CN107945626A - A kind of mechanical fine motion inclined-plane measurement friction coefficient experiment instrument - Google Patents
A kind of mechanical fine motion inclined-plane measurement friction coefficient experiment instrument Download PDFInfo
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Abstract
The present invention relates to a kind of friction coefficient measurement experiment instrument, including horizontal platform and experiment of in dined plane platform, the experiment of in dined plane platform includes base, the rotation inclined-plane being arranged on base, is arranged on the inclined-plane away from horizontal platform one end on base and rotates fixed link, inclination angle of inclined plane coarse screw bar and the thin lead screw of inclination angle of inclined plane.Friction coefficient measurement experiment instrument of the present invention has that precision is high, error is small, the easy to operate, advantage such as manufacture cost is low.
Description
Technical field
The present invention relates to a kind of teaching and experiment equipment, more particularly to a kind of mechanical fine motion inclined-plane measurement friction coefficient are real
Test instrument.
Background technology
The method of measurement kinematics and static friction force coefficient has many kinds, and inclined plane method is undoubtedly most simple, one kind of most convenient.
Although in the market has had the measuring instrument of the kinematics and static friction force coefficient of a variety of materials, just at present
Universities and middle schools laboratory measures the instrument of kinematics and static friction force coefficient using mechanical continuous accurate change inclination angle of inclined plane, also not
See.It is even external also without the instrument using mechanical continuous accurate adjustable inclined surface apparatus inclination angle experiment.Generally using hand
Dynamic lift slope makes it be rotated around low side rotation axis to change the outmoded method that inclination angle of inclined plane measures, and utilizes this operation
Inclination angle of inclined plane precision is low, error is big changing, and the operation for continuously changing inclination angle of inclined plane is difficult control.At present, have on the market
Inclination angle of inclined plane is accurately measured using photoelectric method, not only power consumption, but also it is unfavorable for energy conservation and environmental protection.Applicant is once in Shen on December 2nd, 2015
It please arrive " the quiet dynamic and cylinder rolling friction force coefficient reality of high precision fine tuning inclined-plane measurement of Patent No. ZL201310328276.8
Test instrument " patent of invention, despite the use of mechanical screws come it is continuous accurate change inclination angle of inclined plane and move measuring a variety of materials,
Confficient of static friction, but still have following defect：(1) using bevel termination fixing axle slideway and vernier scale slideway in inclined-plane
Side, causes huge inconvenience to experimenter's operation, is allowed to, experimenter is difficult to observation experiment phenomenon and is measured with being difficult to；(2) using more
A slideway and major diameter main scale, waste of materials, cost are high；(3) it is relatively difficult and unstable in rotation inclined-plane side fixation vernier scale
It is fixed；(4) vernier scale slideway and bevel termination sliding axle slideway shelf are fixed on experiment instrument stent, is also showed to experimenter's observation experiment
As bringing very big inconvenience with parameter measurement；(5) using single vernier reading can to rotate inclination angle of inclined plane measurement bring one can not
The systematic error of elimination；In consideration of it, applicant has invented " a kind of mechanical fine motion inclined-plane measurement friction coefficient experiment instrument " again
Device, in fact, and to existing for the former patent of invention of Patent No. ZL201310328276.8 as above defect carried out it is huge
Improve (innovation), the patent of invention after innovation can be more advantageous to the easy observation experiment phenomenon of experimenter and parameter measurement and conveniently
Hands-on.
The invention can also be used to being engaged in related scientific research personnel by varying inclination angle the association area that goes in for the study.It is based on
This, the instrument and equipment produced using the patented technology, will be able to be that manufacturer brings very abundant economic benefit.
The content of the invention
In order to solve above-mentioned technical problem, the object of the present invention is to provide a kind of small, operation side with precision height, error
Just the friction coefficient measurement experiment instrument for the advantages such as cost is low, is manufactured.
