Method for measuring parameters of a mechanical system that describe an electric motor system

Abstract

A method for measuring parameters of a mechanical system, in particular the moment of inertia and friction effects describing an electric motor system, wherein the method comprises the following steps: - Applying a linear ramp of electric torque to the system according to a current slope h, - Measuring data representing the velocity response of the system, - Fitting the measurement data to a model function by applying a curve-fitting algorithm, wherein a number of fitting parameters correspond to the parameters of the mechanical system, and characterized in that the current slope h is chosen for a single ramp and a guess for the moment of inertia of the mechanical system is calculated by fitting the measurement data with a quadratic equation f(x) = ax² + bx + c.

Description

[0001] The present invention relates to a method for measuring parameters of a mechanical system, in particular the inertia and friction effects that describe an electric motor system. The method comprises the following steps - Applying a linear ramp of electrical torque corresponding to a current gradient h to the system, - Measuring data representing the speed response of the system, - Fitting the measured data with a model function by applying a curve fitting algorithm, where a number of fitting parameters match the parameters of the mechanical system.

[0002] The invention also relates to an electric motor system comprising an electric motor and a frequency converter and a frequency control, wherein the electric motor system is provided for carrying out a corresponding method.

[0003] The invention applies to the operation of electric motors using frequency converters or frequency controllers. The invention can be applied in any industry that uses electric motors. Frequency converters control electric motors in many applications. For high efficiency, precision, and dynamic performance, the parameters describing the physical system of the electric motor must be known.

[0004] These parameters typically need to be determined manually by an operator, which can be problematic because it can introduce human error and complicate the correct operation of the electric motor.

[0005] The aim of the present invention is to overcome this problem and to provide an improved method for autonomously or automatically setting the parameters of a mechanical system of an electric motor system.

[0006] The object is achieved by a method according to claim 1 and an electric motor system according to claim 10. Preferred embodiments of the invention are based on the dependent claims.

[0007] According to claim 1, a method for measuring parameters of a mechanical system, in particular the inertia and friction effects that describe an electric motor system, is provided. The method comprises the following steps - Applying a linear ramp of electrical torque corresponding to a current gradient h to the system, - Measuring data representing the speed response of the system, - Fitting the measured data with a model function by applying a curve fitting algorithm, where a number of fitting parameters match the parameters of the mechanical system.

[0008] At its core, the invention proposes a method for applying a linear ramp of the electrical torque to the motor and measuring its speed response. Based on a physical model of the system, the measured data are fitted with the model functions. The fitting result provides access to several unknown parameters after just a single ramp.

[0009] The electrical torque of an electric motor is proportional to the applied current. While the current can be controlled without knowledge of the mechanical parameters of the motor system, the method can be applied without prior assumptions regarding any of the mechanical parameters of the motor system. The current is then ramped up linearly from zero to a motor-specific maximum. The motor will respond by accelerating, overcoming its inertia and friction effects.

[0010] The current ramp can be limited to a maximum motor speed. The expected speed response is mathematically modeled based on the physics of inertia, static friction, dynamic friction, viscous friction, or any higher-order friction effects. The resulting model provides a function with respect to the motor speed. By applying a curve-fitting algorithm, the measured data points are also adjusted accordingly. The number of unknown fitting parameters coincides with the unknown mechanical parameters of the system. The fitting result will thus allow the parameters to be obtained with an error estimate.

[0011] A natural extension of this procedure is the inclusion of further unknown effects by repeating the measurement with different initial conditions and comparing the differences in the results. Thus, some or all of the procedure steps can be repeated, preferably with different initial conditions, such as different motor speeds, different system inertias, etc.

[0012] The method allows the measurement of a number of mechanical characteristics, such as the motor's moment of inertia and friction effects, using a single torque ramp. It also allows for the compensation of unexpected and unmodeled effects by repeating the individual ramp measurement. In general, the invention contributes to driving electrification in various technical fields, thereby increasing energy efficiency and digitalization.

