder, l, m, r, J, g is constant.
The designed mechanical high-precision continuous-adjustment inclined plane inclination angle accurate measurement experimental instrument for various material dynamic, static and cylindrical rolling friction coefficients can enable the measured angle accuracy to reach 1' and the measured parameter accuracy corresponding to the measured angle accuracy to reach the accuracy of (14), (16), (17) and (18) when the designed instrument is used for measuring the static friction coefficient, the dynamic friction coefficient and the mass center speed and time of the cylinder.
The foregoing description of the invention is merely exemplary of the invention. Those skilled in the art may make various modifications or additions to the described embodiments or substitutions, without departing from the scope of the invention as defined in the accompanying claims.
Claims (5)
1. The utility model provides a mechanical type micro-dynamic inclined plane measurement friction coefficient experiment appearance, includes horizontal stand (1) and inclined plane laboratory bench (2), its characterized in that: the inclined plane experiment table (2) comprises a base (3), a rotating inclined plane (4) arranged on the base (3), an inclined plane rotating fixed rod (5) arranged on the base (3) and far away from one end of the horizontal table (1), an inclined plane inclination angle thick screw rod (6) and an inclined plane inclination angle thin screw rod (7); the lower end of the inclined-plane inclination angle coarse screw rod (6) is connected with the inclined-plane inclination angle fine screw rod (7) through a fine screw rod spiral ring (71), the inclined-plane inclination angle fine screw rod (7) is connected with the base (3) through a rotating shaft I (41), the inclined-plane rotation fixing rod (5) is hinged with the base (3) through a rotating shaft II (42), and the distance between the rotating shaft I (41) and the horizontal table (1) is larger than the distance between the rotating shaft II (42) and the horizontal table (1); one end of the rotating inclined plane (4) is hinged with the horizontal table (1) through a rotating shaft III (43), and the other end of the rotating inclined plane (4) is connected with an inclined plane inclination angle coarse screw rod (6) through a coarse screw rod spiral ring (61); the thin screw rod spiral ring (71) is arranged on the inclined-plane inclined-angle thin screw rod (7) and can move up and down along the inclined-plane inclined-angle thin screw rod (7), and the thick screw rod spiral ring (61) is arranged on the inclined-plane inclined-angle thick screw rod (6) and can move up and down along the inclined-plane inclined-angle thick screw rod (6); a main scale disc (8) and a vernier disc (9) are further arranged on the rotating shaft III (43), wherein the main scale disc (8) is fixed, and the vernier disc (9) rotates along with the rotating inclined plane (4); the main scale disc (8) is circular, a main scale (81) is carved on the outer edge of the main scale disc, a left vernier (91) and a right vernier (92) which are matched with the main scale disc (8) are arranged on the outer edge of the vernier disc (9), and a connecting line at the centers of the left vernier (91) and the right vernier (92) passes through the center of the rotating shaft III (43); a fixed rod sliding groove (51) is formed in the inclined surface rotary fixed rod (5) along the length direction of the inclined surface rotary fixed rod, a fixed rod sliding shaft (52) is arranged in the fixed rod sliding groove (51), and two ends of the fixed rod sliding shaft (52) are fixed on the rotary inclined surface (4); leveling support legs (10) are arranged at the bottoms of the horizontal table (1) and the inclined plane experiment table (2), leveling horizontal bubbles (11) are arranged on the rotating inclined plane (4), the lower end of the inclined plane inclination angle coarse screw rod (6) is kept fixed with the fine screw rod spiral ring (71) through left and right tightening nuts (62), and rotating handles (63) are arranged on the outer sides of the coarse screw rod spiral ring (61) and the fine screw rod spiral ring (71).
2. The mechanical micro-slope friction coefficient measuring experimental instrument according to claim 1, wherein: leveling stabilizer blade (10) include stabilizer blade seat (101), leveling threaded rod (102), leveling lift cover (103) and leveling lifter (104), leveling lifter (104) upper end is fixed in the lower terminal surface of horizontal stand (1) or base (3), and leveling lift cover (103) cover is established on leveling lifter (104) and is connected with leveling threaded rod (102) screw thread, and the lower extreme of leveling threaded rod (102) is fixed on stabilizer blade seat (101).
3. The mechanical micro-slope friction coefficient measuring experimental instrument according to claim 1, wherein: the base (3) is close to one end of the horizontal platform (1) and is provided with a support column (31), the rotating shaft III (43) is arranged on the support column (31), and the height of the position where the rotating shaft III (43) is located is consistent with the height of the horizontal platform (1).
4. A mechanical micro-slope friction coefficient measuring tester according to claim 3, wherein: the main scale disc (8) is axially arranged on the rotating shaft III (43) and is fixed on the supporting column (31) through six screws.
5. The mechanical micro-motion inclined plane friction coefficient measuring experiment instrument according to claim 4, wherein: the vernier disc (9) is axially arranged on the rotating shaft III (43) and is tightly attached to the main scale disc (8).
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| CN201710460447.0A CN107945626B (en) | 2017-06-17 | 2017-06-17 | Mechanical type micro-dynamic inclined plane friction coefficient measuring experiment instrument |
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