Test piece characteristic estimation method and test piece characteristic estimation device

Abstract

A test piece characteristic estimation method includes estimating a moment of inertia of a test piece. A first transfer function G1 from a torque current command for a dynamometer to output from a shaft torque sensor is measured by vibrationally operating the dynamometer. A second transfer function G2 from the torque current command to the output of a dynamo rotation speed sensor is measured by vibrationally operating the dynamometer. A real part and an imaginary part of a ratio obtained by dividing the second transfer function G2 by the first transfer function G1 at a prescribed measurement frequency .sub.k are calculated. A moment of inertia Jeg and a rotational friction Ceg are estimated by using the real part and the imaginary part of the ratio.

Claims

1. A test piece characteristic estimation method which uses a test system comprising: a dynamometer joined with a test piece via a connecting shaft; a shaft torque sensor which detects shaft torque generated at the connecting shaft; and a revolution speed detector which detects a revolution speed of an output shaft of the test piece or the dynamometer, the method estimating a moment of inertia of the test piece the method comprising: measuring a first transfer function from a torque current command relative to the dynamometer until an output of the shaft torque sensor by vibrationally operating the dynamometer; measuring a second transfer function from the torque current command until an output of the revolution speed detector by vibrationally operating the dynamometer; and calculating values of a real part and an imaginary part at a predetermined measurement frequency of a ratio obtained by dividing the second transfer function by the first transfer function, and estimating the moment of inertia using the values of the real part and the imaginary part of the ratio.

2. The test piece characteristic estimation method according to claim 1 wherein, the measurement frequency is defined as .sub.k, a real part and imaginary part of the ratio at the measurement frequency .sub.k are defined as a.sub.k and b.sub.k, a value of the moment of inertia Jeg of the test piece is calculated according to the estimation formula below $\begin{array}{cc}\mathrm{Jeg}=-\frac{b_k}{\left(a_k^2+b_k^2\right){}_k}.& \left(1\right)\end{array}$

3. The test piece characteristic estimation method according to claim 2, wherein a value of rotational friction Ceg with the output shaft of the test piece as a rotation shaft is calculated according to the estimation formula below, using the values of the real part a.sub.k and imaginary part b.sub.k of the ratio at the measurement frequency .sub.k $\begin{array}{cc}\mathrm{Ceg}=\frac{a_k}{a_k^2+b_k^2}.& \left(2\right)\end{array}$

4. The test piece characteristic estimation method according to claim 1 wherein, n-number (n is an integer of 2 or more) of different measurement frequencies are defined as .sub.k_j (j is an integer from 1 to n), a real part and an imaginary part of the ratio at the respective measurement frequencies .sub.k_j are defined as a.sub.k_j and b.sub.k_j, a value of the moment of inertia Jeg of the test piece is calculated according to the estimation formula below $\begin{array}{cc}\mathrm{Jeg}=-\frac{1}{n}\underset{j=1}{\overset{n}{.Math.}}\frac{b_{k\_j}}{\left(a_{k\_j}^2+b_{k\_j}^2\right){}_{k\_j}}.& \left(3\right)\end{array}$

5. The test piece characteristic estimation method according to claim 4, wherein a value of the rotational friction Ceg with an output shaft of the test piece as a rotation shaft is calculated using an estimation formula below, using values of the real part a.sub.k_j and the imaginary part b.sub.k_j of the ratio at the n-number of different measurement frequencies .sub.k_j $\begin{array}{cc}\mathrm{Ceg}=\frac{1}{n}\underset{j=1}{\overset{n}{.Math.}}\frac{a_{k\_j}}{a_{k\_j}^2+b_{k\_j}^2}.& \left(4\right)\end{array}$

6. The test piece characteristic estimation method according to claim 1, wherein the measurement frequency is lower than a resonance frequency of a mechanical system constituted by joining the test piece and the dynamometer by the connecting shaft.

7. A test piece characteristic estimation device for estimating a moment of inertia with an output shaft of a test piece as a rotation shaft, the test piece characteristic estimation device comprising: a dynamometer that is joined with a test piece by a connecting shaft; a shaft torque sensor that detects shaft torque generated at the connecting shaft; a revolution speed detector that detects a revolution speed of an output shaft of the test piece or the dynamometer; a first transfer function measuring means for measuring a first transfer function from a torque current command to the dynamometer until an output of the shaft torque sensor by vibrationally operating the dynamometer; a second transfer function measuring means for measuring a second transfer function from the torque current command until an output of the revolution speed detector by vibrationally operating the dynamometer; and a moment of inertia estimating means for calculating values of a real part and an imaginary part at a predetermined measurement frequency of a ratio obtained by dividing the second transfer function by the first transfer function, and estimating the moment of inertia using the values of the real part and the imaginary part of the ratio.