In order to realize above-mentioned purpose, present invention employs following technical solution：
A kind of mechanical fine motion inclined-plane measurement friction coefficient experiment instrument, including horizontal platform and experiment of in dined plane platform are described oblique
Face experimental bench includes base, the rotation inclined-plane being arranged on base, is arranged on the inclined-plane away from horizontal platform one end on base and rotates
Fixed link, inclination angle of inclined plane coarse screw bar and the thin lead screw of inclination angle of inclined plane；Wherein inclination angle of inclined plane coarse screw bar lower end passes through thin spiral shell
Screw bung flange is connected with the thin lead screw of inclination angle of inclined plane, and the thin lead screw connection of inclination angle of inclined plane is hinged by shaft I with base, and inclined-plane turns
Dynamic fixed link is hinged by shaft II with base, and the distance between shaft I and horizontal platform are more than between shaft II and horizontal platform
Distance；Described one end for rotating inclined-plane is hinged by shaft III with horizontal platform, and the other end for rotating inclined-plane passes through coarse screw bar spiral shell
Circle is connected with inclination angle of inclined plane coarse screw bar；The thin lead screw bung flange is arranged in the thin lead screw of inclination angle of inclined plane and can incline along inclined-plane
The thin lead screw in angle moves up and down, and coarse screw bar bung flange is arranged on inclination angle of inclined plane coarse screw bar and can be along inclination angle of inclined plane coarse screw bar
Move up and down；It is further fixed on main ruler disk and vernier scale disk in shaft III, wherein main ruler disk (8) is fixed, and vernier scale disk (9) is with turning
Move inclined-plane (4) and rotate；The main ruler disk is rounded, its outer rim is carved with master calibration, the outer rim of the vernier scale disk be provided with
The left vernier scale and right vernier scale that main ruler disk matches, line at the left vernier scale and right vernier scale center is through shaft III
Center；The inclined-plane rotates in fixed link on along its length and offers fixed link sliding slot, is provided with fixed link sliding slot
Fixed link rotates slide-bar, and the both ends that the fixed link rotates slide-bar can be fixed on rotation inclined-plane.
Preferably, the horizontal platform and experiment of in dined plane platform bottom are both provided with levelling shoe, set on inclined-plane is rotated
There is leveling spirit bubble.
Preferably, the levelling shoe includes stand bar seat, leveling threaded rod, leveling lifting set and leveling elevating lever,
The leveling elevating lever upper end is fixed on the lower face of horizontal platform or base, leveling lifting set be set on leveling elevating lever and with
Leveling threaded rod is threadedly coupled, and the lower end of leveling threaded rod is fixed in stand bar seat.
Preferably, the base is provided with support column close to one end of horizontal platform, the shaft III is arranged on support column
Upper and III position of shaft height is highly consistent with horizontal platform.
Preferably, the main scale dish axle is located in shaft III and is fixed on the support columns by six roots of sensation screw.
Preferably, the vernier scale dish axle is located in shaft III and is fitted closely with main ruler disk.
Preferably, the inclination angle of inclined plane coarse screw bar lower end keeps solid by left and right banding nut and thin lead screw bung flange
It is fixed, it is both provided with handler on the outside of coarse screw bar bung flange and thin lead screw bung flange.
Compared with prior art, the beneficial effects of the invention are as follows：
(1) rotate between bevel termination and base and to be connected by thickness screw rod using double rotation shaft structures and thickness bung flange
With reference to adjusting, realize and rotate the continuous fine motion that inclined-plane surrounds shaft III；
(2) the cooperation reading of main scale (0~360 °) and vernier scale (0 '~30 ') is employed, rotation inclined-plane is improved and goes to
The pin-point reading (precision up to 1 ') of a certain angle (rotating inclined-plane with respect to the horizontal plane inclination angle)；
(3) new invention patent avoids the former patent of invention of patent No. ZL201310328276.8 by bevel termination shifting axle
With vernier scale installation of slide track in side, the inconvenience brought to experimental implementation with experiment measurement；New invention patent, using 20cm diameters
Main scale, using inclined-plane rotate fixed link come support with stable rotation inclined-plane, do not interfere with the operation and measurement of experimenter；
(4) double vernier ruler system reading is employed, to measure the angle for rotating inclined-plane and turning over, is conducive to eliminate due to rotation
Main shaft and the systematic error caused by geometric principal axis misaligned (i.e. there are centering error)；
(5) in specific experiment, the stability of instrument entirety is ensure that in the banding nut that different parts employ；
(6) the kinematics and static friction force coefficient of a variety of materials can be accurately measured, such as：Various metals, timber, paper, plastics
The test of a variety of materials kinematics and static friction coefficient such as film, thin slice；
(7) special design structure that new invention patent uses, dramatically saves on laboratory apparatus making material, is factory
Family reduces production cost.
