CN103743921B - Based on self-adaptation speed measuring system and the method for inertial sensor - Google Patents
Based on self-adaptation speed measuring system and the method for inertial sensor Download PDFInfo
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- CN103743921B CN103743921B CN201310755470.4A CN201310755470A CN103743921B CN 103743921 B CN103743921 B CN 103743921B CN 201310755470 A CN201310755470 A CN 201310755470A CN 103743921 B CN103743921 B CN 103743921B
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Abstract
The present invention relates to a kind of self-adaptation speed measuring system based on inertial sensor and the self-adaptation rotating speed measurement method based on inertial sensor, measuring system comprises revolution detector and display terminal, be provided with accelerometer, gyroscope, first microprocessor, the first wireless transport module and the first supplying cell in revolution detector, in display terminal, be provided with the second wireless transport module, the second microprocessor, display and the second supplying cell; First wireless transport module and the second wireless transport module wireless connections, the Z axis of accelerometer and gyrostatic Z axis all with the shaft parallel of rotary body.The present invention is in conjunction with the function of gyroscope and accelerometer, when rotary body slowly runs, system self-adaption ground is according to gyrostatic output, calculate the radius of turn of rotary body, output speed simultaneously, when rotary body high-speed rotation, the centripetal acceleration that system self-adaption ground exports according to accelerometer, and export high speed rotating speed in conjunction with the result of calculation computing of low speed.
Description
Technical field
The present invention relates to the tachometric survey technical field of rotary body, particularly relate to a kind of self-adaptation speed measuring system based on inertial sensor and method.
Background technology
Traditional rotating speed measurement method is divided into two large classes, and a class is the tachometric survey based on Hall effect, and another kind of is tachometric survey based on photoelectric reflection.
Hall effect measures rotating speed to be needed to install magnet on rotary body, and installs hall sensing device nearby on the rotational trajectory of magnet, and the switching signal being detected the output of hall sensing device by microprocessor calculates rotating speed.There are 2 deficiencies in the method being measured rotating speed by Hall effect, first installation requirement is high, magnet rotational trajectory installs hall device nearby, distance controlling difficulty, it two is under rotary body low rotation speed, need magnet points much more very to form more switching signal, effectively could measure the slow-speed of revolution, but, when carrying out test of low rotating speed by the method, need the distance of effective controlling magnet quantity and magnet hall device in advance, once design, rotation-speed measuring device can not change, and easily limit the dirigibility of tachometric survey.
Photoelectric reflection measures rotating speed, is on rotary body, stick interruption reflecting strips, and rotating speed is measured in the outside reflective pulse by Photoelectric Detection module detection reflecting strips.Measure rotating speed by photoelectric reflection and also there are following 2 deficiencies, the attachment of first reflecting strips is cumbersome, need tested rotary body to have disc that is parallel and rotation axis, it two is that photoelectricity test test side will stable placement parallel with reflecting strips, otherwise measures unstable or cannot measure at all.
Both rotating speed measurement methods traditional are all difficult to measure the rotating speed of rotary body when slow-speed of revolution campaign flexibly and accurately, while measuring equipment to install complexity high.
Summary of the invention
Technical matters to be solved by this invention there is measuring equipment complex structure for existing rotating speed measurement method, not easily to install and the problem not easily measured of the slow-speed of revolution, provide a kind ofly can arbitrarily to install, structure is simple and have the self-adaptation speed measuring system based on inertial sensor and the self-adaptation rotating speed measurement method in inertial sensor of low, high rotating speed adaptive measuring function.