[0013] In a preferred embodiment of the invention, the linear ramp of the electric torque is applied by ramping an input current from zero to a motor-specific maximum. The motor-specific maximum can be manually entered and / or can be stored on a drive that drives the motor. The drive can include any storage, computing, and power conversion devices required to drive the motor. The electric motor system can include the electric motor and the drive for driving the motor. The electric motor system can include any other components required to perform the presently described method.

[0014] In a further preferred embodiment of the invention, the model function describing the parameters of the mechanical system is: ddtω=32ψpiqJ−MRJ−MHJ where the force of friction and the static friction of the mechanical system form a constant torque M R or a threshold torque M H result.

[0015] In a further preferred embodiment of the invention, the current slope h is chosen for a single ramp and an assumption for the moment of inertia of the mechanical system is made by fitting the measured data with a quadratic equation f(x) = ax 2 + bx +c calculated.

[0016] In a further preferred embodiment of the invention, the moment of inertia is calculated from the equation J=34ψhp1a calculated.

[0017] In a further preferred embodiment of the invention, the force of friction and the static friction of the mechanical system result in a constant torque M R and a threshold torque M H , calculated from the equations MR=−32ψhpt0−bJ and MH=|(32ψhpt0+MR)2−c⋅3Jψhp

[0018] In a further preferred embodiment of the invention, the method is repeated with at least three different current gradients h, the results being calculated using the power law f(x) = ax b + c and the resulting offset c is the real value of the moment of inertia.

[0019] In a further preferred embodiment of the invention, the model function describing the parameters of the mechanical system is ddtω=32ψphtJ−(MRJ−Ae−Bω(t)) where the friction force of the mechanical system is a constant torque M R and where the general solution of this differential equation is ω(t)=1Bln(Bπ2CAeBD22C)+1Bln(erf(B2C(Ct−D))+K)+C2t2−Dt with substitutions C=32ψphJ and D=MRJ

[0020] In a further preferred embodiment of the invention, the measurement data are adapted to a speed profile with the following equations ω(t)=1Bln(Bπ|2C(D−Ct0)eBD22C)+1Bln(ref(B2C(Ct0−D))+K0)+C2t2−Dt with K0=exp((Dt0−C2t02−1Bln(Bπ2C(D−Ct0)eBD22C))B)−erf(B2C(Ct0−D)) where K is the integration constant and the boundary conditions are 0=Ct0−D+A A=D−Ct0

[0021] The invention also relates to an electric motor system according to claim 10. The electric motor system comprises an electric motor and a frequency converter or a frequency drive. The electric motor system is provided for carrying out a method according to any one of claims 1 to 9.

[0022] Further details and advantages of the invention are described with reference to the figures. In the figures: Fig.1: a graphical representation showing a measurement of a linear current ramp; Fig. 2. a power law fit after a set of measurements; Fig. 3: a flowchart of the underlying algorithm of the present invention; Fig. 4: a thin flywheel for testing the underlying algorithm of the invention; Fig. 5: Test results according to Gaussian fittings; Fig. 6: Details of the test results with small moments of inertia; Fig. 7: Test results for a thick flywheel; Fig. 8: Test results for a thick flywheel; and Fig. 9: Test results for a thick flywheel and dynamic friction.

[0023] The method described here for measuring the inertia of an electric motor and its associated system is based on the direct acceleration of the motor. The moment of inertia is the proportionality factor between the desired acceleration and the applied torque. M→=J⋅α→

[0024] The torque itself is directly proportional to the current component orthogonal to the magnetic flux of the rotor magnet i q The corresponding relationship is M→=32ψpiq with the permanent magnet flux ψ (“back EMF constant”) and the number of pole pairs p.

