Research on Tuning Fork Dimension Optimization and Density Calculation Model Based on Viscosity Compensation for Tuning Fork Density Sensor

Table 1

Comparison table of simulation and theoretical results of the first-order natural frequencies of tuning forks with different rectangular structures.

Cross-sectional area c ∗ b (mm^2)	Simulation results (Hz)					Theoretical result (Hz)
	l = 100 mm	l = 80 mm	l = 60 mm	l = 40 mm	l = 20 mm	l = 100 mm	l = 80 mm	l = 60 mm	l = 40 mm	l = 20 mm
20 ∗ 5	84.64	132.92	247.62	536.85	2126.79	82.99	129.05	238.19	516.21	2064.85
20 ∗ 3	109.23	171.51	319.508	692.72	2744.15	107.09	166.52	307.22	666.08	2664.23
20 ∗ 2	133.86	210.18	391.56	848.93	3363.05	131.24	204.06	376.50	816.28	3265.10
16 ∗ 5	94.60	87.31	266.55	599.97	2376.84	92.75	84.77	256.25	576.90	2307.62
16 ∗ 3	122.25	118.96	343.86	774.16	3066.90	119.86	115.50	330.64	744.39	2977.58
16 ∗ 2	149.60	234.89	421.40	948.72	3758.44	146.67	228.05	405.20	912.24	3648.98
12 ∗ 5	109.46	100.92	307.89	693.18	2746.05	107.32	97.99	296.05	666.52	2666.07
12 ∗ 3	141.12	137.53	397.54	894.99	3545.54	138.36	133.53	382.25	860.57	3442.28
12 ∗ 2	172.95	271.55	487.176	1096.80	4345.03	169.56	263.65	468.44	1054.62	4218.48
10 ∗ 5	119.75	188.03	337.35	759.51	3008.82	117.41	182.56	324.38	730.30	2921.19
10 ∗ 3	154.54	242.63	435.30	980.012	3882.36	151.51	235.57	418.56	942.32	3769.29
10 ∗ 2	189.38	297.35	533.45	1201.00	4757.80	185.67	288.69	512.94	1154.81	4619.23