For solving the problem, a kind of technical scheme of the present invention is:
A kind of self-adaptation speed measuring system based on inertial sensor, comprise the revolution detector be arranged on rotary body and the display terminal carrying out with it radio communication, the accelerometer for exporting rotary body 3-axis acceleration is provided with in described revolution detector, for exporting the gyroscope of rotary body three axis angular rate, for controlling and carry out the first microprocessor of data processing, the first wireless transport module transmitted for data and the first supplying cell for powering, first microprocessor respectively with accelerometer, gyroscope is connected with the first wireless transport module, the second wireless transport module transmitted for data is provided with in described display terminal, second microprocessor, display and the second supplying cell for powering, second microprocessor is connected with the second wireless transport module with display respectively, the second wireless transport module wireless connections in the first wireless transport module in described revolution detector and display terminal, the Z axis of described accelerometer and gyrostatic Z axis all with the shaft parallel of rotary body.
Preferably, described gyroscope is three axle micro-mechanical gyroscopes, and accelerometer is three axle micro-mechanical accelerometers.
Preferably, described first wireless transport module and the second wireless transport module are 2.4G module.
Preferably, be also provided with the indicating module for showing revolution detector running status in described revolution detector, indicating module is connected with the first supplying cell with first microprocessor respectively.
Be compared to prior art, self-adaptation speed measuring system based on inertial sensor of the present invention is in conjunction with the function of gyroscope and accelerometer, when rotary body slowly runs, system self-adaption ground is according to gyrostatic output, calculate the radius of turn of rotary body, simultaneously output speed, when rotary body high-speed rotation, the centripetal acceleration that system self-adaption ground exports according to accelerometer, and export high speed rotating speed in conjunction with the result of calculation computing of low speed; Revolution detector in the present invention can arbitrarily be installed on rotary body, easy for installation, directionless and angle requirement, effectively solves the problem that the slow-speed of revolution is not easily accurately measured and revolution detector is not easily installed.
Another kind of technical scheme of the present invention is:
Based on a self-adaptation rotating speed measurement method for inertial sensor, described rotating speed measurement method is based on the self-adaptation speed measuring system based on inertial sensor of the present invention, and described rotating speed measurement method comprises following two kinds of situations:
The first situation: when rotary body is in and slowly runs, tachometric survey is carried out by gyroscope, describedly slowly run for the rotating speed of rotary body is in gyrostatic measurement range, three axis angular rates that gyroscope exports rotary body process in first microprocessor, obtain the tachometer value of rotary body, tachometer value is sent in display terminal by the first wireless transport module and shows by first microprocessor, first microprocessor calculates and preserves the radius of turn of rotary body simultaneously, and described radius of turn is the distance of revolution detector to rotary body rotating shaft;
Second case: when rotary body is in high-speed rotation, carries out tachometric survey by accelerometer, and described high-speed rotation refers to that the rotating speed of rotary body exceeds gyroscope survey scope, comprises the steps:
A) 3-axis acceleration of accelerometer output rotary body is preserved in first microprocessor,
B) radius of turn that calculates according to the first situation of first microprocessor, calculates and preserves the influence value of acceleration of gravity to rotary body,
C) first microprocessor is according to the reverse tachometer value deriving rotary body of the result of step a and step b, and is sent in display terminal by the first wireless transport module and shows.
Preferably, the radius of turn calculated in the first situation described is that radius of turn rotates the calculation expression of centripetal acceleration about axle each on accelerometer, and this calculation expression is obtained by following formulae discovery:
Wherein, ω
x, ω
yand ω
zfor X-axis angular velocity, Y-axis angular velocity and Z axis angular velocity that any time gyroscope exports, R is radius of turn, a
xthe rotation centripetal acceleration in rotary body X-direction, a
ythe rotation centripetal acceleration in rotary body Y direction, a
zit is the rotation centripetal acceleration in rotary body Z-direction;
Separate above-mentioned equation (1) (2) (3) to obtain:
a
X=k
1R…………(4)
a
Y=k
2R…………(5)
a
Z=k
3R…………(6)
Wherein, k
1, k
2and k
3it is the known coefficient calculated.