Brief description of the drawings
Fig. 1 is experiment instrument full figure front view.
Fig. 2 is the structure diagram of levelling shoe.
Fig. 3 is experiment instrument original state full figure top view.
Fig. 4 is that main ruler disk is connected and main ruler disk and vernier scale disk nesting method figure with left support bar, vernier scale disk shaft.
Fig. 5 is that main ruler disk fixes schematic diagram.
Fig. 6 is the structure diagram of vernier scale disk.
Fig. 7 is that experiment instrument rotation inclined-plane turns to a certain angled state figure.
Fig. 8 is the structure diagram of support column.
Fig. 9 is cooperation schematic diagram of the fixed link slide-bar with rotating inclined-plane.
Figure 10 is the structure diagram that inclined-plane rotates fixed link.
Figure 11 is to rotate inclined-plane and inclination angle of inclined plane coarse screw bar connection figure.
Figure 12 is base and the thin lead screw of inclination angle of inclined plane, inclination angle of inclined plane coarse screw bar and the connection of the thin lead screw of inclination angle of inclined plane
Schematic diagram.
Figure 13 is round slider schematic diagram.
Figure 14 is frame of reference accuracy of reading schematic diagram.
Figure 15 is to rotate inclined-plane to go to the corresponding just last position readings view of a certain inclination angle or so vernier scale.
Figure 16 is that double vernier ruler corrects not coaxial schematic diagram.
Figure 17 is to rotate high-acruracy survey kinematics and static friction coefficient instance analysis figure on inclined-plane.
Figure 18 is to rotate cylinder on inclined-plane to roll stress diagram.
Embodiment
The embodiment of the present invention is made a detailed explanation below in conjunction with the accompanying drawings.
A kind of mechanical fine motion inclined-plane measurement friction coefficient experiment instrument as shown in Fig. 1,3,7, including horizontal platform 1 and tiltedly
Face experimental bench 2.Experiment of in dined plane platform 2 includes base 3, sets rotation inclined-plane 4 on the base 3, sets on the base 3 away from horizontal
The inclined-plane of 1 one end of platform rotates fixed link 5, inclination angle of inclined plane coarse screw bar 6 and the thin lead screw 7 of inclination angle of inclined plane.For the ease of adjusting
Level, horizontal platform 1 and 2 bottom of experiment of in dined plane platform are both provided with levelling shoe 10, are rotating inclined-plane 4 with being respectively provided with horizontal platform 1
There is the leveling spirit bubble 11 of same type.
Wherein, 6 lower end of inclination angle of inclined plane coarse screw bar is connected by thin lead screw bung flange 71 lead screw 7 thin with inclination angle of inclined plane,
The thin connection of lead screw 7 of inclination angle of inclined plane is hinged with base 3 by shaft I 41, and inclined-plane rotates fixed link 5 and passes through shaft II 42 and base
3 is hinged.Also, shaft I 41 with the distance between horizontal platform 1 with being more than the distance between shaft II 42 and horizontal platform 1.Rotate oblique
The one end in face 4 is hinged by shaft III 43 and horizontal platform 1, and the other end for rotating inclined-plane 4 passes through coarse screw bar bung flange 61 and inclined-plane
Inclination angle coarse screw bar 6 connects.Wherein, thin lead screw bung flange 71 is arranged in the thin lead screw 7 of inclination angle of inclined plane and can be along inclination angle of inclined plane
Thin lead screw 7 moves up and down, and coarse screw bar bung flange 61 is arranged on inclination angle of inclined plane coarse screw bar 6 and can be along inclination angle of inclined plane coarse screw
Bar 6 moves up and down.
As shown in Fig. 1,4,5,6,7, main ruler disk 8 and vernier scale disk 9 are further fixed in shaft III 43.Main ruler disk 8 is in circle
Shape, its outer rim are carved with master calibration 81.The outer rim of vernier scale disk 9 is provided with the left vernier scale 91 to match with main ruler disk 8 and right vernier
Ruler 92, the line at 92 center of left vernier scale 91 and right vernier scale pass through the center of shaft III 43.
