RPM measurement using MEMS Inertial Measurement Unit (IMU) · They do not work like the digital compass which can generate the RPM signals by itself during rotating. After a lot of

RPM measurement using MEMS Inertial

Measurement Unit (IMU)

Tongjun Ruan, Robert Balch Reservoir Evaluation and Advanced Computational Technologies Group

Of Petroleum Recovery Research Center, New Mexico Tech., Socorro, NM, USA

Abstract- A Small device with MEMS Inertial

Measurement Unit （ IMU ） was designed and

implemented for non-wired sensing and recording of

the RPM (Revolutions per Minute) of mud motor

during Radial Drilling where the wire or wireless

communication ground/surface is impractical or not

feasible. This is accomplished by measuring angular

velocity and accelerations using 3-Axis Gyroscope

and 3-Axis Accelerometer of IMU, store the data on

the device, offloading data to an onsite laptop

computer。Four methods of calculating RPM based

on the outputs of IMU were proposed and the

accuracies of results from different methods were

compared. The measured RPM will be used for the

efficiency analysis and performance analysis of

Radial Drilling.

Keywords: RPM Measurement; MEMS Inertial

Measurement Unit; Radial Drilling;

1. Introduction In 2016-2017, we developed a RPM measurement

device using a 3 –Axis magnetometer and

successfully tested in lab [1]. After Lab test we went

to partner’s test site where the device was mounted

and sealed inside the slot of the steel shaft of mud

motor. The earth magnetic field was disturbed so

much by the steel shaft and steel tube (wellbore) and

the magnetometer could not give the expected

sufficient measurement precision of RPM as it did in

lab test. To improve the measurement precision of

RPM, we tried very hard to find a way (or sensor)

for the on-shaft RPM measurement. There are many

sensors available on market for RPM measurements

for example: photoelectric speed sensor, magnetic

speed sensor, hall speed sensor, eddy current speed

sensor, giant reluctance speed sensor etc. But all of

them require an off-shaft part and an on-shaft part

working together to generate RPM signals during

rotating. They do not work like the digital compass

which can generate the RPM signals by itself during

rotating.

After a lot of searching we think the IMU, which

contains a gyroscope and a accelerometer sometimes

a compass, is perfect for the RPM measurement

since it can measure the angular velocity and

accelerations. The low cost, low power consumption

and small size make MEMS digital output IMU is

very good fit for the On-Shaft RPM measurement. In

this study, MEME Inertial Measurement Unit (IMU)

which contains 3-axis gyroscope, accelerometer and

compass was selected to measure the RPM. After

implementing the prototypes, we tested by putting

the device into the slot of the shaft. The test results

was analyzed and 4 methods to calculate the RPM

based on the outputs of IMU were proposed:

1. Use the angular velocity

2. Use the acceleration

3. Use the quaternion

4. Euler angle

The testing results show the method 3 and 4 have

higher precision and more efficiency than other

methods.

A data processing tool was developed for the

processing and analyzing and visualizing the test

data and calculated results.

2. MEMS Inertial Measurement

Unit

An inertial measurement unit (IMU) is an

electronic device that measures and reports a body's

specific force, angular rate, and sometime the

magnetic field surrounding the body, using a

combination of accelerometers and gyroscopes,

sometime also magnetometers. IMUs are typically

used to maneuver aircraft, among many others, and

space craft, including satellites. Recent developments allow for the production of IMU-enabled GPS devices.

An IMU allows a GPS receiver to work when GPS-

signals are unavailable, such as in tunnels, inside

buildings, or when electronic interference is present.

Int'l Conf. Embedded Systems, Cyber-physical Systems, & Applications | ESCS'18 | 49

ISBN: 1-60132-475-8, CSREA Press ©

But we have not found that the IMU was applied in

RPM measurement.

There are many IMU products in the market: from

customer grade(cheap) to tactical grade(very

expensive). For on-shaft RPM measurement, the IMU

must be small, low cost, low power consumption and

digital output (no extra circuit and power needed).

As modern electronic technology develops,

microchip-packaged digital MEMS IMU have been

developed and popularly used in many electronic

device and customer products for example: smart

phone.

The digital MEMS IMU has following features:

Tiny body

Low single operational voltage

Lower power consumption.

Digital output (analog one needs extra circuit and

power)

Lower price

3 Design and Implementation

Based on the requirements, InvenSense’s MPU-

9250 was selected for this study. MPU-9250 is

InvenSense company’s second generation IMU, also is

the world’s smallest 9-axis IMU with

3mmx3mmx1mm package, low cost and low power

consumption.

The device was designed with the device with

following chips:

MPU-9250 as IMU

Microchip’s PIC16LF18250 as MCU to

configure the sensor and the flash memory, read

data from the sensor and write data into the flash

memory during rotation

IS25LP128 serial flash memory as the data

storage

Lithium Coin battery LR1632 is selected to

provide operating power

Figure 1. Hardware architecture of the device

Figure 2. the implemented prototype and the shaft with

slot.