Preferably, the self-adaptation rotating speed measurement method based on inertial sensor according to claim 5, is characterized in that, described second case
In step a, accelerometer exports the 3-axis acceleration A respectively of rotary body
x, A
yand A
z,
In step b, the influence value of acceleration of gravity to rotary body comprises the gravitational acceleration component g not rotating change with rotary body
xS, g
ySand g
zSand with the gravitational acceleration component g that rotary body rotation period changes
xD, g
yDand g
zD, when rotary body uniform rotation, following formula (7) (8) (9) set up:
A
X=a
X+g
XS+g
XD…………(7)
A
Y=a
Y+g
YS+g
YD…………(8)
A
Z=a
Z+g
ZS+g
ZD…………(9)
By wave filter by g
xD, g
yDand g
zDfiltering, obtains the amplitude g of respective change amount
xDA, g
yDAand g
zDA, to be eliminated g according to formula (7) (8) (9)
xD, g
yDand g
zDa after impact
xA, A
yAand A
zA:
A
XA=a
X+g
XS…………(10)
A
YA=a
Y+g
YS…………(11)
A
ZA=a
Z+g
ZS…………(12)
In step c, the tachometer value of rotary body calculates and comprises the steps:
Formula (4) (5) (6) are substituted into formula (10) (11) (12), obtain:
A
XA=k
1R+g
XS…………(13)
A
YA=k
2R+g
YS…………(14)
A
ZA=k
3R+g
ZS…………(15)
Because g is terrestrial gravitation acceleration, so:
Wherein g
xDA, g
yDAand g
zDAfor known quantity, if
so:
By the g in formula (13) (14) (15)
xS, g
ySand g
zSbe transformed to the equation of R and substitute into formula (17), obtaining the linear equation in two unknowns about R, solve radius of turn R, after R is substituted into formula (13) (14) (15), solve g
xS, g
ySand g
zS;
Radius of turn R, g at any time
xS, g
ySand g
zSfor definite value, and substitute into formula (10) (11) (12), solve the rotation centripetal acceleration a on any time rotary body three direction of principal axis
x, a
yand a
z, calculate centripetal acceleration vector sum and obtain rotating centripetal acceleration a, then basis
draw final tachometer value ω.
Be compared to prior art, self-adaptation rotating speed measurement method based on inertial sensor of the present invention utilizes gyroscope to detect the rotary body slowly run, and export corresponding rotating speed and radius of turn, accelerometer is utilized to detect the rotary body of high-speed rotation, and export high speed rotating speed in conjunction with the result of calculation computing of low speed according to the centripetal acceleration that accelerometer exports simultaneously, there is low speed and high speed detection convenience, the accurate advantage of result; The rotary body that measuring method of the present invention is applicable to different directions, angle is installed, when measuring, only arbitrarily need install revolution detector on rotary body, installing very simple and convenient.
Accompanying drawing explanation
Fig. 1 is the theory diagram of the self-adaptation speed measuring system that the present invention is based on inertial sensor.
Fig. 2 is embodiment one structural representation of the self-adaptation rotating speed measurement method that the present invention is based on inertial sensor.
Fig. 3 is embodiment two structural representation of the self-adaptation rotating speed measurement method that the present invention is based on inertial sensor.
Fig. 4 is embodiment three structural representation of the self-adaptation rotating speed measurement method that the present invention is based on inertial sensor.
Embodiment
Further describe the present invention below in conjunction with drawings and Examples, but protection scope of the present invention is not limited to this.
With reference to Fig. 1, a kind of self-adaptation speed measuring system based on inertial sensor of the present invention, comprises the revolution detector be arranged on rotary body and the display terminal being attached thereto Serial Communication of going forward side by side.Accelerometer, gyroscope, first microprocessor, the first wireless transport module, the first supplying cell and indicating module is provided with in revolution detector, first microprocessor is connected with indicating module with accelerometer, gyroscope, the first wireless transport module respectively, first supplying cell is connected with indicating module with accelerometer, gyroscope, first microprocessor, the first wireless transport module respectively, for the in-line power of revolution detector.The second wireless transport module, the second microprocessor, display and the second supplying cell is provided with in display terminal, second microprocessor is connected with the second wireless transport module with display respectively, second supplying cell is connected with display with the second wireless transport module, the second microprocessor respectively, for display terminal in-line power.Wherein, gyroscope is three axle micro-mechanical gyroscopes, and accelerometer is three axle micro-mechanical accelerometers.First wireless transport module and the second wireless transport module are 2.4G module.