8. A test piece characteristic estimation method which uses a test system comprising: a dynamometer joined with a test piece via a connecting shaft; a shaft torque sensor which detects shaft torque generated at the connecting shaft; and a revolution speed detector which detects a revolution speed of an output shaft of the test piece or the dynamometer, the method estimating a moment of inertia of the test piece, the method comprising: measuring a first transfer function from a torque current command relative to the dynamometer until an output of the shaft torque sensor by vibrationally operating the dynamometer; measuring a second transfer function from the torque current command until an output of the revolution speed detector by vibrationally operating the dynamometer; and calculating a value at a predetermined measurement frequency of a ratio obtained by dividing the second transfer function by the first transfer function, and estimating the moment of inertia using the value of the ratio, wherein, the first transfer function is defined as G1(s), and the second transfer function is defined as G2 (s), a value of the moment of inertia Jeg of the test piece is calculated according to the formula below established for the moment of inertia Jeg and a rotational friction Ceg of the test piece $\begin{array}{cc}\frac{G2\left(s\right)}{G1\left(s\right)}\frac{1}{\mathrm{Ceg}+\mathrm{Jeg}.Math.s}.& \left(5\right)\end{array}$

9. The test piece characteristic estimation method according to claim 8 wherein, the measurement frequency is defined as .sub.k, a real part and imaginary part of the ratio at the measurement frequency .sub.k are defined as a.sub.k and b.sub.k, a value of the moment of inertia Jeg of the test piece is calculated according to the estimation formula below $\begin{array}{cc}\mathrm{Jeg}=-\frac{b_k}{\left(a_k^2+b_k^2\right){}_k}.& \left(6\right)\end{array}$

10. The test piece characteristic estimation method according to claim 9, wherein a value of rotational friction Ceg with the output shaft of the test piece as a rotation shaft is calculated according to the estimation formula below, using the values of the real part a.sub.k and imaginary part b.sub.k of the ratio at the measurement frequency .sub.k $\begin{array}{cc}\mathrm{Ceg}=\frac{a_k}{a_k^2+b_k^2}.& \left(7\right)\end{array}$

11. The test piece characteristic estimation method according to claim 8 wherein, n-number (n is an integer of 2 or more) of different measurement frequencies are defined as .sub.k_j (j is an integer from 1 to n), a real part and an imaginary part of the ratio at the respective measurement frequencies .sub.k_j are defined as a.sub.k_j and b.sub.k_j, a value of the moment of inertia Jeg of the test piece is calculated according to the estimation formula below $\begin{array}{cc}\mathrm{Jeg}=-\frac{1}{n}\underset{j=1}{\overset{n}{.Math.}}\frac{b_{k\_j}}{\left(a_{k\_j}^2+b_{k\_j}^2\right){}_{k\_j}}.& \left(8\right)\end{array}$

12. The test piece characteristic estimation method according to claim 11, wherein a value of the rotational friction Ceg with an output shaft of the test piece as a rotation shaft is calculated using an estimation formula below, using values of the real part a.sub.k_j and the imaginary part b.sub.k_j of the ratio at the n-number of different measurement frequencies .sub.k_j $\begin{array}{cc}\mathrm{Ceg}=\frac{1}{n}\underset{j=1}{\overset{n}{.Math.}}\frac{a_{k\_j}}{a_{k\_j}^2+b_{k\_j}^2}.& \left(9\right)\end{array}$

13. The test piece characteristic estimation method according to claim 11, wherein the measurement frequency is lower than a resonance frequency of a mechanical system constituted by joining the test piece and the dynamometer by the connecting shaft.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) FIG. 1 is a view showing the configuration of a test system according to one embodiment of the present invention;

(2) FIG. 2 is a flowchart showing a sequence of estimating a characteristic of an engine using a ratio of a transfer function;

(3) FIG. 3 is a view showing the result in a case of applying the conventional estimation method for engine specifications;

(4) FIG. 4 is a view showing the result in a case of applying the estimation method for engine characteristics according to the above-mentioned embodiment;

(5) FIG. 5 is a view showing the result in a case of applying the estimation method for engine characteristics according to the above-mentioned embodiment; and

(6) FIG. 6 is a view showing the configuration of a conventional test system.