As shown in Fig. 1,7,9,10, inclined-plane rotate fixed link 5 on along its length on offer fixed link sliding slot 51,
Fixed link slide-bar 52 is provided with fixed link sliding slot 51, the both ends of fixed link slide-bar 52, which are fixed on, to be rotated on inclined-plane 4.Base 3 leans on
One end of nearly horizontal platform 1 is provided with support column 31, and shaft III 43 is arranged on support column 31 and III 43 position of shaft height
It is highly consistent with horizontal platform 1.8 axis of main ruler disk is located in shaft III 43 and is fixed on by six roots of sensation screw on support column 31.Vernier
9 axis of ruler disk is located in shaft III 43 and is fitted closely with main ruler disk 8.Vernier scale disk (9) keeps being relatively fixed with rotating inclined-plane 4,
And it can rotate and rotate with inclined-plane 4 is rotated.
As shown in Fig. 2, levelling shoe 10 includes stand bar seat 101, leveling threaded rod 102, leveling lifting set 103 and leveling
Elevating lever 104.104 upper end of leveling elevating lever is fixed on the lower face of horizontal platform 1 or base 3, and leveling lifting set 103 is set in tune
It is threadedly coupled on flat elevating lever 104 and with leveling threaded rod 102, the lower end of leveling threaded rod 102 is fixed in stand bar seat 101.
As shown in Figure 12,1,7,6 lower end of inclination angle of inclined plane coarse screw bar passes through left and right banding nut 62 and thin lead screw bung flange
71 ends keep fixing, and the outside of coarse screw bar bung flange 61 and thin lead screw bung flange 71 is both provided with handler 63.
The present invention is as follows using double vernier rectifying eccentricity rate principle：
As shown in figure 16, not coaxial schematic diagram is corrected for double vernier.Due to instrument calibration disk main scale center (geometric center)
Not necessarily it is completely superposed with live spindle (i.e. there are centering error), therefore rotates inclined-plane in rotation process, is read from single micro- ruler
Number always there are error (i.e. instrument error), designs for measurement rotation inclination angle of inclined plane and is symmetrically installed two vernier scales, it is possible to
Correct due to instrument error caused by centering error.If O is main scale and main ruler disk geometric center, O1Turn to rotate inclined-plane low side and fixing
Moving axis center, since the two is not necessarily overlapped, according to left and right vernier scale, reads before rotating inclined-plane rotation from left and right vernier scale
Initial reading is respectively θA left side 1、θThe right side 1, it is respectively θ to rotate inclined-plane and go to a certain inclination angle or so vernier scale final readingA left side 2、θThe right side 2, then rotate
Inclined-plane rotate angle be
Prove：As shown in figure 16, if the geometric center of main scale disk is overlapped with rotating inclined-plane low side fixed bias circuit center
Shi Yuanxin is O, and when misaligned, it is O to rotate inclined-plane low side fixed bias circuit center1, it is respectively AC and CD to cross O and do two diameters, crosses O1
It is EF//AB and JH//CD, it can be seen that as long as two centers overlap, the reading AC arc length or BD arc length that any one vernier scale is read
Free from error, if two centers are misaligned, reading is EJ arc length or HF arc length, and two arc length are inaccurate, but EA arc length=FB arcs
It is long；JC arc length=HD arc length, has：AC arc length=BD arc length=(AJ+JC) arc length=(DF+FB) arc length=(AJ+HD) arc length=
(DF+EA) arc length,
Therefore, (1) formula is set up.I.e. instrument calibration disk main scale geometric center is with rotating inclined-plane low side fixed bias circuit not necessarily
When being completely superposed, calculated using double vernier ruler reading, and using 1 formula, it is possible to which accurate measurement rotates inclined-plane and fixed around low side
The angle that rotation axis turns over.