Described accelerometer is for exporting rotary body 3-axis acceleration, gyroscope is for exporting rotary body three axis angular rate, first micro-process is used for controlling and carrying out data place, first wireless transport module is used for data transmission, first wireless transport module and the second wireless transport module wireless connections, indicating module is for showing revolution detector running status, and indicating module is LED.When revolution detector is installed, revolution detector is fixed on rotary body, makes it vibrate, in addition, need the shaft parallel of the Z axis of degree of will speed up meter and gyrostatic Z axis and rotary body to design.
When rotary body is in the slow-speed of revolution, detection output three axis angular rate is carried out by gyroscope, and the rotating speed calculated is exported by first microprocessor, when rotary body is at high rotating speed, carry out detection by acceleration and export 3-axis acceleration, calculated and the rotating speed exported in conjunction with the result that gyroscope detects by first microprocessor.The result of calculation that first microprocessor exports is sent in the second wireless transport module by the first wireless transport module, under the second microprocessor-based control, outputs to display display.
Embodiment one
By the self-adaptation rotating speed measurement method based on inertial sensor that system of the present invention realizes, comprise following two kinds of situations:
The first situation: when rotary body is in and slowly runs, tachometric survey is carried out by gyroscope, describedly slowly run for the rotating speed of rotary body is in gyrostatic measurement range, the measurement range only 2000 degree/second of current three axle micro-mechanical gyroscopes, about 330 revs/min, namely, when the rotating speed of rotary body is less than or equal to 330 revs/min, the scope that slowly runs is belonged to.Now, the vector synthesis of three axis angular rates of gyroscope output is the tachometer value of rotary body.Three axis angular rates that gyroscope exports rotary body process in first microprocessor, obtain the tachometer value of rotary body, tachometer value is sent in display terminal by the first wireless transport module and shows by first microprocessor, first microprocessor calculates and preserves the radius of turn of rotary body simultaneously, and described radius of turn is the distance of revolution detector to rotary body rotating shaft.Wherein, the radius of turn calculated in the first situation is that radius of turn rotates the calculation expression of centripetal acceleration about axle each on accelerometer.
Any time, gyrostatic rotary speed direction is vertical with the direction of centripetal acceleration, so three-dimensional centripetal acceleration and three-dimensional rotating speed meet following formula in space, the calculation expression that radius of turn rotates centripetal acceleration about axle each on accelerometer is obtained by following formulae discovery:
Wherein, ω
x, ω
yand ω
zfor X-axis angular velocity, Y-axis angular velocity and Z axis angular velocity that any time gyroscope exports, R is radius of turn, a
xthe rotation centripetal acceleration in rotary body X-direction, a
ythe rotation centripetal acceleration in rotary body Y direction, a
zit is the rotation centripetal acceleration in rotary body Z-direction;
Separate above-mentioned equation (1) (2) (3) to obtain:
a
X=k
1R…………(4)
a
Y=k
2R…………(5)
a
Z=k
3R…………(6)
Wherein, k
1, k
2and k
3it is the known coefficient calculated.
Second case: when rotary body is in high-speed rotation, detected by accelerometer and rotate centripetal acceleration inverse rotating speed, described high-speed rotation refers to that the rotating speed of rotary body exceeds gyroscope survey scope.Accelerometer detects the prerequisite of rotating centripetal acceleration inverse rotating speed: one is the impact that elimination acceleration of gravity brings, and two is that radius of turn is known.In a first situation, the calculation expression of radius of turn is in known, and the radius of turn that can directly export according to first microprocessor calculates.