PREFERRED MODE FOR CARRYING OUT THE INVENTION

(7) Hereinafter, an embodiment of the present invention will be explained in detail while referencing the drawings. FIG. 1 is a view showing the configuration of a test system 1 according to the present embodiment.

(8) The test system 1 includes: an engine E serving as a test piece; a dynamometer D connected with this engine E via a substantially rod-shaped connecting shaft S; an engine control device 5 which controls the output of the engine E via a throttle actuator 2; an inverter 3 that supplies electrical power to the dynamometer D; a dynamometer control device 6 which controls the output of the dynamometer D via the inverter 3; a shaft torque sensor 7 that detects the torsional torque generated at the connecting shaft S (hereinafter referred to as shaft torque); a dynamo revolution speed sensor 8 which detects the revolution speed of the output shaft of the dynamometer D (hereinafter referred to as dynamo revolution speed); an engine revolution speed sensor C which detects the revolution speed of the output shaft (e.g., crank shaft) of the engine E (hereinafter, to differentiate from dynamo revolution speed, referred to as engine revolution speed); and an arithmetic unit 9 that performs various operations using the outputs of the shaft torque sensor 7, dynamo revolution speed sensor 8 and engine revolution speed sensor C. The test system 1 is also called a so-called engine bench system with the engine E as the testing target.

(9) With the test system 1, tests to evaluate the durability, fuel economy and exhaust purification performance of the engine E are performed by controlling the torque and speed of the dynamometer D using the dynamometer control device 6, while controlling the throttle aperture of the engine E using the engine control device 5. Hereinafter, among the various functions realized in this test system 1, focusing on the functions of estimating a characteristic of the engine E such as the moment of inertia of the engine E and the rotational friction which is substantially proportional to the engine revolution speed, a detailed explanation will be provided centering on the configurations related to the estimation of characteristics of this engine E.

(10) The engine control device 5 starts the engine E at a predetermined timing, and controls the output of the engine E via the throttle actuator 2 in a pre-set mode.

(11) The dynamometer control device 6 generates a torque current command signal to the dynamometer D in a mode determined according to the test. The inverter 3 causes a torque according to this command signal to be generated by the dynamometer D, by supplying electrical power to the dynamometer D based on the torque current command signal generated by the dynamometer control device 6.

(12) While controlling the output of the dynamometer D using the dynamometer control device 6 following the sequence explained by referencing FIG. 2 later, the arithmetic unit 9 acquires data related to the shaft torque detected by the shaft torque sensor 7 at this time, and at least any of the dynamo revolution speed detected by the dynamo revolution speed sensor 8 and the engine revolution speed detected by the engine revolution speed sensor C, and estimates the moment of inertia using this acquired data and the output shaft of the engine E as the rotation shaft, and the rotational friction, which is substantially proportional to the revolution speed. Herein, the concept of the estimation method of the present invention will be explained prior to explaining the specific sequence of estimating the moment of inertia and rotational friction by referencing the flowchart of FIG. 2.

(13) The equation of motion for the test system configured by combining the engine E, connecting shaft S, dynamometer D, inverter 3, etc. such as that shown in FIG. 1 is represented by Formulas (6-1) to (6-3) below, when using the Laplacian operator s.

(14) $\begin{array}{cc}\mathrm{Jeg}.Math.s.Math.\mathrm{weg}+\mathrm{Ceg}.Math.\mathrm{weg}=\mathrm{Teg}+\mathrm{Tsh}& \left(6\text{-}1\right)\\ \mathrm{Tsh}=\frac{\mathrm{Ksh}}{s}.Math.\left(\mathrm{wdy}-\mathrm{weg}\right)& \left(6\text{-}2\right)\\ \mathrm{Jdy}.Math.s.Math.\mathrm{wdy}=-\mathrm{Tsh}+\mathrm{Kinv}.Math.\mathrm{Tdy}& \left(\text{6}\text{-}3\right)\end{array}$

(15) In the above formula, Jeg is the moment of inertia (kgm.sup.2) with the output shaft of the engine as the rotation shaft, Ceg is the rotational friction (Nms/rad) with the output shaft of the engine as the rotation shaft, Ksh is the shaft torque rigidity (Nm/rad), Jdy is the moment of inertia with the output shaft of the dynamometer as the rotation shaft, Teg is the engine torque (Nm), weg is the engine revolution speed (rad/s), Tsh is the shaft torque (Nm), wdy is the dynamo revolution speed (rad/s), Kine is the torque control response coefficient of the inverter, and Tdy is the torque current command value (Nm) of the inverter.