[0025] In general, there are two main components that influence the mechanical dynamics of the system: frictional force and static friction. While the former contributes a constant torque M to this movement, R the latter only locks the motor at standstill until a threshold torque M His reached. Both effects influence any measurement where one wants to measure the acceleration of the system when a constant current is applied. It should be noted that M R is an unknown that is not directly accessible and that contributes directly to the electrical torque of the system.

[0026] The present invention proposes instead a linear current ramp, where the constant acceleration of friction is decoupled from the linear acceleration of the electric torque. The general idea is Fig. 1 shown.

[0027] The differential equation describing the mechanical system is ddtω=32ψpiqJ−MRJ−MHJ where M H only acts while ω = 0. Since the current is ramped up linearly, i q set so that i q = h(t - t0), which leads to a solution of the differential equation (for ω > 0) of ω=34ψpht2J−(32ψpht0+MR)tJ+K

[0028] The integration constant K is used to evaluate the effect of M H The static friction acts until the total acceleration becomes positive, so ddtω>0 what happens at t=t0+23MRphψ+23MHphψ

[0029] At the same point, ω = 0, which is used to calculate C as C=−MH23Jphψ+(123phψJt0+MR3Jphψ)2

[0030] The complete measurement process of the method can consist of two steps: a single ramp to obtain a result for the moment of inertia for a specific gradient h, and a power-law fit to find the real value of the moment of inertia. A single ramp is performed by choosing a gradient h and calculating an estimate for the moment of inertia by fitting the velocity profile with a quadratic equation. f(x)=ax2+bx|+c

[0031] By solving the system equation, the moment of inertia is calculated as J=34ψhp1a

[0032] Analogously, the remaining fitting parameters can be used to obtain estimates for friction, as MR=−32ψhpt0−bJ and MH=|(32ψhpt0+MR)2−c⋅3Jψhp

[0033] Fig. Figure 2 shows the results of the inertial measurements using different current gradients. They decrease monotonically with increasing gradients. Upon closer inspection, they decrease according to the power law f(x) = ax b+ c. To complete the inertia measurement, several ramps (at least three) must be performed and the results fitted using the power law. The resulting offset c is recognized as the real value of the moment of inertia, as it compensates for all the effects that lead to incorrect results at smaller slopes. It can be observed that the best results can be obtained by choosing appropriate slopes to perform the measurements. These depend on the maximum current i q, max at the end of the ramp. It is recommended to choose slopes where this maximum current is between 20% and 80% of the motor's rated current. Within this range, slopes should be chosen that are evenly distributed. A good estimate can be obtained using the relationship iq,max=kh+l and calculating k and I using two random measurements.

[0034] Fig.Figure 3 shows a flowchart of the algorithm. It essentially contains both measurement steps described above. It is supplemented by an introductory step where the initial gradient is assumed. If it is too steep—that is, if the maximum current is reached before the target speed is reached—the gradient is reduced by quartering it until it works.

[0035] At the end of the algorithm, the confidence limits of the adjusted moment of inertia are calculated. These confidence limits are used as a final measure to estimate whether a reliable result has been obtained or whether another measurement is required. At a maximum of 20 measurements, the algorithm stops using the result, as it also considers the final confidence limits.

[0036] The algorithm can be tested and used with an AKM44E motor using an adapter for flywheels with known moments of inertia. In general, the algorithm can be tested with any type of electric motor, such as PMSM-SPM. The wheel is in Fig. 4. In the example given here, two different sized wheels can have a mass of m1 = 0.67 kg and m2 = 1.008 kg. A thinner flywheel can have a width of 5 mm, while a thicker one can have a width of 7.5 mm.