But, there is relation the locus of the impact of acceleration of gravity and the rotating shaft of rotary body, the present embodiment is what to be tilted for the rotating shaft 2.1 of rotary body 2, namely the situation that rotary body 2 is installed arbitrarily is described in detail, concrete with reference to Fig. 2, revolution detector 1 is fixedly mounted on rotary body 2, under the rotating shaft 2.1 of rotary body 2 is inclination conditions, when rotary body 2 does uniform rotation on the direction that certain tilts, acceleration of gravity can produce two kinds of impacts to rotary body 2, and one is on gravity direction, rotate the periodically variable gravitational acceleration component g brought
d, this change in gravitational acceleration cycle is equal with rotation period, can be eliminated by digital low-pass filtering, and another is not with the gravitational acceleration component g rotating change
s, this gravitational acceleration component can be solved by equation.
Rotating speed when rotary body is in high-speed rotation calculates and comprises the steps:
A) 3-axis acceleration of accelerometer output rotary body is preserved in first microprocessor, and 3-axis acceleration is A respectively
x, A
yand A
z;
B) radius of turn that calculates according to the first situation of first microprocessor, calculates and preserves the influence value of acceleration of gravity to rotary body, and the influence value of acceleration of gravity to rotary body comprises the gravitational acceleration component g not rotating change with rotary body
xS, g
ySand g
zSand with the gravitational acceleration component g that rotary body rotation period changes
xD, g
yDand g
zD, when rotary body uniform rotation, rotate centripetal acceleration a
x, a
yand a
zfor the steady state value of the unknown, g
xS, g
ySand g
zSalso be unknown steady state value, following formula (7) (8) (9) set up:
A
X=a
X+g
XS+g
XD…………(7)
A
Y=a
Y+g
YS+g
YD…………(8)
A
Z=a
Z+g
ZS+g
ZD…………(9)
Wherein, by wave filter by g
xD, g
yDand g
zDfiltering, obtains the amplitude g of respective change amount
xDA, g
yDAand g
zDA, amplitude g
xDA, g
yDAand g
zDAfor given value, to be eliminated g according to formula (7) (8) (9)
xD, g
yDand g
zDa after impact
xA, A
yAand A
zA:
A
XA=a
X+g
XS…………(10)
A
YA=a
Y+g
YS…………(11)
A
ZA=a
Z+g
ZS…………(12)
C) first microprocessor is according to the reverse tachometer value deriving rotary body of the result of step a and step b, and is sent in display terminal by the first wireless transport module and shows.Specifically be calculated as follows:
Formula (4) (5) (6) are substituted into formula (10) (11) (12), obtain:
A
XA=k
1R+g
XS…………(13)
A
YA=k
2R+g
YS…………(14)
A
ZA=k
3R+g
ZS…………(15)
Because g is terrestrial gravitation acceleration, again g
sand g
dvector sum equal acceleration of gravity, so
set up, wherein g is terrestrial gravitation acceleration, is known quantity.And
So:
Wherein g
xDA, g
yDAand g
zDAfor known quantity, if
so:
By the g in formula (13) (14) (15)
xS, g
ySand g
zSbe transformed to the equation of R and substitute into formula (17), obtaining the linear equation in two unknowns about R, solve radius of turn R, after R is substituted into formula (13) (14) (15), solve g
xS, g
ySand g
zS;
Radius of turn R, g at any time
xS, g
ySand g
zSfor definite value, and substitute into formula (10) (11) (12), solve the rotation centripetal acceleration a on any time rotary body three direction of principal axis
x, a
yand a
z, calculate centripetal acceleration vector sum and obtain rotating centripetal acceleration a, then basis
draw final tachometer value ω.
The present invention utilizes gyroscope to detect the rotary body slowly run, and export corresponding rotating speed and radius of turn, accelerometer is utilized to detect the rotary body of high-speed rotation, and export high speed rotating speed in conjunction with the result of calculation computing of low speed according to the centripetal acceleration that accelerometer exports simultaneously, there is low speed and high speed detection convenience, the accurate advantage of result; The rotary body that measuring method of the present invention is applicable to different directions, angle is installed, when measuring, only arbitrarily need install revolution detector on rotary body, installing very simple and convenient.