(16) When solving this equation of motion (6-1) to (6-3) for shaft torque Tsh, dynamo revolution speed wdy and engine revolution speed weg, and extracting only terms proportional to the torque current command value Tdy, the following formula is derived.

(17) $\begin{array}{cc}\mathrm{Tsh}\frac{\mathrm{KinvKsh}\left(\mathrm{Ceg}+\mathrm{Jegs}\right)}{\mathrm{CegKsh}+\mathrm{JdyKshs}+\mathrm{JegKshs}+{\mathrm{CegJdys}}^2+{\mathrm{JdyJegs}}^3}.Math.\mathrm{Tdy}& \left(7\text{-}1\right)\\ \mathrm{wdy}\frac{\mathrm{Kinv}\left(\mathrm{Ksh}+\mathrm{Cegs}+{\mathrm{Jegs}}^2\right)}{\mathrm{CegKsh}+\mathrm{JdyKshs}+\mathrm{JegKshs}+{\mathrm{CegJdys}}^2+{\mathrm{JdyJegs}}^3}.Math.\mathrm{Tdy}& \left(7\text{-}2\right)\\ \mathrm{weg}\frac{\mathrm{KinvKsh}}{\mathrm{CegKsh}+\mathrm{JdyKshs}+\mathrm{JegKshs}+{\mathrm{CegJdys}}^2+{\mathrm{JdyJegs}}^3}.Math.\mathrm{Tdy}& \left(7\text{-}3\right)\end{array}$

(18) In the above formula, when defining the ratio of torque current command value Tdy to shaft torque Tsh as a first transfer function G1(s), defining the ratio between torque current command value Tdy and dynamo revolution speed wdy as a second transfer function G2(s), and defining the ratio between torque current command value Tdy and engine revolution speed weg as a third transfer function G3(s), these first to third transfer functions can measure by acquiring the outputs of the shaft torque sensor, dynamo revolution speed sensor and engine revolution speed sensor when vibrationally operating (i.e. oscillating the torque current command value Tdy) the dynamometer.

(19) Herein, as shown in the above Formulas (7-1) to (7-3), the first to third transfer functions are proportional to the torque control response coefficient Kinv of the inverter, respectively. Therefore, when dividing the second transfer function by the first transfer function to cancel out the influence of this torque control response coefficient Kinv, the following Formula (8-1) is derived. In addition, the low-frequency performance of Formula (8-1) is as in Formula (8-2).

(20) $\begin{array}{cc}\frac{G2\left(s\right)}{G1\left(s\right)}=\frac{1}{\mathrm{Ceg}+\mathrm{Jeg}.Math.s}+\frac{s}{\mathrm{Ksh}}& \left(8\text{-}1\right)\\ \frac{G2\left(s\right)}{G1\left(s\right)}\frac{1}{\mathrm{Ceg}+\mathrm{Jeg}.Math.s}& \left(8\text{-}2\right)\end{array}$

(21) Herein, when defining the real part of a predetermined frequency .sub.k (rad/s) of the ratio of the second transfer function to the first transfer function (G2/G1) as a.sub.k and defining the imaginary part as b.sub.k, the following Formula (9) is derived from the above Formula (8-2). Herein, i is an imaginary number.

(22) $\begin{array}{cc}\mathrm{Jeg}.Math.{}_k.Math.i+\mathrm{Ceg}=\frac{1}{a_k+b_k.Math.i}=\frac{a_k}{a_k^2+b_k^2}-\frac{b_k}{a_k^2+b_k^2}.Math.i& \left(9\right)\end{array}$

(23) Therefore, when comparing the real part and imaginary part of Formula (9), respectively, the following Formula (10) relative to the moment of inertia Jeg and rotational friction Ceg is derived. Herein, the first and second transfer functions and the ratio of these are respectively measurable in the aforementioned way; therefore, when using the measurement results of the frequency .sub.k, it is possible to specify the values of the coefficients a.sub.k and b.sub.k on the right side. Consequently, when using the measurement results of the first and second transfer functions, it is possible to estimate the moment of inertia Jeg and rotational friction Ceg of the engine by the following Formulas (10-1) and (10-2).