Figure 1 shows the device’s architecture. Figure 2

shows the implemented prototype and the shaft with

slot. During the testing, the device with coin battery

will be sitting inside of the slot.

4 Methods of computing RPM

Based on the possible outputs of MPU-9250, we

proposed 4 methods to compute the RPM.

4.1 Use the angular velocity

MPU-9250 has 3 –axis gyroscope. According to its

function (measuring the angular velocity), gyroscope

should be perfect for the RPM measurement. The

angular velocity can be easily converted into RPM.

The gyroscope’s highest Full-Scale range, is +/-

2000 Degree/Second, the range of RPM should be 0--

---60*2000/360, thus the maximum RPM which could

be measured by this device is about 333 RPM.

Normally the RPM of the downhole mud motor, which

drives the drilling head, is between 0 and 250, so the

sensor is suitable to measuring its RPM.

If the angular velocity is the rate of change of angle

with respect to time. Unit of angular velocity is ω

radians per second (rad/sec). The relationship of ω and

RPM can be descripted as formula (1) and (2)

ω=2πN/60 (1)

N= 60 ω/2π=30 ω/ π (2)

Where: ω is the angular velocity in radians per

second, N is Revolutions per Minute (RPM).

Figure 3 show the angular velocity when the device

rotates at 60 RPM

Figure 3. Angular velocity

-300

-200

-100

0

100

17

31

45

21

72

89

36

14

33

50

55

77

64

97

21

79

38

65

93

7

Series1 Series2 Series3

50 Int'l Conf. Embedded Systems, Cyber-physical Systems, & Applications | ESCS'18 |


4.2 Computing RPM based on

accelerations

The IMU can measure the acceleration; according

to physics we can use the accelerations to calculate the

RPM respectively:

The gravity is removed by low-pass digital filter

from the 3-Axis accelerations to get the linear

accelerations. And linear accelerations were

transferred from body frame to global frame. They

became sinusoidal signal (see figure 4). Then the

linear-global accelerations are integrated twice to get

the trajectory of the movement that consists of many

circles. RPM will be calculated based on the

period/time (between the two peaks) of the device

moving one circle(the linear-global accelerations,

linear-global velocity or position). Figure 5 show the

trajectory of the movement is circles. (see Figure 5)

Fig. 4 Linear/Global Accelrations (removed

gracity and transfereed from body/device fram to

global frame)

Figure 5 Computed circular paths

4.3 Computing RPM based on quaternions

Quaternion is calculated from angular velocity

and acceleration, below is popular used codes[6] to

calculate quaternion based on the angular velocity and

acceleration:

// variable definitions

// quaternion elements representing the estimated

orientation

float exInt=0,eyInt=0 , ezInt=0;

// scaled integral error

//gx, gy, gz------angular velocity

//ax, ay, az -----acceleration

IMUUpdate( float gx, float gy, float gz, float ax, float

ay, float az )

{

float norm;

float vx, vy, vz;

float ex, ey, ez;

// normalise the measurements

norm = nr_sqrt((ax*ax) + (ay*ay) + (az*az));

ax = ax / norm;

ay = ay / norm;

az = az / norm;

// estimated direction of gravity

vx = 2*(q1*q3 - q0*q2);

vy = 2*(q0*q1 + q2*q3);

vz = q0*q0 - q1*q1 - q2*q2 + q3*q3;

// error is sum of cross product between reference

direction of field and direction measured by sensor

ex = (ay*vz - az*vy);

ey = (az*vx - ax*vz);

ez = (ax*vy - ay*vx);

// integral error scaled integral gain

exInt = exInt + ex*Ki;



eyInt = eyInt + ey*Ki;

ezInt = ezInt + ez*Ki;

// adjusted gyroscope measurements

gx = gx + Kp*ex + exInt;

gy = gy + Kp*ey + eyInt;

gz = gz + Kp*ez + ezInt;

// integrate quaternion rate and normalise

q0 = q0 + (-q1*gx - q2*gy - q3*gz)*halfT;

q1 = q1 + (q0*gx + q2*gz - q3*gy)*halfT;

q2 = q2 + (q0*gy - q1*gz + q3*gx)*halfT;

q3 = q3 + (q0*gz + q1*gy - q2*gx)*halfT;

// normalise quaternion

norm=nr_sqrt((q0*q0)+(q1*q1)+(q2*q2)+(q3*q3));

q0 = q0 / norm;

q1 = q1 / norm;

q2 = q2 / norm;

q3 = q3 / norm;

}

Comparing figure 4 and figure 6, the period of

quaternion’s sinusoidal signal and is half of the period

of acceleration’s sinusoidal signal. We can use the

same method to calculate the RPM. For quaternion we

need to double it to get correct RPM.

Figure. 6 Quaternion sinusodal wave

4.4 Euler angles

Euler angles, ie Roll, Pitch and Yaw, can be callated

from quaternion using forllown formulas :

Euler angles change during the device rotating. Its

period is the same as that of the acceleration. Figure 7

shows the changes.