Embodiment two
With reference to Fig. 3, revolution detector 1 is fixedly mounted on rotary body 2, and the difference of the present embodiment and embodiment one is, the rotating shaft 2.1 of rotary body 2 is vertical, the XY direction of principal axis induction centripetal acceleration of accelerometer.Now, acceleration of gravity is in the Z-direction of accelerometer, and unchanged, so the rotating speed within the scope of gyroscope survey equals ω
z, during uniform rotation
wherein A
xand A
yfor the XY axle of accelerometer exports, ω
zfor gyroscope Z axis exports, radius of turn R can be calculated.The rotating speed of follow-up any moment rotary body can according to R and A
xand A
yvalue calculate, concrete computation process, with reference to embodiment one, does not repeat them here.
Embodiment three
With reference to Fig. 4, revolution detector 1 is fixedly mounted on rotary body 2, and the difference of the present embodiment and embodiment one is, the rotating shaft 2.1 of rotary body 2 is levels, now, and the XY direction of principal axis induction centripetal acceleration of accelerometer, XY axle has the Orthogonal Periodic of acceleration of gravity to affect simultaneously, Z axis acceleration A
z=0.So the rotating speed within the scope of gyroscope survey equals ω
z, during uniform rotation, first to A
xand A
ycarry out digital filtering, eliminate the acceleration of gravity of cyclic effects, obtain A
xAand A
yA, and have
set up, wherein ω
zfor gyroscope Z axis exports, A
xAand A
yAbe the value that XY axle exports that data eliminate gravity effect through digital filtering, solve an equation and can obtain radius of turn R.Follow-up any moment can according to R, A
xAand A
yAvalue calculate rotating speed, concrete computation process, with reference to embodiment one, does not repeat them here.
In above-mentioned explanation, all special instructions that do not add, all adopt technological means of the prior art.
Claims (5)
1. the self-adaptation speed measuring system based on inertial sensor, comprise the revolution detector be arranged on rotary body and the display terminal carrying out with it radio communication, it is characterized in that, the accelerometer for exporting rotary body 3-axis acceleration is provided with in described revolution detector, for exporting the gyroscope of rotary body three axis angular rate, for controlling and carry out the first microprocessor of data processing, the first wireless transport module transmitted for data and the first supplying cell for powering, first microprocessor respectively with accelerometer, gyroscope is connected with the first wireless transport module, the second wireless transport module transmitted for data is provided with in described display terminal, second microprocessor, display and the second supplying cell for powering, second microprocessor is connected with the second wireless transport module with display respectively, the second wireless transport module wireless connections in the first wireless transport module in described revolution detector and display terminal, the Z axis of described accelerometer and gyrostatic Z axis all with the shaft parallel of rotary body, described gyroscope is three axle micro-mechanical gyroscopes, accelerometer is three axle micro-mechanical accelerometers, the indicating module for showing revolution detector running status is also provided with in described revolution detector, indicating module is connected with the first supplying cell with first microprocessor respectively, tachometric survey is carried out by gyroscope when the rotating speed that rotary body is in the i.e. rotary body of slowly running is in gyrostatic measurement range, tachometric survey is carried out by accelerometer when the rotating speed that rotary body is in high-speed rotation and rotary body exceeds gyroscope survey scope.
2. the self-adaptation speed measuring system based on inertial sensor according to claim 1, is characterized in that, described first wireless transport module and the second wireless transport module are 2.4G module.