(24) 0$\begin{array}{cc}\mathrm{Jeg}=-\frac{b_k}{\left(a_k^2+b_k^2\right){}_k}& \left(10\text{-}1\right)\\ \mathrm{Ceg}=\frac{a_k}{a_k^2+b_k^2}& \left(10\text{-}2\right)\end{array}$

(25) It should be noted that the above Formulas (10-1) and (10-2) are formulas established relative to the measurement point of one frequency .sub.k; however, when defining this as the average value for the measurement points of a plurality of n-number (n is any integer of 2 or more) of different frequencies .sub.k_j (j is an integer between 1 and n), the following Formulas (11-1) and (11-2) are derived. It should be noted that, in the following formula, the real part and imaginary part of the ratio between the second transfer function and first transfer function at each measurement frequency .sub.k_j were defined as a.sub.k_j and b.sub.k_j, respectively. Therefore, in the case of the measurement points of the first and second transfer functions being plural, it is possible to estimate the moment of inertia Jeg and rotational friction Ceg with higher precision, by using the following Formulas (11-1) and (11-2) in place of the above Formulas (10-1) and (10-2).

(26) $\begin{array}{cc}\mathrm{Jeg}=-\frac{1}{n}\underset{j=1}{\overset{n}{.Math.}}\frac{b_{k\_j}}{\left(a_{k\_j}^2+b_{k\_j}^2\right){}_{k\_j}}& \left(11\text{-}1\right)\\ \mathrm{Ceg}=\frac{1}{n}\underset{j=1}{\overset{n}{.Math.}}\frac{a_{k\_j}}{a_{k\_j}^2+b_{k\_j}^2}& \left(11\text{-}2\right)\end{array}$

(27) Although a case of estimating the moment of inertia Jeg and rotational friction Ceg using the ratio of the second transfer function to the first transfer function was explained above, alternatively, even if using the ratio of the third transfer function to the first transfer function, it is possible to estimate the moment of inertia and rotational friction by almost the same sequence. More specifically, when dividing the third transfer function by the first transfer function, the following Formula (12), which is the same as the above approximate Formula (8-2), is derived. For this reason, when specifying the values of the real part a.sub.k (or a.sub.k_j) and imaginary part b.sub.k (or b.sub.k_j) using the ratio of the third transfer function to the first transfer function, it is possible to estimate the moment of inertia Jeg and rotational friction Ceg, using the above Formula (10-1) (or Formula (11-1)) and Formula (10-1) (or Formula (11-2)).

(28) $\begin{array}{cc}\frac{G3\left(s\right)}{G1\left(s\right)}=\frac{1}{\mathrm{Ceg}+\mathrm{Jeg}.Math.s}& \left(12\right)\end{array}$

(29) FIG. 2 is a flowchart showing a sequence of estimating the characteristics of the engine using the ratio of transfer functions such as Formula (8-2) or Formula (12).

(30) In S1, the first transfer function G1(s) is measured from the torque current command value Tdy until shaft torque Tsh, by vibrationally operating the dynamometer under a predetermined excitation frequency.

(31) In S2, the second transfer function G2(s) (or third transfer function G3(s)) is measured from the torque current command value Tdy until dynamo revolution speed wdy (or engine revolution speed weg), by vibrationally operating the dynamometer under a predetermined excitation frequency.

(32) In S3, the values of the real part a.sub.k and imaginary part b.sub.k in the predetermined measurement frequency .sub.k, of the ratio G2/G1 (or G3/G1) obtained by dividing the second transfer function G2(s) (or third transfer function G3(s)) acquired in S2 by the first transfer function G1(s) acquired in S1 are calculated. It should be noted that, in order to avoid the resonance phenomenon from influencing the estimation result, the above-mentioned measurement frequency .sub.k is preferably made lower than the resonance frequency of the mechanical system constituted by joining the engine E and dynamometer D by the shaft S. In addition, since Formula (8-2) is an approximate formula holding true is a low region as mentioned above, the measurement frequency .sub.k is preferably made lower than the resonance frequency also from such a viewpoint.

(33) In S4, by substituting the values of the real part a.sub.k and imaginary part b.sub.k of the ratio G2/G2 of transfer functions calculated in S3 and the value of the measurement frequency .sub.k into the aforementioned Formulas (10-1) and (10-2), the values of the moment of inertia Jeg and rotational friction Ceg of the engine are calculated.

(34) It should be noted that, a case of estimating the moment of inertia and rotational friction based on Formulas (10-1) and (10-2) using the ratio of transfer functions at one measurement frequency .sub.k is exemplified in the flowchart of FIG. 2; however, it may be estimated based on Formulas (11-1) and (11-2) in the aforementioned way. In this case, the values of the real part a.sub.k_j and imaginary part .sub.bk_j of the ratio G2/G1 (or G3/G1) of transfer functions should be calculated under a plurality of n-number of different measurement frequencies .sub.k_j (all preferably made lower than the resonance frequency in the aforementioned way), and the values of the moment of inertia Jeg and rotational friction Ceg of the engine should be calculated by substituting these into Formulas (11-1) and (11-2).