Mechanical fine motion inclined-plane measurement friction coefficient experiment instrument of the present invention, its adjusting method are as follows：
(1) the leveling lifting set 103 and change coarse screw bar bung flange first on four levelling shoes 10 of adjustment base
61, change thin lead screw bung flange 71, be allowed to rotate the leveling spirit bubble 11 on inclined-plane 4 and be in circle center, rotate inclined-plane and be in
Horizontality, reads A, B window initial reading α respectively1、β1, as shown in Figure 1, 2, 3；If measuring the coefficient of kinetic friction, also to adjust
The level of water-saving platform 1, i.e., by the leveling lifting set 103 for four levelling shoes 10 for adjusting horizontal platform.Such as the institute of Fig. 1,2,3
Show；
(2) material of kinematics and static friction force coefficient to be measured is made into the same size tabular that matches with experiment instrument, and is pacified
Pre-designed relevant position is filled to, makes diameter 50.00mm, thickness 10.00mm round sliders (its center band has pore),
And the sliding block is put in and is rotated on inclined-plane predeterminated position；
(3) lock screw for the terminal rotation axis 2-21 lead screw 7 thin with inclination angle of inclined plane for rotating inclined-plane is loosened, is allowed to change
Thicker lead screw bung flange edge changes the radially lasting rotation of inclination angle of inclined plane coarse screw bar, waits to be put in rotation inclined-plane material round slider
After slip, then retract coarse screw bar bung flange is changed a little, be allowed to the material sliding block 11 it is just static untill, then rotate change
The thin lead screw bung flange of inclination angle of inclined plane, is allowed to detected materials sliding block and is just slightly moved along rotation inclined-plane, at this time sliding block gravity edge
The sliding force for inclined-plane is equal to maximum static friction force F of the cunning quality of materials block relative to inclined-planei, such as Fig. 1,3,7,12,15
It is shown；
(4) read that to rotate inclined-plane to go to A, B window reading of a certain angle be respectively α by measuring scale system2、β2, then rotate oblique
Angle that face turns over (rotating inclined-plane relative level inclination angle) isAs Fig. 1,4,
7th, shown in 15；
(5) in specific experiment, also to lock rotate 4 terminal of inclined-plane inclined-plane rotate fixed link hold-doun nut 8-4 and
Rotate the left and right banding nut 2-21 for rotating Beveled ends connecting shaft 2-2 and the thin lead screw of inclination angle of inclined plane and shaft of bevel termination
I left and right banding nut 62 (as shown in Figure 11,12), and inclined-plane rotate the inclined-plane rotation fixed link hold-doun nut of fixed link 5
8-4 (as shown in Figure 7), to meet the stability of measuring device.Meanwhile if also to measure kinetic force of friction coefficient, it is also necessary to allow and turn
The beginning of dynamic Beveled ends and horizontal platform 1 is identical.
The precision index of the present invention is as follows：
1. experiment instrument structure composition：It is mainly thick by rack, WidFin combined knob, measuring scale system, rotation inclination angle of inclined plane
Fine adjustments system, experimental level face etc. are formed.
2. rotate inclined-plane and horizontal plane size：500.0mm(L)×300.0mm(B)×15.0mm(H)；
3. sliding block specification：Diameter 50.00mm (D), the round slider of thickness 10.00mm (h) are made, in actually measuring
Visual specific measurement material is different and carries out flexible design, thickness generally in 10.00~15.00mm, and is applied in its circular central
Have and clearly indicate, to facilitate being convenient for measuring for starting and end of a period sliding block position, and weigh up its standard quality；
4. angular range：0 °~85 °；
5. precision：1′.
