MPU6050 returns unreal values

Yesterday I have tried to use a MPU6050 with ESP32 in arduino IDE.
I've tried several ways to get the acceleration data from the sensor.
At first I used the Adafruit MPU library. The sensor laid flat on a surface but X showed me -3m/s², Y something around 1m/s² and Z ~0m/s². I Expected X:0, Y:0, Z:9,81.

// Arduino Guide: https://RandomNerdTutorials.com/arduino-mpu-6050-accelerometer-gyroscope/

#include <Adafruit_MPU6050.h>
#include <Adafruit_Sensor.h>
#include <Wire.h>

Adafruit_MPU6050 mpu;

void setup(void) {
  Serial.begin(115200);
  while (!Serial) {
    delay(10); // will pause Zero, Leonardo, etc until serial console opens
  }

  // Try to initialize!
  if (!mpu.begin()) {
    Serial.println("Failed to find MPU6050 chip");
    while (1) {
      delay(10);
    }
  }

  mpu.setAccelerometerRange(MPU6050_RANGE_16_G);
  mpu.setGyroRange(MPU6050_RANGE_250_DEG);
  mpu.setFilterBandwidth(MPU6050_BAND_21_HZ);
  Serial.println("");
  delay(100);
}

void loop() {

  /* Get new sensor events with the readings */
  sensors_event_t a, g, temp;
  mpu.getEvent(&a, &g, &temp);

  /* Print out the values */
  Serial.print(a.acceleration.x);
  Serial.print(",");
  Serial.print(a.acceleration.y);
  Serial.print(",");
  Serial.print(a.acceleration.z);
  Serial.print(", ");
  Serial.print(g.gyro.x);
  Serial.print(",");
  Serial.print(g.gyro.y);
  Serial.print(",");
  Serial.print(g.gyro.z);
  Serial.println("");

  delay(10);
}

Next, I used another example-code to get the raw sensor data. The results were nearly the same, like X: -5000, Y: 1500 and Z: 300. I don't know the exact values but they were in this magnitude.

So I installed a calibration library and have done the calibration. After this, X and Y were ~0 and Z ~16,000. (I think this should be the real values).
After turning the sensor 90°, Y was 16,000, X ~0 but Z keeps at 16,000.
It seems like the sensor is always returning values near 0 for Z and the calibration-offset adds 16k to Z, so Z is always 16k.

Is this sensor broken?
Thank you!

Look at the raw data, using this minimal example, while orienting the MPU-6050 with X, Y or Z up.

If it is working correctly, the axis pointing up or down should show a large number representing +/- 1 g, and the other two axes should be around zero.

If not, it is broken. But then, the MPU-6050 was discontinued years ago, so what you have is some sort of clone or counterfeit.

// MPU-6050 Short Example Sketch
// By Arduino User JohnChi
// August 17, 2014
// Public Domain
#include<Wire.h>
const int MPU_addr = 0x68; // I2C address of the MPU-6050
int16_t AcX, AcY, AcZ, Tmp, GyX, GyY, GyZ;

void setup() {
  Wire.begin();
  Wire.beginTransmission(MPU_addr);
  Wire.write(0x6B);  // PWR_MGMT_1 register
  Wire.write(0);     // set to zero (wakes up the MPU-6050)
  Wire.endTransmission(true);
  Serial.begin(9600);
}

void loop() {
  Wire.beginTransmission(MPU_addr);
  Wire.write(0x3B);  // starting with register 0x3B (ACCEL_XOUT_H)
  Wire.endTransmission(false);
  Wire.requestFrom(MPU_addr, 14); // request a total of 14 registers
  int16_t t = Wire.read();
  AcX = (t << 8) | Wire.read(); // 0x3B (ACCEL_XOUT_H) & 0x3C (ACCEL_XOUT_L)
  t = Wire.read();
  AcY = (t << 8) | Wire.read(); // 0x3D (ACCEL_YOUT_H) & 0x3E (ACCEL_YOUT_L)
  t = Wire.read();
  AcZ = (t << 8) | Wire.read(); // 0x3F (ACCEL_ZOUT_H) & 0x40 (ACCEL_ZOUT_L)
  t = Wire.read();
  Tmp = (t << 8) | Wire.read(); // 0x41 (TEMP_OUT_H) & 0x42 (TEMP_OUT_L)
  t = Wire.read();
  GyX = (t << 8) | Wire.read(); // 0x43 (GYRO_XOUT_H) & 0x44 (GYRO_XOUT_L)
  t = Wire.read();
  GyY = (t << 8) | Wire.read(); // 0x45 (GYRO_YOUT_H) & 0x46 (GYRO_YOUT_L)
  t = Wire.read();
  GyZ = (t << 8) | Wire.read(); // 0x47 (GYRO_ZOUT_H) & 0x48 (GYRO_ZOUT_L)
  t = Wire.read();
  Serial.print("AcX = "); Serial.print(AcX);
  Serial.print(" | AcY = "); Serial.print(AcY);
  Serial.print(" | AcZ = "); Serial.print(AcZ);
  Serial.print(" | Tmp = "); Serial.print(Tmp / 340.00 + 36.53); //equation for temperature in degrees C from datasheet
  Serial.print(" | GyX = "); Serial.print(GyX);
  Serial.print(" | GyY = "); Serial.print(GyY);
  Serial.print(" | GyZ = "); Serial.println(GyZ);
  delay(333);
}

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