[0037] The moments of inertia of the adapter, thin and thick flywheels, and the screws used to attach them are known. They are J a = 0.00044kgm 2 , J1 = 0.00236kgm 2 , J2 = 0.00353kgm 2 and Js = 0.000038kgm 2 in this order. However, a careful calculation of the moments of inertia of both flywheels was also carried out based on the formula J=mri2+ro22 with the inner radius r i and the outer radius r0. Taking into account the holes for the screws, this formula gives J1 = 0.002335kgm 2 and J2 = 0.00350kgm 2 for the two flywheels. The engine itself has a moment of inertia of J m = 0.00027kgm 2 obtained from its data sheet. Four cases are treated as follows: case construction Data sheet value [kg cm 2 ] Calculated value [kg cm 2 ] 1 Adapter only 7,10 7,10 2 Adapter with screws 7,48 7,48 3 Thin flywheel 31,08 30,83 4 Thick flywheel 42,78 42,50

[0038] The test was carried out with several hundred measurements for each case to obtain statistically reliable data. The results are shown in Fig. 5. The scale for the moment of inertia is discretized with 0.05 kg m 2 The test determines how often each position on the scale has been measured and fits the result using a Gaussian distribution. The results are also shown in the following table: case construction Measured value [kg cm 2 ] Standard deviation [kg cm 2 ] 1 Adapter only 7,335 0,059 2 Adapter with screws 7,655 0,074 3 Thin flywheel 30,92 0,23 4 Thick flywheel 42,40 0,24

[0039] The statistical error of the standard deviation of the recorded measurements is shown to be less than 1%. Compared to the theoretical values, the measurement results deviate within the range of uncertainty between the datasheet value and the calculated values. Some information regarding the precision of the given values, as well as the values ​​used in the measurement process, is missing, namely the back EMF constant. Nevertheless, the measurement compares well with the given theoretical values ​​and demonstrates not only the good precision of the measurement process but also good accuracy. As described in Fig. As shown in Figure 6, the moment of inertia of the adapter attached only to the motor and the adapter with six screws added to it can be clearly distinguished.

[0040] These statistical considerations can serve as a guideline for how the measurement should be used and what can be expected from it. Ultimately, applicability depends significantly on the use case in which the inertial measurement is to be used. Under certain circumstances, the approach may not be suitable overall. For these cases, other measurement principles could be applied.

[0041] The presently described invention can be extended under certain circumstances. The inclusion of a tight shaft seal can influence the dynamic friction of the entire system in such a drastic way that the resulting dynamics from a linear current ramp cannot be reliably described by a quadratic velocity response. Extensive investigations show a velocity dependence of the dynamic friction, which can be described to a certain extent by an exponential function. This observation leads to the extension of the mechanical model to the differential equation ddtω=32ψphtJ−(MRJ−Ae−Bω(t)) with some unknown factors A and B. For simplicity, the substitutions C = 3.2 ψph / J and D = M R J. Using a computer algebra system, the general solution of this differential equation can be found as ω(t)=1Bln(Bπ2CAeBD22C)+1Bln(erf(B2C(Ct−D))+K)+C2t2−Dt with the integration constant K. The integration constant can be used to obtain a condition for the real root t0 of the function. For this purpose, the condition ω(t0)=0 be used to 0=1Bln(Bπ2CAeBD22C)+1Bln(erf(B2C(Ct0−D))+K)+C2t02−Dt0(Dt0−C2t02−1Bln(Bπ2CAeBD22 C))B=ln(erf(B2C(Ct0−D))+K)K=exp((Dt0−C2t02−1Bln(Bπ2CAeBD22C))B)−erf(B2C(Ct0−D)). This function can be directly applied to describe the velocity response of a constant current ramp with an exponential velocity-dependent dynamic friction. However, extensive testing has shown that the small velocity response introduces more uncertainties, so a different restriction must be applied, with the disadvantage of truncating the first peak of the velocity profile and considering only the regime where the influence of static friction can be neglected.