Example measures
(1) the leveling lifting set 103 and change coarse screw bar bung flange first on four levelling shoes 10 of adjustment base
61, change thin lead screw bung flange 71, be allowed to rotate the leveling spirit bubble 11 on inclined-plane 4 and be in circle center, rotate inclined-plane and be in
Horizontality, it is α to read A, B window initial reading respectively1、β1, as shown in Fig. 1,3 (rotating slope level initial position)；If survey
The coefficient of kinetic friction is measured, the level of horizontal platform 1 is also adjusted, i.e., set be lifted by the leveling of four levelling shoes 10 of horizontal platform
103.As shown in Figure 1, 2, 3；
(2) material of kinematics and static friction force coefficient to be measured is made into the same size tabular that matches with experiment instrument, and is installed
To pre-designed relevant position, diameter 50.00mm, thickness 10.00mm round sliders (its center band has pore) are made, and
The sliding block is put on the predeterminated position rotated on inclined-plane；
(3) lock screw for the terminal rotation axis 2-21 lead screw 7 thin with inclination angle of inclined plane for rotating inclined-plane is loosened, is allowed to change
Thicker lead screw bung flange edge changes the radially lasting rotation of inclination angle of inclined plane coarse screw bar, waits to be put in rotation inclined-plane material round slider
After slip, then retract coarse screw bar bung flange is changed a little, be allowed to the material sliding block 11 it is just static untill, then rotate change
The thin lead screw bung flange of inclination angle of inclined plane, is allowed to detected materials sliding block and is just slightly moved along rotation inclined-plane, at this time sliding block gravity edge
The sliding force for inclined-plane is equal to maximum static friction force F of the cunning quality of materials block relative to inclined-planei, as Fig. 1,3,7,11,12,
17th, shown in 15；
(4) inclined-plane is read by measuring scale system go to the reading of a certain inclination angle (i.e. angle with horizontal plane) A, B window and be respectively
α2、β2, then rotating the angle (rotating angle between inclined-plane and horizontal plane) that inclined-plane turns over isAs shown in Fig. 7,15；
(5) in specific experiment, also to lock rotate 4 terminal of inclined-plane inclined-plane rotate fixed link hold-doun nut 8-4 and
Rotate the left and right banding nut 2-21 for rotating Beveled ends connecting shaft 2-2 and the thin lead screw of inclination angle of inclined plane and shaft of bevel termination
I left and right banding nut 62 (as shown in Figure 11,12), and inclined-plane rotate the inclined-plane rotation fixed link hold-doun nut of fixed link 5
8-4 (as shown in Figure 7), to meet the stability of measuring device.Meanwhile if also to measure kinetic force of friction coefficient, it is also necessary to allow and turn
The beginning of dynamic Beveled ends and horizontal platform 1 is identical, and the adjusting to horizontal platform 1 is horizontal.
(6) in specifically measurement kinetic force of friction coefficient experiment, the sliding block on inclined-plane can be fabricated to circle, and the Bing Qi gardens heart is beaten
Perpendicular to garden face pore, so that when using sliding block experiment, initial position stops position finally with movement and facilitates trace mark, so
Sliding block displacement distance is measured using vernier caliper afterwards；
(7) the stiction coefficient (μ of respective material is measureds).As shown in Fig. 7,17；
(8) the kinetic force of friction coefficient (μ of respective material is measuredk).As shown in Fig. 7,17；
2. actual measurement mechanical analysis and the derivation of equation
(1) measurement of confficient of static friction
Equipped using the design, as long as respective material is made size identical with rotating its horizontal plane of inclined-plane and is installed.It is sliding
Block is made by suitable dimension, and puts it into inclined-plane relevant position to be rotated.If sliding block and two surface of contact position are static each other,
Two interfacial contact places can form one and relatively combine power --- stiction by force, unless the table can just be made with reference to power by destroying this
The relatively another surface in face is moved, to realize that destroying this combines power --- the ratio of power before movement to the vertical force on its surface
It is referred to as confficient of static friction μsIf fsFor stiction, F2For vertical force, which is also the maximum, force for starting the object,
That is maximum static friction force, is formulated as：
fs=μsF2……(1)
We will can be decomposed into along parallel to the component F on inclined-plane in the sliding block rotated on inclined-plane1, perpendicular to inclined-plane
Component F2, i.e.,
F1=mg sin α ... (2)
F2=mg sin α ... (3)
During inclined-plane is rotated, if sliding block just glides along inclined-plane, the inclination alpha on inclined-plane at this time0, sliding force at this time
F1(α0) just with maximum static friction force fsIdentical, the power on inclined-plane is F2(α0) obtained by (1) formula and (2) formula：
As shown in figure 17.
(2) measurement of the coefficient of kinetic friction
Rotate inclined-plane and go to a certain angle [alpha]1, due to α1＞ α0(precision up to 1 '), inclined-plane position (l) is put in by sliding block, by
Acted in gravitional force, start to glide at sliding block this this, moved in the horizontal direction again to surface bottom, in whole motion process
It is subject to force of sliding friction to act on, its direction is with slide block movement direction on the contrary, finally sliding to along the horizontal plane static at s.If slip rubs
Wipe force coefficient μk；Away from the bottom of the slope position l (using vernier caliper measurement), potential energy mgl possessed by the sliding block of initial position
sinα0, sliding block institute's resistance work done f in inclined-plane sliding processkL=μkFj0=μkmg cosα0, sliding block from the bottom of the slope again
Move to s (use vernier caliper measurement) place, resistance work done mgs.Obtained according to law of conservation of energy：
mgl sinα0=μklmg cosα0+mgs……(5)
It can thus be concluded that sliding friction force coefficient is
μk=(l sin α0-s)/l cosα0……(6)
Thus, it can also prove that maximum static friction force coefficient is more than kinetic force of friction coefficient by being measured as above.I.e.
