Transport resistance versus lever arm rolling friction EN
AKB Report
Transport resistance versus lever arm of rolling
friction
1) Introduction
The stationary torque requirement of a roller application (roller conveyor; travelling drive) can be
determined in different ways. This report describes two commonly used ways ("specific travelling
resistance or transport resistance"; "lever arm of rolling friction") and compares them with regard to
their effects on the drive dimensioning process.
For determining the specific transport resistance (... which is independent of the payload) of roller
conveyors (Fig. 1.1) or travelling drives, DSD queries the "lever arm of the rolling friction" (Fig. 1.3).
DSD uses this entry and the diameter of the transport rolls to determine the transport resistance to
be provided as stationary load by the drive.
Furthermore, DSD contains a travelling resistance calculator (Fig. 1.4) in the "Tools" menu.
Fig. 1.1: Typical roller conveyor for Euro pallets
Fig. 1.4: Travelling resistance calculator in DSD
Fig. 1.2: DSD Input dialog box for travelling drives
Fig. 1.3: DSD input dialog box for roller conveyors
Transport_resistance_versus_lever_arm_rolling_friction_EN_17.03.2015.docx
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2) "Lever arm of rolling friction" versus "Specific transport resistance"
Basically, both methods can be used to determine the absolute transport or travelling resistance.
Specific transport or travelling resistance
In many cases, the specific transport or travelling resistance (N/t) is based on known empirical values
or can be determined in DSD (Fig. 1.3/1.4).
Lever arm of rolling friction
The physical way of determining the absolute transport resistance is based on the "lever arm of the
rolling friction" of two known material pairs (Fig. 2, e.g. wooden pallets on steel rolls) and the
payload. DSD uses an integrated auxiliary calculator to determine the absolute transport resistance
(Fig. 1.3/1.4).
Fig. 2: Lever arm of rolling friction, physical principle
Determining the transport resistance (FTr) from the "lever arm of the rolling friction" (f)
The transport resistance FTr (= frictional resistance) is the resistance to be provided to move the
payload on the transport rolls. It is determined via Equ. 2.1a or via the DSD auxiliary calculator.
Equ. 2.1a
Special case:
- β = 0 degree (horizontal conveyor line)
- bearing friction is very low and can be neglected
With this, the equation is simplified to Equ. 2.1b
Equ. 2.1b
By rearranging Equ. 2.1b, you will obtain the relationship between the "lever arm of the rolling
friction" (f), the "diameter of the transport rolls" (daux) and the specific transport resistance kF_Tr.
Equ. 2.1c
The material pair (f) has a linear influence and the radius of the transport rolls (daux) has a reciprocal
influence.
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For dimensioning example 3, the "specific transport resistance" (kF_Tr) results as follows:
= 0.235 N/kg= 235 N/t
Fig. 2.1 / 2.2 show the relationship of equation 2.1c. You can see that the "wheel diameter" and the
"lever arm of the rolling friction" have a significant influence on the specific transport resistance kF_Tr.
f = 1.2 mm
(steel – wood)
kF_Tr =
235 Nm / t
Fig. 2.1: Relative transport /travelling resistance as a function of "lever arm of rolling friction" for different
wheel and roll diameters
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Fig. 2.2: Relative transport/travelling resistance as a function of "lever arm of rolling friction" for different
wheel and roll diameters for different material combinations
3) Dimensioning example – roller conveyor
- Diameter of drive roll
- Payload
- max. system speed
- Acceleration / deceleration
- Acceleration / starting time
- Lever arm of rolling friction
100 mm
4000 kg
0.45 m/s = 27 m/min
0.45 / -1.0 m/s2
1.0 / 0.45 s; linear profile
1.2 mm
(wooden pallet on steel rolls)
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4) Comparison of "specific transport resistance" versus "acceleration"
In general, horizontal roller conveyors are typical acceleration drives; i.e. the "acceleration
component" is predominant compared to the "stationary torque" and determines the drive size. A
comparison of the two components is interesting.
The specific transport resistance (kF_Tr) is specified in N/kg. Thus, it has the same physical unit "m/s2"
as the translatory acceleration (a).
A comparison of the two components is a good indicator to show which component is dominant.
With the data from dimensioning example 3, the situation is as follows:
- Deceleration af = 1.0 m/s2
- Specific transport resistance kF_Tr = 0.235 m/s2
af / kF_Tr = 1.0 / 0.235 = 4.25
Conclusion: The acceleration component is 4.25 times higher than the component of the travelling
resistance and thus determines the drive size.
Transport_resistance_versus_lever_arm_rolling_friction_EN_17.03.2015.docx
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AKB Report
Based on the DSD results, this is clearly shown in Fig. 4.1.
47 Nm
200 Nm
Fig. 4.1: Comparison of dynamic and stationary torque; 200 Nm / 47 Nm = 4.25
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