[0042] For this additional restriction, the currently used model states: ω˙=Ct−(D−Ae−Bω)

[0043] For a negligible static function, one expects ω˙(t0)=0 and, ω(t0)=0 so that 0=Ct0−D+A A=D−Ct0

[0044] Under this condition, the final velocity profile can be obtained: ω(t)=1Bln(Bπ2C(D−Ct0)eBD22C)+1Bln(erf(B2C(Ct−D))+K0)+C2t2−Dt, with K0=exp((Dt0−C2t02−1Bln(Bπ2C(D−Ct0)eBD22C))B)−erf(B2C(Ct0−D)).

[0045] Thus, a function with four unknowns is obtained, which can be solved by fitting a velocity profile with the currently used model.

[0046] Fig. Figures 7 to 9 document a further test of the presently described invention, wherein 300 fitting cycles were used and the final sum of residual values ​​was tracked to obtain an estimate of the quality of the fitting.

[0047] The current was ramped up at a constant rate of h = 0.11 A / s. The fit was obtained for 64 measurement points between 20% and 95% of the normal speed.

[0048] The results shown were obtained for a run of 500 consecutive measurements, starting with a cold engine and using the thick flywheel. The results show some overshoot for intermediate temperatures at the beginning of the test. Once the system has reached its steady-state temperature, a flattening of the curve is observed in the expected regime of J = 42 kg cm. 2 The actual value is well within the error limits. The parameters and steps described with reference to the possible tests may represent features of the presently described invention.

Claims

[1] A method for measuring parameters of a mechanical system, in particular the inertia and friction effects describing an electric motor system, the method comprising the following steps - Applying a linear ramp of electrical torque corresponding to a current gradient h to the system, - Measuring data representing the speed response of the system, - Fitting the measured data with a model function by applying a curve fitting algorithm, where a number of fitting parameters match the parameters of the mechanical system. [2] Method according to claim 1, characterized by that the linear ramp of the electrical torque is applied by changing an input current from zero to a motor-specific maximum. [3] Method according to claim 1 or 2, characterized by that the model function describing the parameters of the mechanical system is: ddtω=32ψpiqJ−MRJ−MHJ where the friction force and the static friction of the mechanical system form a constant torque M R or a threshold torque M H result. [4] Method according to one of the preceding claims, characterized by that the current gradient h is chosen for a single ramp and an assumption for the moment of inertia of the mechanical system is made by fitting the measured data with a quadratic equation f(x) = ax 2 + bx +c is calculated. [5] Method according to claims 3 and 4, characterized by that the moment of inertia is calculated from the following equation J=34ψhp1a [6] Method according to claims 3 to 5, characterized by that the friction force and the static friction of the mechanical system produce a constant torque M R and one based on the equations MR=−32ψhpt0−bJ and MH=|(32ψhpt0+MR)2−c⋅3Jψhp calculated torque. [7] Method according to claims 3 to 6, characterized by that the procedure is repeated with at least three different current gradients h, the results being calculated using the power law f(x) = ax b + c and the resulting offset c is the real value of the moment of inertia. [8] Method according to one of claims 1 to 3, characterized by that the model function describing the parameters of the mechanical system is ddtω=32ψphtJ−(MRJ−Ae−Bω(t)) where the friction force of the mechanical system is a constant torque M R and where the general solution of this difference equation is ω(t)=1Bln(Bπ2CAeBD22C)+1Bln(erf(B2C(Ct−D))+K)+C2t2−Dt with substitutions C=32ψphJ and D=MRJ [9] Method according to claim 8, characterized bythat the measured data are fitted to a velocity profile with the equations ω(t)=1Bln(Bπ|2C(D−Ct0)eBD22C)+1Bln(ref(B2C(Ct−D))+K0)+C2t2−Dt with K0=exp((Dt0−C2t02−1Bln(Bπ2C(D−Ct0)eBD22C))B)−erf(B2C(Ct0−D)) where K is the integration constant and the boundary conditions are 0=Ct0−D+A A=D−Ct0 [10] Electric motor system comprising an electric motor and a frequency converter or a frequency control, characterized by that the electric motor system is provided for carrying out a method according to one of claims 1 to 9.

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