μs＞ μk……(7)
As shown in figure 17.
(3) cylinder rigid body rolls application on inclined-plane
If cylindrical Rigid Mass is m, radius r, the rotary inertia around its center axis is J.We use " one
The mechanical fine motion inclined-plane measurement friction coefficient experiment instrument of kind " is tested, and carries out corresponding operating according to its step, works as cylinder
When making pure rolling on inclined-plane, the movement of the translation of barycenter and the rotation around barycenter, such as its stressing conditions, Figure 18 are can be regarded as
It is shown.
Obtained by center of mass motion law and law of rotation
Mg sin θs-f=mac……(8)
Fr=J βc……(9)
And ac=βcR, a in formulacFor the translatory acceleration of barycenter, βcFor the angular acceleration of rotation around center of mass, obtain
If the length on inclined-plane is l.The then cylinder speed of barycenter and rolling when bottom is rolled to by top static
Time is
With phase homogenous quantities and radius, but when the different cylinder of rotary inertia makees pure rolling from same inclined-plane, its matter
Speed and required time when acceleration that the heart is obtained, movement same distance are all different, and rotary inertia J is bigger, matter
The speed when acceleration and movement same distance of the heart is smaller, but it is then longer to move the same distance required time.
9th, mechanical high accuracy continuously adjusts inclination angle of inclined plane accurately to measure a variety of materials dynamic and static with cylinder force of rolling friction
The precision analysis of the example measurement of coefficient experiment instrument
1st, to the precision analysis of stiction coefficient
To (4) μs=tan α0Carry out differential and obtain μ 's=(sec α0)α′0.Allow μ 'k=Δ μs、α′0=Δ α0, then the knot tested
The corresponding error of fruit is
Wherein：
2nd, to the precision analysis of kinetic force of friction coefficient
To (6)Differential is carried out to obtain
Allow μ 'k=Δ μk, α '0=Δ α0.Then the corresponding instrument error of experimental result is
Wherein：L, s is constant.
2nd, to the precision analysis of rolling friction force coefficient
(1) to the precision analysis of Mass Center of Circular Column speed
To (11) formulaDifferential is carried out to obtainAllow v '0
=Δ v0, then Mass Center of Circular Column velocity error is θ '=Δ θ
(2) to the precision analysis of Mass Center of Circular Column rolling time
To (12) formulaDifferential obtainsAllow t '
=Δ t, θ '=Δ θ, then cylinder rolling time error be
Wherein：For definite cylinder, its l, m, r, J, g are constant.
Design should " mechanical high accuracy continuously adjusts inclination angle of inclined plane and accurately measures that a variety of materials is dynamic and static to be rolled with cylinder
Friction coefficient experiment instrument " instrument and equipment, measurement stiction coefficient, kinetic force of friction coefficient and Mass Center of Circular Column speed with
Time, by using the design instrument when, enable to institute's measuring angle precision to reach 1 ', and corresponding survey parameter
The precision that precision reaches (14), (16), (17), (18) are reached.
Above content described in this specification is only illustration made for the present invention.Technology belonging to the present invention
The technical staff in field can do described specific embodiment various modifications or additions or in a similar way
Substitute, content without departing from description of the invention or surmount scope defined in the claims, this should all be belonged to
The protection domain of invention.