(35) Next, the effects of the above such estimation method for the engine characteristics will be explained while comparing with the results for a case of estimating by the conventional method.

(36) FIG. 3 is a graph showing the results for a case of applying the conventional estimation method of engine characteristics to an engine having known characteristics. Herein, conventional estimation method of engine characteristics specifically refers to the method described in Patent Document 1 (i.e. Japanese Unexamined Patent Application, Publication No. 2006-30068) by the applicants of the present application. In addition, the real value for the moment of inertia of the engine serving as the test piece is 19 (kgm.sup.2), and the real value for the rotational friction of the engine is 0.64 (Nms/rad). Herein, FIG. 3 shows the results obtained from the conventional estimation method (more specifically, results obtained by substituting the moment of inertia EG.J obtained by the conventional estimation method into the above Formula (8-2)) by a bold dotted line. In addition, for comparison with this, the measurement results for the ratio of the second transfer function to the first transfer function (i.e. transfer function from the output of the shaft torque sensor until the dynamo revolution speed sensor) is shown by a fine line.

(37) First, the rotational friction of the engine is not taken into account by the conventional estimation method. For this reason, with the conventional estimation method, it may capture a gain decline in the low region due to engine friction as that due to an increase in the moment of inertia. For this reason, the estimation result for the moment of inertia by the conventional estimation method is 0.25 (kgm.sup.2), which is larger than the real value (0.19 (kgm.sup.2)).

(38) FIGS. 4 and 5 are graphs showing results for cases of applying the estimation method for engine characteristics of the present invention to the same known engine as FIG. 3. More specifically, FIG. 4 shows the results for a case of estimating the moment of inertia Jeg and rotational friction Ceg using the measurement results of the ratio of the second transfer function to the first transfer function, and FIG. 5 shows the results for a case of estimating the moment of inertia Jeg and rotational friction Ceg using the measurement results of the ratio of the third transfer function to the first transfer function. In addition, the bold dotted lines in FIGS. 4 and 5 show the results obtained by substituting the results obtained by the respective methods into the above Formula (8-2) and Formula (12). In addition, the fine line in FIG. 4 shows the measurement results of the ratio of the second transfer function to the first transfer function, similarly to FIG. 3, and the fine line in FIG. 5 shows the measurement results for the ratio of the third transfer function to the first transfer function (i.e. transfer function from the output of the shaft torque sensor until the engine revolution speed sensor).

(39) As shown in FIG. 4, by using the ratio of the second transfer function to first transfer function, the moment of inertia Jeg of the engine is 0.18 (kgm.sup.2), and compared to the results obtained by the conventional estimation method in FIG. 3, a value sufficiently close to the real value was estimated. In addition, the rotational friction Ceg was 0.66 (Nms/rad), and thus a value sufficiently close to the real value was also estimated. In addition, as shown in FIG. 4, the bold dotted line and fine line in the low range roughly match. This indicates that the approximate Formula (8-2) is sufficiently close to the measurement result in the low range. Therefore, with the estimation method of the present invention, it is considered to appropriately distinguish the moment of inertia and rotational friction of the engine.

(40) In addition, as shown in FIG. 5, by using the ratio of the third transfer function to the first transfer function, the moment of inertia Jeg of the engine became 0.18 (kgm.sup.2), and the rotational friction Ceg became 0.68 (Nms/rad). Therefore, even when using the ratio of the third transfer function to the first transfer function, it is possible to estimate the moment of inertia and rotational friction with sufficient precision. In the above way, it is possible to measure the moment of inertia in a short time, while taking account of the loss due to rotational friction, according to the present invention.

(41) Although an embodiment of the present invention has been explained above, the present invention is not to be limited thereto. The detailed configurations may be modified as appropriate within the scope of the gist of the present invention.

EXPLANATION OF REFERENCE NUMERALS

(42) 1 test system (test piece characteristic estimation device) 7 shaft torque sensor 8 dynamo revolution speed sensor (revolution speed detector) 9 arithmetic unit (first transfer function measuring means, second transfer function measuring means, moment of inertia estimating means) C engine revolution speed sensor (revolution speed detector) D dynamometer E engine (test piece) S connecting shaft