Experimental characterization and numerical determination of the rigidity of a Binder Magnetic synchronous belt transmission type AT10

doi:10.21203/rs.3.rs-389844/v1

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Experimental characterization and numerical determination of the rigidity of a Binder Magnetic synchronous belt transmission type AT10

https://doi.org/10.21203/rs.3.rs-389844/v1

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Given the important role of synchronous belts in the functioning of mechanisms, they are the subject of numerous studies and researches in order to define them more and more finely. Their mechanical characteristics influence the behavior in operation of the mechanisms that they entail. Also, the measurement of the characteristics of the longitudinal stiffness of the belt and the stiffness of the teeth is necessary to better control their behavior. In addition, these parameters constitute input data for models of lifetime and dynamic behavior of synchronous transmissions. An approach for the determination of longitudinal stiffness is presented. We have demonstrated a study comparing the measurement of the rigidity of a toothed belt by two methods. This is to qualify the first method of measurement through experimentation. And the second measurement method using the simulation of this toothed belt by SOLIDWORKS software.

Mechanical Engineering

Materials Engineering

Synchronous belt

Measured

Rigidity

Effort

Displacement sensor

Stiffness

Table 1. Characteristics of the belt AT 10

Profile	Belt width [mm]	Weight [kg/m]	Cables: standard steel - polyurethane: TPU ST1²
			Allowable effort F_N [N]	the armature stiffness constant [N/m]
AT10	16	0,093	2750	0,69 .10⁶
	20	0,120	3400	0,85 .10⁶

Table 2. Test result AT10 belt (width 16 mm).

Test N°	Charge [N]		Elongation [µm]		Effort [N]		Rigidity [10⁷.N/m]
Test N°	Max	Min	Max	Min	Max	Min	Max	Min
1	1200	305	337	40	1002	107	9.28	8.03
2	1205	305	352	44	1012	112	8.96	7.76
3	1204	305	361	49	1006	107	8.36	6.55
4	1204	295	342	35	1011	102	9.84	8.47

Table 3. Test result AT10 belt (width 20 mm).

Test N°	Charge [N]		Elongation [µm]		Effort [N]		Rigidity [10⁷.N/m]
Test N°	Max	Min	Max	Min	Max	Min	Max	Min
1	1199	300	305	35	1006	107	11.8	9.17
2	1229	339	339	45	1001	112	8.86	7.33
3	1233	320	354	54	1011	98	8.57	5.44
4	1228	320	3.41	40	1006	98	8.85	6.38

Table 4. Rigidity of the core of the two AT10 belts

Test N°	Rigidity belt width 16 mm [10⁷.N/m]	Overall rigidity	Rigidity belt width 20 mm [10⁷.N/m] [10⁷.N/m]	Overall rigidity
1	8.78	8.71.10⁷	9.75	9.37.10⁷
2	8.93		9.23
3	8.58		9.31
4	8.62		9.21

Table 5. Measured and simulated core stiffness of the two AT10 belts

Rigidity of the belt width 16 mm [10⁷.N/m]		Rigidity of the belt width 20 mm [10⁷.N/m]
Measured	Simulated	Measured	Simulated
8.71	8.79	9.37	9,03

Table 5. Variation of the stiffness of the tooth as a function of the radial load and the displacement of the tooth u for the two belts AT10 of width 16 mm and 20 mm

Déplacement de la dent u [µm]	Charge radiale Q_y[ N]	La raideur de la dent [10⁷.N/µm]		Rapport k₁/ k₂
Déplacement de la dent u [µm]	Charge radiale Q_y[ N]	k₁[16mm]	k₂[20 mm]	Rapport k₁/ k₂
0	0	0	0	-
	24	0.20	0.20	1.02
	48	0.37	0.37	1.00
	72	0.56	0.54	1.04
	96	0.75	0.72	1.04
	120	0.94	0.90	1.05
150	0	0	0	-
	24	0.10	0.13	0.80
	48	0.18	0.22	0.82
	72	0.27	0.33	0.82
	96	0.38	0.45	0.84
	120	0.47	0.57	0.82
300	0	0	0	-
	24	0.04	0.08	0.53
	48	0.06	0.12	0.50
	72	0.10	0.18	0.56
	96	0.13	0.24	0.54
	120	0.17	0.34	0.50

Table 6. The stiffness as a function of the radial charge for a displacement = 0 μm

Radial Charge Q_y[ N]	Stiffness of the belt tooth [10⁷.N/m]		Rapport k₁/ k₂
Radial Charge Q_y[ N]	k₁ [width 16 mm]	k₂ [width 20 mm]	Rapport k₁/ k₂
0	0	0	0
24	0.26	0.18	0.69
48	0.52	0.36	0.69
72	0.76	0.54	0.71
96	1.02	0.7	0.68
120	1.26	0.88	0.69

Table 7. The stiffness as a function of the radial charge for a displacement = 100 μm

Radial Charge Q_y[ N]	Stiffness of the belt tooth [10⁷.N/m]		Rapport k₁/ k₂
Radial Charge Q_y[ N]	k₁ [width 16 mm]	k₂ [width 20 mm]	Rapport k₁/ k₂
0	0	0	0
24	0.13	0.09	0.69
48	0.29	0.21	0.72
72	0.43	0.31	0.72
96	0.56	0.4	0.71
120	0.72	0.51	0.71

Table 8. The stiffness as a function of the radial charge for a displacement = 200 μm

Radial Charge Q_y[ N]	Stiffness of the belt tooth [10⁷.N/m]		Rapport k₁/ k₂
Radial Charge Q_y[ N]	k₁ [width 16 mm]	k₂ [width 20 mm]	Rapport k₁/ k₂
0	0	0	0
24	0.08	0.05	0.63
48	0.17	0.1	0.59
72	0.24	0.15	0.63
96	0.36	0.21	0.58
120	0.58	0.35	0.60

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Experimental characterization and numerical determination of the rigidity of a Binder Magnetic synchronous belt transmission type AT10

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