Claims (7)
1. a kind of mechanical fine motion inclined-plane measurement friction coefficient experiment instrument, including horizontal platform (1) and experiment of in dined plane platform (2), its
It is characterized in that：The experiment of in dined plane platform (2) includes base (3), and the rotation inclined-plane (4) being arranged on base (3), is arranged on base
(3) inclined-plane away from horizontal platform (1) one end rotates fixed link (5), inclination angle of inclined plane coarse screw bar (6) and the thin spiral shell of inclination angle of inclined plane on
Screw (7)；Wherein inclination angle of inclined plane coarse screw bar (6) lower end passes through thin lead screw bung flange (71) and the thin lead screw of inclination angle of inclined plane (7)
Connection, the thin lead screw of inclination angle of inclined plane (7) connection is hinged with base (3) by shaft I (41), and inclined-plane rotates fixed link (5) and passes through
Shaft II (42) is hinged with base (3), and the distance between shaft I (41) and horizontal platform (1) are more than shaft II (42) and horizontal platform
The distance between (1)；Described one end for rotating inclined-plane (4) is hinged by shaft III (43) and horizontal platform (1), rotates inclined-plane (4)
The other end be connected by coarse screw bar bung flange (61) with inclination angle of inclined plane coarse screw bar (6)；The thin lead screw bung flange (71) is set
Put in the thin lead screw of inclination angle of inclined plane (7) and can move up and down along the thin lead screw of inclination angle of inclined plane (7), coarse screw bar bung flange (61) is set
Put on inclination angle of inclined plane coarse screw bar (6) and can move up and down along inclination angle of inclined plane coarse screw bar (6)；Also set in shaft III (43)
Main ruler disk (8) and vernier scale disk (9) are equipped with, wherein main ruler disk (8) is fixed, and vernier scale disk (9) is rotated with inclined-plane (4) are rotated；
The main ruler disk (8) is rounded, its outer rim is carved with master calibration (81), and the outer rim of the vernier scale disk (9) is provided with and main ruler disk
(8) the left vernier scale (91) and right vernier scale (92) to match, the company at the left vernier scale (91) and right vernier scale (92) center
Line passes through the center of shaft III (43)；The inclined-plane rotates in fixed link (5) on along its length and offers fixed link sliding slot
(51), fixed link slide-bar (52) is provided with fixed link sliding slot (51), the both ends of the fixed link slide-bar (52), which are fixed on, to be turned
On dynamic inclined-plane (4).
A kind of 2. mechanical fine motion inclined-plane measurement friction coefficient experiment instrument according to claim 1, it is characterised in that：Institute
State horizontal platform (1) and experiment of in dined plane platform (2) bottom is both provided with levelling shoe (10), leveling is provided with inclined-plane (4) are rotated
Spirit bubble (11).
A kind of 3. mechanical fine motion inclined-plane measurement friction coefficient experiment instrument according to claim 2, it is characterised in that：Institute
Stating levelling shoe (10) includes stand bar seat (101), leveling threaded rod (102), leveling lifting set (103) and leveling elevating lever
(104), leveling elevating lever (104) upper end is fixed on the lower face of horizontal platform (1) or base (3), leveling lifting set (103)
It is set on leveling elevating lever (104) and is threadedly coupled with leveling threaded rod (102), the lower end of leveling threaded rod (102) is fixed
In stand bar seat (101).
A kind of 4. mechanical fine motion inclined-plane measurement friction coefficient experiment instrument according to claim 1, it is characterised in that：Institute
State base (3) and one end of horizontal platform (1) is provided with support column (31), the shaft III (43) is arranged on support column (31)
And shaft III (43) position height is highly consistent with horizontal platform (1).
A kind of 5. mechanical fine motion inclined-plane measurement friction coefficient experiment instrument according to claim 4, it is characterised in that：Institute
Main ruler disk (8) axis is stated to be located in shaft III (43) and be fixed on support column (31) by six roots of sensation screw.
A kind of 6. mechanical fine motion inclined-plane measurement friction coefficient experiment instrument according to claim 5, it is characterised in that：Institute
Vernier scale disk (9) axis is stated to be located in shaft III (43) and fit closely with main ruler disk (8).
A kind of 7. mechanical fine motion inclined-plane measurement friction coefficient experiment instrument according to claim 1, it is characterised in that：Institute
State inclination angle of inclined plane coarse screw bar (6) lower end to keep fixing by left and right banding nut (62) and thin lead screw bung flange (71), thick spiral shell
Handler (63) is both provided with the outside of screw bung flange (61) and thin lead screw bung flange (71).
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Cited By (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN108766141A (en) * | 2018-08-09 | 2018-11-06 | 浙江大学城市学院 | A kind of mechanical accurate fine motion inclined-plane mechanics series experiment instrument |
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