Figure 7a. Euler angles

Figure 7b. Algorithm Examples

The peak value should be

𝜋(𝑅𝑜𝑙𝑙72 − 𝑅𝑜𝑙𝑙71)

𝑇72 − 𝑇71= (𝜋 − 𝑅𝑜𝑙𝑙72)/(𝑇𝑝 − 𝑇72)

Then we can get

𝑇𝑝 = 𝑇72 + (𝜋 − 𝑅𝑜𝑙𝑙72)(𝑇72 − 𝑇71)/(𝑅𝑜𝑙𝑙72− 𝑅𝑜𝑙𝑙71)

𝑅𝑃𝑀 = 60/𝑇𝑝

Or we have another simplified algorithm which

directly use the Euler change between two nearest

points to calculate the RPM :

RPM= 60*(Rolli+1-Rolli)*sampling-rate/(2 𝜋)

52 Int'l Conf. Embedded Systems, Cyber-physical Systems, & Applications | ESCS'18 |


5 Estimate the period of the signals

of Accelerations, quaternion and

Euler angles

It is very clear that these three signals, global

linear acceleration, quaternion and Euler angle, are

periodic signals. We can use a method to estimate the

periods and convert them into RPM.

In the test the sampling number (Ns) of a period

was counted. Thus

Tp= Ns x (1/sampling rate)

RPM=60/Tp

Where Tp is the time of one period

We specifically used the following calculation

process to calculate the RPM from one of

Accelerations, Quaternion and Euler angles:

1. Select the signal S with max peak values(for

example the Roll signal in Euler angles)

2. Select two nearest peak values of signals S

3. Count the sampling number ( Ns) between the two

peak values

4. Calculate the time Tp of between the two peak

values ( one period):

Tp= Ns x (1/sampling rate) 5. Calculate the RPM :

If signal is acceleration or Euler angle

(method 2 and 4) RPM=60/Tp

If signal is quaternion: RPM=2*60/Tp

To get more accurate results, Interpolation

calculation was used in finding the positons of peak

value and computing the Ns.

6 Test results Methods 1 and 2 give the RPM 58.9 when the shaft

turns at RPM=60.

The error is (60-58.59)/60.00 = 2.35%

Methods 3 and 4 give the RPM 60.60 when the

shaft turns at RPM=60.

The error is (60.60-60)/60.00 = 1%

Thus the method 3 and 4 have higher accuracy and

more efficiency than method 1 and 2.

7 Conclusion and future work

7.1 Conclusion

Test results show MEMS IMU is a perfect device

for on-shaft RPM measurement.

1 It does not need accurately positing on the

rotator or shaft. Because RPM computation does

not rely on the line speed of the rotation

2 It depend on the period of a rotation from

angular velocity.

3 It does not require a specific angle or a position

on rotator or shaft. It can be mounted on any

position and any angle on the shaft or rotator

which will not affect the RPM measurement

accuracy.

4 The measurement range will decided by the

gyroscope’s highest Full-Scale range, if the

highest Full-Scale range is +/- A Degree/Second,

RPM range should be {-60*A/360-60*A /360}.

The Gyroscope of IMU with the higher Full-Scale

range can have the larger RPM measurement

range.

5 Proposed methods of RPM computing based on

the IMU’s output all work well ,but method

3(quaternion ) and 4(Euler angles ) give higher

accuracy ( 1% error )and more efficiency than

method 1 and 2.

7.2 Future work Future work: more tests will be done next

month to get more results and to improve the

RPM computational methods and data analysis.

8 Reference

[1] Tongjun Ruan, Robert Balch,”RPM measurement

using 3-Axis Digital. Magnetometer.” Int'l Conf.

Embedded Systems, Cyber-physical Systems, &

Applications (ESCS'17 ), Las Vegas NV,July.

2017.

[2] Micochip Technology Inc, “PIC16F1825 data

sheet,” 2012,pp.1-5

[3] Integrated Silicon Solution Inc.“IS25LP128

128M-BIT 3V Serial Flash Memory datasheet”,

10/3/2014

[4] InvenSense Inc., “MPU-9250 Product

Specification Revision 1.0”, 2014

[5] P Cheng, Y Yang, B Oelmann,”design and

implement of a stator –free RPM sensor prototye

basedon MEMS accelerometers” IEEE

Transactions on Instrumentation and

Measurement 61 (3), 775-785,2012.

[6] https://github.com/dancollins/Quad-

Rotor/blob/master/QuadRotor/imu.c, April, 2018



https://github.com/dancollins/Quad-Rotor/blob/master/QuadRotor/imu.c

https://github.com/dancollins/Quad-Rotor/blob/master/QuadRotor/imu.c

Documents

RPM measurement using MEMS Inertial Measurement Unit (IMU) · They do not work like the digital compass which can generate the RPM signals by itself during rotating. After a lot of