3. based on a self-adaptation rotating speed measurement method for inertial sensor, it is characterized in that, described rotating speed measurement method is based on the self-adaptation speed measuring system based on inertial sensor according to claim 1, and described rotating speed measurement method comprises following two kinds of situations:
The first situation: when rotary body is in and slowly runs, tachometric survey is carried out by gyroscope, describedly slowly run for the rotating speed of rotary body is in gyrostatic measurement range, three axis angular rates that gyroscope exports rotary body process in first microprocessor, obtain the tachometer value of rotary body, tachometer value is sent in display terminal by the first wireless transport module and shows by first microprocessor, first microprocessor calculates and preserves the radius of turn of rotary body simultaneously, and described radius of turn is the distance of revolution detector to rotary body rotating shaft;
Second case: when rotary body is in high-speed rotation, carries out tachometric survey by accelerometer, and described high-speed rotation refers to that the rotating speed of rotary body exceeds gyroscope survey scope, comprises the steps:
A) 3-axis acceleration of accelerometer output rotary body is preserved in first microprocessor,
B) radius of turn that calculates according to the first situation of first microprocessor, calculates and preserves the influence value of acceleration of gravity to rotary body,
C) first microprocessor is according to the reverse tachometer value deriving rotary body of the result of step a and step b, and is sent in display terminal by the first wireless transport module and shows.
4. the self-adaptation rotating speed measurement method based on inertial sensor according to claim 3, it is characterized in that, the radius of turn calculated in the first situation described is that radius of turn rotates the calculation expression of centripetal acceleration about axle each on accelerometer, and this calculation expression is obtained by following formulae discovery:
Wherein, ω
x, ω
yand ω
zfor X-axis angular velocity, Y-axis angular velocity and Z axis angular velocity that any time gyroscope exports, R is radius of turn, a
xthe rotation centripetal acceleration in rotary body X-direction, a
ythe rotation centripetal acceleration in rotary body Y direction, a
zit is the rotation centripetal acceleration in rotary body Z-direction;
Separate above-mentioned equation (1) (2) (3) to obtain:
a
X=k
1R…………(4)
a
Y=k
2R…………(5)
a
Z=k
3R…………(6)
Wherein, k
1, k
2and k
3it is the known coefficient calculated.
5. the self-adaptation rotating speed measurement method based on inertial sensor according to claim 4, is characterized in that, described second case
In step a, accelerometer exports the 3-axis acceleration A respectively of rotary body
x, A
yand A
z,
In step b, the influence value of acceleration of gravity to rotary body comprises the gravitational acceleration component g not rotating change with rotary body
xS, g
ySand g
zSand with the gravitational acceleration component g that rotary body rotation period changes
xD, g
yDand g
zD, when rotary body uniform rotation, following formula (7) (8) (9) set up:
A
X=a
X+g
XS+g
XD…………(7)
A
Y=a
Y+g
YS+g
YD…………(8)
A
Z=a
Z+g
ZS+g
ZD…………(9)
By wave filter by g
xD, g
yDand g
zDfiltering, obtains the amplitude g of respective change amount
xDA, g
yDAand g
zDA, to be eliminated g according to formula (7) (8) (9)
xD, g
yDand g
zDa after impact
xA, A
yAand A
zA:
A
XA=a
X+g
XS…………(10)
A
YA=a
Y+g
YS…………(11)
A
ZA=a
Z+g
ZS…………(12)
In step c, the tachometer value of rotary body calculates and comprises the steps:
Formula (4) (5) (6) are substituted into formula (10) (11) (12), obtain:
A
XA=k
1R+g
XS…………(13)
A
YA=k
2R+g
YS…………(14)
A
ZA=k
3R+g
ZS…………(15)
Because g is terrestrial gravitation acceleration, so:
Wherein g
xDA, g
yDAand g
zDAfor known quantity, if
so:
By the g in formula (13) (14) (15)
xS, g
ySand g
zSbe transformed to the equation of R and substitute into formula (17), obtaining the linear equation in two unknowns about R, solve radius of turn R, after R is substituted into formula (13) (14) (15), solve g
xS, g
ySand g
zS;
Radius of turn R, g at any time
xS, g
ySand g
zSfor definite value, and substitute into formula (10) (11) (12), solve the rotation centripetal acceleration a on any time rotary body three direction of principal axis
x, a
yand a
z, calculate centripetal acceleration vector sum and obtain rotating centripetal acceleration a, then basis
draw final tachometer value ω.
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